How I Rewired My Brain to Become Fluent in Math - <AUTHOR> http://nautil.us/issue/17/big-bangs/how-i-rewired-my-brain-to-become-fluent-in-math-rd <comment><USER3> My observation from years of experience teaching calculus and mechanics is that every student has a different learning style. In particular, there are "theory people" who need to understand the reasoning behind the concepts first and "practice people" who best understand concepts by looking at worked examples. There may be other subdivisions, but these are the main types.

I had two cases when my students showed no signs of progress after hours of theory-style training, and then became Einsteins after solving some practice problems. I was like... why did we waste so much time with the theory???

I don't necessarily agree with the OP that rote memorization is for everyone. Ultimately both the theoretical/symbolic understanding and the "doing"-experience are necessary, but the order in which students acquire these skills is up to them.

Here's a nice quote:

        不闻不若闻之,      Not having heard is not as good as having heard,
        闻之不若见之,      having heard is not as good as having seen,
        见之不若知之,      having seen is not as good as mentally knowing,
        知之不若行之;      mentally knowing is not as good as putting into action;
        学至于行之而止矣    true learning is complete only when action has been put forth
               -- 荀子                                    -- Xunzi

<comment><USER4> 不: not

闻: hear

若: good

见: see

之: have

知: know

looks easy :)

<comment><USER5> That's not as easy as it seems.

若 literally means [some kind of] "if", 之 is not "have" but rather "the" [?]. The last line is completely obscure for my very beginner Chinese skills.

I'd be glad if someone explained this.

<comment><USER3> My chinese is probably more rudimentary than yours, but I often use a firefox plugin that helps you get _some_ idea of what the sentence means: [https://addons.mozilla.org/en-US/firefox/addon/perapera- kun-...](https://addons.mozilla.org/en-US/firefox/addon/perapera-kun-chinese- popup-tra/) (note it recognizes expressions, instead of working only character by character ... )

</comment></comment></comment></comment><comment><USER6> I come from a very similar background as the writer. As a young man, I showed high potential for languages. So when I went to college, I loaded up on languages, graduating with 6 different languages at at least the 200-level and fluency in 3 of those languages. Unlike the writer, I chose neither military nor government work upon graduation, but instead worked as an ATA-certified translator for 10+ years, primarily translating pharmaceutical documentation and medical studies.

I've since moved into professional software development and am now rusty in the spoken languages I used to be fluent in. I work with a number of different programming languages, primarily doing web development since that's where the money is in remote work (although I also have a strong interest in embedded programming). In between, I also finished graduate school in public health (don't ask!), taking multiple upper-level biostats and epidemiology courses.

Anyway, people were always interested in how I learned so many languages. As it turned out, I used similar techniques as what the writer describes to not only learn languages, but also learn graduate-level quantitative coursework, and now programming languages, algorithms, and data structures (an ongoing task!). People are taking exception to her description of the technique as "rote learning". Perhaps a better emphasis would be on repetition, drilling, and fluency. But for me at least, this did entail things like flash cards -- Quizlet is a godsend -- and repeated, focused practice of short problems.

I have found that the technique doesn't seem to work as well for complex algorithms as it did for math and languages. Maybe because it's difficult to break down some algorithms into small parts, perhaps because I just haven't figured out how to do so yet, or maybe I'm just getting older.

But I am in total agreement with the writer that modern education does a grave disservice to young learners by discarding rote learning and repetition.

<comment><USER7> > But I am in total agreement with the writer that modern education does a > grave disservice to young learners by discarding rote learning and > repetition.

I've come to appreciate the importance of rote learning over the past couple of years... but despite its simplicity, I would call it a very advanced technique.

You don't need rote learning to get to understand something. You don't even need rote learning to become very good at something. You only ever need it to be able to think faster about certain advanced topics or if you'd like to become fully fluent in a language.

These are not things a high school student should necessarily spend much time on. Especially considering that rote learning, if not self-motivated, can be incredibly demotivating and have the opposite effect of what was intended.

<comment><USER8> I disagree. We are expecting students to learn more than ever before. Math is a great example. Their ability to handle even a simple concept like multiplication requires fluency in addition. The ability to learn algebra requires fluency in arithmetic. The ability to learn calculus requires fluency in algebra. Tons of kids pass one grade but emerge unprepared for the next. The author hits the nail on the head: they understand the material at the time, but never develop fluency. Then next year when they try to build on that foundation it has evaporated. Rote learning should begin in elementary. I am thankful that I was required to learn my multiplication tables.

Yes, we need to tailor our teaching to the attention span and abilities of our students, but that doesn't mean we shouldn't be using this powerful tool of fluency through rote learning.

<comment><USER9> It really depends on the goal. From a mathematician's perspective Engineering is still part of the kiddie pool of math. The kind of things some people did in high school mostly though route memorization.

However, for ~98% of the population it's by far the most useful parts of math. Then again you can also say the same thing about just Arithmetic, basic Algebra, Logic and Statistics. So, it's really a question of what your goals are.

There is actually a lot of Math that's been dropped from K-12 education. EX: Understanding logarithms is really fundamental for using a slide rule or understanding floating point arithmetic, but it's not really that useful for most people.

</comment></comment></comment></comment><comment><AUTHOR> As a thank-you present to our readers on HN, Nautilus wanted to give you exclusive full access to this Prelude article from our latest print Quarterly online "preview". Subscriptions to our print edition are how we make all our online content free. We thought the HN audience would like this piece so in appreciation for your traffic and your comments, here it is.

<comment><USER10> I love Nautilus! Gorgeous layouts (print & online) with engaging and opinionated content.

I notice that you only sell print subscriptions. Do you plan on selling any digital-only subscriptions? I would sign up in a heartbeat because your online layout is Really That Good (TM).

<comment><AUTHOR> We are planning to have ebooks of each issue available next month. Thanks

</comment></comment></comment><comment><USER11> I can recognize some of my experience in what she's saying -- as I've been told several times in math/stats "you don't understand this, you just get used to it."

That's a bit of troubling statement at first, but I think it's sortof a shorthand way of saying that much of the understanding available comes through the process of repeated manipulation and observing outcomes.

I've also noticed that a decade or two after going through a math undergrad, the limited material I've retained best was the stuff I learned my freshman year and had to repeatedly re-apply in other coursework.

Still, I think she may be overstating the case about the limits of conceptual understanding, though (or perhaps bringing an engineer's perspective to the discussion rather than a mathematician's. ;)

Practice is crucial, but when I need to dredge old mostly-forgotten material up out of my brain, the interconnections formed by the mapping of conceptual space we call "proofs" often turn out to be pretty helpful. There's plenty of things I can't remember that I can derive from what I can recall.

<comment><USER12> I got tired of not having an intuitive understanding of particular mathematical concepts. The rote memorization was very limiting for be because I wasn't as easily able to grasp when it might apply to certain concepts.

Pretty sure Kalid is a commenter here, but I have to give him a huge thanks and plug for BetterExplained.com--really helped me grasp some of these higher- level concepts in a more intuitive manner, even if I didn't walk away with a full understanding of the intricacies.

His Cheatsheet is a great starting point if you are interested in a particular topic: [http://betterexplained.com/cheatsheet/](http://betterexplained.com/cheatsheet/)

<comment><USER13> Wow, thanks for the plug and the kind words! Glad to hear the site is helping -- most of the time I miss the intricacies too, and end up adding things years later [after a re-read] or in response to a comment from the article.

As a more general reply to the article, I was fortunate enough to work with Prof. Oakley on her Coursera Class ([https://class.coursera.org/learning-001/lecture](https://class.coursera.org/learning-001/lecture), I'm the last guest interview at the bottom) and I really, really like her learning strategy.

Her article didn't use the exact phrase "deliberate practice" but I think that captures the essence of what she means by repetition. You need enough conceptual understanding to make sure you're following the path correctly, but then you want to practice -- at the edge of your comfort zone, with feedback, etc. -- to make sure it's really clicking.

It's really easy to fool yourself into thinking "I've got this" when it's untested. In my own case, I realized I didn't "get" imaginary numbers and exponents when I couldn't estimate a^b [a raised to the bth power] in my head with equal fluency for all numbers a and b. I had never really tested every type of number in every type of exponent position (base and power).

For example,

3^4 => this should be a positive real number greater than 1

3^(-4) => this should be a positive real number, very close to 0.

3^i => Hrm.

i^i => Uh oh.

I knew that unless I had fluency with all of these scenarios, I didn't truly "get" exponents or complex numbers. Sure, maybe I had a baby version where I could use them in well-defined ways, but I had a subconscious fear of i appearing as a base and/or exponent. I had to challenge myself and practice thinking through the various permutations before I recognized the gaps. Then I had to deepen my conceptual understanding, and practice again.

(For the previous questions, 3^i should be a complex number on the unit circle, maybe around 50 or 60 degrees, but less than 90, and i^i should be a real number, greater than 0 but less than 1. I can estimate these without calculating them, see [http://betterexplained.com/articles/intuitive- understanding-...](http://betterexplained.com/articles/intuitive- understanding-of-eulers-formula/) for more details.)

Again, thanks for the mention!

<comment><USER14> The entries on complex number, exponential functions & e, and many other subjects at betterexplained.com are simply amazing! It helped to clear my decade-long confusions or fears when dealing with them, Thank you for the great work.

In my opinion the three essential characteristics of a great teacher are expert level in the subject at hand, great communication skill and enthusiasm for teaching. Possessing two of them already makes a good teacher. You have all three.

