The language brain matters more for programming than the math brain? (2020)

Most coding doesn't need much of any math past boolean logic and very basic set operations. I'm much more likely to spend my time studying DB and interface schemas to understand how something works than doing a lot of mathy fiddling. Sure, some people write game engines and such, but even much of 3D graphics doesn't need anything more complicated than the first half of a linear algebra course.

Organization may also benefit from spacial skills.

Regarding mathematical

> concepts that are intrinsically complicated,

I'm not a mathematician, but I figure mathematicians aim for clean, composable abstractions the same way programmers do. Something complicated, not just complex in its interactions with other things, seems more useful as a bespoke tool (e.g. in a proof) than as a general purpose object?

> Whereas programming has more “small steps”: even someone who’s not smart (but has grit) can write an impressive program, if they write one component at a time and there aren’t too many components that rely on each other.

This is well put. I often wonder if a merely average working memory might be a benefit to (or at least may place a lower bound on the output quality of) a programmer tasked with writing maintainable code. You cannot possibly deliver working spaghetti if you can't recall what you wrote three minutes ago.

This is a baldly self-serving hypothesis.

> Good code doesn’t just solve a problem, it solves it in a way that’s readable and modular.

Strongly disagree.

There are plenty of cases where non-modular code is more readable and faster than modular code (littered, presumably, with invocations of modular logic).

There are also countless cases, particularly in low-level languages or languages with manual memory management, where the best solution -- or the correct solution -- is far from readable.

Readability is anyways in the eye of the beholder (My code is readable. Isn't yours?) and takes a back seat to formal requirements.

Just as a matter of personal style, I prefer long, well-organized functions that are minimally modular. In my experience, context changes -- file boundaries, new function contexts, etc -- are the single greatest source of complexity and bugs, once one has shipped a piece of code and needs to maintain it or build on it. Modular code, by multiplying those, tends to obscure complexity and augment organizational problems by making them harder to reason about and fix. Longer functions certainty feel less readable initially but I'd wager they produce better, clearer mental models, leading to better solutions.

> Whereas programming has more “small steps”: even someone who’s not smart (but has grit) can write an impressive program, if they write one component at a time and there aren’t too many components that rely on each other.

... In my experience, learning to write one component at a time (and try the code, and make sure it works before proceeding) is itself a skill that many struggle to develop. Similarly for avoiding unnecessary dependencies between components. Oh, and also being able to analyze the problem and identify separable components.

One of the most frustrating things about teaching programming, for me, is the constant insistence from other teachers that you have to maintain an "absolutely everyone can learn to program" attitude at all times. Many people who start to learn programming have misguided or confused reasons for doing so and - to say the least - could make much more effective use of their time developing other skills. (It's not a question of elitism; I'd surely flounder at some tasks that others find natural.)

Its very rare imo that computational problems emerge fully formed & ready to be tackled like proofs.

Usually even deciding what the problem is is in part an art, requires an act of narrativization, to shape and form concepts of origin, movement, and destination.

A good problem solver has a very wide range of abstract ideas and concepts and concrete tools they can use to model and explain problem, solution, & destination. Sometimes raw computational intellect can arrive at stunningly good proposals, can see brilliant paths through. But more often, my gut tells me it's about having a breadth of exposure, to different techniques and tools, and being someone who can both see a vast number of ways to tackle a situation, and being able to see tradeoffs in approaches, being able to weight long and short term impacts.

+1. Excellent description of how the skills relate. I often read, listen to poetry when stuck in a math or programming problem. ... or just talk to the rubber duck. :-)

The problem with doing things right the first time is some people look at it and just say, “well of course it should work that way.” Yes but did you think of doing it that way?

> I've always been a very good / fast reader, which has been incredibly useful in my programming career. I had a good SAT math score (710) but got a perfect score (800) on the SAT verbal (in the late 90s).

This is me and also many of the CS students in my cohort, and AFAIK something that universities actively selected for, and students also self-selected around in an era of RTFM/MUDs/IRC before LLMs or youtube. The best programmers I've worked with are still always very linguistically brained.. polyglots even when they didn't have to be, or with a long track record of engaging with difficult literature. If nothing else.. just very witty in that certain way that's meta-cognitive, meta-linguistic.

This is still true I think but it's much harder see out in the wild due to the degree/career trajectory popularity. Plus as long we're optimizing for leet-coding even though built-from-scratch algorithms are a very rare need compared to skills with good design/exposition.. naturally the math-brain is favored.

Also checking in as someone with strong language skills. When I was a kid in school a million years ago I was actually rather weak in math and crapped out around trig, but excelled in English, Spanish and C. Now I'm a senior web dev, and I still can't do much math beyond the basics required for everyday living (though 18 years in food service means I'm really quick at estimating percentages to within delta)

Early, strong reader here. Off-the-charts spatial reasoning, as measured by tests.

