Is programming experience relevant in a pure Math graduate program?

Question: Programming skills such as experience with Java, Python, C++ or work experience as a software developer can be indispensable for applied mathematicians. How useful is it to have such experiences as a pure Math graduate student where the focus tends to be on proofs and rigor rather than computation?
Comment: Define "useful" and "programming experience."
Comment: I would look at this from a different perspective: programming requires a certain kind of logical, mathematical reasoning and thinking, so if you have programming experience then that should count as a point in your favour for a pure mathematics course, whether or not the course itself might involve any programming.
Comment: one thing i think everyone missed is, theorem provers ([example](https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_game/) of their usage for math) are (i hope) being used increasingly often - since it's nice to have a permanent, verifiable record that a certain theorem is true. (of course, i suspect this is far enough from convention that it won't be particularly common for a long while yet)
Comment: I don't have the rep here to post an answer, but if I did it would be a form of my answer to the opposite question "Is mathematics necessary for learning to program?" which you can read at https://softwareengineering.stackexchange.com/a/137075/48582 ; a point I haven't seen yet in the answers here is that the _skills_ you have developed from programming will help you considerably with learning Mathematics even with topics that have no visible link to programming.
Comment: Two applications come to my mind, and these should be two of possibly many: 1- one may use programming languages to numerically calculate results of integrations, expansions, formulas, etc; 2- there are packages like Mathematica which do analytical expansions and calculations. So, my answer is, Yes! Programming is a good skill to have, these days.
Comment: if in [pure physics](https://academia.stackexchange.com/questions/27047/what-are-the-available-non-academic-careers-to-a-newly-minted-phd-in-theoretical) the answer is no, then probably for pure maths it's also no?
Comment: What is "pure" math to you?
Comment: Even when it seems contradictory at first, there exists a branch of mathematics called "Experimental mathematics", math is not purely deductive. Such that experimentation is performed by computers, using for example CAS systems. In fact, there is a journal for it.
Comment: The Mathematics Masters (not necessarily pure math) had a required computer course.  Not sure everything it covered, but it included IEEE number format, tolerances and accumulated rounding error and presumably a programming language.
Answer: Not really an answer to what you asked, but: Look beyond grad school as well. Most math PhDs do not actually stay in academia but end up in industry in one way or another. Nearly every job mathematicians will eventually take on outside academic pure math research will benefit from having computer programming experience. So there may not be an advantage to knowing programming when you apply for grad school, but it will be useful to you in the future anyway.
Comment: "nearly every" ... True.  But current math Ph.D. students (and their advisors) often do not want to admit it.
Comment: @GEdgar Yes, but ignoring or denying the fact doesn't make it any less true :-)
Comment: +1, it's super important to hedge.  They don't like to admit it probably because the main point of a pure math education is to work in academia.  It's kinda like admitting a lot of what you are doing is not really going to be of value to you in the long run.  There are exceptions of course, but for many of the types of jobs people end up in there was probably a more useful field they could have enrolled in (eg if you end up as a programmer or developer more than likely cs would have been a more useful path [or stats/DS if they end up in prediction/modeling/database admins.])
Answer: In many parts of pure mathematics you use software to calculate examples that a while ago you could do only with pencil and paper. That's particularly true in combinatorics (my field) and number theory.
There is a tradeoff. Sometimes you learn from the slow process that forces you to see what happens at each step - like looking at a program with a debugger. But you get a lot more data in a lot less time, so are less likely to be misled by the law of small numbers.
I have taught an undergraduate course whose purpose was to expose students to the possibilities of calculation: python, symbolic manipulation (mathematica and sage), spreadsheets, LaTeX for writing mathematics.
You may not need programming skills to be admitted to graduate school, but any on your cv would be a plus. You might well have to learn some
when you start your researchl
Comment: Even limited programming skills make a huge difference when it comes to learning LaTeX, and LaTeX seems to be even more widely used in maths than physics
Comment: I once looked for certain paths in certain graphs with a computer and was then able to show their general existence after noticing patterns for small examples. However, even for those small examples, the graphs were not actually small (they were graphs of graph homomorphisms between small graphs), so I could not just have looked for the paths by hand. (A smarter person might of course have found a better proof, who knows.)
Comment: Beyond Mathematica/Maple and the like, there're tools such as [PARI/GP](https://en.wikipedia.org/wiki/PARI/GP) for number theory and [GAP](https://en.wikipedia.org/wiki/GAP_(computer_algebra_system)) for discrete algebra (group theory).
Answer: Maybe, maybe not. Ignoring some of the more obvious expectations such as LaTeX, you might consider becoming familiar with Pari as well as Mathematica programming and Sage/Python. Apart from that the cognitive development that comes from learning both procedural and declarative programming can be fruitful in unexpected ways.
Answer: Computers are sometimes used to solve complex mathematical problems because it's impractical for humans to enumerate all the cases and combinations. Famously, the Four Color Theorem was proved using a computer.
There's a list of proofs that used computers in this Wikipedia article: Computer-assisted proof
And while the eventual proof of Fermat's Last Theorem was purely mathematical, computers were used by many researchers to confirm the conjecture for many cases.
Answer: Long-term usefulness aside - during your PhD, you might have to teach a class that is not pure math and may require you to know how to program...
Answer: Yes. For example, in my case Matlab programming was quite helpful for plotting figure. The latex language Tikz/PGF the is almost very essential in plotting figures, diagrams in commutative algebra, algebraic geometry, number theory etc. The Language like PARI/GP and SAGE are very helpful in algebra and number theory.
Answer: Having a familiarity with programming languages is useful in pure math too. It is easy to observe some patterns by plotting a suitable graph.
For example in number theory,  if we are studying a particular type of prime number and we want to see how they are distributed, the first step I would do is to plot the counting function to get an intuition which can not be done by hand. If this function is not studied before it is unlikely that you will find an existing inbuilt function in standard programming languages. In this situation, if you are familiar with programming then you have an advantage.
Also, we can do various calculations using a computer which would be laborious to do manually.
Answer: As someone who is currently doing a PhD in mathematics, yes, it is definitely useful to have a prior understanding of programming. However, I don't think it is necessary - if you can keep up with the maths, the coding will follow.
A lot of people keep mentioning Latex. I wouldn't really call this programming per se, but you will definitely need to learn it. This is not very hard though.
You will almost definitely use some sort of programming language in a PhD for  visualisation or computation (yes, computation is common even in pure maths these days). Exactly what languages/programming you will do is difficult to say with out more information about the project. 'Pure maths' is extremely general and can cover a vast range of fields.
Answer: Practical programming experience is very useful for any high-educated worker that spends most of their time behind a computer, and for a PhD-student in particular. Why?
Automation
As a PhD student, you will increasing likely be working with software systems in order to do basic tasks such as writing, literature search, interacting with students, having meetings, administration, grading homework. Some of this systems have a well designed UX (user experience) and allow you to tell the computer what to do at the speed of either your thoughts or your typing.
However, many of these systems can be rather painful. Often these are simple things, such as dragging the cursor all over the screen rather than pressing a key, or waiting 10 seconds on a page to load that could have been loaded while you were doing something useful. These are minor things, but when you have to do them ~200 times on a day, these annoyances add up. So, what to do?
Do it yourself
You could ask someone else to solve this issue, such as the developers of the software. However, this is a task more difficult for them than it is for you (assuming you have the practical programming experience): they need to change it (if they agree to change it at all!) and make it work for all users, you only need to make it work for yourselves.
This may sound a lot of work, but it's not bad at all, time-wise. It's a time investment that has paid of for me within a week, whenever I improved some frequent painful processes. And while the time gained may be peanuts, the main purpose is to remove annoyances, which allow more enjoyable and more focused work.
It's not particularly difficult, either, if you have some practical programming experience and know what tools are out there. A web-app drives you crazy? Write a user-script with Greasemonkey/Violentmonkey/Tampermonkey. Some simple DOM-manipulation often works, I personally use  MDN as a reference. An application can use more keyboard shortcuts? AutoHotkey can help.
Answer: Well, in addition to other good points raised, in these days if a math/tech-oriented person is clueless about talking to computers in any serious way, they're just a babe-in-the-woods. Almost immediately incompetent in various sorts of not-strictly-math ways.
As many of us have noticed, "computers" are a big deal, as is the internet. Not all of that is relevant to "doing mathematics", but quite a bit is. I use Perl to rearrange text/TeX files, Python for basic computations, Sage for subtler computations and graphs... even if none of those computations or graphs enter in any public-facing paper I write.
Also, many notions from Computer Science, such as "scope of a variable-name", are quite valuable in understanding mathematical writing (and in writing more clearly). And in teaching more clearly, and understanding that most undergrads do not have the same sense of "scope of a variable" that mathematically trained people do.
One last thing: I myself would not want to be making choices based on weakness, rather than on interest and preferences. If one shuts oneself out from understanding how computers seriously work, ... well, maybe you'll be an "end-user". No reason to solicit that.
Answer:
how useful are they when applying to pure a Math program?

Having to contend with (La)TeX to typeset your publications already means you'll be doing a bit of programming; and if you're even the least bit finicky, creative or perfectionistic, it will be more than a bit.
... you might think this answer is tongue-in-cheek, but many a grad student has TeX battle scars they could tell you about :-(
Want another example? Well, will you have a personal website? That often benefits from being able to program. Is there any chance you might want to demo some of the abstract concepts you work on for a wider audience? That would require programming. Will you be using abstract/symbolic math software packages? Another case programming comes into your life. Hell, if I could, I would reprogram my alma mater's math department building elevator, the logic of which I couldn't figure out.
So, programming is (nearly) everywhere, for pure mathematicians as well.
(Also, what @EthanBolker and @WolfgangBangerth said.)
Answer: Obviously having a skill is better than not having that skill. As far as direct applicability to a PhD in pure mathematics, Python and possibly C++ might be useful for certain kinds of computational work (such as generating examples or testing hypotheses) mentioned by other commenters here. But this is usually done using packages tailored more specifically for mathematics such as Magma or Sage.
If what you're really asking is whether experience as a Python or C++ programmer is going to boost your application, the answer is probably not, unless the advisor you're planning to work with wants someone who can do that (e.g., if they don't want to do coding themselves).


