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

https://massivesci.com/articles/programming-math-language-python-women-in-science/

by smusamashah • 1 year ago

415 453 1 year ago

Qem3• 1 year ago

I wonder if this finding hold across programming languages. I suspect the conclusions would be different for people programming in APL instead of Python, for example.

floxy• 1 year ago

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?

codr73• 1 year ago

Low level requires more discipline, similar to math, that's about it.

graemep• 1 year ago

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.

jimbokun• 1 year ago

I would take the other side of the bet.

jp573• 1 year ago

After I started my PhD program in CS/AI (late 90's), one of the faculty told me that the GRE verbal score was thing on the application most predictive of student success in the program. Of course, most applicants had perfect or near perfect GRE math scores, so there was no predictive power there. But the application also included the GRE subject test, transcripts, and letters of recommendation.

georgeburdell• 1 year ago

The GRE math bar for excellence was quite low and so a perfect score was only the 92nd percentile or so. It’s not surprising that other metrics correlated better with success

beambot• 1 year ago

Putnam exam score might be more predictive?

jp573• 1 year ago

Sure, but also, if you can't read and write well, you're going to struggle in a PhD, because that's really a lot of what you have to do.

philipkglass• 1 year ago

I also seem to recall from The Making of the Atomic Bomb that the theoretical physicists of the era were noted as having the highest verbal intelligence of any group of scientists. That struck me since I would not have expected it.

EDIT: I found the quote, from chapter 6:

Psychometricians have closely questioned American scientists of this first modern generation, curious to know what kind of men they were—there were few women among them—and from what backgrounds they emerged. Small liberal arts colleges in the Middle West and on the Pacific coast, one study found, were most productive of scientists then (by contrast, New England in the same period excelled at the manufacture of lawyers).

...

Theoretical physicists averaged the highest verbal IQs among all scientists studied, clustering around 170, almost 20 percent higher than the experimentalists. Theoreticians also averaged the highest spatial IQs, experimentalists ranking second.

tomjakubowski• 1 year ago

I'd think strong verbal skills would make for better collaboration between scientists.

jp573• 1 year ago

In order to solve what are essentially "word problems" -- i.e. reading a verbal description of a problem and translating it to math -- you have to have very good reading comprehension.

Qem3• 1 year ago

Perhaps survivorship bias explain part of it. Many of those scientists arrived at US fleeing their home countries in WWII. Migrating under those circumstances is tricky, lacking the necessary support network or failing to successfully negotiate an encounter with border patrol may be the difference between reaching a safe place and being dragged to rot in the trenches. Good verbal intelligence is very helpful in this process. Perhaps the same way good verbal intelligence is over-represented in those who escaped the war, the trait of being taciturn was over-represented in all the scientists that got stuck and died in WWII[1].

[1] https://worldscientific.com/worldscibooks/10.1142/q0436#t=ab...

lgiordano_notte• 1 year ago

Makes sense that verbal ability would line up more with success in CS, especially when math scores are already high across the board. A lot of programming leans on language-type skills: reading and understanding code, navigating docs, naming things clearly, writing maintainable logic etc.

The field probably does itself a disservice by overemphasising math. That framing can push people away who might actually do really well, especially those strong in reasoning, abstraction, or communication. Linked study is a good reminder to rethink how we present programming imo.

jart• 1 year ago

It does. The majority of what's popular and gets attention in programming is things like languages and frameworks which do the best smooth talking. The whole point of CS is to focus on the aspects of programming that aren't just vogue trends. With any field or aspect of modern life, language skills are the gateway to privilege and software engineering is no exception. But here it's respect for the math that stops it all from spiraling into a bunch of bs. You can't fool the math people.

swayvil• 1 year ago

Math is a subset of language, surely.

kanbankaren• 1 year ago

Probably true. Math used to be written in prose style before we invented symbols to compress the prose. Most of the symbols are very recent just in the last 200 years or so.

klipt• 1 year ago

Some types of math benefit a lot from visual reasoning. Like geometry.

ducttapecrown2• 1 year ago

Geometry only benefits from visual reasoning in 3d and lower, and there are a lot of dimensions above that!

You can see visual reasoning as a little cheat computation, you can run math problems through your sense-determining brain, which is what brains are really good at (robots struggle with our levels of dexterity). But the fact remains that you can only visualize in low dimensions, and there are infinitely many dimensions.

Note: You can reduce many problems to 3d, but also many problems in 3d have configuration spaces with much higher dimension, so there's some nuance.

bell-cot• 1 year ago

It's easily argued that languages are subsets of math.

del_operator2• 1 year ago

Left as an exercise for the reader.

ulbu• 1 year ago

and both are instances / processes of symbolic composition.

DiscourseFan2• 1 year ago

Before Godel, yeah. Many in math departments would like to believe that claim but would not accept it when pressed.

js8• 1 year ago

Easily? Not sure. But perhaps it's a linguistic version of the Skolem paradox. Looks like Hilary Putnam had some things to say on that..

jboggan• 1 year ago

I have found a fairly interesting correlation between people who are good at learning programming and people who are good at English spelling bees. Something about holding a lot of anecdotes and esoteric rule exceptions when performing an otherwise algorithmic process.

QuercusMax6• 1 year ago

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.

nemosaltat• 1 year ago

I can’t decide if you’ve cheekily included the classic homophonic there-error. This isn’t technically an issue with English spelling, but I think you intended to communicate that CLI interfaces have idiosyncratic command structures, not that they are idiosyncratic structures themselves. If I’ve been taken in by pedant-bait, I apologize.

deeThrow9415• 1 year ago

I'm a terrible speller; it's taken me ten years of typing "ammend" to learn its proper spelling. It also sort of goes against the "programmers are lazy" meme: why memorize what a computer can detect and correct?

FjordWarden• 1 year ago

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?

ducttapecrown2• 1 year ago

They get it from being an engineer!

senderista• 1 year ago

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.

QuercusMax6• 1 year ago

This totally makes sense to me. 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).

I remember when I first started working on my Master's project on wireless sensor networks, my advisor sat me down and said "I think I know a good project for you. I want you to print out the source code for TinyOS, study it for a week, and come back to me when you think you know enough to make these changes." This was a sort of formative experience for me, and ever since when joining a new project I made sure to take the time to read through the code to understand how things fit together.

alabastervlog3• 1 year ago

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.

tapoxi• 1 year ago

Same but I am literally math dyslexic (formal diagnosis of dyscalculia).

It prevented me from having a CS degree, I was unable to complete the math courses, but as far as actual programming and "software engineering" goes (design, etc) it's never hindered me. I can work out the logic and I let the computer do the math.

Edit: I'm downvoted below zero for this comment. I don't know what people are so offended by?

lubujackson• 1 year ago

Very interesting, as I am nearly the opposite. Bad spatial reasoning though pretty good at most other things. In school, geometry was fun and interesting - I enjoyed proofs. And I majored in English in college with a CS minor, so I think there must be a variety of in-roads for programming.

I think one "verbal" skill that has served me well is fast reading. When I had to read a 300 page novel once a week you learn how to skim for key elements, which is immensively useful for getting up to speed in a new codebase/language or locating a bug.

reverendsteveii3• 1 year ago

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)

throwaway20372• 1 year ago

    > though 18 years in food service means I'm really quick at estimating percentages to within delta

This is an interesting comment! No trolling: Were you a bread or pastry baker? I am curious to hear more about this experience.