Terrible at math, I hate it and feel dyslexic trying to read most mathematical writing. I excelled at it in elementary school, then quickly came to feel frustratingly stupid at it as it became less about algorithms (more on that in a bit...) and all about equations and abstract stuff with unknown applications.

However, programming was natural and easy to pick up. I've repeatedly had to take more time convincing myself I actually understand some supposedly "hard" thing, like pointers or recursion, than it took to learn them in the first place, because they were in fact very easy to understand so I kept second-guessing myself—"I must not get it, because that was easy". I've been the go-to guy for "hard" and "low-level" problems basically everywhere I've worked.

What I've noticed is that when I must read math, the only way I can get any headway is to turn everything into steps, through which some example values may pass and affect one another. I have to turn it all into algorithms. Algorithms, I can get. Attempts to express meaning through equations and proofs, no, I have to painstakingly turn every single boundary between every symbol into a step and "walk through" it to have any hope of understanding it, and once I do, this new understanding only barely illuminates the original representation.

I think programming clicked for me because, as typically encountered and taught, it's very heavy on algorithms and very light on other varieties of mathematical presentation. Plus, having so very much more context available about what variables represent and what routines do, than a jumble of letters and symbols. FFS, if we say Perl is line noise, what's mathematical writing? Straight gibberish from a brain-wrecked Cthulhu cultist? Perl's the clearest thing in the world by comparison!

... where I do run into trouble is languages with "mathy" syntax, where the idiomatic style favors single-letter variables and accomplishing-things-by-asserting-equality. I can't read Haskell to save my life. Put the same supposedly-tricky concepts (monads, type classes) in any more-ordinary language, and it's easy, but when I tried to learn them using Haskell, I couldn't get anywhere at all. Shit, it takes me forever just to understand fizzbuzz-level programs written in Haskell.

Oh wow, are you me - I had an almost identical SAT experience. Oddly enough compared to another poster in this thread, I love functional programming and Haskell and studying things like dependent types in a programming context has helped me patch up my crappy understanding of "actual math", proofs, etc.

Dyscalculia, dysgraphia and dyslexia can all present independent of one another, heavily implying that different processes govern math, reading and writing. To call them "language brain" and "math brain" is simply a useful fiction, whether they're actually separate piles of meat is irrelevant.

"language brain" or "math brain" are obviously non-scientific terms.

I think most people would agree that problem solving, expressing ideas verbally, and expressing ideas in math are very different skills.

The other thing I don't like about this framing is the implicit false dichotomy. The best programmers I've met often have strong language and math skills.

Poetry is the art of giving different names to the same thing. Mathematics is the art of giving the same name to different things. (Henri Poincaré)

It's basically being good at "naming things", in particular abstractions.

> unless you show experimentally that those bunch of neurons can be grouped into two non-overlapping regions

A good place to look is after brain trauma. Where people end up with weird missing functionality.

Oliver Sacks writes about some of the weird side effects of brain trauma.

We could experiment on mathematicians or writers by causing trauma to different parts of the brain...

Or neural stimulation/anaesthetic of brain regions might show something.

I wanted to say something like this, but in the opposite direction. I think perhaps more so there’s a difference between abstract and concrete thinking? But tests like the SAT in my experience (which is now 20 years out of date) treat the verbal section as more of a set of abstractions (analogies, for instance) and the math the same. I got almost equal marks in each (660 verbal/650 math) on my only try.

Yeah, the brain is a sparse MoE. There is a lot of overlap in the hardware of the "language brain" and the "math brain". That being said, I can discuss software concepts in a foreign language, but struggle with basic arithmetic in anything but English. So while the hardware might be the same, the virtualization layer that sits on top might have some kind of compartmentalization.

Yes, but there is a visual/spatial ability and a verbal/mathematical, and you can do maths with the visual/spatial ability or with the verbal/mathematical ability.

It leads to different styles of thinking and problem solving.

> There is no such thing as a "language brain" or a "math brain"

Tell that to the people who designed the study, the people that approved the study, and the people that funded the study.

At the end of the day, the study set out certain criteria for assessing certain skill types/competencies and divided the people by those well defined criteria. I think it’s pretty hard to argue against the idea that people might have at least some level of aptitude for different types of activity and skill.

It took me a long time to realize math consisted of abstractions.

I was never told, for example, that matrices are a useful abstraction (shorthand?) for representing linear equations.

Or that imaginary numbers were an invented abstraction that made certain calculations easier.

It would have been nice to learn it from the perspective of how those abstractions came into being and why they're useful.

If we taught music the way we teach math. No wonder so many people are "bad at math".