Logic Pro X flex markers

Question: I love Flex Time (Polyphonic) in Logic Pro X – it saved my off-beat playing a lot of times. Of course it's very interesting to move markers right on the hits (aka. quarter note hit, 8th note hit, 16th, so on) but sometimes I just have a pattern played using only 8th notes (quavers, whatever you call them) and sitting and snapping each off-beat 8th note to grid becomes not so interesting. So... is there any automatic approach to snap all off-beat markers perfectly to closest on-beat grid position? Of course this doen't apply to triplets, quintuplets, sextuplets and some other tuplets because they can fall on a tick instead of even beat.
Comment: Is there a reason why you don't want to just use quaver quantization?
Comment: @BobBroadley  How to apply that?
Comment: Hey there. I'm sat in an airport waiting for a flight, with no computer, so I won't post either an answer or detailed comments. However, I would say that, if you don't know much about what quantisation is, or how to do it to audio and midi in a DAW, you should definitely read up on it. It is one of the most fundamental aspects of creating music in DAWS.
Comment: TLDR: select passage of audio you want to snap to grid and press Q.
Answer: For the most part, you should do it yourself, as sometimes you want to leave a certain transient as it is, because it might create a vital artifact that can easily spoil the sound in a place, where it is snapped to grid. But in most cases, you can use quantization and then listen while correcting the transient that are quantized off (this happens especially with triplets of any type, mostly 16th note triplets though) or those that sound bad due to created artifact.

Logic Pro X flex markers


Ore Reserve Definition

Question: I've seen many papers on mineral deposits say something along the line of "a 100,000 tonne deposit of Zn, 1% grade." Does this mean there is 1% of 100,000 tonnes which is 1000 tonnes pure zinc, or does it mean there is a total zinc deposit of 100,000 which is 1% of the total giving 10,000,000 tonnes including the waste material?
Comment: When I went to school , an ore was a deposit from which something could be produced at a profit. A mineral deposit was everything else.  As economic conditions change , a deposit may change back and forth between "ore"  and "mineral".
Answer: Ore reserves represent the economic portion of a mineral deposit. They are reported as tonnes and grade above a minimum value (cut-off grade).
Irrespective of whether the ore reserve will be mined by surface or underground methods the deposit is blocked out and the mass of each block and the mass of the valuable commodity (zinc, copper, gold, etc.) is calculated for each block. From this the grade of each block is also determined. The reserve is determined by summing the masses of all the blocks and determining the overall grade of the total.
In your example, a deposit of 100,000 tonnes grading 1% zinc means there is 100,000 tonnes of rock that can be mining and treated by a processing plant (mill). The amount of zinc metal contained within that 100,000 tonnes of rock is 1000 tonnes.
Similarly, a gold deposit that contains 2 Mt @ 8 g/t, contains 2 million tonnes of rock grading 8 grams per tonne, or 8 parts per million. The amount of gold contained in that 2 million tonnes is 16,000,000 g (16,000 kg or 16 t).
Answer: It means there is an estimated 100,000 tonnes of recoverable zinc in the lifetime of the mine, and the ore it produces is 1% zinc. As zinc ores usually contain other metals such as lead, it is not necessarily the case that this ore is 99% waste material.
Comment: As someone who has spent decades determining ore reserves for various commodities & mining methods, you answer is wrong.

Ore Reserve Definition


Electronic cigarettes on Yom Tov

Question: Let's say someone quits smoking, and that person smokes electronics cigarettes. So regarding yom tov (chag), the only prohibition I can think of is Nolad every time you activate the heating element within the electronic cigarette. Doing this is a rabbinic prohibition. However what if the person did it in an abnormal manner (Shinui) or better yet if it's yom tov sheini. So in those two cases it's a shvus dshvus, and it's for tza'ar because lack of nicotine in a smoker causes many unpleasant side affects such as light headedness and nausea. Would the manner of using the electronic as listed above be permitted under those circumstances?
Comment: Well, the difficulty is that you can also get nicotine from a tablet, a gum, or from a normal cigarette on Yom Tov, so it's not really a case of health issues. Activating the heating element may constitute the melocho of ma'avir, depending on what opinion you follow, and many e-cigarettes have a sponge-like material in the cartridges from which the vapor is released, possibly being an issue of dosh. Like all issues related to electronics on shabbos or yom tov, e-cigarettes are something that require case-by-case and device-by-device analysis by a qualified rav.
Comment: http://chat.stackexchange.com/transcript/message/15993155#15993155 et seqq.
Comment: Its hard enough getting a hetter for the regular ones.....
Comment: @David Feigen Molid or Nolid?
Answer: Electronic cigarette

An electronic cigarette (e-cig or e-cigarette), personal vaporizer (PV) or electronic nicotine delivery system (ENDS) is a battery-powered device which simulates tobacco smoking by producing a vapor that resembles smoke. It generally uses a heating element known as an atomizer, that vaporizes a liquid solution. Solutions usually contain a mixture of propylene glycol, vegetable glycerin, nicotine, and flavorings,[1] while others release a flavored vapor without nicotine.[2]

As a matter of logic, the heating element can be considered to be like a fire that is "lit". This is not only a matter of completing a circuit, but of causing something to heat up. While you might say that "cooking" the nicotine out of is sufficiently "like" ochel nefesh to be mutar, you are still creating a new "fire". Since you are producing heat, this is not like the other types of electricity uses that some people say are mutar on Yom Tov (or Shabbos) because they do not turn on a light or produce heat.
This would be analogous to turning on the stove from a completely off position and not just raising or lowering the flame.
Comment: @DavidFeigen We don't usually use Yom Tov Sheni as a Shevus.
Comment: I understand that there is an issue of creating a new flame. But a theoretical loophole would be to do it in an abnormal manner (derech Shinui) because then it becomes a shvus dshvus or better yet at least it should be more meikel regarding the second day of yom tov in the diaspora
Comment: @DavidFeigen since the device is not set up to allow a "shinui" then it would not apply.
Comment: You can use a Shinui if you use your knuckles
Answer: Shalom u'vracha! Strictly speaking, it is forbidden because smoking is not ochel nefesh.
There is no issur of nolad with electronic devices or electricity, as explained by Chacham Ben-Tzion Meir Chai Uziel ztz"l in shu't Mishpetei Uziel and R' David Shlush ztz"l in shu't Chemda Genuza, among other poskim. Although their psak was specific to electric switches, the same can be applied to battery-powered electronic devices because the battery "contains" the power and merely transfers it to the parts of the device. Another reason for nolad to be applicable, is that it must be visible to the eye; like an egg coming out of a chicken or sparks coming out between two rocks when bringing them together(microscopic vision doesn't count in Talmudic law).
However, only ochel nefesh was permitted on yom tov and the rule is that for a non-ochel nefesh melacha to be done on yom tov is that it must be enjoyable to the general population on a similar level, which doesn't apply to smoking(cigarettes or e-cigs); rendering smoking a forbidden act on yom tov. So too, was the psak of Rav Elyashiv ztz"l.
It is my opinion that electricity is permitted on yom tov when used for ochel nefesh(like the poskim listed above and my personal reasoning), even though this is not my practice. Even though the tzibbur is machmir, it is due to the doubt of the nature of electricity and not a gezera; rendering it permitted due to it being accepted as a matter of doubt and minhag ta'ut.
For detailed sources, please comment. Not a psak! Merely my humble opinion on the issue
Comment: Comments are not for extended discussion; this conversation has been [moved to chat](https://chat.stackexchange.com/rooms/82105/discussion-on-answer-by-chacham-nisan-electronic-cigarettes-on-yom-tov).
Answer: using the electric function is also a problem of binyan, at least according to the chazon ish
Comment: @YEZ I suppose.....
Comment: Did the Chazon Ish say that about battery operated portable devices or only devices that are attached to a house?
Comment: Was this answer meant to be a comment? It doesn't really answer the question...
Comment: @Shokhet It answers the question by challenging its assumptions.  This answer is suggesting that it is a Biblical violation, not Rabbinic, and therefore the reasoning offered would not apply.

Electronic cigarettes on Yom Tov


How to create the   part in "scriptSig"?

Question:
I've decoderawtransaction and see in the vin part a "scriptSig" ,which
I believe to be the "unlocking script"  . Assuming I have
the private key in a paper wallet and someone send me transaction to
my bitcoin address, How do I generate the    to unlock it
?
My second question is: after I generated it, can someone copy this
part and use it in the future to unlock a future transaction made to
my same bitcoin address ?
Comment: For the 1st question I'm looking for a mathematical answer, i.e: take PK hash 160 extra. don't send me to some library.
Answer: First question has a long answer, because it depends on the scriptPubKey, but also of the sigHash flag, I assume you are speaking about classic P2PKH transactions. (ScriptPubKey expose the condition for "unlocking", while ScriptSig satisfies them for "unlocking". It can use signature... or not, but will assume you are using P2PKH scriptPubKey, so it does)
So the scriptPubKey is
OP_DUP OP_HASH160 <PubkeyHash> OP_EQUALVERIFY OP_CHECKSIG

Where PubkeyHash is given by your bitcoin address.
The scriptSig should be
<Sig> <PubKey>

The PubKey is simple. From your Private key, you can get the public key (curve secp256k1)
Q = dG

where d private key : int, Q public key : EC Point, G : ECPoint given by curve.
<sig>

is composed of 2 components
<ecdsaSig> <sigHash>

ECDA Sig is the signature of a hash of the transaction in DER encoding. sigHash is a byte that specifies how to generate this hash (ie: what is actually signed).
sigHash itself contains 2 informations.
<AnyoneCanPay><All|None|Single>

So what is signed is a calculated hash of your transaction depending on the sigHash. The human friendly explanation is here, and the most readable code doing that is here.
Once you calculated the hash, you need to sign it according to this math on elliptic curves.
Due to the need in the algorithm of a random K value, it supposes a fair RNG.
So RFC6979 describes a way for finding a K value that is not random but secure to use.  (implementation here)
So here is what is signed, depending on the sigHash you choose:
AnyoneCanPay : You allow someone to modify any input in the transaction. (don't sign inputs, except yours)
All : You deny modification of outputs in the transaction. (sign outputs)
Single : You deny modification of the output having the same index as you input (sign one output)
None : You allow modification of any output in the transaction. (sign no output)
Second question :
No, whatever the sigHash you use, part of your signature contains the previous output reference you are spending. Since you can't double spend, you can't reuse the signature.
However, if you really want to do that, then use the same K value for signing 2 different hashes, then you basically leaked your private key. So anyone would be able to "unlock" a future transaction made to your bitcoin address by knowing the two signatures.
Comment: Yes, if sigHash = None (with AnyoneCanPay), then basically anyone can take the input you sign and put it in whatever transaction they like.