_dwt• 1 year ago

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.

photonthug• 1 year ago

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.

GoblinSlayer17• 1 year ago

Remember people whining about weak ecosystems? That's a lot of opportunity to build things from scratch instead of making another - for real this time - IRC clone with Electron.

ezekiel68• 1 year ago

I came here to comment the same -- also ready to share my SAT scores from the 1980s. I was also much highter on the verbal side and I have had an awesome software engineering career using many, many languages (often together) on large, professional projects at large companies anybody here would recognize.

abraxas• 1 year ago

This mirrors my personal experience. My writing skills have been above average and my parents' presumption was that I would pursue some humanistic studies. I ended up studying software engineering and made a career out of it of almost three decades and counting. Meanwhile my wife who always had a "math brain" has struggled to learn to program at a decent competency level.

paride5745• 1 year ago

Interestingly, I became better at learning human languages after learning a couple of programming languages. I was good at math at the beginning. I guess programming kinda bridged the gap.

p0nce• 1 year ago

Programming education should have more humanities such as writing, sociology, epistemology and design, and not nearly as much maths.

Jtsummers• 1 year ago

How much math is in a typical CS program these days? Calc 1-3 (maybe 3, varied by school), Linear Algebra, Statistics (inconsistent across programs), Discrete were pretty much it when I was in school 25+ years or so ago. That's only 4-6 courses depending on the university, though some where the CS dept was more strongly associated with an engineering college might have added Diff Eq and others. (I got interested in CS education and reviewed a lot of curricula in the US at the time, this is from memory.)

Some schools like MIT might have required more, but on average what I wrote was about it. Has it increased since then? Based on the new hires I've seen the last decade I'd have guessed the math requirements were mostly the same.

deeThrow9415• 1 year ago

I'd argue none of that math is really necessary. While I have used most of my classes at least once, it was never a barrier to advancement in my career. Hell you could say the same thing about any of the theory. Like yea it's cool I know what a "merkle tree" is but it ultimately is a distraction from most of the skills you need to work with git.

Anyway, both computation and math are grouped under "apriori" knowledge. Any semantic distinction is ultimately silly. But we could just as easily be teaching programming as a craft in the context of the real world—I think this is closer to how it's done outside the US. I am not at all convinced the American style is what people ought to be paying for.

cognisent• 1 year ago

It was my grades in math that ultimately failed me out of my undergraduate CS program. My university had: Calculus 1, Calculus 2, Linear Algebra, Vector Geometry, Multi-Variable Calculus, Applied Combinatorics, Discrete Math, Differential Equations and maybe more that I don't remember. So many that CS majors could take one more math class and get a minor.

Yeah, I never thought this made sense, but so many people did; and, I always hear people on Slashdot talking about how programming IS math. None of that has been my personal experience, and I'm coming up on 21 years as software engineer. Discrete was the ONLY math course that I really enjoyed and did well in the first time around. For me, this always made sense.

canjobear• 1 year ago

This makes sense for my path to math. In high school I was bad at math and good at learning languages. Then I started learning Python and realized that it was just like learning a language. Then at some point I realized math notation was just another language for expressing the kinds of things you could express in Python. Now I'm in a job where I do math every day and I read math textbooks for fun.

It helped that Python was meant to resemble natural language. I had learned C++ and Perl before but they never stuck, because I never made the connection to language. Ironically, since Perl was designed by a linguist!

odyssey72• 1 year ago

And yet CS grad programs seem to care about only the math section of the GRE

ivape2• 1 year ago

Societally we made that association, so it's not the programs fault, they simply live the same world we live in.

Kurt Vonnegut: See, I came up through a chemistry department.

Charlie Rose: Yeah, right.

Kurt Vonnegut: And so I wrote and there was nobody there to tell me whether it was any good or not. I was just making my soul grow, writing stories.

There's some stuff about his opinion on training for writing that could be relevant:

https://charlierose.com/videos/25437

I don't think it's fair to attribute anything to anything. Stuff comes from all over the place. In other words, attributing programming prowess to math was a mistake, and we are making the same mistake again attributing it to language.

---

Just one more:

Kurt Vonnegut: --consider himself in competition with a world's champion. And this is one reason good writers are unlikely to come from an English Department. It's because the English Department teaches you good taste too early.

I think his main point is when we put something on a pedestal, we actually limit people, whether that be math or language.

latexr• 1 year ago

Video isn’t loading for me. But from the still frame of the preview, it seems to be this one on YouTube:

https://www.youtube.com/watch?v=ROyr83rib3Q

odyssey72• 1 year ago

Maybe they didn’t invent the problem, but the admissions priorities are theirs to repair

contravariant• 1 year ago

Learning mathematics is likely to benefit more from whatever a language brain is as opposed to whatever a math brain is.

divbzero• 1 year ago

So maybe it makes sense that LLMs do okay at programming even though they lack the ability to reason?

77pt774• 1 year ago

They don't do okay. Quite on the contrary.

My experience is that they spit out reasonably looking solutions but then they don't even parse/compile.

They are OK to create small spinets of code and completion.

Anything past that they suck.

It's actually hilarious that AI "solved" bullshiting and and artistic fields much better and faster than say reasoning fields like math or programming.

It's the supreme irony. Even 5 years ago the status quo was saying artistic fields were completely safe from the AI apocalypse.

NickM3• 1 year ago

I disagree that the current generation of AI has "solved" artistic fields any more than it's solved math or programming.

Just as an LLM may be good at spitting out code that looks plausible but fails to work, diffusion models are good at spitting out art that looks shiny but is lacking in any real creativity or artistic expression.

codr73• 1 year ago

I would say the fact they do better than anyone could have imagined using just language points in the same direction, okay is very much up for debate imo.

It's like people enjoy extrapolating their surprise when it comes to LLMs, and I don't think it's very helpful.

deeThrow9415• 1 year ago

100% agree, I've been saying this for years. I'm terrible with arithmetic but great with symbols and relations. Recursion is also fundamentally linguistic, and although our internal "stacks" for processing it naturally are quite small, language remains the easiest demonstration of recursion in our daily lives.

Oddly, I also use spatial intuition when thinking about stuff like stacks and the shape of data structures.

karmakaze6• 1 year ago

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.

deeThrow9415• 1 year ago

How do you communicate an inductive proof without language? Even formal symbolic logic is fundamentally linguistic.

retrac• 1 year ago

Language has an inherently recursive structure: I saw the man who saw the man who saw the man who saw the man who saw the man who... While our brains have practical limits to how deeply such things can actually be nested, language has a recursive tree-like aspect to it.

trealira• 1 year ago

This is just a guess on my part, but I'd also bet that writing inductive proofs (or proofs in general) require more of the language brain than just doing math problems.

umanwizard4• 1 year ago

Recursion is also fundamentally linguistic

What does this mean exactly?

hbn• 1 year ago

> Recursion is also fundamentally linguistic
What does this mean exactly?

What does this mean exactly?

karmakaze6• 1 year ago

This says more about our programming languages than it does about the brain.