<comment><USER13> That is really humbling and gratifying to hear, thank you.

</comment></comment></comment></comment></comment><comment><USER15> I found the article rambling and mostly pointless...

However, if you have a weak background in math and want to get up to speed before going into calculus and beyond, I have 2 suggestions.

1) Lial's Basic College Math[1] is adequate and will get you up to speed. 2) Serge Lang's "Basic Mathematics" is great and will cover all you need to go into a rigorous theory based college math class.

[1] [http://www.amazon.com/s?ie=UTF8&field- keywords=lials%20basic...](http://www.amazon.com/s?ie=UTF8&field- keywords=lials%20basic%20college%20math&index=blended&link_code=qs&sourceid=Mozilla- search&tag=mozilla-20) The editions basically the same... pick the cheapest

[2] [http://www.amazon.com/Basic-Mathematics-Serge- Lang/dp/038796...](http://www.amazon.com/Basic-Mathematics-Serge- Lang/dp/0387967877/ref=sr_1_1?ie=UTF8&qid=1412284774&sr=8-1&keywords=serge+langs+basic+mathematics)

<comment><USER3> Since we are on the topic of math textbooks, I will suggest the _No bullshit guide to math and physics_ which is a math textbook written specifically for adult learners. See [http://minireference.com/](http://minireference.com/) for more info.

<discl>I'm the author</discl>

<comment><USER16> It's an interesting looking book, and I'm somewhat inclined to buy it. Bookmarked!

I agree that you don't need to read thousands of pages to learn calculus. However, I don't want to stop at calculus. Basically, what I'd really love to have is a "mother of all maths textbook" \-- a thick and heavy tome that compacts information from all the other thick and expensive books (which I'm never going to read) and different fields of mathematics. With enough detail that you can actually learn from it -- so it shouldn't be just for review and looking up formulas you couldn't memorize. I'd like to call it a reference book I can forever keep in my bookshelf (under my bed) and always look in it if I'm unsure about something...

If someone has book suggestions, I'm all eyes.

<comment><USER3> I've looked at a bunch of these math compendiums while researching what to include in my book, and this one seemed the best so far: [http://www.amazon.com/Mathematics-Content-Methods-Meaning- Do...](http://www.amazon.com/Mathematics-Content-Methods-Meaning- Dover/dp/0486409163) The writing isn't very hand-holdy, but it covers a lot of important topics, and without too much fluff.

For a more "math for general culture" I'd recommend this one: [http://www.amazon.ca/Mathematics-1001-Absolutely- Everything-...](http://www.amazon.ca/Mathematics-1001-Absolutely-Everything- Explanations/dp/1554077192) which covers a lot of fundamental topics in an intuitive manner.

I have both books on the shelf, but not finished reading through all of them so I can't give my full endorsement, but from what I've seen so far, they're good stuff.

</comment></comment></comment></comment><comment><USER17> She never really gave a definition of "understanding". Personally, I see "understanding" as exactly the way she described her method of learning. When I learned f=ma I did it the same way she did, but I would've called it "understanding".

In fact, "rote memorization" is the opposite of how I'd describe her method of learning. She says she learns language by using it in many different situations and learning the situations when it's usable and when it's not to be used. That sounds exactly like a search for intuitive understanding to me.

Rote memorization is more like using flash cards or scanning over a list of words and memorizing their definitions.

Contrast this with her method. She's playing with the subject matter.

I find that playing with a subject is the best way to understand it and to be able to apply it.

</comment><comment><USER18> A similar comment Joel Spolsky from years ago always stuck with me.

"... Even though I understand all the little bits, I can't understand them fast enough to get the big picture. And the same thing happens in programming. If the basic concepts aren't so easy that you don't even have to think about them, you're not going to get the big concepts."

[http://www.joelonsoftware.com/articles/GuerrillaInterviewing...](http://www.joelonsoftware.com/articles/GuerrillaInterviewing3.html):

</comment><comment><USER19> As someone who graduated with a math minor and promptly forgot the vast majority of what he learned, something that really messed me up were gaps in my education.

For example, I took a graduate level course in the foundations of mathematics (proving natural numbers and arithmetic). I grasped the lectures, but one day I was completely stumped by a step in the proof where algebra was performed across an inequality.

I had never in my life seen algebra across an inequality! As an undergrad senior in a 500-level course.

I grew up moving a few times, and even within single schools I found the teachers weren't on the same page in terms of how math would be taught. For this alone, the Common Core sounds like a good idea to me.

<comment><USER20> What do you mean by "algebra across an inequality"? (Does this mean things like "x < y is equivalent to 5 + x < 5 + y"?)

<comment><USER21> Or perhaps more likely, multiplying with a negative number which involves changing the ordering relation in the inequality.

</comment></comment></comment><comment><USER22> Take a look at Daniel Willingham's material and his book "Why Don't Students Like School"

Here's a review of the book: [http://ed-policy.blogspot.com/2009/04/one-of- handfull-one-of...](http://ed-policy.blogspot.com/2009/04/one-of-handfull-one- of-most-important.html)

Here's Dr Willingham's web site with a lot of articles worth reading: [http://www.danielwillingham.com/articles.html](http://www.danielwillingham.com/articles.html)

Here's his credentials: Earned his B.A. from Duke University in 1983 and his Ph.D. in Cognitive Psychology from Harvard University in 1990. He is currently Professor of Psychology at the University of Virginia, where he has taught since 1992.

</comment><comment><USER23> What an incredibly short-sighted sentence: "Sorry, education reformers, it's still memorization and repetition we need.".

I could not disagree more with this article. Memorization helps, but MAKING CONNECTIONS between concepts is _HOW YOU MEMORIZE EFFECTIVELY_.

Memorizing is great for learning different languages. NOT MATH.

Sure, maybe students are bullshitting in understanding concepts, and forgot quickly since they didn't learn anything. However, just memorizing shit doesn't do anything. So many students in other cultures are being forced to memorize everything, and since they don't understand the connections, they cannot come up with the answer on their own. There was a piece on HN about a math teacher that was amazed by how little students knew: They memorized how to solve a particular problem instead of actually knowing _why_ something was true, and therefore couldn't work through basic proofs and stupidly basic, foundational stuff.

A terrible article!

<comment><USER24> This is why the education system will never ever change. Too many people learn too many different ways. Some people can read a formula and instantly memorize it. Other's need a connection to that formula. Some need to figure out how that formula was derived in order to understand and memorize it. And some know the formula before you even show it too them.

Not to rehash what you hashed, but it depends who you are. If you are really good at memorizing, you may not need to make connections. You may just be able to memorize everything. Some people can.

<comment><USER25> This is very true. A corporate trainer once told me there's specific kinds of learners. They've actually identified each type, and which specific methodologies you need to reach each one. The best teachers find a way to synthesize it all into an effective single presentation. (This may also be why tutors are so helpful -- they can customize their material to the audience...)

<comment><USER26> Although there is ample evidence that individuals express preferences for how they prefer to receive information, few studies have found any validity in using learning styles in education.[2] Critics say there is no evidence that identifying an individual student's learning style produces better outcomes. There is evidence of empirical and pedagogical problems related to the use of learning tasks to "correspond to differences in a one-to-one fashion".[3] Well-designed studies contradict the widespread "meshing hypothesis", that a student will learn best if taught in a method deemed appropriate for the student's learning style.[2]

<comment><USER25> Heh. Okay, that's good to know. These comments prompted me to look up "Learning Styles" on Wikipedia, which confirms that scientific studies have not confirmed the validity of the "different learning styles" theory.

[http://en.wikipedia.org/wiki/Learning_styles#Criticism](http://en.wikipedia.org/wiki/Learning_styles#Criticism)

That probably says something about corporate trainers. I still remember the HR department at one company where I worked that insisted on giving the Myers- Briggs personality test to every employee. So maybe this also says something about junk science and the way it lingers on in our workplaces...

</comment></comment></comment></comment></comment><comment><USER14> I am interested in this kind of topic, but came away disappointed. Not only is it long-winded, but also she never gave clear definitions of 'fluency' and 'understanding', which are the key ideas in the article.

I think the reason she has succeeded is quite simple: she is an avid learner. She has put in huge amount of effort into learning. It's not about some magic methods she discovered.

Carrying the formula f=ma in head all day long, thinking about it, practicing its various forms in different situations, that is not rote learning or simple repetition (as the author claims), it is working one's a$$ off to understand something.

</comment><comment><USER27> It's always the combination of conceptual learning and memorization when it comes to learn math. It's like performing a complex computation job once, and then caching the result for fast retrieval. Memorization is for efficiency: it clears the way for our brains to focus on higher-level thinking. The great Euler "memorized not only the first 100 prime numbers but also all of their squares, their cubes, and their fourth, fifth, and sixth powers. While others are digging through tables or pulling out pencils and paper, Euler could simply recite from memory...". Besides, math is all about making invisible visible, about discovery patterns, or about connecting dots. That means we need to have dots to connect, and need to have patterns to work with. If we don't remember them, what the hell can we use for?

On the other hand, there's no need for rote memory. Just practice by solving interesting problems. There are plenty of opportunities to use math every day. There is also a very effective way of learning: work on slightly harder than usual problems. When learning calculus, I started to work on Demidovich's Problems in Mathematical Analysis, and I thought it was hard. Then, I stumbled upon solution book for college math competitions. Man, that was a huge help. After working through the problems, a lot of concepts became clear to me, and Demidovich's problems became reasonably easy too. It turned out the hard problems were hard because they required me to make non-obvious connections, which nudged me to really understand, from different angles, the concepts that I learned in the classroom.