If sigHash=None without AnyoneCanPay, then someone can only change the other inputs.
Comment: If I sign sigHash=None then anyone can change the transaction to receive the bitcoin ?
Answer:
How to redeem a basic Tx?
The question is not clear to me. Do you want to send your transaction after signing? Or do you want to hold the signature for later use?

How to create the   part in "scriptSig"?


What are the easiest/most suitable fruits and vegetables to grow in an apocalyptic scenario?

Question: My story is set in a sort of apocalyptic world, the main characters live in an old house and they're too afraid to go out as there're creatures hunting them. They obviously still need to eat so my question is what kind of fruits, vegetables, roots, or just anything edible at all, can they grow inside a house with very little resources?
Comment: Without a reliable source of clean water, they will die of dehydration or disease before they get the opportunity to starve in their (giant) house. Similarly, they will need a way to safely dispose of trash and sewage to avoid contaminating their food/water supply and living space and doesn't attract the hunting creatures. Of course, humans are themselves devastatingly efficient predators...so if those hunters taste yummy served with a nice sauce and some potatoes on the side, their days are numbered.
Comment: You are not going to grow enough food inside a house to support even one individual.  There simply isn't enough area exposed to sunlight.  It takes about 0.5 acre or more per person.
Comment: They probably need a greenhouse and even with one, weather is an important consideration.
Comment: Where is this old house?  Finland?  Egypt?  Beijing?  While there may be imported plants, the climate will have a massive impact on what can be grown.  Temperature, sunlight, humidity, availability of water, and altitude are all important in determining what plants are viable.
Comment: Also refer to [What do stranded astronauts eat in space](https://worldbuilding.stackexchange.com/questions/178874/what-do-stranded-astronauts-eat-in-space/). Even if a different question, many of the concerns are the same (e.g. small population, limited space, closed system). Well, at least a house on earth (presumably) has unlimited ventilation and can capture rain/precipitation - makes some things easier.
Answer: My money is on potatoes, for the following reasons:

They are sturdy plants with a good output. From Wikipedia:

According to conservative estimates, the introduction of the potato was responsible for a quarter of the growth in Old World population and urbanization between 1700 and 1900. In the Altiplano, potatoes provided the principal energy source for the Inca civilization, its predecessors, and its Spanish successor. Following the Spanish conquest of the Inca Empire, the Spanish introduced the potato to Europe in the second half of the 16th century, part of the Columbian exchange. The staple was subsequently conveyed by European mariners to territories and ports throughout the world. The potato was slow to be adopted by European farmers, but soon enough it became an important food staple and field crop that played a major role in the European 19th century population boom.

They are nutritious. Wikipedia also compares it to other staple foods, and while they  not the ones with the most of any given nutrient per portion, they do have a relatively good amount of vitamin C while being comparatively low on carbs and fats (as in they have less carbs per weight than rice, but please notice they are still really high in carbs anyway).

They are DELICIOUS[citation needed]. You can boil'em, mash'em, stick'em in a stew. They are also very good in french fries format, which is healthy because cooking does not kill all germs (to be really healthy, take this with a grain of salt).

While potatoes are really good, don't rely just on them. Ireland learned this the hard way once due to a potato blight.
Also, to really meet their nutrition requirements in the long run, your people will need to vary the plants they eat. A house may not provide adequate environment for maize (corn), wheat and specially soy and rice. They will need some fields for those.
There is a novel called The Martian, which was also made into a movie starring Matt Damon. It is about an astronaut/botanist stranded in Mars, surviving alone on a diet mostly based on potato. The book aims to be as scientifically correct as possible and is really pedantic about every tiny scientific detail. The rocket science and chemistry in the novel are precise and correct, but the fact that the protagonist survived for months on potatoes alone is the one thing that is off in that book.
Comment: Iirc, Mark Watney was able to survive for a year plus on potatoes  because he was supplementing it with small portions of NASA issue rations and a lifetime supply of multivitamin pills. If you pay attention in the film though, you will see that he still goes from a healthy body weight to clearly malnourished by the end of the story, so its evidently not a sustainable diet.
Comment: *"Potatoes being relatively low on carbs":* This is in complete contradiction with reality. Potatoes are almost *pure carbohydrates* (= starch) and water. (Only *"almost"* pure because they also have a little indigestible fiber if you are in the habit of eating the skin.) They have just about zero protein and fat. Great as an energy source, absolutely lousy as long-term diet. You *need* fats and proteins, and potatoes just don't have them in any appreciable quantity.
Comment: @Kyyshak yep, they had enough supplements to fulfill all his nutrient needs, the potatoes were strictly for calories. The book is very explicit about this. He was malnourished at the end because he didn't have enough potatoes to eat due to... complications.
Comment: and you can make [alcohol](https://en.wikipedia.org/wiki/Fruit_brandy) out of it . [here](https://de.wikipedia.org/wiki/Kartoffelschnaps) is a german entry extra for potatoes
Comment: Trust on this man, Ana Clara. Galacticus Renan is expertise in apocalypses and other kind of destructions!
Comment: Also agreeing with his argument, there this [article](https://theconversation.com/can-you-survive-eating-nothing-but-potatoes-54262).
Comment: @AlexP the devil is in the details. I meant they are low on that when compared to other staple foods - but to make that clear, I've edited my answer.
Comment: Potatoes are about 80% water and 20% carbohydrates. I hope you agree that water doesn't count as food. Yes, rice has less water, but I don't see why it matters. I have looked at that table and it is misleading; you need to take out the water content and compare the nutrients in the dry food. (Ah, and it also have a note saying that it referes to raw potatoes; I didn't even know that potatoes *could* be eaten raw. I tried a raw potato once when I was a child: it was horrible.)
Comment: Potatoes can be grown from potatoes, so they may have what they need to get started in the kitchen.
Comment: Do potatoes grow without sunlight?
Answer: Wine cellar

A different way to get calories.  An old house might have a wine cellar.  A bottle of wine has about 700 calories and safe water.  People do live on wine.      The depicted wine cellar must have several hundred bottles which would be enough for months.  If there is some hard liquor that has even more calories - maybe 1600 kcal / bottle.  I think you would need some water with that but the scotch should kill any germs if you leave them together for a minute or 2.
The living on liquor angle also potentially makes things scarier for your story.  Drunk people can be more emotional, or have lapses of judgement, or perceive things in an altered way.  If they run out of liquor they will have withdrawals and that would be really scary.
A wine cellar is not going to sustain you for years.  I cannot think of anything that could provide adequate calories able to grow in the area provided by a house, with no outside inputs except sun.  We need a lot of calories; especially me.  If it could be done I think people would be doing it all over the world.
Comment: *"People do live on wine."* I was going to contest this but my alcoholic relatives provide factual support for this claim.
Answer: Potatoes are a good choice if you ask me. Same with yam and ube. Make candy out of ube you can.
Also, since I live in Alaska, you can grow raspberries, strawberries, blueberries, and blackberries indoors. I hear people do this.
The part where potatoes are grown on Mars is one of my favorite parts of the movie "The Martian".
Answer: You need to decide how strict you want to be on the 'inside the house' part. If you don't have some fancy green house or halls with a lot of artificial light, you can't really grow any plants indoor in sufficient quantities to feed people. In that case your best bet would be mushrooms which will grow well in any damp dark cellar. It's hard to make a balanced diet out of that.
If you are willing to handwave that, I would recommend a combination of rice and soy beans. This is a historically well proven combination that already gives you all nutrients that humans need in significant quantities. Supplement with a small amount of salt and you are essentially good to go. Note that you need a few hectar of farm land per person to grow enough to feed them.
Answer: In your scenario, is there still running water and electricity?
If so, there are many plants that we can grow in our homes.
There are types of cucumber and tomatoes are rather simple.
There are home hydroponic setups like the aerogarden, but those grow herbs and spices, and a few small salad  ingredients, nothing substantial.
You might have your character be someone who is already growing marijuana in his basement with grow lights, so he just has to add some variety to his crops!
Answer: I agree with the answer that potatoes are going to be a good vegetable to grow.
However, as pointed out, it only provides carbohydrates- no protein or fat.
depending on how you define "grow" i think it's worth raising chickens in the house.
If you raise a few chickens you'll have a supply of eggs. Plus if you let some eggs hatch and raise new chickens, you can eat the older chicken and get some meat.
You can use the chicken dung to fertilize the potato crop, thus both adding nutrients to your crop as well as disposing of the waste.
and if you create a compost pile of the dung to break it down, you'll end up with worms and bugs which will be more food for the chicken.
Answer: I live in warmer weather (it only occasionally reaches to freezing in winter) so my suggestions may be tainted by that background.
Also, I think it stands to reason that a variety of corps would be more beneficial from a nutrition and also crop seasonality standpoint. One would obviously have to incorporate storage techniques like fermenting, dehydration, and cool storage to preserve a part of the in-season overproduction for leaner times.
I am thinking that it would be really useful to have access to a flat roof space (like a commercial building rooftop) where they would, amongst others, have

access to sunlight
growing space
space for greenhouses
space and ventilation for livestock e.g. chickens or pigeons
space and ventilation for a composting operation, which may (probably should) include a way to treat/recycle human waste (urine, feces)