I've always wondered why FP isn't more popular. I concluded it's because most folks don't like thinking like abstract math.

deeThrow9415• 1 year ago

I can't speak for other forms of FP, but symbol operators make communicating about haskell very annoying. Outside of that FP seems to be doing fine, IMO.

karmakaze6• 1 year ago

Try APL, you'll be begging for FP.

armchairhacker2• 1 year ago

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

I think the problem-solving part of coding requires math skills, while the organization part requires writing skills. The organization part affects the problem-solving part, because if you write messy code (that you can’t reread once you forget or extend without rewriting) you’ll quickly get overwhelmed.

Writing large math proofs also requires organization skills, since you’ll refer to earlier sections of your proof and may have to modify it when you encounter issues. But to me, math seems to have more “big steps”: sudden insights that can’t be derived from writing (“how did you discover this?”), and concepts that are intrinsically complicated so one can’t really explain them no matter how well they can write. 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.

QuercusMax6• 1 year ago

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.

ajuc• 1 year ago

The difficulty is in how many relationships you need to keep in mind, not in how hard each of them are.

Just like in math.

BTW relational DBs are math.

Someone1234• 1 year ago

Now we're getting into the "define maths" part of the discussion which is always where these discussions die. It can be argued that turning a kettle on and boiling some water is "maths" or it can be as narrow as "everything above basic arithmetic is logic, not maths."

So how much of programming is maths? Before we answer that, let's answer: How much of maths is actually maths? Because first we define maths, and then we define programming based on whatever that is, but until we have that first concrete definition this discussion cannot occur.

I will add that "it is taught by the maths department in college" is a flimsy argument, and frankly one the Physics department in particular would mock.

switchbak3• 1 year ago

It's definitely a gray area. Is a DAG traversal algo "math", or is it more computer-sciencey? What if you do it in SQL? Certainly there's a mix of more or less concentrated logic/math vs glue code, and most of that is very dependent on the domain you're working in.

I find this distinction useful in the abstract, that one can engage different parts of the brain for different components of development. This probably explains why a well-written DSL can be so powerful in the right context.

godelski46• 1 year ago

  > Most coding doesn't need much of any math past boolean logic and very basic set operations

Coding IS math.

Not "coding uses math", I mean it is math.

  Mathematicians do not deal in objects, but in relations among objects; they are free to replace some object by others so long as the relations remain unchanged. Content to them is irrelevant; they are interested in form only.
  - Poincare[0]

I don't know how you code, but I don't think I'm aware of code that can't be reasonably explained as forming relationships between objects. The face we can trace a program seems to necessitate this.

[0] https://philosophy.stackexchange.com/questions/22440/what-di...

hinkley3• 1 year ago

Boolean logic and set theory are very important to computer logic, and graph theory is not far behind. But you can also learn Boolean logic in the philosophy dept. Which I unfortunately learned the hard way by taking Philosophy 101 after already having the CS class on logic. Took a semester to go over what we did for the midterm. Got a lot of naps that semester.

yubblegum• 1 year ago

Probability is math and there you have caching, hashing, etc. Then there are permutations, combinations, etc. with a lot of usecases in software. Distributing graphs across nodes? More math.

zahlman• 1 year ago

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.)

tetha• 1 year ago

I dislike "everyone can learn to program" because it conflates many, many levels of skills and expertise.

I very much think many people could learn the more advanced Excel Formulas, Power Automate and even simple Bash/PowerShell scripting to make their work more effective. I've met quite a few folks who had been intimidated out of trying who could do it.

On the other hand, how many people on this site could bootstrap a linux kernel on either very new or very old hardware? I know there are some, but they are certainly not the majority. I certainly won't be the first person to get linux and doom to run on a quantum computer.

But that is similar to other professions. Everyone with a largely functioning body can learn to turn a few planks and some metal parts into a functional shed door with some basic tools or to put up a decent brick wall that won't topple over in a month.

That doesn't mean everyone is qualified to pour concrete for a dam or a bridge foundation, or to re-do some historical work in original style.

switchbak3• 1 year ago

I mean - not "absolutely everyone" can learn to do just about anything. There's a wide distribution of intelligence, aptitude/ability and desire amongst folks amongst all of the various things that you might learn (not to mention learning disabilities, impairments, etc).

I might be capable of learning advanced accounting, but that sounds like torture to me and I'll be damned if I'll ever take that on! I'm sure programming feels like that to a wide variety of people, and I don't see any need for us to try to pretend otherwise - outside of a bizarre ideological desire for equivalent outcomes from disparate groups.

HarHarVeryFunny3• 1 year ago

I guess it depends on what is meant by "everyone can learn to program". It's a bit like saying everyone can learn to write, or to do math, or play tennis, etc.

I'm sure everyone is capable of learning some basic level of programming, just as they are able to learn a basic (high school) level of any subject. However, not everyone is going to have the aptitude to take that to an advanced professional level, however hard they try. We're not all cut out to be artists, or writers, or doctors, or scientists, or developers, etc.

HideousKojima• 1 year ago

"absolutely everyone can learn to program"

Personally I've always considered a solid grasp of algebra to be the minimum bar for being able to program, at least for anything that isn't utterly trivial. Being able to take a word problem and turn it into a system of equations and solve it is a pretty close analog to being able to take some sort of problem or business requirement and turn it into code.

And the sad truth is that a huge percentage of the population struggle with just arithmetic, let alone algebra.

magicalhippo• 1 year ago

I recall reading about a professor at uni which carefully designed his tests throughout the year so he could determine if a student had grasped a certain programming topic. He also tracked effort, through handins and such.

After collecting data for a few semesters he concluded his students could be clearly divided into three categories: those who just "got" programming, those who understood it after working hard, and a small group that just didn't grasp regardless of effort.

ivape2• 1 year ago

What do you mean by math? Abstractions or calculations? The effort it takes me to do long division in my head matches the effort it takes me to follow some obtuse spaghetti code. See, I can get good and fast at long division in my head, but I may never understand the fundamental theorem of calculus. Some people are really good at mucking around garbage code (they have no choice, they get paid to), but what part of programming did they get good at? Obviously, some part of it, but nothing to write home about. Whenever I sense that I'm just getting practice at doing the equivalent of mental long division at work, that's when I always seek a new job. No amount of money is worth falling behind like that.

armchairhacker2• 1 year ago

I'm thinking of "computation", "intuition", and "organization".

Computation is following an algorithm. e.g. long division or computing a derivative.

Intuition, AKA brilliance, is finding a non-obvious solution. Think "solving an NP problem without brute force"*. e.g. solving an integral (in a form that hasn't already been memorized) or discovering an interesting proof.

Organization is recording information in a way that a) is easy for you to recall later on (and get insights from) and b) is digestible by others**. e.g. explaining how to compute a derivative, solve an integral, or anything else.

Math, programming, and writing each require all skills. The kind of math taught in school (e.g. long division) and your boring jobs are primarily computation. I believe advanced math (e.g. calculus) is primarily intuition; it requires some organization because big theories are broken into smaller steps, but seems to mostly involve smart people "banging their head against the wall" to solve problems that are still quite unclear***. Programming is primarily organization. It requires some intuition (I think this is why some people seemingly can't learn to code), but in contrast to math, most programs can be broken into many relatively-simple features. IMO implementing all the features and interactions between them without creating a buggy, verbose, and unmaintainable codebase is programming's real challenge. Writing is also primarily organization, but finding interesting ideas requires intuition, and worldbuilding requires computation (even in fiction, there must be some coherence or people won't like your work).