By the way, when did arithmetic become so hard? It seems kids nowadays are being spoiled by their parents...

</comment><comment><USER28> He highlights one of the problems I had with mathematics when I reached University. I was in the top 2% of students in the first few months. I considered it a trivial subject. "Here's a class of problems, here's how you solve them." Easy peasy. Then we started integrating and differentiating forms of problems we weren't familiar with. All of a sudden, everything we were taught didn't seem to apply any more.

Our lecturer told us: "I can see that some of you are struggling and are confused. You want to know how you become skilled at solving these problems? Forget your social life. Solve every problem in that 900 page textbook of yours. When you've done that, come to me and I'll give you another 900 page text book and finish that as well."

In one fell swoop Mathematics had lost all its appeal. I switched to Applied Math and aced it.

On the other hand, my brother actually followed this advice. For an entire year he spent a few hours every night doing Calculus till he recognized every different form they could conceivably throw at him. I asked him how he knew how to solve some problems. He said he didn't. It was all just memorization and recognition.

<comment><USER29> >> I switched to Applied Math and aced it.

What sort of integration and differentiation were you doing originally that is not included in an applied math curriculum?

<comment><USER28> My Applied Math curriculum (roughly):

\- Logic of Compound/Quantitative statements.

\- Elementary Number Theory and Proof Methods

\- Sequences and Mathematical Induction

\- Graphs/Tree/Set theory

\- Algorithms

\- Functions and Application

</comment></comment></comment><comment> B-Con > memorized the equation so I could carry it around with me in my head and > play with it. If m and a were big numbers, what did that do to f when I > pushed it through the equation? If f was big and a was small, what did that > do to m? How did the units match on each side? Playing with the equation was > like conjugating a verb. I was beginning to intuit that the sparse outlines > of the equation were like a metaphorical poem, with all sorts of beautiful > symbolic representations embedded within it.

I cannot emphasize how useful this approach is. What's more, I am very surprised by how many students lack the basic ability to sit and "play around" with math concepts.

I used to tutor algebra, trig, and pre-calc. I was surprised by how few students had the ability to look at something and break it into pieces. If you gave them piece A which they knew, piece B which they knew, and put them together, the result was something new the student couldn't understand and they'd sit and wait for an explanation.

This was sad because this is largely what math learning is. Given pieces you do understand, you put together bigger pieces and then build an understanding of those bigger pieces.

I have always advocated something similar to what what the author said here:

> What I had done in learning Russian was to emphasize not just understanding > of the language, but fluency. Fluency of something whole like a language > requires a kind of familiarity that only repeated and varied interaction > with the parts can develop.

I love this point. I am borderline convinced it it is near impossible to learn math concepts more than one or two steps beyond the point that you are _fluent_ in. Beyond that, it's just memorization, guessing, and poor heuristics that just get you to skate past the test and do little or nothing for understanding or retention.

The bigger picture here is that the author has learned how to learn. It amazes me how significant a divide there is between people who know how to learn and people who don't. Forget IQ or test scores, I think knowing how to learn is the biggest indicator of how far someone will go in life. So perhaps most of all I love the fact that they began this journey relatively late (most students going through a similar math path would have done in their late teens or very early 20s what the author was doing in their late 20s).

</comment><comment><USER30> Case studies in education as applied to non-atypical brains are essentially worthless. You'd think that someone with a newfound scientific disposition might realize that you probably shouldn't make sweeping prescriptions based on personal anecdotes (though honestly, based on the quality of the educational literature I've seen, it's not uncommon even for professional education researchers).

</comment><comment><USER31> I think those of us who aren't a fan of "memorize/repeat" is that it is extremely inefficient. And you lose as many people as you gain.

The classic example is long division. In elementary school I did a thousand long division problems, but I never understood it. I just knew the pattern. I didn't really know the math. It wasn't until much later did I learn how and why it worked. Having done those thousand problems didn't really help my understanding at all. And honestly, it's not a skill I use today.

Rote learning is useful when what you memorize is useful in itself. Learning what 2+2 is useful, but because adding 2 to another small number, including itself, is something you do a lot.

Addition/times tables are great because the scope of numbers is something you will run across a lot of day to day. A thousand long division (or multiplication) problems is just rote work for little benefit. It's better to teach the concepts, and then build on them.

<comment><USER32> I can relate to your long division example. In grade school my mom helped[1] me put in a ridiculous amount of effort in order to get through my school's spelling tests. I have come to believe that the reason that I couldn't spell was because at the time I did not understand the rules behind how the letters form together to get words. Simply memorizing how words are spelled took a lot of painful practice.

A more recent example is when I was first learning lambda calculus I wanted to understand how church encoding worked to allow basic integer operations with just function abstraction and application. Most of the operators are easy except for predecessor, which is absolutely nightmarish to get on your own. I tried memorizing the definition I found on wikipedia for over a year to no avail, but once I understood how it was working ...

      pred = λ n . λ f . λ v.
               n ( λ a . λ b . b (a f) )
               λ k . v
               λ i . i

I haven't yet forgotten what it is.

[1] - well, basically dragged me kicking and screaming

EDIT: formatting

<comment><USER6> > I couldn't spell was because at the time I did not understand the rules > behind how the letters form together to get words.

One of the main goals of this kind of learning (at least for me) is to recognize patterns and rules on your own. When I repeat something often enough, patterns and rules began to jump out at me.

</comment></comment></comment><comment><USER33> Just saw that the author, Barbara Oakley, has a (free) Coursera course titled "Learning How to Learn" starting Oct 3. Sign-up here - [https://www.coursera.org/course/learning](https://www.coursera.org/course/learning)

</comment><comment><USER34> For those interested in this learning approach, I recommend the book "The Talent Code" by Daniel Coyle [1] which covers 3 areas for mastering new skills.

Here the author only mentions about the importance of repetition (which she refers to as fluency). In the Talent code book Repetition is the first step, but we can learn that the brain is wired to master new skills by taking advantage of 2 others areas as well: A/ Ignition (or passion and motivation), and B/ Discipline and long term commitment.

[1] [http://www.amazon.com/The-Talent-Code-Greatness- Grown/dp/055...](http://www.amazon.com/The-Talent-Code-Greatness- Grown/dp/055380684X)

</comment><comment><USER35> Understanding is "facile" [superficial], but rote learning is the real way....?

Seems reversed. An explanation is she's in Electrical Engineering - my ugrad experience of EE was a emphasis on _using_ tools (formula etc) as opposed to understanding them (that's for Science). Engineers, after all, are paid to get stuff done, not just sit there and grok it. "Fluency" with tools works well for EE.

OTOH, all discplines have "tools" \- even pure maths has algebraic manipulation. If you're not fluent, it will slow you down (fortunately, you'll have years of algebraic practice from school).

OAH, most professional mathematicians don't _think_ symbolically (a survey found, IIRC, about 70% visual, 25% kinesthetic, 5% linguistic) - notation not so much a tool of thought as a serial representation (serialization/data format), for recording/communicating. So practice in thinking is what's helpful.

I think fluency with "standard" modes of thought is a double-edged sword. Yes, you become expert with those tools, fast and able. But that very expertise biases your perception and reasoning in terms of them. Thus, it's hard for you to see another way; you'll tend to build on top of them instead. Fortunately, since our tools are pretty good, this approach works well. It's just that you're less likely to see fundamentally new approaches (though to be fair, that's pretty damn unlikely anyway).

</comment><comment><USER36> >>student may have thought he'd understood it at the time, and perhaps he did, but he'd never practiced using the concept to truly internalize it.

I'm changing jobs and I've interviewed at quite a few places off late. Having faced with so many Algorithm and Data Structure questions, I took it upon myself to read upon a good deal of material before I started interviewing. So I did the usual approach one takes while studying math, understand all the basic concepts and look for places where you could apply them, rather than studying individual problems.

Recently I interviewed at one place, where I guess a guy who was just out of college asked a few questions. My general approach is to look for how the problem would fit in the concepts I've learned. I gradually derived the solution out of the concepts I knew. And to my surprise, the solution was simply unacceptable to the interviewer, he just clung to his position that I was wrong. He then proceeded to write the answer, he even wrote the test cases.

Now I go back home and check it out of the internet and it was hardly surprising for me to see what I had suspected. The guy didn't want the answer to the question. He wanted exactly the same answer he had memorized. The guy had even memorized the variable names, even the exact input values.

Most people interviewing you on your Algorithm and Data structure skills. They are simply testing your algorithm and data structure rote memorization skills. The same goes in exams.

<comment><USER37> And isn't that completely bogus too - you don't want programmers who can regurgitate algos you want ones that can take an overview and know which algos to apply and how to implement them in a timely way using reference material if needs be ... perhaps it's too hard to test for that ability in interview?

It's like upthread someone talked about engineering exams - seemingly you don't need working engineers to run through equation derivations and do arithmetic. You want them to understand the basis for the derivations and to have a mental model that will spot if the calculations are way out, for sure, but really you want them to be able to take an overview: know which factors are important, use the engineering tools they have. A practical engineer is going to be using computers to perform calculations (be that chemical processes or electronics or civil structures or whatever).

In a way I think we're on the cusp of a change in how we need to approach job focused learning. We're getting to the point where we've stood on the shoulders of so many giants that if you want to operate at the top you can't see the floor any more. By which I mean that maybe the human mind can't cope with the full vertical stack in some fields, that we need to have people either focus at the bottom - understanding the basis on which particular knowledge is built. Or understand the top - be able to work with the tools for implementation.