Otherwise, if your old mansion has a lot of balconies, especially towards the sun, these will come in handy for the same reasons. Or sunrooms/large windows, which will double as greenhouses.
I hear the potato proponents, but in warmer weather sweet potatoes are a better option: they are more drought resistant, one can also eat the shoots and leaves (which are poisonous in the potato), and (arguably) are slightly better nutrient wise. Be aware that both crops need a lot of space. Even though both are touted to be some of the most nutrient-dense crops per ground area covered. Also keep in mind that potatoes (and root crops in general) are slow-growing, so while it may be a good long-term sustainability option, for the first 3-5 months there won't be much to eat. On the positive side they can be made to store well for 6-8 months with just a little labor and know-how.
Since your setting is space-restricted, your gardening would probably rely heavily on plants that use vertical space: think vining crops like (some varieties of) squash/melons/cucumbers, beans, peas, tomatoes, etc. One related concept you may want to read up on some in this regards is the so-called Food Forest, which combines plants at different heights in the same space to use the soil to its maximum potential; the plant interaction often has mutually beneficial effects too. Up to 7 "layers" are often defined, obviously some won't be possible in your setting due to space constraints and time needed to establish:

trees (fruit and nuts)
vines (as mentioned)
scrubs (berries)
perennial vegetables
herbs
ground covers (e.g. strawberries)
root crops ([sweet] potatoes, beetroot, carrots, onions, ...)

Do note however that one of the main limiting factors would still be light: all leaves need sufficient light even up on a wall or in a tree. "Light in" is pretty much proportional to the amount of "food out".
Another way to make use of vertical space, would be to have tiers of hydroponics/aquaponics/vermiponics channels mounted on walls.
And remember, for all vertical/wall-mounted growing systems above, you would not be limited to inside walls (depending on your type of monster). Systems mounted high enough on outside walls to be out of reach of monsters will create a lot of space and access to sunlight. The characters will need some pre-existing or jury-rigged walkways to access them, though.
I've mentioned pigeons. So plant food could be supplemented from birds such as these that could be caught by the inhabitants. Another way to supplement plant food would be through Entomophagy, in other words, Insects as food.
How much space do you need?
This obviously depends on a lot of factors (like light, water and temperature) and thus no two sources agree. I'd say you could get away with around 2m² per adult for year-round production under conditions including:

maximum soil fertility, which can be improved with additions of earthworm compost, bone meal and other nutrient sources, the targeted improvement of microbial/fungal soil activity, mulching, and a minimum-till approach.
(healthy soil like this that produces healthy strong plants will also do much to avoid plant diseases and pest insects.)
multi-tier production like in the Food Forest concept, or similar.
efficient recycling of nutrients back into the soil.
optimal light, moisture, temperature.


How to prevent a 1-year-old from getting hurt while learning to walk?

Question: My 1-year-old child is now trying to walk. She got hurt many times. Sometimes we had to rush her to the pediatrician. Mostly she used to hurt her tongue, cheek and head. My parents and I cannot prevent her from falling. Sometimes out of frustration I used to think we should put some kind of helmet on her. Please suggest some thing which will protect her from getting hurt.
Answer:
Watch her and catch her when you can, and comfort her when you don't.
Learn how to judge the severity of the fall. Generally, if she cries, the fall isn't too bad. If she is groggy and does not respond, then you need to contact a doctor.
Also carefully monitor the state of your child after a fall to make sure her condition returns to normal. If anything seems wrong or if you feel worried, just contact your doctor.

Our little one has had some nasty falls – face hitting both shelves of the coffee table, face into a fence pole (blood nose, trip to hospital), falling backwards off couch – and many many smaller ones. For the smaller ones, like the ones you describe, she sometimes cries, sometimes just says "bonk" and sometimes is furious. But she always reacts promptly and normally, so we know that nothing is wrong, even though it looks bad.
Kids fall. It's a part of learning about the world. Just may your world safe so that when they fall, they are less likely to do any severe damage. Ironically, they will learn to walk better if the environment is not too 'padded'. They might start tripping over the edge of the rug, but don't take the rug away, as it acts as a device to teach them how to walk more stably. Same goes with socks and somewhat slippery floor, and sand and bark, and walking on a trampoline. They're all more difficult than basic walking, but they help the child learn to walk better.
And learn to worry less about it.
Comment: +1 to this. I am also the parent of a non-walker and have heard in several places anecdotally (so not from an authority) that the falls are an essential part of learning to balance and therefore an essential part of learning to walk without falling *faster*.
Answer: While falling and getting hurt are part of learning to walk. Here are a few tips that may help:

She needs furniture without sharp edges to pull up on and help her
balance. Keep a close eye on her to prevent her grabbing onto unsafe or unstable surfaces.
A carpeted surface (short nap so it doesn't trip her) is a softer
landing spot than ceramic tiles.
Keep the floors clear of things she could trip on.
Block off unsafe areas, like stairs.
Practice walking with her, holding her two hands. The more practice she gets, the sooner she will gain her balance.
Until she is walking outside, let her walk barefoot. If it is cold, consider soft booties with leather or leather-like soles where she has full range of motion in her feet and reasonable grip.

A helmet is not advised as it could slip and cause injury to head or neck.
Comment: In my experience assisted walking practice has not reduced falls with a new walker. My child preferred to walk assisted rather than cruise before walking and still often does despite the fact that she can walk unassisted. She still falls as regularly as any other new walker.
Answer: Trying to entirely prevent her from hurting herself will be futile and even if you could, it may ultimately do her more harm in the long run. I will explain...
Getting slightly hurt when she falls is crucial to her development. She will not learn to protect herself from falling, if falling apparently has no unpleasant consequences.
If you put a helmet on her, for example, she would learn that hitting her head on things is perfectly fine. This obviously not something you want her to learn.
Having said that. Obviously you need to do what you can to avoid serious injuries, by blocking off stairs etc.
A normal fall from toddler height, onto the floor usually wouldn't require a hospital visit. You do however need to learn what to look for to make this determination.


internet explorer on ubuntu

Question: I need IE on my Ubuntu Karmic, better yet various versions of IE at the same time. What's the best and most reliable solution? Tx
Comment: Internet Explorer. The only reason I think that excusable is if you are design websites in Ubuntu.
Comment: xhtml/css is not the main part of my job, but still...
Answer:
Install some kind of virtual machine (e.g., vmware, virtual box)
Install a version of Windows in the virtual machine
Install Sandboxie in the virtual machine
Upgrade IE within the individual sandbox.
Answer: the most reliable method would be a VBox with Windows XP, if you don't have a license, you may use a  Internet Explorer Application Compatibility VPC Image, although designed for MS VPC, these virtual hard disks work with VirtualBox.
Internet Explorer Application Compatibility VPC Image are free time-limited virtual machines, either XP or Vista with IE6, 7 & 8 , the current set is valid until April 1st, 2010.
Answer: Install wine, and install each version in a separate wine "bottle".
IEs4Linux ( http://www.tatanka.com.br/ies4linux/page/Main_Page ) does a bunch of the work for you, but it can be challenging to extend the installation to other applications
Alternatively, use Cross-over Linux - they roll in some of the Windows stuff that IE needs. It has worked well for me.
Answer: At work we have an old machine running Ubuntu with lots of VMs on it. One runs IE6 on XP and another runs IE8, again on XP. The IE8 browser can be put into IE7 mode with the developer toolbar.
To access the VMs we use Remote Desktop. This works very well within the team as we can get someone else to easily log in and see 'the problem', hopefully to fix it.
The main benefit of the Remote Desktop approach is that one's machine is not slowed down by running a native copy of Virtualbox.

internet explorer on ubuntu


Plotting multiple, separate, closed Bezier objects from dataset of xyz coordinates

Question: I am new to blender and am using python within blender to do the following:

Read in list of coordinate data for bezier curve objects - DONE
For each unique object within the dataset, take that objects multiple xyz coordinates and plot a connected closed bezier curve from it. - NOT DONE

My Code for Point 2 is shown below:
<code>for i in unique_plotables:
# Creating CurveData
    curveData = bpy.data.curves.new('Slice Object %s' %(i), type='CURVE')
    curveData.dimensions = '3D'
    curveData.resolution_u = 20
# Subsetting my dataset of xyz coords to only coords belonging to desired object
# When the blender_id variable in my dataset = the unique_plotable value the loop is on
    df_object = object3_df[object3_df['blender_id']==i]
# Dropping variables not needed from dataset
    df_object = df_object.drop(['blender_id'], axis = 1)
# Remaining variables left in dataset include x_coord, y_coord, z_coord
# Convert this to a array
    coords = df_object.to_numpy()
# Create new spline for CurveData of Bezier type
    bez = curveData.splines.new('BEZIER')
# Add a number of bezier_points equal to the number of coordinates we have
    count = len(coords)
# Add this many points to the Bez spline
    bez.bezier_points.add(count-1)
    bezier_points_range = range(count)
    bez_points = bez.bezier_points
# For each point in the bezier points, make the .co for the point be equal to the vectorized version of coordinates when the index of coordinates is equal to the bezier point number.
    for j in bezier_points_range:
        bez_point = bez_points[j]
        coord = coords[j]
        bez_point.co = Vector(coord)
# Create the object and link it to the scene
    od = bpy.data.objects.new('Slice Object %s' %(i), curveData)
    od.location=(0,0,0)
    od.data.resolution_u=20
    od.data.bevel_resolution=20
    #od.data.fill_mode = 'FULL'
    od.data.bevel_depth=0.1
    bpy.context.scene.collection.objects.link(od)
</code>
In my test data, there are 4 variables: x_coord, y_coord, z_coord, and blender_id.  There is one blender_id thus one unique plotable object with 406 rows of x,y,z coordinates. So imagine this loop firing once and making one object with 406 points
When I run this code, it executes fine, but the resulting image in my active screen appears to show each point of the bezier spline not connecting to the previous or next, but rather, leading in a straight line back to 0,0,0
What I would like: Each point to connect to the next and prior point, not extending back to the 0,0,0.
Example image:

I have hand drawn in the red line indicating what I am trying to have done, and you can hopefully see that instead of this, each point is separate and alone and extending back to 0,0,0
Resources I have checked with include the python blender API documentation,
this other post: Poly / Bezier curve from a list of coordinates and Creating curves in Python as well as this medium article https://behreajj.medium.com/scripting-curves-in-blender-with-python-c487097efd13 particularly this persons code snippets when they discuss closed bezier curves from data.
I am unfortunately unable to figure out what is wrong with my code and would appreciate assistance. If I am lacking in any required info please let me know and I apologize.
Answer: I found a fix to this I believe, credited to rfabbri on another post here (First link in my question)
Comment:
"For Bezier, the default (0,0,0) handles won't be adequate, you may want to set them to the points as well: .bezier_points[i].handle_left = .bezier_points[i].handle_right = .bezier_points[i].co"
So I added the last line you see here:
<code> for j in bezier_points_range:
        bez_point = bez_points[j]
        coord = coords[j]
        bez_point.co = Vector(coord)
        bez_point.handle_left=bez_point.handle_right = bez_point.co
</code>
And the resulting image appears to be what I am aiming for.


Why do some assemblers require an odd-length kmer for the construction of de Bruijn graphs?

Question: Why do some assemblers like SOAPdenovo2 or Velvet require an odd-length k-mer size for the construction of de Bruijn graph, while some other assemblers like ABySS are fine with even-length k-mers?
Answer: From the manual of Velvet:

it must be an odd number, to avoid palindromes. If you put in an even
  number, Velvet will just decrement it and proceed.

the palindromes in biology are defined as reverse complementary sequences. The problem of palindromes is explained in this review:

Palindromes induce paths that fold back on themselves. At least one
  assembler avoids these elegantly; Velvet requires K, the length of a
  K-mer, to be odd. An odd-size K-mer cannot match its reverse
  complement.

It is possible to construct graph with palindromes, but then the interpretation will be harder. Allowing only graphs of odd k-mers is just an elegant way to avoid writing a code for interpretation of a more complicated graph.
Comment: Lest someone in the future misinterpret this, it should be noted that [palindrome](https://en.wikipedia.org/wiki/Palindromic_sequence) in this context has a slightly more specific meaning than it [normally would in English](https://en.wiktionary.org/wiki/palindrome).
Answer: To expand on the answer above, in case it isn't clear, we show:

Why palindromic sequences must be even in length
Why palindromic sequences induce self-loops in a de Bruijn graph
Why self loops in a de Bruijn graph are problematic

1. Palindromic sequence ⇒ sequence is of even length

Idea: in an odd-length k-mer, its middle nucleotide is 'flipped' in its reverse complement, so the two can never be equal.

Suppose you have a palindromic sequence $X$. Then $X$ is identical to its reverse complement, which we will label $\bar{X}$.
Suppose $X$ is of odd length. Then it is of the form $AbC$, where $len(A) = len(C) = \frac{len(X)-1}{2}$, and $len(b) = 1$.
Then
$X = \bar{X} \implies AbC = \overline{AbC} = \bar{C}\bar{b}\bar{A}$
And hence:
$b = \bar{b}$
(since $len(A) = len(C) = len(\bar{C}))$. But this is a contradiction, since $b$ is a single nucleotide, and cannot be equal to its complement. Therefore k-mers of odd length cannot form palindromes.
Hence the length of a k-mer that forms a palindrome must be even.

2. Why palindromic k-mers induce self loops
Each node in a traditional de Bruijn graph is a unique string, but in most bio-informatics implementations each pair of reverse-complementary k-1-mers are identified as a single node, e.g for $k=6$:

A palindromic k-mer (of $k \geq 2$) is of the form:
$xAy$
where $len(A) = k-2$, $x=\bar{y}$ and $A=\bar{A}$ (possibly the empty string).
Hence it will contribute two nodes in the de Bruijn graph:

its left k-1-mer $xA$
its right k-1-mer $Ay$

And an edge going from 1 to 2.
But since this k-mer is palindromic, $xA = \overline{Ay}$ and hence these two nodes are reverse-complementary, and thus the 'same' node, and so this edge is a self loop at this node.

3. Why are self loops problematic?
Self-loops (if they occur in a node with $in\_degree \geq 2$ and $out\_degree \geq 1$) increase the number of possible Eulerian paths in a de Bruijn graph (or more specifically, in the connected component containing this node, which represents a contig, of which their may be multiple), as you have an additional possible Eulerian path for each time you traverse this node.
This increases ambiguity in reading the graph, as each possible Eulerian path is an extra possible reconstruction of the full sequence.
Consider the example:

There is only one possible Eulerian path:

$A B C D B E$

However, if we include a self loop at $B$, which is visited twice above, this doubles to two possible Eulerian paths:

$A B B C D B E$
$A B C D B B E$

Depending on whether we traverse the self loop during the first time we reach $B$, or the second.
Comment: https://homolog.us/Tutorials/book4/p2.4.html "Genome assembly programs also avoid even k, because with even k, many k-mers become reverse complements of their own sequences. **That causes ambiguities in the strand-specificness of the graph.** Therefore, odd k-values are preferred."
Comment: Nice answer @ukemi. It took me a while to understand the conclusion of the point 1, so I have added there a sentence that would have helped me. I you don't like it you can reverse the change, but I would say that a small clarification would be good there.
Comment: @KamilSJaron no worries, the clearer the better - yeah, technically I should have also shown existence for the implication that they must be even to follow (as opposed to just not-odd), but showing existence is trivial via example (e.g. AT, ATAT etc).


How to convert LEGO base plate to a DUPLO base plate?

Question: How can I convert a regular LEGO base to a DUPLO base? I have a table that cannot be changed and it has built-in LEGO baseplates, but I need it to be 100% DUPLO compatible. Any LEGO to DUPLO baseplate converters?
Comment: See also: [Are DUPLO blocks compatible with LEGO blocks in any way](https://bricks.stackexchange.com/q/38/56) and [Are there any LEGO baseplates that are compatible with DUPLO](https://bricks.stackexchange.com/q/2583/56)
Answer: The table IS already cross compatible, even though it doesn't look it. The tabletop or LEGO baseplate is cross molded for DUPLO pieces to fit and lock in on top of the regular LEGO baseplate.
PART ONE: THE PICTURED PROOFS...

So, let's imagine the top of your table is my unopened gray baseplate.

We'll use a DUPLO Cock-A-Doodle-Doo for an example DUPLO model.

Sorry, but I don't want open my baseplate just yet, so in the next four shots we'll use these green plates to show the cross interlocking magic of LEGO and DUPLO.

PART TWO:  THE WHAT IFs...

Now, I did say the magic was cross interlocking, so... WHAT IF your tabletop HAD started off DUPLO and we wanted it to be, in our minds, 100% compatible with regular LEGO.

You see, it is compatible, again, it may not look it at first glace, but as we can see using these White 2x4 LEGO bricks with a Bright Yellow 2x2 DUPLO brick things are indeed cross compatible.

I'm gonna get uber geeky here, but the harder to imagine negative space inside the White 2x4 LEGO brick interlocks beautify with the easier to see studs of the 2x2 Yellow DUPLO brick.

Well, hey!  Hoped to have saved you time, money and effort in fabricating a new table.  Later!
Comment: Thanks for the clear pictures.  They really drive your point home.
Comment: Now you have to tell us what the black, white and grey thing is. :)
Comment: A highly glorified garbage can, that's what it is!  Well, it's a trash receptacle. LEGO themed after an enemy from Super Mario World, called a Thwomp. https://www.youtube.com/watch?v=Yxr5WEYJ-6s.


How long do amaryllis bulbs live?

Question: I've had an amaryllis bulb in a pot for about 5 years now and the bulb hasn't been doing much for, I reckon, over 6 months. When should I consider getting rid of it? Could it have run its course?
Comment: To clarify, do you mean *Hippeastrum*? - most cultivars sold as "amaryllis" are actually Hippeastrum. Historically botanists confused the two genera.
Comment: Here in central North Carolina they can be planted outside.
Answer: My amaryllis bulb is about 26 years old and blooms twice every year without fail. I have it in an east facing window, and I water it as and when I remember!  I feed it with Gro-more twice a year as the main stalk starts to show (only adding to one watering each blossoming time).  I honestly do not pamper this bulb, never take it out of the window (even in winter but central heating usually keeps house at about 20 degrees), forget to water regularly (sometimes the leaves start to droop a little) and yet it still gives me 2 beautiful displays every year.  The bulb has almost filled the pot for the last 6 years, so I took it from the pot 6 weeks ago, cut back the roots (there was very little soil left anymore) and put some new soil in. I thought I had killed it but it is proudly showing 4 deep red blooms on the stalk. I do strip off the dead 'skins' on the bulb when it gets very flaky - a gentle pull brings most of it off.  Hope this helps.
Answer: I would re-pot it and fertilize it and keep it moist for a while, and if nothing happened in a couple of months, I would get rid of it.
Answer: my amaryllis bulb is now 21 years old I leave it in a pot year round in the house some years it blooms twice
Comment: You would improve this answer if you described how you care for your plant: the amount of light it receives, temperatures, feeding and watering schedule, etc.
Comment: @NiallC. is right, Lori. Please give us some more detail on how you keep them, what temperature, etc.
Answer: My Grandpa has one in his living room that belonged to his mother. She has been gone for 38 years, so we figure at the minimum it is 40 years old. He said it had 9 different blossoms this year but only blooms once per year.
Answer: My mother started her Amaryllis in 1942. My sister and I divided the bulbs maybe 15 years ago. They didn't bloom for a few years. Now mine blooms every year and my sister's has only bloomed a few times. No explanation... I remember it blooming as a child and I'm 63. So given its history it's 75 years old this year.
Comment: That surely would be a great picture to share.
Answer: I have an Amaryllis plant. It is planted in the ground in the back yard and has been there for over 50 years. No special care, just watering.
Answer: I'm going to guess it's a Hippeastrum as you're keeping it in a pot - Amaryllis is often planted outside, whereas Hippeastrum are not. They can live for decades (my mum has one that is at least 50 years old). They will go dormant for part of the year. The main thing is not to overwater them or bury them too deep - my mum's has been half out of the soil. If they sit in cold, damp soil they will rot. Do not water them when they are dormant. Six months sounds like a long time to be dormant. Try shifting it to a warmer, brighter spot. If nothing happens, try lifting the bulbs and have a look - are they firm and plump (like a fresh onion) - if so, plant them again and be patient. If they're rotten or hollow, then I'm afraid you're out of luck.