Some people are really good at mucking around garbage code (they have no choice, they get paid to), but what part of programming did they get good at? Obviously, some part of it, but nothing to write home about.

I agree that work you find boring should be avoided, and I also try to avoid working with it. But some people really seem to like working on esoteric code, and I think there are some skills (beyond computation) developed from it, that even apply when working with good code. Building a mental model of a spaghetti codebase involves organization, and if the codebase uses "genius hacks", intuition. Moreover, the same techniques to discern that two code segments in completely different locations are tightly coupled, may also discern that two seemingly-separate ideas have some connection, leading to an "intuitive" discovery. There's an MIT lecture somewhere that describes how a smart student found interesting work in a factory, and I think ended up optimizing the factory; the lesson was that you can gain some amount of knowledge and growth from pretty much any experience, and sometimes there's a lot of opportunity where you'd least expect it.

* Or maybe it is just brute force but people with this skill ("geniuses") do it very fast.

** These are kind of two separate skills but they're similar. Moreover, b) is more important because it's necessary for problems too large for one person to solve, and it implies a).

*** And whatever method solves these problems doesn't seem to be simplification, because many theories and proofs were initially written down very obtuse, then simplified later.

hinkley3• 1 year ago

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?

jauntywundrkind2• 1 year ago

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.

throwaway20372• 1 year ago

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

In my generation, the perfect example is Python's Timsort. It is an modest improvement upon prior sorting algorithms, but it has come to dominate. And, frankly, in terms of computer science history, it was discovered very late. The paper was written in 1993, but the first major, high-impact open source implementation was not written until 2003. Ref: https://en.wikipedia.org/wiki/Timsort

It has been reimplemented in a wide variety of languages today. I look forward to the next iteration: WolfgangSort or FatimaSort or XiaomiSort or whatever.

owl_vision• 1 year ago

+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. :-)

leptons6• 1 year ago

Good code

"Good code" is very subjective. Even readability and modularity can be taken too far.

walleeee• 1 year ago

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.

MaxBarraclough• 1 year ago

You cannot possibly write or deliver spaghetti, working or otherwise, if you're not capable of remembering what you wrote three minutes ago.

Forth programmers make a similar point. Forth is stack based; you typically use stack operations rather than local variables. This is ok when your 'words' (analogous to functions/procedures) have short and simple definitions, but code can quickly become unreadable if they don't. In this way, the language strongly nudges the programmer toward developing composable words with simple definitions.

(Of course, Forth sees little use today, and it hasn't won over the masses with its approach, but the broader point stands.)

globnomulous• 1 year ago

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.

quails8mydog• 1 year ago

I think the important concept that "readable and modular" is trying to get at is how easy is it to continue working on the code in future. There's definitely codebases that are easier to work on than others, even when the domain is the same.

I'd say that readability, which often boils down to consistency, and modularity are ways to do this, but they aren't the only ways. And as you say, sometimes there's a need for "unreadable" code, so not everything can be easy.

heisenbit• 1 year ago

Organization may also benefit from spacial skills.

sebastialonso4• 1 year ago

A lot of people in this type of threads always makes the same mistake: confusing what math is with branches of math, or rather, ways in which math is used. The way the education system is built certainly contributes to this.

I've always found the car metaphor to work very good to understand this: A car is a machine that can transport itself to point A to B (some other rules apply). There are different types of cars, but you certainly haven't understood the definition of you say that something is not a car because is not a Volvo, or because it doesn't look like a Ford, when it's clearly able to transport itself.

Math is the study of ideal objects and the way they behave or are related to each others. We have many branches of mathematics because people have invented so many objects and rules to play with them. Programming is nothing if not this very definition. The fact that you don't have to "use math" when programming is not really addressing the point, it's like saying a car is not a car because it has no discernible brand.

GoblinSlayer17• 1 year ago

Declarative construct is made of relations, but imperative execution isn't, rather it's a process in time, but time is not a thing in math.

flkiwi• 1 year ago

I tell people all the time that the single greatest tool an aspiring lawyer can have is a background with programming, as the analytical and algorithmic mindset is FAR more important than being "good at public speaking" or any of the other base skills often cited as desirable for lawyers. I've also said the second greatest tool an aspiring lawyer can have (in my personal opinion) is a significant background in foreign language learning, as that is a skill that is closely related to programming, though a bit abstracted and coming from a different angle. I'm going to see if I can use this article to support that.

rowanG0772• 1 year ago

The article is extremely misleading, I dare even say almost malignant.

The study itself claims:

- fluid reasoning and working-memory capacity explained 34%

- language aptitude (17%)

- resting-state EEG power in beta and low-gamma bands (10%)

- numeracy (2%)

They take math skills to equal numeracy. The study itself implies this too. I disagree on a fundamental level with that. Math skills align much more closely to fluid reasoning than to numeracy.

del_operator2• 1 year ago

This is largely true, but also, the dynamic shifts depending on how learners engage with peers as they move from understanding to synthesis.

In small peer groups (“pods”) that debug and learn together, communication becomes a core skill—and that can actually change how math skills are applied and developed. Language doesn’t just support learning; it reshapes the process.

matt3210• 1 year ago

You guys have more than one brain?

casey2• 1 year ago

For learning a programming environment*

This has the effect of making programming easier, but don't confuse it.

scotty79• 1 year ago

I feel like I'm using language part of the brain for almost everything. My performance at any task (except purely manual and automatic ones) drops to 0-15% when I can hear someone talking. Alternatively if I manage to focus on the task I immediately stop understanding what's being said.

shadowgovt• 1 year ago

You know where we got a lot of really solid programmers before we had formal computer science degrees?

English majors.

ulrischa• 1 year ago

The best programmers were good in Latin at school

roopekangas• 1 year ago

If you grew up where it was in the curriculum ;)

eximius• 1 year ago

I'm very curious what this math pretest looked like, whether it was "proper" high level math or, like, computing some trig problems. Folks who have aptitude with algebra or number theory or topology, I'd expect that to be correlated, but not to rote computational math.

gowld• 1 year ago

It was arithmetic. The study is n=42 p-hacking nothingness, and then a highly misleading misinterpretation by the junk popsci website.

mtmickush• 1 year ago

I don't find this too surprising. The study itself was primarily just testing a students ability to identify syntax and remember what various functions do. I wouldn't expect math proficiency to help much in this area vs I would very much expect language to.

It'd be interesting to see correlations (language brain vs math brain) for how easy or hard it is for people to solve new problems with language after they already know the basics.

adamc• 1 year ago

Strangely (I was a math major as an undergrad), I never doubted this. It just feels more like writing.

makk• 1 year ago

Those long held assumptions were held by people who aren't professional programmers, right?

Because, if you do what we do, it's obvious that language > math for most of this stuff.

I'd go so far as to say that music > math for programming.

shayneo• 1 year ago

As a self taught programmer with a Communication Studies degree, this definitely resonates. The ability to articulate the problem in code is kind of the starting point for most productive development work.

77pt774• 1 year ago

Any experienced programmer will be able to tell what kind of person another programmer is just by the way they write their code.

Code written by programmers with humanities backgrounds is easily identifiable as being of bad quality.