Maybe.

</comment></comment><comment><USER38> I have a crappy memory. I tried med school for a year. In all my pre-med and medical courses, they constantly warned us to understand, not memorize. I gladly took their advice, tried to understand rather than rote-memorize, and I ended up flunking 5 exams, which finished my medical career.

The fact is, in many fields of human endeavor, you need to memorize before you can think. Would we have better physicians if they weren't required to memorize and spit out so much rote information? Not sure about that. I think a good doc not only has great personal and intuitive skills, he or she needs good analytical skills and a "think outside the box" problem solving mentality similar to that of a really good computer programmer (which I thought I had, hence crossing over into medicine from computers).

But, a doc also needs to _remember_ stuff. There's so much data and you need to remember signs and symptoms, case histories, and see the similarities and differences with previous cases you've had.

The OP was about math, and I'm definitely in the memorize-the-formula camp; I've never really grasped the theoretical niceties of mathematics and am more of a connect-the-dots kind of guy. But definitely there are similarities between learning math and learning the physical and biological sciences. Some of it is intuitive, but some of it is just wacky stuff out of left field and you have to just take it on faith.

I think we need to emphasize critical thinking and analysis more, but we also need to teach the ancient Greek and Roman methods of memorizing, e.g. the memory palace method -- see _Moonwalking with Einstein_ for more details.

</comment><comment><USER39> It reminds me a lot of the Pimsleur method.

[http://en.wikipedia.org/wiki/Pimsleur_method](http://en.wikipedia.org/wiki/Pimsleur_method)

It's rote memorization and repetition, but it also incorporates interaction and active thinking. Additionally, the repetition is non linear. As you learn new terms they throw old terms at you once in a while to make sure you remember them, and the spacing is set out for maximum retention.

</comment><comment><USER40> I believe that math is something a lot of people can learn and become effective at using, way more than Americans currently believe about themselves.

I think it all comes down to making sure people understand the actual abstractions and concepts rather than formulas and rote learning. The advantage of math is that you can figure stuff out using what you already know, without having to learn every little detail - while that's impossible in other subjects, such as history.

The missing piece is, in fact, granularity and feedback. And real world studies support my position:

[http://opinionator.blogs.nytimes.com/2011/04/18/a-better- way...](http://opinionator.blogs.nytimes.com/2011/04/18/a-better-way-to-teach- math/)

[http://opinionator.blogs.nytimes.com/2011/04/21/teaching- mat...](http://opinionator.blogs.nytimes.com/2011/04/21/teaching-math- advanced-discussion/)

If you want to read how I'd reform education and improve the economy, these are my thoughts:

[http://magarshak.com/blog/?p=158](http://magarshak.com/blog/?p=158)

</comment><comment><USER41> Assuming the author's convictions are true, how would one apply a 'rote learning' technique to programming?

I believe in repetition, but, personally haven't been able to find a useful way of implementing it to become a top-notch programmer.

Why? Well, take calculus. Buy a book, pound problems. Do 1,000 derivatives. Next chapter. 1,000 integrals.

Is there a similar "exercise" for programming?

<comment><USER42> Depending on what you want to learn, sure. Googling for "[someLanguage] practice problems" appears to turn up good results for most languages.

For data structures, write some unit tests and then make them pass.

I personally wouldn't recommend you bother learning the implementation details of algorithms: just learn the names and use-cases. Make some Quizlet flash cards and you're good. If you're having trouble finding some to learn, try Googling "sorting algorithms" or "sorting algorithm for [someDataStructure]". Go from there. I'd recommend a similar approach for design patterns.

If you want to get better at building applications, practice by reimplementing apps you use every day in your favorite language (or just come up with your own). "Building applications" encompasses a wide variety of things not mentioned above that you'll only be exposed to by building stuff, so do that.

<comment><USER43> > "[someLanguage] practice problems" It might also be fall under "Études"

such as 'Études for Elixir' [http://chimera.labs.oreilly.com/books/1234000001642](http://chimera.labs.oreilly.com/books/1234000001642)

which is a collection of exercises that slowly introduce you to a programming language.

I can read stuff out of a book, but I won't have that 'muscle memory' until I've spent that time in Vim and the compiler/REPL. So that when something new gets thrown my way, I'm not having to think back to the basics.

</comment></comment></comment><comment><USER44> "Sorry, education reformers, it's still memorization and repetition we need." This is very true. For example, doing the advanced engineering calculus can often boil down to manipulating polynomial, which are still arithmetic. A person with "understanding" but no fluency in basic arithmetic is setup to fail.

<comment><USER45> If your work seriously involves manipulating polynomials, install some software.

Done, and done better and faster than you could possibly do it.

</comment></comment><comment><USER46> I thought thus would be about the guy on HN who used a psychedelic trip to gett over math anxiety. Still a good read.

</comment><comment><USER47> I think that it is strange that she is saying that there is too much focus on understanding at school. From what I could see, most people learned maths by just memorising the process. Except for a few who invested an exceptional amount of effort, they scored poorly. In contrast, everyone who I knew who focused on gaining a deep understanding was able to pick up maths quickly.

There is one area, though, where there is probably too much focus on understanding at the cost of memorisation and that is in the Olympiads. I remember that many of us held the rather uncharitable attitude that the people who tried to succeed in maths by memorising it were 'stupid'. But clearly, understanding combined with targeted memorisation of the key building blocks will lead to the most success.

</comment><comment><USER48> How is "rewiring your brain to become fluent in maths" different from "learning maths"? Can someone explain this? I read the article, and I don't understand it. To me it sounds like she learned maths, in much the same way one learns anything else.

<comment><USER49> Authors usually don't get to pick the titles of their articles. That's the editor's job and they try to pick headlines which will attract readers.

</comment></comment><comment><USER50> It's not so hard:

(1) Pick a topic at about the right level.

(2) Get one main, maybe plus a few extra, good books on the topic.

(3) In a good chair in a quiet room, in the good book, read the material on the topic and try to understand it well enough to make sense. Then work the exercises.

If something doesn't make sense, look in one or more of the other books.

(4) At times, review the last several topics and try to get more understanding, e.g., what else is true, what is not true, what makes the true statements true and the false statements false.

Maybe take a class that covers the main book and check work and understanding with the professor.

Rinse, repeat with other topics.

Done.

Worked for me.

</comment><comment><USER51> I liked her point of repetition being the main problem. It makes sense as we strengthen the new synopsis that are made. Josh Foer author of moonwalking with Einstein proposed an interesting theory that, essentially fucked up imagery of any kind helps increase and strength synaptic connections.

Interesting watch (first 5mins gives good context) [http://books.google.com/books/about/Moonwalking_with_Einstei...](http://books.google.com/books/about/Moonwalking_with_Einstein.html?id=f_0XXXjJk3gC)

</comment><comment><USER52> I don't understand why there seems to be a languages/math dichotomy. I remember in school teachers used to bucket people in one or the other.

But from what I can tell, and also from the article, they have a lot of common ground. Learning either requires understanding of structure, but also a fair bit of memorization. Learning conjugations by heart is not all the different to learning trig relations. You also need both on the fly when you're using your language/calculus.

</comment><comment><USER53> Memorization is not learning. It is a part of learning. Being able to memorize things and understand their relationships in context is learning.

<comment><USER54> My German teacher at school did an accelerated course from scratch at university (no previous knowledge) - a full language degree. It involved rote memorisation of German texts. It worked! She said that the advantage was that you later recognised phrases and grammar and were able to analyse what was previously just rote memorisation.

I spent a couple of years in Italy in my early 20s and learnt fluent Italian in that time. I took a couple of classes a week in the evenings, but spent the day programming with a team of English colleagues and perforce spoke English. I made an effort to socialise with Italians outside of work.

I went out with groups of Italians many a time, and experienced many a boring evening where if people didn't speak to me specifically I couldn't understand a thing.

I realised that after 9 months I could hold a good 1-to-1 conversation but that it was another 9 months before I was comfortable in a group situation - in your native tongue you can keep tabs on the various threads of a group conversation with ease, whereas if you are having to explicitly process it, it's so easy to fall behind and then you're lost.

<comment><USER55> From experience with exchange students, staying with families and going to regular local secondary school (ages 15-18, look at www.afs.org for more information) -- that sounds typical for an adult in a non-native work setting, making an effort.

Generally students starting at zero will use 3/5/7 months to approach fluency, approaching native level at the end of a stay. The difference being the "jump distance" \-- so German to Norwegian or Spanish to Italian is 3 -- Arabic to Norwegian might be 5 -- and Japanese to Norwegian might be closer to 7.

Coming to Norway, sometimes students with poor English skills will do better - not being tempted to fall back to English, breaking the immersion - and not having such a hard time "forcing" class mates to speak Norwegian.

Having spent a year in Japan myself, it's fascinating how one can go from seemingly "nothing" to fluent after those months of no apparent progress. But language learning tends to be like a staircase -- you can feel stuck at one level for a long time (and being in a foreign setting it can be incredibly frustrating to be constrained to a preschool level of speech) -- only to seem to jump up a level. And then you'll be stuck there... etc

</comment></comment></comment><comment><USER56> I wonder if part of the effect is simply studying a lot. It sounds as if she devoted a lot of time to studying Russian and then maths. Perhaps the actual way she spent the time is not that relevant? Not saying it is irrelevant, but for example maybe simply doing problems in maths for the same amount of time would have been just as effective?