How long do amaryllis bulbs live?


Why was this question voted down?

Question: I'm new to the site - wondering why this question: Database Design Query (not mine) was voted down.  Seems on topic.  Is it not specific enough?  If so, should folks be making comments on how to improve it?
Answer: It was put on hold for being too broad.
Asking for the best-practice for an employee database is not exactly a clear-cut problem to tackle, especially since there isn't really a problem even being stated. It reads more like, "what's your favorite way to do this?" If you check the help-center, it seems questions like that aren't desired in this part of Stack Exchange.
If the question was framed differently, such as,

"I do X to achieve Y. Do you see a cleaner/more maintainable way to do it?",

that would be an actual question that could be answered, objectively. That would probably get a better response from the community.
Answer: Look at the first half of this meta-answer.
The question, which you're asking about, looks like (I'm not saying that it is) an example of "I have a problem (i.e. a database to design), how do I solve it?"
Maybe, theoretically, a question about "design" should be on-topic.
But there's e.g. another question here where someone commented,

Just because the OP used a diagram to describe some classes, rather than code, suddenly they feel entitled to use the "design" tag.

Which implies that users have this site have some opinions that specific types of "design" question are on- and off-topic.

Also, the last time I asked a database-related question here, users seemed to have trouble reading it.
I asked how to improve it and this meta-answer suggested the question would be easier to understand with pictures (e.g. ascii art), or code (e.g. DDL).

It may be that people want a more-general question ... about a more-specific class of problem:

No: "how to solve my problem?"
Yes: "how to solve this class of problems?"

If I look at the titles of other questions tagged database-design recent titles include:

How can I appropriately model relationships that have a cyclical dependency?
Best way to structure many-to-one allocation of users to projects in NoSQL
NoSQL data modelling for multi level nested documents

... which are, more-or-less, general problems. Someone else might have the same type of problem.
Whereas the question you're asking abot doesn't have a good title like that: its title is currently Database Design Query.
Maybe the title should be changed to ask something about (*reads the question body*)  storing sparse (i.e. frequently-missing) or non-homogenous data -- figure out a general question to ask about the specific question.
This meta-answer reads the question as "best-practice for an employee database" ... the question needn't (shouldn't) be specific to an employee database; perhaps it should be phrased to that its being an employee database is a specific example of some (to be defined) more general problem description.

This meta-answer includes,

With a design question, it is expected that the person asking the question has taken some time to sketch out the design that they have come up with and identify the problem they are encountering with the design.

So if the question is going to be about my design(s) I guess it should at least be specific about what the various problems are, that I've identified, with my various designs.
But here the OP was asking, "Here are requirements and here are designs, which design is better?" ... maybe they should have been asking, instead. "Here are requirements and here are designs, and here are problems with the designs."
Actually in this case I think the problems with the designs are obvious, but anyway I think these are various reasons why people might have downvoted.

Why was this question voted down?


Mathoverflow and the mathematical community

Question: What is the general point of view of the mathematical community about MO ?
Do you talk about MO with your colleagues non-"MO users" ?   What are their views?
   Is it acceptable to cite MO's posts in a paper for a peer-review journal ?
Comment: I don't think "acceptable" really makes sense here. In academia, you *must* adequately report all your sources no matter what or where they are. If you make use of an equation from a graffiti on a pillar of the Brooklyn Bridge, then you have to figure out a way to cite it. A journal may require a specific mechanism for unusual citations but they can't reject the citation itself.
Comment: The part about citing MO posts has been effectively answered by the multitude of references to MO in existing mathematical papers (do a search on arXiv).
Comment: Your post includes at least two questions that are somehow unrelated. When I talk to my non-MO colleagues, I usually tell them it is very interesting forum, in particular, if you use one question per post! :)
Comment: "In academia, you *must* adequately report all your sources no matter what or where they are" Ah-oh, given that I got the key idea for one lemma from a Russian street song with words not quite suitable to reproduce in print and another from a friend who, in my student years, challenged me to compete who can say more of abacabadabacabaeaba... without mistake or a break to inhaling (no jokes: he second paper can be found at http://arxiv.org/abs/1008.3077 and the connection is obvious, though I'll abstain from demonstrating the first one),  I'm in big trouble now...
Comment: @SébastienPalcoux: When you wrote "acceptable", the last thing I had expected was for it to mean "accepted by publishers".
Comment: Perhaps, but what choice do they have? You always can just copy (with all required attributions, etc.) the corresponding part of the discussion into the paper and say that it is the only source currently available, so no "respectable reference" is forthcoming within the next several years. Of course, like with every other citation, you have the responsibility to check that the argument you cite is correct and here you *cannot* rely on the "historical acceptance" and on other people doing this work for you.
Comment: I think you may have misunderstood what @darijgrinberg meant. I think he meant that there are several papers on the arXiv which reference MO (in the same way one would reference another paper), not that there is a paper specifically about MO.
Comment: @FrançoisG.Dorais, interestingly, I've had a journal (PNAS) reject, in any form, a citation to notes published on a web page.
Comment: @Mark Meckes In both cases it was more than "inspiration". Understood correctly, it was a full solution modulo routine (for a professional analyst) technical details. If we go into inspiration, the list will be endless. Renyi said that a mathematician is a machine for turning coffee into theorems but he mentioned only the fuel, not the raw material consumed by this machine. Starting at some point, you take in just everything (like any other good artist) and see the whole world as *inspiration*. If you want, we can talk more about that when you drive 30 miles South or I go 30 miles North :-).
Comment: @fedja: I think you're being rather too modest in your personal role in "understanding correctly".  Maybe we can compromise and agree that in any case the song was more than "inspiration" but still less than a "source".  I'd be happy to talk more about the subject with you sometime, though if I drove 30 miles south right now I'd be in the Pyrenees.
Comment: @AmirAsghari : if you prefer, the second question is a specialization of the first, in the sense that something is "acceptable" if it's accepted by the community. So the views of the mathematical community contains this acceptability. What do your colleagues respond to you, are they curious,
unconcerned, afraid ? Is there a natural difference between your young and old colleagues ?
Comment: The part about citing MO posts has been discussed before, either here or on tea (I will try to dig up the relevant posts when I have the time unless someone does it before I get around to it).
Comment: @darijgrinberg, yes thanks. Here is the arxiv's paper (4 May 2013) :
[What does mathoverflow tell us about the production of mathematics?](http://arxiv.org/abs/1305.0904)
Comment: @TobiasKildetoft : oh ok, I understand.
Comment: @darijgrinberg : But everyone can post a paper on arxiv with MO's reference, this does not show that it's acceptable. *Acceptable* means *accepted* for a peer-review journal. Perhaps some journals accept and others not, in this case, which ?
Comment: @darijgrinberg : I'm sorry to have been unclear on this point. So what do you think now ?
Comment: @ScottMorrison: Really? They didn't suggest using footnotes or something else?
Comment: @fedja: I don't think François meant you must also report all your sources of *inspiration*.
Comment: @Mark Meckes "though if I drove 30 miles south right now I'd be in the Pyrenees" Not a bad place for a conversation either :-). I guess I should visit Europe too sometimes though I will, most likely, go to Barcelona and then it'll be 170 miles North for me...
Answer: In my experience, MO mainly satisfies the following need that conferences used (for me) to fill: After thinking about a question for a long time, usually something technical that is holding you up, you have the opportunity to directly ask an expert. At the conference you'd think really carefully about what you say and brace yourself for the answer, hold your breath, and then ask. You'd have to be very careful when you ask, because the expert might have a Fields medal or be a rising superstar...they were, after all, invited to speak at a conference. So you only have one shot to get a good answer and the question should be formulated very carefully.
The community is now the expert, but the idea is the same.
A second fortunate function of MO is the presence of the CW option. We can ask experts about their ideas that might direct or affect our, and the community's, approach to mathematics in general...as well as glean ideas that don't appear in papers. The answers to these are like the things speakers will mention in a talk that are complementary to, or that motivate, their results.
The second feature has developed despite the intention of the site playing the first role. I think this is mainly because a few high-profile members (like Bill Thurston) have opened the door to broader questions.
The strongest criticism of MO by certain of my colleagues is that MO might discourage young mathematicians (graduate students, for example) from thinking hard enough about their problems before looking for help with them. This is a valid criticism, if you believe in the mathematical process as put forward by Hadamard/Poincaré for example. Briefly put: long periods of being stuck after working hard with no progress at all are often critical to kick the subconscious into high gear.
Colleagues have also advised me to refrain from asking questions too frequently (understandably, if you regard MO community as a fields medalist...for example). They have advised that it looks more appropriate to answer questions more often, since it doesn't appear that I'm trying to take an undue amount of attention from the community on the front page. This was good advice for me, since I'm rather excited about MO, don't have graduate students, and have a lot of questions that I'll probably never get around to working on.
Comment: "it might discourage young mathematicians (graduate students, for example) from thinking hard enough about their problems". Only those who are not willing to think from the beginning (and, frankly speaking, I do not really care what happens to them). Those who are willing to think and, especially, those who are willing to think of *other people's* problems may find it rather stimulating (plus much more exciting than Fox news or Obama speeches as a topic of the afternoon tea discussion). ;)
Comment: @Yemon I come from the culture where future mathematicians were supposed (and taught) to think from day one of their undegraduate studies for sure and from the 7-8th grade of school en masse. If you were to get the idea that you should think and solve problems by yourself only as a graduate in Leningrad, you just wouldn't be in the graduate school. Most likely, you wouldn't be in the undergraduate school either but I admit that this may be questionable. We asked each other and shared our ideas much more than it is customary here and yet, we knew that we should be able to hold on our own.
Comment: @fedja That is laudable (I mean this with utter sincerity) but that's not the "initial condition" that I find myself in as a teacher and supervisor :( As it happens my own mathematical origins are closer to what you describe.
Comment: @fedja I agree to some extent with your underlying sentiment, but there are those who start their graduate studies without having been told/taught to think from the beginning, yet on suitable encouragement will develop such skills. For those, I think there is some merit in encouraging them not to use MO as their own Jeeves, at least not at the start.
Comment: Thank you very much for this witness ! I didn't know the book of Hadamard/Poincaré, it looks very interesting, I just buy it on ama---.
Comment: @fedja: A nice point!
Comment: @Yemon Yeah, I know it is different here and now from how it was there and then. However, I sincerely see little chance that somebody whom you drag through the graduate school and whose first impulse when presented with a challenge is to pass it to somebody else will ever become anything worth of being called a professional. If I had an infinite lifespan and 200 hours in a day instead of 24, I would, maybe, show more "humanism" and less desire to "cut corners". As it is, however, I prefer to take care of those who, I believe, deserve it, and simply leave the rest to kinder souls. :)
Comment: @fedja: (Sorry to "eavesdrop") Arguably, it is not kinder to encourage the weaker students you describe. It is kinder to be honest with them.
Comment: @Jon Bannon Perhaps, but since those are pretty much exactly to whom the "most valid criticism of MO" applies, and since it was not I, who invented this criticism, I suspect that it is also not I, who should be convinced here :-).
Comment: @fedja: That is why I think your original comment above was an appropriate one!
Answer: What is the general point of view of the mathematical community about MO ?
The community I am going to talk about is just a handful of mathematician colleagues of mine whom I was talking with today about a "simple" mathematical problem.  I think it is worth hearing.
We tried to solve the problem and we failed. I suggested: okay, I'll ask the question on MO. Their reaction was telling: "What if the question is so simple?" Somehow, they was afraid of asking a probably "simple" though for us a genuine question on MO. It is interesting that It was me who was at danger of losing reputation!! I don't know how this fear of MO is general, but I think MO should encourage genuine questions more. Although, I don't know how.
Answer: Is it acceptable to cite MO's posts in a paper for a peer-review journal ?
Currently neither more nor less acceptable than citing other web sources in a paper.
We hope MO will be around for many years to come.  But many other resources which had that same hope invested in them have now faded away, making papers that cite them less helpful.  If MO is still going strong in 10 years, then a citation to it may be as acceptable as a citation to a paper journal.
Working on fractals, I had once a reference to HAKMEM ... which fortunately was found on microfilm in the basement of a university library.
Answer:
I do talk to my friends about Overflow. I find it somewhat entertaining and sometimes
useful. Some of my friends (a minority) like it, others (a majority) are indifferent,
but nobody said that it makes any harm.
I do cite several MO entries in my papers intended for publication in journals. (Not published yet).
Why not, if we can cite arXiv? The only objection that I know against citing such sources
is that there is no certainty that they will be available in the future in exactly the
same form. I mean people can edit or withdraw entries, or the whole site may disappear.
The last possibility does not seem to be very probable.