Kind of like vibe coding meets programming by accident, before vibe coding was really a term.

It's a faux pas to even mention this IRL, but good coders know what's up.

Those "coders" usually get promoted to people managers, which is usually what they want anyway because their self-worth relies on abusing others to mitigate the correct self-perception they have of being "inferior".

The problem is, things need to be solved and vibe+accident programming can only go so far.

But fear not, they can always scapegoat whoever solves the problems, because if they were not to blame, how could they know what was up or even feel the need to correct it?

daedrdev• 1 year ago

This is a high level of bias and generalization about an enormous group of people with varied backgrounds and experiences, not to mention selection bias as you don't know many good coders backgrounds who may in fact be from humanities.

Even if many of the bad coders are those who were in humanities and don't have coding experience because they just entered the field (because once you get it you are no longer a humanities background)

taeric• 1 year ago

I'm strong in the belief that kids having lower reading scores is directly related to lower math scores. Learning to decode words is directly translatable to learning to decode equations. Down to some of my favorite math passages would include how to read something as it introduces a symbol or other construct.

linguae• 1 year ago

(2020)

As a new computer science professor at a community college, this is a timely article for me that may end up influencing how I teach, especially my introductory programming course as well as my discrete mathematics course.

darkerside• 1 year ago

Couldn't this difference be explained by the fact that the lessons were in English? If your language skills are poor, it's going to be hard to read the directions. You'll definitely be slower, which was the primary finding around language.

That side, I wonder if early programming was much more math heavy, and higher level languages have successively reduced that need over time.

jll29• 1 year ago

There is no such thing as a "language brain" or a "math brain" unless you show experimentally that those bunch of neurons can be grouped into two non-overlapping regions dedicated to "language" and "mathematics".

Mathematics itself is a human-made formal language that can be bootstrapped from definitions and axioms of logics and set theory, which have to be given in human language first.

Experienced mathematicians read formal theorems written in Greek letters off their blackboards as if it was normal English, suggesting they think about it like it was just normal English. This is not to say they cannot also view in front of their mental eye visual representations isomorphic with that language if they chose to.

reverendsteveii3• 1 year ago

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.

danielmarkbruce5• 1 year ago

math != calculation.

It's an actively stupid fiction for people who don't understand what math is.

karmakaze6• 1 year ago

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.

pier252• 1 year ago

"naming things" is really about "recognizing things" and/or "understanding things". It much deeper than just language.

hirvi745• 1 year ago

Poetry is the art of giving different names to the same thing.

Did Robert Frost say something like, "all language is poetry?" A chair is the term I learned to describe the object I am currently sitting on while typing this comment. Germans might call the same object a 'Stuhl', the French might call it a 'chaise', etc.. My point being that the object isn't technically any of those words, but rather those words symbolically map to that object.

scripturial• 1 year ago

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.

chrisfosterelli• 1 year ago

I think its worth noting the study did not actually make this claim, the news article did. I suspect the study authors would agree the term "language brain" or "math brain" is misleading.

danielmarkbruce5• 1 year ago

The types of people who do these types of experiments almost never have a real understanding of math. They equate arithmetic with math.

buffalobuffalo• 1 year ago

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.

impossiblefork• 1 year ago

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.

pier252• 1 year ago

"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.

twodave2• 1 year ago

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.

perrygeo• 1 year ago

What about Wernicke's area and Broca's area? If damaged they produce causal changes to our use and processing of language. I agree it's not as simple "language brain" but there are physical structures in the brain that are directly related to language.

robocat• 1 year ago

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.

swinglock• 1 year ago

I figure the programming brain matters the most for programming.

CobrastanJorji• 1 year ago

Makes sense to me. "Language" is an oft-forgotten part of "programming language." I'm sure math skills probably would better predict, say, ability to do well in advanced theory classes, but programming doesn't require that. It DOES require learning a specialized language.

RHSeeger3• 1 year ago

It DOES require learning a specialized language.

Which... is what math is, too.

qwerty456127• 1 year ago

This sounds obvious. To me it seems the majority of developers hardly use any math.

fjfaase• 1 year ago

I did not read any mentioning of testing non-verbal IQ. Many math skills also depend on verbal IQ. Verbal IQ correlates strongly with academic performance and probably also with learning new programming languages. I personally have a much stronger non-verbal IQ than a verbal IQ. Often when I think about algorithms, it is all about abstract blocks moving around even before I have written a single line of code. I usually see multiple solutions in my head and often find myself being stuck because I cannot make a choice. I always takes some effort to code the solutions and weed out stupid bugs due to spelling errors mixing up varisbles, but then things work correctly.

hunkins• 1 year ago

Interesting. I grew up most of my life overseas learning various different languages. Anecdotal, but most of the best coders I know are talented writers and often are multi-lingual.

janalsncm2• 1 year ago

language ability and problem solving skills

First red flag is here. The title rewrote this to be language only. That problem solving skills are relevant is pretty obvious, but language less so.

I’ve been programming for most of my life and I don’t consider myself a very good speaker. My language skills are passable. And learning new languages? Forget it. So I’m skeptical. Let’s look at the study.

First of all, “math” becomes “numeracy”. But I think programming is probably closer to algebra, but even then it’s less strict and easier to debug.

Assessed using a Rasch-Based Nuemracy Scale which was created by evaluating 18 numeracy questions across multiple measures and determining the 8 most predictive items.

Also, the whole thing is 5 years old now.

deeThrow9415• 1 year ago

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.

janalsncm2• 1 year ago

There are different ways of solving a problem though, some which require more critical thinking than others. Trial and error (in industry you can sound fancy by calling it “choosing parameters empirically”) requires no understanding of the underlying process, only the ability to measure the outcome.

If you’re debugging, you can get by for a long time by trying things until the compiler shuts up. It’s not efficient or good but people do it.

karmakaze6• 1 year ago

The article is from 2020. Recent LLM developments show that a model trained on math and code is better at coding than one that's trained on language and code without math.

gitremote• 1 year ago

Absolutely. That's why people can be perfectly fluent in a programming language and a high performer at work, but fail an interview algorithms/leetcode problem in that language, as algorithms are math problems that programmers almost never see at work.

The recruiter labels an algorithm problem as a "coding" test, but it's a math test, and concludes that most applicants who claim to be fluent in a programming language can't code and must have lied on their resume.

For context, I don't mind algorithm tests, but I strongly disagree with recruiters presenting it as a coding assessment.

qwertytyyuu• 1 year ago

Computer science definitely requires math brain

_ache_2• 1 year ago

Yes, nobody doubt about that. The article is about programming, which, even if it requires some math skills, require more an ability to deal with a language system.

_ache_2• 1 year ago

That is now obvious, any LLM is able to code, and is usually very bad at math. This alone proves that a good part of programming is linked to language not math.

Even if CS is sort of applied mathematics.

godelski46• 1 year ago

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." I'll also claim that most people don't know what math is, and that their evidence supports a "math brain".

Math isn't about calculations/computations, it is about patterns. You get to algebra and think "what are these letters doing in my math" but once you get further you think "what are these numbers doing in my math?"