</comment><comment><USER57> Reading this reminds me of how much I really want to be better at math, and especially the quick fire recall and understanding. I'm taking courses with a lot of math that I've learned before, and encountering similar struggles this time around as last time. Maybe I'll try a new approach, one such as this, to insure my success.

</comment><comment><USER58> I get this sense that mathematicians tend to focus on abstracting relationships, whereas programmers tend to focus on abstracting objects/entities. Hard to explain though. Like programmers are constantly building models of the world, whereas mathematicians are constantly building new functions and general transformative techniques.

<comment><USER59> This is the general idea behind category theory: it describes relations and not objects themselves.

That's quite a shift from set theory, where the core idea is that objects can be described with what's inside of them (and building the whole idea of relation as a set of tuples).

</comment></comment><comment><USER60> Author makes generalizations based on her own individual experience - <USER2> process which she doesn't understand. Rot-learning in music (mentioned as example of good practice) produces millions of classically-trained musicians that don't understand anything about music, and can't play even Christmas song by ear.

</comment><comment><USER61> so many aspects of this article echo my own experiences, though i was likely a far worse example of a student than the author of this article. i excelled at literature (and took this talent for granted) and i had a vicious disdain for math. my time in high school was spent anticipating a "mathless" career in the NHL that never quite came to fruition… sometimes you just don't grow any taller after your freshmen year :)

here's how a gift can actually be a curse: i've always had an extremely strong visual memory and it enabled me to get by (and sometimes even excel) at courses like algebra and pre-calc. i'd simply memorize the exact structure of a solution, and "plug and play" from memory when teacher asked identical questions on exams with different numbers. it wasn't until i was an undergrad and i decided to do my own "rewiring" experiment that i realized i hadn't ever learned a thing about math my entire academic career. it made for quite the rude awakening, being that i was a college sophomore who'd just switched from pre-med biology to electrical engineering!

i struggled with basic problems that required even a little bit of mathematical intuition because i'd never developed an intuitive understanding of anything–to paraphrase bart simpson, it was like i was cheating on tests by using my own mind, since i could remember my notes with such vivid detail.

how'd i fix it? i became a voracious reader. i started reading "popular" science books about math that actually interested me, and i realized that textbooks were only part of the puzzle. once i was able to grasp the theoretical concepts (aided by the "pop" books) i could return to the textbooks without being bored to tears with the dry, abstract concepts–i could actually relate the concepts to reality! i also took a keen interest in physics because it connected calculus to the real world. when i realized that a parabola could actually be the path of a cannon ball, it changed my entire outlook on math. things started to click.

so how'd it work out? getting through b.s. degrees in both electrical and biomedical engineering (i was a masochist and picked up a second degree) was nonetheless a struggle, due to the fact i was essentially several years behind my peers in terms of my mathematical ability. also, i constantly had to fight the urge to rely on my memory. old habits die hard or simply just go into remission, but i made it!

where am i now? as an MBA student (please bear with me here) i was fortunate enough to be at a university that recently embraced data science. i fell in love with the field because data can tell a story, and my (now) strong mathematical background enabled me to grasp the underlying math & algorithms that yield the wonderful insights you can uncover if you look in the right places.

was it worth it? absolutely. i feel as though i am a different person that's capable of using both sides of their brain! although i must admit i'm still a natural "right brainer" and i need to use a calculator more frequently than i'd like to admit. i'm an engineering manager at a 9-5, i work as a data science lead for a startup, and i dabble with inventing products. i'm convinced that had i not put myself through the wonderful torture that was rewiring my brain, i'd likely not have achieved a single thing in my career.

if you're really curious to see how someone like me thinks i've done some writing here: www.takeiteasythursday.com/liox

</comment><comment><USER62> I remember struggling with Calculus in high school. I sat in the library next to the smartest guy in the class and explained to him that I couldn't figure out why a certain formula was to be used to solve a problem. It went something like:

Steve: "You have to use that formula to solve this."

Me: "I understand that but why do we use that formula?"

Steve: "Cause that's the only formula that works."

Me: "OK but how did they come up with that one formula?"

Steve: "Cause it just works!!"

He didn't know. That's when I first realized a lot of his knowledge was just memorization while I needed to know the why. It wasn't till my first year in college that I finally found a math instructor who always shows us the reasons why that I was able to take off and grasp math by connecting the dots.

So, no, I do not think memorization is the key but, like most zen things, understanding is.

<comment><USER63> I've constantly struggled with something along these lines too. I've always had a difficult time in Chemistry because i wanted to know the why's of things as opposed to just memorizing things. Even in programming, my intro Java class everyone learned the basic public static void main(String[] args){} and we were expected to take it for granted. The first Hello World assignment took most students a few minutes to complete, but sent me researching the Oracle docs, which led me to the java trail, which made my assignment like a week late lol.

If there's any life hacks on how to minimize this mindset, I'd love to hear about it. I'm constantly struggling to find this balance of memorizing abstractions vs digging in the details.

<comment><USER64> YMMW, but I use "I can always fill in that gap later if I have the time" and move on. Later, if I do indeed have the time or I find out that I'm struggling because of missing details, I'll get back to it.

Its like making a temporary mess in a project while trying to understand the problem you are solving and making a promise that you will refactor it later, once you get to something that works.

<comment><USER65> This is where OCD really kicks my ass. I want to understand everything that I'm typing, and it's a major hurdle to have to accept that, no, I just can't have all the answers.

</comment></comment></comment></comment><comment><USER66> Theorems are muscles of the mind.

</comment><comment><USER67> Nice!

<comment><USER68> FYI: This comment will get downvotes. Not because people here are senselessly mean. But, because the HN community takes a strict approach to comments that add noise without contributing signal to the conversation. Downvotes on "Nice article!" comments frustrate many new users. So, here's your explanation. Welcome to Hacker News!

<comment><USER67> I was simply replying to the explanation that the article is available for free and I care nothing for points or votes, thanks anyway

</comment></comment></comment><comment><USER69> I could hardly stomach the self-congratulatory tone of the introduction. Jeez.</comment>


Meetings are Toxic - <AUTHOR> http://gettingreal.37signals.com/ch07_Meetings_Are_Toxic.php

<comment><USER2> Meetings aren't the problem, in my opinion. People who don't know how to properly run meetings are.

I spent some time in the military, and one of the best skills that experience ever taught me was how to properly prepare for and run a meeting.

Some people prepare too much for meetings with useless props/aids that aren't required, some people allow the attendees of the meeting to derail the subject uselessly, and so on and so on.

I'm a consultant in a large game company right now, and there are too many "emails instead of meetings" types. It's amazing how a quick 10 minute discussion at someone's desk can replace a solid day of useless and confusing email "discussions".

Meetings and email threads are simply tools to get the job done, and as with everything, it's a matter of picking the right tool for the job at hand.

</comment><comment><USER3> "Every minute you avoid spending in a meeting is a minute you can get real work done instead."

I'm probably being a bit too nitpicky but this statement stuck out to me. Two sentences before that the author tells you to do x instead of having a meeting, so you're not going to get every minute back by simply not having meetings. There's no need to exaggerate like that.

Although I do agree meetings are time sinks, and are overused.

</comment><comment><USER4> Meetings can most definitely be a huge time-waster, but not always. Sometimes a few minutes of face-to-face will resolve issues faster than an extended email/im/campfire exchange.

 _They're usually about words and abstract concepts, not real things (like a piece of code or some interface design)_

They have got to be trolling.

In short, this is typical linkbait backed by the faintest smell of truth.

</comment><comment><USER5> "The greatest myth that exists about meetings is that they are inherently bad." -- Patrick Lencioni in "Death by Meeting"

The real problem is not meetings themselves, but that most meetings are run ineffectively. Contrary to what one might expect based on the title, "Death by Meeting" recommends having more meetings, but gives guidelines on how to run them effectively.

</comment><comment><USER6> Meetings are necessary to get everyone on the same page. Short term it is difficult to see the benefits of meetings, but long-term success is only achievable if everyone is cohesively chasing the same goal.

I completely agree that meetings need to have a concrete agenda and should not allow anyone to monopolize air time. But they are important.

</comment><comment><USER7> "Never have a meeting without a clear agenda."

This is the only one that I agree with.

I hate meetings. But I have to admit that they serve a purpose: Getting people to spend some time thinking about a problem and working on it collectively.

When I send out an email, I get very few responses until I start poking people. And then I get just enough to get me to go away.

When a meeting is called, people are forced to be attentive and actually contribute because their boss is in the room. (And yes, their boss was CC'd on the emails above.)

For some things, meetings are the only way to progress them. For others, email works just fine. The key is to figure out which are which and act appropriately.

</comment><comment><USER8> A good set of guidelines on how to run meetings effectively:

<http://artofmanliness.com/2009/11/17/how-to-run-a-meeting/>

(Not a joke, despite the whimsical domain name)

</comment><comment><USER9> Groundbreaking post 37signals has right here. Switching styles away from inflammatory trying to generate some traffic?

<comment><USER4> From "inflammatory" to "so far beyond obvious that it ventures back into the patently false".</comment></comment>


U.S. Military Sees Future in Neuromorphic Computing - <AUTHOR> https://www.nextplatform.com/2017/06/26/u-s-military-sees-future-neuromorphic-computing/ <comment><USER2> I've said it before and I'll say it again, neuromorphic computing is a fun side research topic, but at this point, nothing more.

NOTE: All of this completely changes if neuromorphic chips would put up benchmark results, as of now, the neuromorphic flagship, "TrueNorth" takes a heavy accuracy hit on CIFAR compared to contemporary DL techniques (~5-8% IIRC), imagine how bad it will be on real world datasets!