Against the first possibility, perhaps it is worth to consider making some questions
and answers impossible to edit or remove.
Say after 3 months since a question or an answer is posted.
We can allow the author of the question/answer to exercise this option.
This is my suggestion to those who run MO.
Comment: So MO, like the planet Earth, is mostly harmless. http://en.wikipedia.org/wiki/Mostly_Harmless
Comment: It does suggest that we should think about long-term archiving of MathOverflow. Perhaps we should print the entire site to a giant PDF and put it on the arXiv. (This is at least half-serious.)
Comment: @ScottMorrison: I agree that there should be a long-term archiving plan (but putting it on the arXiv wouldn't make sense, or even be particularly useful if it lost all the structure).  Convincing a university library to archive it would be a good start.  There are probably people who have more useful contacts than I do, but I'd be happy to help with this.
Comment: I think the first thing to do is to introduce a special status of problems/answers that cannot be altered, edited or removed.
Comment: I do not think that putting a giant pdf file on the arxiv is a good idea. It will be impossible to find anything interesting in this hudge file. When I started using MO a year ago, I first tried to search for interesting problems, but soon gave up, and now I am only checking the new ones. What interests me in MO makes < 1% of all problems, and I think this is the case for most users. Tags do not help much.
Comment: @AlexandreEremenko I do not consider it as necessary to enforce that some posts cannot be edited. You mentione arXiv, also there people can and do post updated version (that is 'edit' their paper). Of course, old versions are preserved on the arXiv and if one wants to be sure one will mention the precise version. *And* this is exatly the same for MO. The full revision history stays visible. If you are worried about later edits mention the revision number of the post/the date.
Comment: Deletion could be a problem; but I think it should be quite rare and undeletion (which is always possible) could be handled on a case by case basis; every post is undelete-able. Also, it would seem better to me rather than to alter the functionality of the main site for some rare cases to perhaps create a mechanism to 'save a frozen copy' as a backup of something one quoted. If one does not insists on automating this a lot, it seems easy to do this.
Comment: All that is needed (for citing MO entries) is the ability to fix these entries, so that they are never altered/deleted, and their URL is fixed. The main principle with references in a published paper is that every cited reference must be available to any reader in the future.
Comment: You can cite a specific version of a post, like arXiv, so future edits should not be a problem. In fact, if you are using the cite link under the questions it contains the date of the revision you are citing.
Comment: @quid - If questions or answers are deleted (which the users can do for their own content more or less as they please), then that content will not be generally visible through the site, and good content does sometimes get deleted.  It is possible to externally "back-up" site contents by using the site's data dump, but this is not useful for the community until someone (better, some institution) makes the effort to regularly keep and make visible their own mirror of the site contents.
Comment: @CharlesStewart 'more or less as they please' seems like quite an exaggeration. For questions it seems *completely* false as one can **not** delete ones aquestions as soon as it has an answer(s) with some upvote(s) (I do not know the precise thresholds by heart yet could looke them up but they are *very* low, something like one answer with score +1 or +2 suffices). I highly doubt there are that many questions that are so worthy of preservation that do not meet this. Also accepted answers cannot be deleted, which often will suffice in standard usecase for quoting (quote 'the' answer to ones q)
Comment: @quid: I should have recalled the point about questions with answers, and I did not know that accepted answers could not be deleted - you are right.  That said, I think that Stack Exchange policy and implementation mean the site is not good as a reference resource without some kind of external archiving.  Some questions of interest to me on the Stack Overflow site were deleted, because despite their interest and quality of answers, they were regarded as being too "soft" some years later.  What happens to our high-quality soft questions if we have a regime change here?
Comment: @CharlesStewart yes I do not disagree that MO in its current form is not optimal regarding archiving. Meanwhile there is a meta-thread dedicated to this. My point here is mainly that in practice the problem is not that big in my opinion and in any case I am against changing the core functionality of the site for what is actually (regarding frequency) a corner case. (In addition to me not following some of what is claimed in comments by OP, there are plenty of reference in the literature to private communcication, letters and what not where it is not at all true that they are available)


Can patent owner sue if a product is made, but never sold (only rented out)?

Question: If a new product infringes upon a patent, but is never sold (only rented out), can the patent owner sue?
Answer: I am not a lawyer so this answer isn't based on direct legal knowledge. That said, I would be very surprised if the patent owner couldn't successfully sue anyone using the patented technology whether or not it is sold or rented. There is a research exemption, but that has nothing to do with renting vs. selling a patented technology. So to be explicit:

If a new product infringes upon a patent, but is never sold (only
  rented out), can the patent owner sue?

Yes
Answer: I am an attorney (though this is not my specialty). But yes, you can be sued for patent infringement if you are renting the product out. The key is that you are earning money (or better said, depriving the patent owner of making money). It helps to think of it like, "am I possibly taking money out of their pocket? If yes, it's probably patent infringement."
As Eric Shain mentioned, there is generally an exception for development/testing (which isn't taking any money away from the patent owner), versus selling, renting, giving away, etc. - all of those are going to take money out of the owner's pocket (theoretically - you can always argue that they wouldn't have gotten this business anyway, but that's a hard argument to win).
Comment: Thanks for confirming my assumption. I do believe the research exemption is very narrow and basically limited to pharma companies.
Answer: If you're in the USA and the question is "if I do X, can person A sue", the answer is always "yes".  But in this case, it would be a legitimate answer. You can infringe a patent all by yourself, sitting at home, without ever leaving the house or selling the product.


How to make a transparent image a non transparent one?

Question: I am a newbie to Photoshop and I have a PSD file that contains a transparent button. Now I want to duplicate that button and move it to somewhere else. When I moved it I realized that the button is transparent, and the place where I move it, has another color, so the effect is that original button changes its color in destination place. Now I want to make it nontransparent. How I can do that?
Answer: I would probably leave the button transparent, but add a layer below it with the desired (or solid black with a blend option of color overlay), place the two layers in a group, and then add a layer mask (the same shape as the button) to the group. This way it is trivial to change the color of the button later by changing the color of the new layer I just created below it.
Answer: Layer → Flatten image.
Comment: When I flatten I lose all the other layers. Why? It becomes only one layer and tells me that it can not do the operation because the layer is locked.
Comment: Oh, I got the problem, my layer was ok, the layer on which I was moving was transparent and in layer list was upper that my dublicated layer. So it was just overlapping. Thanks!
Comment: I don't think that flattening an image should be the first course of action, especially when you want to duplicate the layer onto another document. Checking transparency, layer style, and blend mode should be done first. Then trying another alternative, as Horatio suggested, is a better tactic than flattening an image.