A great tragedy we have in math education is that we focus so much on calculation. There's tons of useful subjects that are only taught once people get to an undergraduate math degree or grad school despite being understandable by children. The basics of things like group theory, combinatorics, graphs, set theory, category theory, etc. All of these also have herculean levels of depth, but there's plenty of things that formalize our way of thinking yet are easily understandable by children. If you want to see an example, I recommend Visual Group Theory[0]. Math is all about abstraction and for some reason we reserve that till "late in the game". But I can certainly say that getting this stuff accelerates learning and has a profound effect on the way I think. Though an important component of that is ensuring that you really take to heart the abstraction, not getting in your own way by thinking these tools only apply in very specific applications. A lot of people struggle with word problems, but even though they might involve silly situations like having a cousin named Throckmorton or him wanting to buy 500 watermelons, they really are part of that connection from math to reality.

This is why "advanced" math accelerating my learning, because that "level" of math is about teaching you abstractions. Ways to think. These are tremendously helpful even if you do not end up writing down equations. Because, math isn't really about writing down equations. But we do it because it sure helps, especially when shit gets complicated.

[0] https://www.youtube.com/watch?v=UwTQdOop-nU&list=PLwV-9DG53N...

danielmarkbruce5• 1 year ago

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).

godelski46• 1 year ago

Yeah, certainly we'd need to adapt classes to match their level, but we've tried before[0]. While it "failed" it also seemed pretty successful, especially in France and the USSR.

I mean is it any surprise kids get bored in math? They spend years learning the same thing. You spend years learning addition and multiplication (subtraction and division are the same operators). I sure as hell hated math as a kid. Especially doesn't help that it is always taught by someone who's also dispassionate about the subject. You really can get a process going where most middle schoolers are doing calculus and linear algebra (and advance ones are doing this in elementary). It isn't as far fetched as many would believe.

[0] https://en.wikipedia.org/wiki/New_Math

waynesonfire• 1 year ago

what is the name / curriculum of such a class?

belinder• 1 year ago

Do you recommend any other resources for children to learn the basics of those theories?

PartiallyTyped2• 1 year ago

A book of abstract algebra is very approachable!

godelski46• 1 year ago

Unfortunately I don't know any direct resources. I really do hope they are out there and some will share.

But if you're willing to hunt, I know that this idea was attempted before[0]. France and USSR had better success than the US. I'm sure there are still people working in this direction. I don't have children, but fwiw I've taught my nieces and nephews algebra and even some of calculus before they were 10 just in visiting time during vacations. They were bored and it seemed more fun than talking about the drama, politics, and religion that the rest of my family likes to spend most of their time on. Kids were similarly disinterested in that stuff lol. I've also seen my god{son,daughter} be able to learn these types of skills, so I'm highly confident it is doable.

[0] https://en.wikipedia.org/wiki/New_Math

mrexroad• 1 year ago

Thank you. I’ve long held that calculus, formal logic, combinatorics, etc. should be started in elementary school, separate from arithmetic. Even after stripping away the numbers and procedural knowledge, there is tremendous real world value in simply understanding many of the concepts. Plus, (and I say this half-jokingly) won’t we all be using llms to vibe-math everything that needs math-ing anyway?

vendiddy3• 1 year ago

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.

Nevermark3• 1 year ago

Even if we narrow math to numbers, what many people thing of as "math", we quickly move from arithmetic to patterns.

The patterns of repetitions of single things, repetitions over different things, repetitions between different things, repetitions over repetitions, ...

Natural/counting numbers are just the simplest patterns of repetition.

Jensson6• 1 year ago

Numbers are an abstraction, not just "imaginary" numbers, all numbers are imaginary they don't exist in reality.

bee_rider2• 1 year ago

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

Congratulations on overcoming the (very weird) choice of whoever taught your intro to linear algebra class.

PartiallyTyped2• 1 year ago

I am willing to bet good money that teaching pure mathematics like group theory, abstract algebra, or stuff like big Oh and combinatronics will do our kids a lot more good and advance them far more than calculus or geometry as taught in schools will.

I have the same experience as you did, in that studying by myself abstract algebra accelerated my learning and reasoning skills.

godelski46• 1 year ago

I think differential equations was where the switch from "I'm good at math" to "I think I want to actually know more of this" happened. I changed my major from engineering to physics. But agreed, abstract algebra was another big change and after that I took every class my university would let me and the chair of the department even made some new ones for me and some others.

I don't think this experience is uncommon (among people who get to these levels). Which is why it is really sad. Especially given how linear algebra and abstract algebra are in a lot of ways easier than calculus. I also think they should be taught earlier purely due to the fact that they teach abstraction and reasoning.

lo_zamoyski• 1 year ago

Math is about form and traditionally the science of quantity. It is called a formal science for this reason.

Language also concerns form. Grammar has form. Concepts are forms.

Math is language. 'Everything' is language. Language is the image of reality.

In the beginning was the Logos...

godelski46• 1 year ago

  > Math is language.

Facts. I think it is hard to disagree with this, and it seems like a rare opinion to be held by people at high levels.

  > Language is the image of reality.

An image?[0] ;)

[0] https://ncatlab.org/nlab/show/image

hdkdicnsnjes• 1 year ago

Real

NickM3• 1 year ago

I think you might be missing the point of the article: the study being cited isn't trying to establish the existence of a "language brain" or a "math brain", that's just the way the headline editorialized it to help people understand the conclusions.

The conclusion of the study was that linguistic aptitude seemed to be more correlated with programming aptitude than mathematical aptitude, which seems fairly interesting, and also fairly unconcerned with which specific physical regions in the brain might happen to be involved.

godelski46• 1 year ago

I understood it.

  > The conclusion of the study was that linguistic aptitude seemed to be more correlated with programming aptitude than mathematical aptitude

And this is what I'm pushing back against and where I think you've misinterpreted.

  > They found that how well students learned Python was mostly explained by general cognitive abilities (problem solving and working memory), while how quickly they learned was explained by both general cognitive skills and language aptitude.

I made the claim that these are in fact math skills, but most people confuse with arithmetic. Math is a language. It is a language we created to help with abstraction. Code is math. There's no question about this. Go look into lambda calculus and the Church-Turing Thesis. There is much more in this direction too. And of course, we should have a clear connection to connect it all if you're able to see some abstraction.

prmph• 1 year ago

The point is that linguistic aptitude _is_ math aptitude, and vice versa.

From my experience, my ability to articulate myself well is bound up with my ability to abstract and detect patterns. It is the same thing I apply to crafting software, the same thing I apply to creating visual art.

I think high-cognitive-ability people segregating themselves into artsy vs mathy people has more to do with their experiences in their formative years.

necovek• 1 year ago

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?

godelski46• 1 year ago

  > the original study uses "numeracy"

That's fair, although I don't think it changes my response. And the article still really leads to the wrong conclusions. You want to teach children abstraction and reasoning? You teach them math. Not numeracy, math.

apeescape2• 1 year ago

Finland tried teaching maths to children using Group Theory in the 70s [1], but the results weren't that good; it proved to be too abstract for young kids.

Ultimately, I believe basic algebra and geometry are the most important takeaways from math classes for most people.

[1] https://www.hs.fi/tiede/art-2000004823594.html (sorry, it's in Finnish and behind a paywall)

hirvi745• 1 year ago

I am no expert in pedagogy of mathematics, and I am sure someone will correct me if I am wrong, but I think there was/is a Russian academic program in which students were/are basically only taught algebra in an iteratively increasing manner.