The essence of my opposition to neuromorphic computing can be approximately distilled to the following exchange:

Neuromorphic architecture: "Here's this really efficient 1-bit/analog computer we made!"

Programmer/AI Researcher: "Cool, does it do anything useful? Have you tried it on benchmarks?"

Neuromorphic Architect: "Well, it doesn't work on benchmarks, but that's your problem, you just don't understand the genius!"

AI researcher: -_- So you made a very efficient chip that doesn't do any useful computation? So an inefficient heater?

Later sometime, neuromoprhic architect to media: "These people just don't understand the genius of neuromorphic, it's the future of chip design and will auto-magic away our problems!"

Media: "OMG Yes, stoopid programmers inhibiting adoption"</comment>


Infectious Theory of Alzheimer's Disease Draws Fresh Interest - <AUTHOR> https://www.npr.org/sections/health-shots/2018/09/09/645629133/infectious-theory-of-alzheimers-disease-draws-fresh-interest?ft=nprml&f=1001 <comment><USER2> Dupe</comment>


Modified radar gun identifies suicide bombers up to ten meters away - <AUTHOR> http://www.engadget.com/2010/11/27/modified-radar-gun-identifies-suicide-bombers-up-to-ten-meters-a/ <comment><USER2> I'm struggling to see the usefulness of this technology. If an attacker is within 10 meters, it is simply too late. The average human can cover 10 meters (~30 ft) in 5 seconds or less. Not to mention, detonation of a well designed explosive at 10 meters is still going to severely injure or kill a lot of people.

<comment><USER3> Place the gun somewhere everyone must walk past and then stand further back.</comment></comment>


GitHelp – Ask the authors - <AUTHOR> https://githelp.io/?ref=hackernews

<comment><USER2> This service has been spamming developers, harvesting emails from open source repos and then emailing them, advertising the service. Really not cool.

Even though it looks like quite a cool service, honestly I wouldn't use them on principle.

Here's the email I received: [http://i.imgur.com/Kf9Nv3F.png](http://i.imgur.com/Kf9Nv3F.png)

<comment><AUTHOR> We were not advertising, we're inviting the hackers to join if they are interested to send they help requests from their communities based on their contributions.

We understand that it's not acceptable by some people and that's why we're going to change that.

<comment><USER2> Well that is advertising. You run the service, you're emailing people to tell them about the service. You phrased it in a way that implied it was doing the developers a favour (and I'm sure that you feel that you are - your software looks good) but nevertheless, it's advertising.

It's also spamming. Harvesting email addresses from people contributing to open-source isn't cool. I'm glad to hear you'll be changing that.

I know it's competitive out there but your app looks good, let it speak for itself. You don't need to stoop this low.

<comment><AUTHOR> Thank you for your feedback, and I hope we see you on GitHelp someday :)

</comment></comment></comment></comment><comment><USER3> Questions:

1) Why would I want people submitting a request through this application rather than just using Github issues tracking? Using them would create an additional channel of communication that I now have to not only check but sync. Rather have one channel of communication for my projects

2) I don't see anywhere that the questions and answer will be share with the community like they are with StackOverflow. Why would I want to hide valuable information behind a curtain that no one can see unless they sign up?

3) I personally see no benefit for a CLI interface. I don't see the value in learning a non-standard interface just to get help with something. Yea I can see the "look this is cool" factor, but honestly, I think that's all it is.

I can't even count how many of these startups have come and gone since the time I've been on Hacker News. They never seem to be around long and, quite honestly, I don't think the creators get that they are fixing something that isn't broken.

</comment><comment><USER4> Since it was mentioned on the title, here's a tip

Don't sign up for the ZenDesk trial, unless you are sure of what is it about and that you want it.

You'll spend 10% of your time evaluating their product and 90% of the time dealing with their aggressive sales team and tactics

<comment><AUTHOR> We've compared GitHelp to ZenDesk in the since that can help people serve their customers in a better way. The people here are the open source maintainers and the customers are the developers who are using their projects.

</comment></comment><comment><USER5> It seems like your goal is to be a better search engine than Google, and focusing primarily on the command line.

What is the reason for a developer not wanting to type into a normal search engine a few keywords about a coding issue?

This concept just doesn't make sense to me: "Describe your problem in details with markdown supported. GitHelp will use your description to find you the most relevant content and resources to help you solve your problem instead of Googling."

Here is a suggestion, show us an example (with screenshots or a video) of a query or question using Google search and using GitHelp, then we can properly see the value of the service.

The "getting stuck" part is the most fun for me personally. It means I've hit a challenge that I've not faced before and have to do something thinking and research to solve it.

</comment><comment><USER6> Summing up: you are harvesting identities and then spam them. It is not just unethical, is ilegal under the CAN-SPAM act.

</comment><comment><AUTHOR> Hey there, Thanks for checking us out :)

We have multiple goals we want to achieve with GitHelp, the first one is helping busy open source maintainers to manage all the questions and support requests that comes to them from different sources like GitHub issues, Twitter, Mailing lists, StackOverflow, forums, or even requests for audio and video conversation in one place. You can think of it as ZenDesk for open source projects.

The other side of that is for the benefit of developers, by matching them with the best experts and increase their chance of getting the best answers they need as fast as possible. But we don't just depend on matching developers requests with experts. We think there's enough content on the internet from resources like Documentation, Tutorial sites, StackOverflow questions, and blogs that we can match your request with a content/link that can help you without nagging someone.

This beta version of GitHelp have the core of the product. Developers can create help requests and we match them with the open source maintainers and maintainers/hackers can reply.

What's next for GitHelp is the dashboard for maintainers to manage the all requests and collaborate on that, the matching with content, also the payment is coming up very soon. We focused on the Ruby community right now, but we'll expand to other communities soon like JavaScript. Please let us know what you think!

<comment><USER7> > Hey there Product Hunt!

Wrong site! This might be why you're being downvoted.

<comment><AUTHOR> Sorry about that!

</comment></comment></comment><comment><USER8> What's the difference to Stackoverflow? Code oriented help platform for developers sounds like Stackoverflow.

Edit: Finished googling ZenDesk. If I understand correctly then what you are doing is a platform independent ticket system for open-source developers? Then that's not what the title says.

</comment><comment><USER9> `solve your problem instead of Googling.`

Better to google first then ask, or it could be a spam platform.

</comment><comment><USER10> "...before grating us any access..." *granting

<comment><AUTHOR> Yeah, thank you :)

</comment></comment><comment><USER11> What is it different form AirPair besides the Git pedigree & GitHub integration?

<comment><AUTHOR> It's different in multiple ways, but some of the features that distinguish us from others is under development. But with the current features we different with things like GitHub integration, and also and that's the big difference is the Expert criteria on GitHelp is that you have to be an open source hackers, someone have contributed to open source project, but not any project. We match your request with the people who contributed to the projects that your using in your decencies.</comment></comment>


Relationship between Education and Mental Health: New Evidence from Twin Study - <AUTHOR> http://sf.oxfordjournals.org/content/early/2016/05/20/sf.sow035.abstract <comment><USER2> The study argues that the positive relationship between mental health and higher levels of education is due to confounding factors. The take home message seems to be that higher levels education is not important to mental health.

I think the larger narrative here is that higher education is not as important to success as previously believed. Was someone successful because they went to college, or were they already on a trajectory for success, and they just happened to attend college because they were offered a free ride?

<comment><USER3> It's all statistics, I would think the highly educated has a higher probability to be more successful then the less educated when a large sample pool is used?

<comment><USER4> It's turtles all the way down.

</comment></comment></comment><comment><USER5> Full text on SciHub: [http://sci-hub.cc/10.1093/sf/sow035](http://sci- hub.cc/10.1093/sf/sow035) (PDF)

</comment><comment><USER6> So in short, by comparing identical twins, this study found that people with better mental health tended to achieve a higher education, meaning that the arrow of causality doesn't go the other way: education doesn't necessarily improve mental health.

</comment><comment><USER7> TL:DR "If there are social factors that systematically drive differences in mental health within pairs of MZ twins, our findings suggest that education is not among them."

<comment><USER8> If every article on HN had a TL:DR, I'd be a happy camper.

</comment></comment><comment><USER9> "confounding factors. "

I'm going to go ahead and state the obvious. School systems (all social systems) filter for (relatively) functionally stable individuals. This is the case with the work-force too, and easily explains the correlation between the unemployed and the mentally ill. One does not cause the other, one filters out the other.

I guess it's easy to ignore this dark possibility; it would imply deep, and possibly irreparable facts of human nature.

<comment><USER10> I wonder if this a relatively new phenomenon, or if it has always been the case.

</comment></comment><comment><USER11> Nice to see this linked to the original article rather than to a pop article misrepresenting it.

</comment><comment><USER12> I don't see the surprise however.

<comment><USER13> it's spelt out in the abstract, no?

 _> Prior research has documented a strong and positive correlation between completed education and adults' mental health.

...

> Results from our analyses suggest that the observed association between > education and mental health is attributable to confounding on unobserved > variables._

</comment></comment><comment><USER14> The title is misleading, though the original is not descriptive. Suggestion: "Higher education does not improve mental health, twin-study proves"

<comment><USER15> It's a journal article title, not linkbait. Most scientific articles don't give away the ending, they're just a statement of what is. The idea presumably being, you must read at least the abstract

</comment></comment><comment><USER16> sociology was right.</comment>


Franka: A Robot Arm That's Safe, Low Cost, and Can Replicate Itself - <AUTHOR> http://spectrum.ieee.org/robotics/industrial-robots/franka-a-robot-arm-thats-safe-low-cost-and-can-replicate-itself <comment><USER2> Everything was pretty standard until I got to the price. This robot is a nice improvement, but there's already many good collaborative robots (i.e. [http://preciseautomation.com/PF400.html](http://preciseautomation.com/PF400.html)).