“Music class is where we take out our staff paper, our teacher puts some notes on the board, and we copy them or transpose them into a different key. We have to make sure to get the clefs and key signatures right, and our teacher is very picky about making sure we fill in our quarter-notes completely. One time we had a chromatic scale problem and I did it right, but the teacher gave me no credit because I had the stems pointing the wrong way.”

https://en.m.wikipedia.org/wiki/A_Mathematician%27s_Lament

> It think this is silly on multiple accounts. I'll claim that there's not real thing such as a "language brain" or "math brain."

It seems plainly obvious that this language just means “areas of brain that activate when dealing with math problems” vs “areas of brain that activate when dealing with language problems” and yes there is hard evidence that there is a difference between them.

By the very expansive definition that you advocate for, what exactly do we do that isn't math?

One could argue that all we do is turn thoughts, senses, and memories into further thoughts and appropriate actions, which is applying a pattern, which is math. But at that point the definition is too broad to be helpful for anything but playing word games.

Just anecdotally based on my 2000something kid high school, the copious amount of tiering of math classes seemed to indicate to me that either we're really bad at teaching math to 80% of people, or only 20% of people will be able to handle precalculus.

We had basically 4 tracks: one ended with you doing algebra 1 in senior year, another ended with you doing trig in sr year, yet another that ended with trig (no precalculus), and then one that ended with you doing trig and precalc. That final class then had further subdivisions that were too small to have their own full classes: some kids just did precalc, some did calc 1 and took the AP Calculus AB exam and/or IB Math SL, while even even smaller group took AP Calculus BC and/or IB Math HL. The total number of kids who took the AP Calc AB exam in my year was 20ish, out of a graduating class of 500-600.

To be fair, the original study uses "numeracy", and the correlation numbers are almost exactly like the ones for "language aptitude".

At the same time, the study excluded "five participants ... due to attrition (not completing the training sessions), and one participant ... because he was an extreme outlier in learning rate (>3 sd away from the mean)." I mean, if you are to exclude 15% of your subjects without looking at their aptitude (maybe they didn't do it because it was too hard to pass the training tests to move to the next lesson, yet their language aptitude is high?), with only 36 subjects of which 21 are female (it's obvious programming is male dominated, so they only had 15 males: maybe it doesn't matter, but maybe it does), how can you claim any statistical significance with such small numbers?

100%. I have 2 kids and what they learn at school is absurd... I have to put them in an extra class outside school where they learn a lot of the more abstract stuff, albeit as you say at a level which makes sense (not too deep).

Interesting to me how Wernicke’s Aphasia works then (which I have occasionally; my epilepsy stems from there + broca’s area). Could you explain that?

Are you a teacher and/or someone that runs spelling bees or otherwise someone that has done the proper statistics to distinguish this correlation with generalised intelligence. Just wondering where you get this anecdata from?

Makes sense to me; I've always been a naturally good English speller. My brain just knows how to store and retrieve this type of data, which has a high correlation with e.g. CLI interfaces and their idiosyncratic command structures.

I had a CS prof who couldn't spell to save his life and caught a lot of good-natured flak about it from his students.

> That problem solving skills are relevant is pretty obvious, but language less so.

To me, problem solving ability is precisely the same as the ability to articulate the problem and a solution. I don't see a major difference.

If you can solve a problem but you can't articulate what the problem is or why the solution will address it, I wouldn't call you a good problem solver. If you can articulate the problem well but not come up with a solution, you're already doing better than a lot of programmers in the world, and I'd probably prefer working with you over someone who presents the solution without "showing their work".

In fact, what is problem solving without such articulation? It's hard to even grasp what the skill means in a raw sense. Arguably creativity in this context is just the ability to reframe a problem in a more approachable manner. Many times, if not most times, such framing implies some obvious solution or sets of solutions with clear tradeoffs.

> Recursion is also fundamentally linguistic

You sure about that? How about inductive proofs?

I would just say that language is more familiar to most. Mathematics are also languages, but more formal and foreign to most.

> Recursion is also fundamentally linguistic

What does this mean exactly?

Going further, it seems like Language Aptitude was primarily significant in explaining variance in learning rate, measured by how many Codecademy lessons they completed in the allotted time, but wasn't explanatory for learning outcomes based on writing code or answering multiple-choice questions.

Seeing as Codecademy lessons are written in English, I would think this may just be a result of participants with higher Language Aptitude being faster readers.

I do think that language skills are undervalued for programming, if only for their impact on your ability to read and write documentations or specifications, but I'm not sure this study is demonstrating that link in a meaningful way.

And/or application domain. Lower level programming might lean more on the math side? Wasn't the modulus operator a common complaint about fizz-buzz?

I was thinking about whether it would vary with task, but I think you have a good point and it would vary even more with the language.

I would take the other side of the bet.