As it was explained to me, one wouldn't take a "Calculus I" class as a prerequisite for say an entry-level engineering course. One typically had such a strong foundation of algebra, that when encountering a problem that required calculus, the student would just learn the necessary calculus at that point in time. In other words, with such a strong algebraic background, other aspects of math, within reason, were much easier to grok.

godelski46• 1 year ago

  > the results weren't that good; it proved to be too abstract for young kids

You cannot make that conclusion as a result of the evidence. Yes, the evidence might support that conclusion, but there are many others that also could. For example, they could have just been really bad at teaching. This even seems like a likely one as it is difficult to perform such a reformulation and to do so broadly and quickly.

The other reason I'm willing to accept alternative conclusions is that France and the USSR had far more success than Finland (or even America). Their success contradicts a claim that "[it is] too abstract for young kids". You'd need to constrain it to something like "[it is] too abstract for Finish kids" which I think both of us would doubt such a claim.

florbnit2• 1 year ago

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.

godelski46• 1 year ago

Please reread my comment in full. I'm willing to bet we disagree on the definition of math. I'll strongly insist that the one I'm using is common among mathematicians. If you'd like to retort by saying it's about semantics then congrats, we're on the same page (and can be verified by reading you sibling comments and/or my replies to some of them)

jeffhuys• 1 year ago

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?

godelski46• 1 year ago

What is the question asking? Why do you have Aphasia? I'm not sure what the relationship here is. Or are you suggesting you're good at math but not good at language?

I feel weird answering even if I infer the right question because it feels tautological. If you have Wernicke's Aphasia does it not create the possibility that I already have but your condition resulted in misunderstanding. Given the condition does it not create a high probability that a response will similarly be misunderstood? Is not Anosognosia quite common?

Maybe I'm really misunderstanding but honestly I'm not sure what you're asking

atomicnumber3• 1 year ago

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.

godelski46• 1 year ago

In either case it would seem to suggest we should radically change the system

serial_dev• 1 year ago

This system sounds extremely complicated.

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

Or maybe it indicates that the people designing this system should be fired? Job security through complexity?

(Or maybe I’m just biased by the system I know… I’m just asking questions)

thaumasiotes8• 1 year ago

I went to a small high school; my graduating class was around 30 people.

Math classes weren't separated by grade. So, I took Algebra 2 in 8th grade alongside a cross section of the school; there was one other 8th grader, two seniors, and a selection of people in between.

There was no path to take the AP Calculus AB. Trig / Calc A was offered as two semesters, and then Calc B / Calc C was offered as two more semesters, after which you'd take the BC test. There was also no such thing as "precalculus". Trig followed Algebra II.

In my Calc C class, there were probably 8ish people, of which one or two (besides me) would have been in my grade.

HarHarVeryFunny3• 1 year ago

I'll claim that there's not real thing such as a "language brain" or "math brain.

Did you even read beyond the silly headline?

The article itself is about pre-testing subjects on a range of capabilities from problem solving ability to second (foreign) language learning ability, and then seeing how these correlated to the ability of the test subjects to learn to code.

The results were basically exactly what might be expected - people who learned Python the quickest were those who scored the best at learning a second language, and those who learned to wield it the best were those who had scored the best at problem solving.

Not surprisingly math ability wasn't much of a predictor since programming has little to nothing to do with math.

ubercow13• 1 year ago

I think the above comment stands. The point is, what do they consider maths ability? High school maths has very little to do with programming but university-level maths certainly feels very similar to it in structure. Many of my (good) classmates in my maths degree were very bad at things like mental arithmetic. So maybe "maths ability" (defined some way) isn't very important for being good at "maths" (proper).

godelski46• 1 year ago

  > Did you even read beyond the silly headline?

Yes. I'll also refer you to the HN guideline on this manner. You're welcome to disagree with me but you must communicate in good faith and unless you have a very specific reason for thinking I didn't "RTFM" then don't make the accusation.

I'm happy to continue discussing, but only on those terms. In fact, I think we're in far more agreement than your tone suggests. But I think you missed the crux of my point: math isn't number crunching

hydrogen7800• 1 year ago

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

thomasikzelf• 1 year ago

Of course Brett Victor has the essay on his website: https://worrydream.com/refs/Lockhart_2002_-_A_Mathematician'...

It is a great read!

seba_dos17• 1 year ago

Frankly, with all the mess that music notation is and the way it's often being taught, this may actually be a slight upgrade over status quo. I have never experienced more "that's just how it is" than in music.

thaumasiotes8• 1 year ago

most people don't know what math is

It's surprisingly common. Case in point: "The unreasonable effectiveness of mathematics in the natural sciences".

A normal person wouldn't be surprised that describing how something works is a good way to understand it.

LegionMammal978• 1 year ago

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.

godelski46• 1 year ago

There are no rules. On the other hand, code is very formal. It is a set of rules. It has structures. There is wrongness and you can do verification that is not the result of opinion nor is it subjective.

But yes, math is very broad. But it doesn't cover everything. At least not at this time.

ohgr• 1 year ago

As a mathematician by trade, the math brain is a language brain. Mathematics is about abstract communication rather than mechanics.

Oh wait neuroscientists, explains it all. A statisticians favourite target for being unable to interpret data correctly.

725686• 1 year ago

For the 99% of programming I come across, I need about 0% math.

hinkley3• 1 year ago

I’m old enough to have caught the tail end of CS being an offshoot of the Math department and I had a gaggle of fellow undergrads who were happy ours had been moved to the Engineering college and upset to know other students at other schools who were still in Math.

I don’t know about for learning but definitely for collaborating and mentoring. And it’s difficult to make a definition of mastery that excludes both of those, so I suppose after a fashion it’s right.

Despite being a professed lover of math, I scored higher on the verbal than the math SAT. There’s a lot of persuasive and descriptive writing in software, particularly if you’re trying to build a team that works smarter instead of finding more corners to cut.

quantadev• 1 year ago

There's only a handful of key concepts people need to learn to understand the basics of 'coding'. If you understand what a variable is, how they're scoped, how step-wise transformations happen, and what loops are, you know 90% of "coding". I knew it at age 13 in 1981 doing "Basic" programming. Sure mastery of the art of coding does take decades, but that's just just adding polish, rather than capability.

Math is VASTLY different with VASTLY more concepts that are all much more abstract in nature and harder to understand the infinite numbers of different ways one mathematical construct can be applied to another. A person can "master" coding, but no one ever masters math.

So comparing math to language or to coding is silly. They're completely separate domains. Just because each of the three can encode and represent the other two doesn't make them similar in any way whatsoever.

JohnMakin• 1 year ago

There’s a lot of people out there who “aren’t math people,” but they just might be computer science people

This is beyond silly from my perspective. I know the field of CS is vast, but this seems to conflate programming with CS. My school was more theory heavy but there definitely came a point in certain paths of study where I didnt touch a line of code for a year, just pure math. I struggle to even understand how someone can think of this sentence - computer science at its core is underpinned by mathematics.

rowanG0772• 1 year ago

They call "numeracy" math skills. From that perspective it seems not that weird to call programming CS.

calebm• 1 year ago

This is why women are so dominant in the software development field - because women are known to have higher language skills than men.

tmaly• 1 year ago

I just started reading this. Only 42 people in this study and only 36 completed the activity. I am a bit skeptical about the findings with such a small sample size.