But if they can actually hit the price point it will be game changing:

"Another factor that will make Franka stand out is cost. At the time of this writing, the robot was available for preorder at a yet-to-be-confirmed price of €9,900, or about $10,500. That's a startlingly low figure for such a capable robotic arm. For comparison, Rethink's Sawyer sells for $29,000, and Universal Robots' best-selling UR5 costs even more, at $35,000."

Heck, even $15K vs the standard $30K would be a big improvement.

<comment><USER3> Agreed this could change the game. I think there is a large network effect to this type of product. Once people get used to it, learn how to code it, build tutorials, start using it on projects, and tell their friends about it, they won't want to switch. Right now Universal Robots seems to have a large share of the existing market, but many small shops are still just getting their first robotic arm. Will be very cool to watch.

<comment><USER4> I agree that effect will exist, but it remains to be seen when it will kick in.

Ie, if there are big improvements left to be made then that network effect can be overcome a few times by each 'big leap' change. Once the market matures though, you probably will see strong lock-in as you describe.

</comment></comment></comment><comment><USER5> "Replicate itself" is a bit much. It's used on its own assembly line. Fanuc has done that for two decades. Here are Fanuc robots making more Fanuc robots.[1] Robots are pouring molten metal for casting, loading and unloading CNC machine tools, and making many of the parts. Then robots assemble the parts.

[1] [https://www.youtube.com/watch?v=pgzrkwXV- bY](https://www.youtube.com/watch?v=pgzrkwXV-bY)

<comment><USER6> Not quite skynet yet then

<comment><USER7> This is an ancient video about KUKA robot production [1]. While it's not very automated at all, some things are done with robots because no human has the required strength or precision.

Truth is, robots have been building robots since the 60s or so, long before I was born, and long before skynet was a fictional gleam in some author's eye.

[1] [https://www.youtube.com/watch?v=0qM0znv70IA](https://www.youtube.com/watch?v=0qM0znv70IA)

</comment></comment></comment><comment><USER8> "Clone itself" as long as you get gearboxes, actuators, bearings, bolts, and any other part already made by other machines. "Assemble a copy of itself from parts" would be more accurate, but of course less attention grabbing.

<comment><USER9> I'm guessing it could 3D print/CNC quite a few of its own parts?

<comment><USER10> Unlikely - seven axes is very flexible, but it can't lift more than 3Kg, I suppose a very small handheld router could allow it to do some CNC, though the precision would suffer compared to a normal CNC; by the same token, it could hold a 3D printer's extrusion nozzle, but the accuracy would be poorer than a dedicated printer. It sounds like they are hoping to drive their production line entirely with their own robots, not to manufacture all the parts needed in-house.

<comment><USER11> The key is to design it in a way that such precision isn't really necessary. It probably isn't for most of it. Some things are, and for that, it puts the part on a precision jig or whatnot, rather than relying on it's own precision.

Also, if it works the way they say it does, where it is constantly comparing what it measures against its internal model and adjusting the model (similar to how our own arms and brain works), again, precision (in the geometry of the parts) isn't so necessary.

</comment></comment></comment></comment><comment><USER11> One thing it doesn't do, that would be particularly powerful, is emulate the geometry of the human arm. If it did, and it if it was typically paired with a mirror image arm, you would be able to very easily train it to do most tasks that can be done by a human. Instead of "programming" it to, say, iron a shirt, you just get someone who is good at ironing shirts to do the task over and over while it copies them, gradually improving its abilities.

Combine that with designing it in a way that it can do a large part of making new robot arms, and the costs should drop and the capabilities should increase....dramatically.

<comment><USER12> The very easily trained arm depends on a lot of precision of the surroundings to repeat the process. Knifes and ingredients at the same spots.

Else you enter the World of cameras and image processing. A expensive world still.

<comment><USER11> Yes I assume there are cameras, and that it isn't copying exact moves but actually learning. I'm not suggesting it would figure out how to iron a shirt quickly, it would take thousands upon thousands of hours of watching/copying as someone is ironing. But hey we were worried about robots taking jobs...and there's a job! (and they are also producing ironed shirts!)

Cameras aren't particularly expensive, the ones made for cell phones can do fine and they are a couple bucks. The software is hard but machine learning is improving by leaps and bounds. And software may be expensive to develop, but it isn't expensive to make another copy of.

<comment><USER13> The problem isn't the hardware here, the problem is the software. Robots just aren't smart enough to perceive the world around them yet. People are working on it, but it's still _very much_ in the research phase at universities. You should check out HERB at Carnegie Mellon (1), which is working on things just like this. A fun anecdote - all the students spent forever trying to get the robot to open a microwave (and keep in mind this is a highly controlled environment and they knew exactly where it was). Eventually they gave up and modified the microwave.

Robotics is really, really hard.

(1) [https://www.personalrobotics.ri.cmu.edu/](https://www.personalrobotics.ri.cmu.edu/)

<comment><USER11> True. I bet if the hardware was cheap enough, the software would advance a lot quicker.

I mean, imagine the only really useful thing one of these things can do is make a copy of itself. And it might takes it a month running non-stop to do it, but the parts are cheap so it only costs a few hundred bucks for a new one. Would you want one of these things in your basement working away? I sure would. And I'd be pretty interested in tweaking its software and training data and whatnot to make it faster and better.

Sure it'll be a good while before it is folding laundry or picking weeds in the garden or whatever, but I think the pace of improvement would pick up quick once these things are available in mass.

</comment></comment></comment></comment></comment><comment><USER14> I'm curious if there's a small population of people (with the means) that buy these robots for private/hobby use, and if so, what they do with them in their house/workshop?

Cause honestly, I would love to play and experiment with a few of these to see what I can automate around the house and maybe if I was inclined create a mini-assembly line for "etsy" like products.

<comment><USER15> I suspect that most of them compete in the Amazon picking challenge - [http://spectrum.ieee.org/automaton/robotics/industrial- robot...](http://spectrum.ieee.org/automaton/robotics/industrial-robots/team- delft-wins-amazon-picking-challenge)

</comment></comment><comment><USER16> Man, $10K - soon we're going to hit a threshold of some sort, and automation is going to explode.

</comment><comment><USER17> 10500€ for 7 degrees of freedom is awesome. Usually you get small 6 axis bots for 20k - 40k, without collision detection. Not to mention user friendly software.</comment>


Seeking the Lost Art of Growing Old with Intention - <AUTHOR> https://www.outsideonline.com/2267886/last-naturalist <comment><USER2> I just returned from a Christmas weekend back in Minnesota - and saw my beloved 93 year old great aunt and 86 year old grandfather. Both now live in the same old persons home.

I left my visits to them saddened and somewhat depressed. These vibrant and influential souls reduced to a small studio apartment to live out their days, wracked with the infirmaties of old age. While old age is still a distant horizon for me, I'm leery of what it means given how I see my relatives living.

Yet, this article - and remembering the intentional lives my aunt and grandfather lived - gave me a new, hopeful perspective.

Life doesn't have to end when you start collecting your social security check. You may finally have the freedom to realize your purpose on earth.

</comment><comment><USER3> This is a great story about a great man, but the post title / url slug "The Last Naturalist" really misses the point. Living close to nature is something that we must bring to the fore for those of us who have lost it. We reach universal ecological literacy not by suggesting that it's dead but by teaching it, and living it.

<comment><USER4> I'm not quite sure how that title made it in there (unless the submitter broke the HN guidelines by editorializing) but we've restored the article's title above.</comment></comment>


Ask HN: Does it feel like there's been more tech layoffs lately? - <AUTHOR> Feel like I've seen a lot of layoffs lately, across a lot of different companies (not just overfunded unicorns)... <comment><USER2> Layoffs become a trend and there is a cascading effect. One company does it because they have to and others start doing it because they think they should too. The public companies start doing it to cull their ranks because they want to.

</comment><comment><USER3> When in doubt make a spreadsheet.</comment>


Show HN: A site that lets you predict when Elon Musk will land on Mars - <AUTHOR> https://www.muskonmars.space/ <comment><USER2> Such a cool idea but, isn't a bit too obvious that the people reserving a day on the calendar showed but the website are not real? The calendar has only 3 days booked, what about the other people that every second are reserving a day?

Also, you need to think about what you are going to do with the money if no- one picks the right date, otherwise there might be legal issues...

</comment><comment><USER3> LMAO. Love this. Reminds me of what AirBnB did with Obama Os. Even better cos its a digital product.

</comment><comment><USER4> The ultimate troll would be Elon Musk buying a day lol

</comment><comment><USER5> Get rid of the calendly calendar. It's a massive pain it the ass on mobile.

<comment><USER6> Yeah the mobile version is trash

</comment></comment><comment><USER7> There needs to be a choice for never.</comment>


Localizing "Jump Up, Super Star" - <AUTHOR> https://nintendotreehouse.tumblr.com/post/167703261242/localizing-jump-up-super-star <comment><USER3> Interesting peek behind the veil, localization goes far beyond simple translation but that's not immediately obvious to most, unless they're playing a poorly localized game!