How much lift is lost by wing dihedral, and can it be fixed?

Question: The loss of lift, though negligible, was mentioned in another thread regarding the angle of dihedral wings. Not knowing the coreect name but will external "ribs" on the wing surface reduce that loss? Also, is that lift loss less or greater with forward swept wings than straight or rear swept? And is that loss due to the dihedral angle of the wings increase with a greater angle?
Comment: The title of your post should reflect your actual question.
Answer:
The amount of lift lost to dihedral is because of a trigonometrical condition, and cannot be fixed by ribs.
Lift is always perpendicular to the local surface, and each wing half develops lift at the dihedral angle. Only the vertical bit is useful for suspending the aeroplane weight.
In order to quantify:

Cos 5° = 0.9962, so less than 0.4% of lift is not useful.
Cos 10° = 0.9848, meaning a 1.5 % loss.

Wing sweep has the same roll/sideslip stabilising effect as dihedral does (this answer), so less or no dihedral is required if the wing is swept. But there are many other considerations related to lift and drag with a swept wing.
Answer: Dihedral is included in many wing designs because it is very useful in making the plane fly in a stable, comfortable manner.  As Koyovis explained, lift loss is minimal, and if more lift is needed, simply make the wings larger (or reduce weight!).  This is called wing loading.
Is far as external "ribs", these are called wing fences, and are not usually needed on top of the wing unless you plan to fly near the speed of sound.
However, wing fences underneath the wings, at the wing tips, are very useful for slow flight.
These are seen with many Short Take Off and Landing kits.  Bottom wing tip fences, along with flaps and slats, help increase the Lift Coefficient and maximum Angle Of Attack of your wing.


How many photos will fit on a 16 GB  iPad?

Question: I am interested about an iPad for my mom and can't decide whether to go for 16GB or 32GB. Assuming no movies on it, and minimal amount of apps (she will use it mainly for browsing and skype) how many photos can fit on a 16GB?
Answer: Short answer: 16GB should be fine for photos.
Long Answer: Your question is hard to answer with any accuracy as photos come in a variety of sizes depending on resolution, subject matter etc. For example, a photo taken on your 3GS iphone will be smaller than one taken on your 4GS iphone, which will also be smaller than one taken on your nikon DSLR digital camera. And as you could also reduce the image size based on how you want the photos to appear on your ipad, it becomes a bit more complicated to answer.
However, some math might give you a better idea at least.
1GB = 1024 MB so 16GB is 16384MB. Assuming you lose say 4GB for the in built apps and skype etc. we could say you might be left with 12GB or 12288MB.
Let's assume your mother isn't a professional photographer with a 30 megapixel dslr camera, but for the sake of being conservative we'll say all of her photos are taken on a hi definition camera, like the iPhone 4s. Depending on a variety of factors the photo size will range from about 1.5mb to 3mb at full size (bearing in mind these are still HUGE photos at full res.) If we say 2.25 is an average photo size, you're still left with roughly 5,500 photos on your spare 12GB of space.
Bearing in mind this is still pretty conservative the answer is that your mum can store literally thousands of photos in her 16GB iPad. If you weren't using a really hi def camera like the 4s iPhone, your photo sizes could be as small as 100 or 200 kb's each and the number is more like 50,000 photos.
Hope that's helped.
Answer: It depends on how big each of the photo files are. If they are all exactly the same, you can get a rough estimate by dividing the hard drive size by the file size.
If each photo is 120kb in size, and the operating system on the iPad is 3.4 gb, you can use the formula:
(16-3.4)gb/120kb = 105,000 photos
(32-3.4)gb/120kb = 238,333 photos.
Or more generically:
(Hard-Drive-Size - 3.4gb) / (Average-photo-file-size) = estimated photo capacity
Comment: one question. is it true the thing about overheating that Ipad 2nd gen does not have?
Answer: It will probably be able to hold a couple hundered pictures, because on my 16gb iPad, I have 125 photos, but it still keeps saying "storage almost full." Still, I am taking pictures, which means I can still keep taking as many pictures as I want to until my iPad gets up to 16gb's.
Answer: Back up to Google photo - The free cloud.
Comment: could you expand on how this addresses the count of images?


Order of HTML meta tags

Question: A SEO company suggested we change the order of our HTML meta tags so that <title> and <meta name="description"> are the first two. They say this is to ensure search engines can utilize these two tags. I've been under the impression that the order of tags inside the document's head is not significant. Have I been wrong? Are there really search engines that assume that the first two tags are always title and description and give up looking for them if they aren't?
Comment: See also on Stack Overflow: [Can the order in which adding link and meta tags on head of a webpage have any adverse effect?](https://stackoverflow.com/q/27576959/1591669)
Answer: You are correct. The order of those tags do not matter for SEO. They just need to be present. Whomever said that is obviously clueless (and of course running an SEO business. Sigh).
Comment: Just opinion based on experience. Here's a SearchEngineWatch discussion on the topic - order doesn't matter: http://forums.searchenginewatch.com/showthread.php?t=16452
Comment: Can you provide a source or case study?
Answer: While for the purposes of SEO, it may be true that the order is not significant, it is not true when considering other things like security, content (character) display, or loading speed. It is a good idea to order your page's head roughly thus (presuming HTML5 for syntax):

So far in the document, you should not have used any non-ASCII characters, so character encoding is not an issue yet. But the likelihood of using non-ASCII characters goes up markedly once you open that head tag. Accordingly (and assuming that you are not declaring your character encoding programmatically or at the server level), you should make the next statement your character-encoding declaration. This also satisfies parsers/browsers/agents that would be sniffing for character encoding statements:
  <meta charset="utf-8">

The following two (X-UA-Compatible and viewport) are recommended by the folks at Bootstrap (as recently as v3.3.4). While I am nearly positive that these recommendations are based on performance, most of what I would say would be speculative:
  <meta http-equiv="X-UA-Compatible" content="IE=edge">

If you are thinking about device-agnostic design/development (inclusive of smaller, non-desktop user agents), you should include the following:
  <meta name="viewport" content="width=device-width, initial-scale=1">

Finally, the title:
  <title>Ingenious Page Title</title>

Next, you offer the CSS as soon after the title as possible (no 'daylight' between them):
  <link rel="stylesheet" href="stylesheet-1.css">
  <link rel="stylesheet" href="stylesheet-2.css">

If you are using page-level styles, they would go here. This is largely because of the 'cascading' nature of CSS: namely the last style declaration of identical levels of specificity (such as two statements that target a paragraph p). In order to make overriding external styles easier (i.e. without using greater specificity, or !important), you should put page-level styles after external styles (<link>s).  Also, it is generally inadvisable to use the @import directive in page-level styles, because it will impede the concurrent downloading of other style assets:

This is the point where it seems most appropriate to put meta tags, favicons, and other cruft. It is arguable that favicons or similar assets (e.g. iOS app images) would be loaded before most meta tags, because it gets the downloading of those assets started marginally sooner.
  <link rel="shortcut icon" href="favicon.ico">
  <link rel="apple-touch-icon" href="apple-icon.png">
  <meta name="description" content="Some information that is descriptive of the content">
  <meta name="generator" content="Microsoft FrontPage 2002">

Because it blocks/delays rendering, if you intend to require scripts, load them as late as is reasonable. If they must be in the head, you might load them before the close of the head (). If you can load them later, put them before the close of the body tag ().

It seems unimportant in most cases to pay much attention to the order of meta tags for SEO purposes, given that indexing bots (i.e. search engine spiders) are going to consume the whole page. Otherwise, how would they index a page's content, or update that index later?
It is notable to me that for all that we think we know, and all the recommendations that we find on the web (even from places like Google and Bing Webmaster Tools, etc.), sites like Amazon, Google and other folks who clearly care about such minuscule performance gains don't follow these rules.
Comment: Good answer @DavidEldridge. But would you mind updating your answer to include `application/ld+json` scripts for structured data? For speed purposes. Where would it be best to put it? Should we treat it as external `JavaScript` files?
Comment: While `X-UA-Compatible`, [`viewport`](http://stackoverflow.com/questions/1230019/how-to-set-viewport-meta-for-iphone-that-handles-rotation-properly) and Apple touch icons were still (relatively) new in 2010, all were in use. HTML5 only affected the charset declaration's length. CSS, JS and image pipelining was a concern back then, as well as the (re-)rendering of pages subsequent to the application of CSS and JS. Notwithstanding that, I couldn't find this information in one place (outside of the `head`s of html documents), and after stumbling across this question, it seemed good to do it here.
Comment: All CSS in the header is no longer a best practice for CWV.
Comment: @Bangkokian are you talking about style using the
Answer: From a functionality point of view the following from Bootstrap seems to be the better order of the meta tags:
    1) <meta charset="utf-8">
    2) <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1">
    3) <title></title>
    4) <meta name="description" content="">
    5) <meta name="viewport" content="width=device-width, initial-scale=1">

According to the people at Google, what matters for SEO is

being mobile friendly
title and description
unique and worthwhile content

If your site is not mobile friendly they do not even look at 2) or 3). If it is mobile friendly they may use the title and description when they list your site. No guarantees on that. They may decide to come up with their own description based on what they find on your site.
If your content is plagiarized or repetitious and if you try to stuff it full of keywords or use other 'BlackHat' techniques, those things will hurt you and possibly ban you.
Comment: +1 this [video](https://developers.google.com/search/docs/advanced/crawling/special-tags) from Google confirms much of what you said.

Order of HTML meta tags