I don't have much else to to add except to say that Odyssey is a fantastic game and you should buy it. I'm a PC gamer and have no nostalgia goggles for any Nintendo property except Pokémon - I don't even like platformers! - <USER2> that game is a joy to play. The section where the song in TFA played was particularly stand out.

<comment><USER4> I'm a big Nintendo fan. Other than that, I came to say almost exactly what you did. Including the recommendation!

Localization in entertainment is often more about preserving the conveyed feelings than translating the words themselves. During the recent development of Need for Speed: Payback, I happened to sit next to two people working on dialogue and localisation. I'm a software engineer working on the UI team, but for a few months, these wonderful guys were seated in the UI room.

I learned a bunch from them, especially when they discussed how to translate things like common sayings and cultural references.

</comment></comment><comment><USER5> Song translation is a really interesting "intelligence-complete" [constrained] optimization problem. You have an objective function that needs to take into account:

\- closeness of meaning to the source language for each line or group of lines

\- rhyme scheme in the target language (often completely absent in the source language)

\- meteor/scansion in the target language (i.e. strong syllables on downbeats, see: [http://www.patpattison.com/perfectmatch/](http://www.patpattison.com/perfectmatch/) \- and, as is often the case when the source language is a language like Japanese where syllable stresses are ignored, the melody is not written to make this easy)

\- if the target language is tonal or semi-tonal, the degree to which words match the melody increasing/decreasing in pitch

\- overall natural feel of the lyrics as dialogue

So the song re-writing is an iterative process as indicated here: over time, you explore the space of possible translations, evaluating against these metrics, and recognizing that changing one line could have higher-order effects, i.e. you need to change the rhyme scheme and therefore require a reordering of two other previous lines, leaping out of a local optimum and throwing out a lot of progress to make the overall song even better!

Skilled songwriters, of course, can instantly discard huge portions of the space, and know intuitively where to begin. But even the best still need to iterate. And I find translation a great exercise for songwriting, since it lets me practice navigating this subspace of the much more complex general problem: how do you write a song starting with a blank page?

</comment><comment><USER6> If you're interested in video-game localisation, you'll get a kick out of Legends of Localization. It's a site run by professional translator and amateur game-translator Clyde "Tomato" Mandelin, and it has a bunch of articles examining the translation of particular well-known scenes¹ as well as in-depth comparisons between different versions of a single game, like The Legend of Zelda².

¹: [http://legendsoflocalization.com/articles/recommended/](http://legendsoflocalization.com/articles/recommended/) ²: [http://legendsoflocalization.com/the-legend-of- zelda/](http://legendsoflocalization.com/the-legend-of-zelda/)

<comment><USER7> Interesting site.

I immediately thought of the All Your Base Are Belong To Us meme. [https://en.m.wikipedia.org/wiki/All_your_base_are_belong_to_...](https://en.m.wikipedia.org/wiki/All_your_base_are_belong_to_us)

<comment><USER6> There's an article about that, too!

[http://legendsoflocalization.com/lets-take-a-peek-at-zero- wi...](http://legendsoflocalization.com/lets-take-a-peek-at-zero-wings-all- your-base-translation/)

</comment></comment></comment><comment><USER8> I didn't even know there was a Japanese version of the song. I set my game- language to Japanese, but the song was in English.

I'd enjoyed a link to the Japanese version and lyrics as part of an otherwise very interesting article.</comment>


Asm.js Chess Battle - <AUTHOR> https://dev.windows.com/en-us/microsoft-edge/testdrive/demos/chess/ <comment><USER3> The code they are benchmarking is written in C, then compiled to asm.js (presumably with Emscripten). In one version, they remove the "use asm" header, but the code appears identical.

That seems like a strange test. They aren't testing JS against ASM, or even compiled-to-vanilla-JS vs compiled-to-ASM. Both versions are compiled to ASM (complete with all strange annotations like num|0), only one has the asm optimizations disabled. I don't know enough about asm to know if their annotations are slower than vanilla JS in unoptimized engines, but I suspect they might be.

I was also surprised that asm still won in Chrome - I thought Chrome optimized for asm-like code without checking for the "use asm" flag.

<comment><USER4> > I don't know enough about asm to know if their annotations are slower than > vanilla JS in unoptimized engines, but I suspect they might be.

The opposite is true, for the most part. JS engines, even without asm.js optimizations, utilize the fact that the | operator emits a 32-bit integer (per the JS semantics), so it helps their type inference.

(The engine needs to be good enough to get rid of the actual 0 value in the |0 coercions, but JS engines have been that good for several years now anyhow.)

> I was also surprised that asm still won in Chrome - I thought Chrome > optimized for asm-like code without checking for the "use asm" flag.

Chrome detects "use asm", and enables TurboFan on such code. All JS engines today detect "use asm", except for JavaScriptCore.

</comment></comment><comment><USER5> > Refresh page to play again

This was very infuriating. The server seemed to be under load and took several minutes to load. I was not going to wait for it load again to retry the simulation.

<comment><USER6> Seriously. Came here to say this. How hard is it to add a button that says "play another".

<comment><USER7> FWIW, I put this in console so I could click the banner at the end to start over:

      $('#chess__board-message').click(function() { var m = new ChessDemo.Match(); m.$boardOverlay.hide(); m.startNextTurn(); });

</comment></comment></comment><comment><USER8> Interesting. I slowed a game down to 1000ms per move so I could realistically follow what was going on. The game started 1.Nf3 Nf6 2.e4?

So White sacrifices (loses?) a pawn for no compensation on move 2. Not really sure what this says in respect of the experiment in general, but it does smell a little.

Also; Showing the dark squares would be a massive usability advance! And it would be nice if they respected some simple and fundamental chess conventions (for example presenting the moves in the way I did in my comment above - <USER2> numbers increment after whole moves not half moves)

<comment><USER9> It's almost certainly playing out of an opening book.

There is a move history, but you have to expand it.

<comment><USER10> How does playing out of an opening book explain the opening blunder 2. e4?

<comment><USER11> Well, I guess if it really was out of a book, it would imply that the quality of the engine itself wasn't at fault, but rather a bad opening book. Also, without that line being thoroughly researched, it'd be difficult to say whether it's a blunder, or a clever sacrifice. Again, it could be an incomplete opening book which led the engine to offer the sacrifice, but then didn't have info on how to capitalise on it.

Though in this case, I think it's almost certainly a blunder, that line does not appear to be a well known opening.

<comment> V-2 There are opening books, and there are opening books. 1. Nf3 Nf6 2. e4 can no doubt be found in some opening books due to the sheer fact that someone, somewhere, played it, and it got archived. Then yes it's a line that could get selected at random.

It's not a serious opening though, it looks frivolous - could be played in simultaneous games, or in bullet chess for its surprise value etc.

If you optimize the opening book to include serious games only, you're unlikely to come across this line. [http://www.chessgames.com/perl/explorer?node=98&move=2&moves...](http://www.chessgames.com/perl/explorer?node=98&move=2&moves=Nf3.Nf6&nodes=74.98)

Given the insame amount of opening theory research humanity has done by now, if e4 on the third move here was even remotely close to a clever sacrifice, chess community would have noted it by now.

</comment></comment></comment></comment></comment><comment><USER12> I set it to as slow as it could go so I could watch the game. It was weird because it got to a point where it declared a draw, but the pieces were still moving around so I left it alone. Eventually a couple more pieces were captured and the non-optimized side managed to win, so it updated from "draw" to "checkmate".

</comment><comment><USER13> Interestingly, asm.js has an advantage in Firefox and Chrome for me, but not in Safari.

<comment><USER14> Safari doesn't implement an asm.js backend, presumably?

<comment><USER13> Nor does Chrome, but I think Chrome takes the `"use asm";` as a hint to use certain optimisations.

<comment><USER15> Chrome should enable turbo fan with the "use asm"; set. Though the only confirmation of this is saying it's tested in beta. [https://code.google.com/p/v8/issues/detail?id=2599#c77](https://code.google.com/p/v8/issues/detail?id=2599#c77)

<comment><USER4> It's in release Chrome currently.

</comment></comment></comment></comment></comment><comment><USER16> Link to source: [https://github.com/MicrosoftEdge/Demos/tree/master/chess](https://github.com/MicrosoftEdge/Demos/tree/master/chess)

</comment><comment><USER17> So does this mean that asm.js is good for longer operations? Because I tried reducing the think time and the engine lost.

<comment><USER18> I think it rather means that the search time was short enough that neither search tree got deep enough to form advantageous moves. (When I check the detailed output, it seems that the asm.js version visits at least 2x as many nodes as the un-optimized version, independent of Time-per-turn)

</comment></comment><comment><USER19> An interesting tidbit (chrome):

When you push it up to 1000ms per move, since the difference between 15 moves ahead and 16 moves ahead is so large, both engines end up making 15 moves ahead and win / lose about half the time, even though asm.js is visiting more nodes.

<comment><USER20> I noticed the same behavior by hobbling their time down to 10ms for each.

</comment></comment><comment><USER21> At high level chess (which this is), white has a significant advantage over black. Always picking asm.js as white (and not providing a setting to change it) is a bit disingenuous.

<comment><USER22> I don't know if it's updated but here asm.js is the black (or blue) player.

</comment></comment><comment><USER23> Ran it in chrome and it came out to a draw.

<comment><USER24> Of course, even a chess engine that is stronger will sometimes draw or lose to a weaker one.

</comment></comment><comment><USER25> "Checkmate! The non-optimized JavaScript wins!"

That's funny.</comment>