3pt14159• 1 year ago

That's what I was going to say. Big conclusions based of tiny sample sizes are ridiculous.

alexpotato• 1 year ago

This reminds me of the following quote:

"Coding largely involves the 'logical part' of your brain. It tends to not include the 'language part' of your brain.

This is one reason why comments you add to code are so useful: they force you to engage both parts of your brain and therefore get better results.

This is also why when you go to explain a problem to a colleague, you often have a flash of brilliance and solve the problem: you are reframing the problem using a different part of your brain and the different part of your brain helps solve the problem."

I'm sure some readers here will say this is preposterous and there is no such thing as having "two parts of your brain".

To them I suggest watching:

1. "You are are two" (about people with their corpus callosum being severed) https://www.youtube.com/watch?v=wfYbgdo8e-8

2. "Conscious Ants and Human Hives" by Peter Watts https://www.youtube.com/watch?v=v4uwaw_5Q3I

TheGrognardling2• 1 year ago

I certainly don’t dispute the empirical validity of the findings from the study - but there are important nuances to consider as well. I am certainly more naturally-attuned to languages as-far as language-learning and reading than mathematics, but I have also found myself understanding more mathematical and theoretical linguistics as well. I also love programming.

It wasn’t until high school, when I tested-into the highest math class that the school offered, that I began to unlock (with some initial struggle) more logical and procedural reasoning specific to mathematics that I had always done well in, but never explicitly went above-and-beyond in, despite hints of such in arithmetic competitions that my school would hold and that sort of thing. I just think my brain works well for both the linguistic aspects of programming (more naturally) and the computational problem-solving aspects of programming. Certainly there are individuals who have strengths in both cognitive aspects, despite being more naturally-attuned to one versus the other, at least presumably.

Perhaps this shows a cognitive profile that has natural strengths in both "brains", or maybe this highlights limitations of the article's potentially narrow definitions of "language" and "math", implying a more complex intellectual landscape.

Interesting findings nonetheless.

john-h-k3• 1 year ago

I certainly don’t dispute the empirical validity of the findings from the study

You absolutely should. Tiny sample size and poor statistical method. It is p-hacking plain and simple

TheGrognardling2• 1 year ago

Okay, yeah - fair point. I admittedly didn't look too closely at the article before posting this - and I'm not too statistically-minded in many respects. But upon further investigation, yeah, you seem to be right. I think this article is really just promotional material for something.

resters• 1 year ago

I've noticed that the people who initially grok programming language syntax are often better at learning new symbolic systems, but I think this is actually due to a persistent type I error their brains make that is OK for early learning.

People who end up being the best programmers have a deeper appreciation for semantics and information flow, but tend to commit more type II errors early on, making them inferior intro CS students.

Much of the CS curriculum (and typically also the required maths curriculum) in universities still favors the first type of student over the second, driving out the most capable and creative minds.

osigurdson• 1 year ago

If you are bad at math, don't assume you will be bad at programming. Similarly, if good at math, don't assume you will be bad at programming.

If you try programming and you don't like it chances are you won't be very good at it.

randerson• 1 year ago

As an accomplished programmer who is not great at language nor math, I feel like my "modeling brain" is the key to success. I can envision all the aspects of an architecture, its data shapes and program flow, making it obvious which data structures and algorithms to use, or where to look for a bug. I did spend a lot of time naming things though... until ChatGPT replaced the need for a thesaurus.

hirvi745• 1 year ago

Isn't math somewhat a language in of itself? If not, a language has surely derived from math.

tgv• 1 year ago

Hold your horses. The summary of that article does not offer any proof of what the title says.

* It's a small sample, and they did not analyze the people who didn't complete the course. That's dubious. Those 6 could have had a massive influence on the outcome.

* The summary does not present the actual numbers. These are: "fluid reasoning and working-memory capacity explained 34% of the variance, followed by language aptitude (17%), resting-state EEG power in beta and low-gamma bands (10%), and numeracy (2%)". Note: numeracy, not math.

* The test result was only partially programming related. 50% consisted of the results of a multiple choice test with questions such as What does the “str()” method do?. Linguistic knowledge indeed.

* It's about completing a 7.5 hour Python course. That's learning indeed, but only the very beginning, where abstraction is not in play. The early phase is about welding bits of syntax into working order.

* The numeracy skills required are very low for such tasks, as the tasks are simple, and mainly require thinking in steps and loops, whereas numeracy aptitude is generally measured on rather problems involving fractions.

Edit: the paper uses the Rasch-Based Numeracy Scale for this, which seems to involve estimation and probabilities.

* 17% explained variance is a rather minimal result, and you cannot easily compare factors in such a small design, even if the other one is only 2%. That's a rather hairy statistical undertaking.

* Linguistic expedience might be explain the speed with which the course was followed, since the instruction is, obviously, linguistic. Hence, this factor is not necessarily related to the actual learning or programming.

* The argument from beta waves is clutching at straws.

* The argument that "perhaps women should have more of a reputation for being “good” at programming" because they score better on tests, is --however well meant-- utterly ridiculous. It reverses correlation to causation and then turns that into a fact.

* That linguistic skills are useful for programmers is widely understood. However, this is not because of the actual coding, but because the coder needs to understand the environment, the specs, the users, etc., all of which is transferred via language.

* And of course, the statistical result relies on Null Hypothesis Test Significance, which is rotten in its very foundations.

* Note that the CodeAcademy course "Learn Python 3" is 23 hours in 14 lessons.

msvana• 1 year ago

At the beginning, the article mentions correlation with language skills AND problem-solving. Focusing only on language skills in the second half is misleading. According to the abstract of the original paper, problem solving and working memory capacity were FAR MORE important.

Also, the article doesn't mention "math skills". It talks about numeracy, which is defined in a cited paper as "the ability to understand, manipulate, and use numerical information, including probabilities". This is only a very small part of mathematics. I would even argue that mathematics involves a lot of problem solving and since problem solving is a good predictor, math skills are good predictor.

scarecrw• 1 year ago

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.

BXLE_1-1-BitIs1• 1 year ago

Started programming over half a century ago. The insurance company I was working for gave me a joint life actuarial evaluation problem for which I wrote a Fortran program, picked up from a book. My uni student buddy let me use his ID so I could drop decks into their IBSYS. Turnaround was about a day. My career as a professional manual reader began.

Well yes, my high school maths were in the high 90s - more than my language scores in French, German and Latin with some off curricular Russian. I guess being a polymath helps.

Unless you are doing an engineering or mathematical application you don't need much math, especially as you can just call a function in the vast majority of the time.

I did a number of software products and operating system modifications without using any math beyond arithmetic operations.

I was a resource for other programmers including the odd math PhD.

dismalaf• 1 year ago

Notwithstanding Puritanism like "language is maths" or "logic is maths" I definitely agree.

I learned to program when I was a kid and my maths skills were super basic. Programming can almost be distilled to something as basic as "if this, then do that", plus "do this x times". Then read API documentation and call functions that do what the docs say.

With just this basic understanding you can create a lot of stuff. The maths is obviously the foundation of computation, but to be a programming language user and build stuff, you don't actually need to understand most of it.

In university I did eventually do some math-y stuff (econ degree so prerequisites in stats, maths and even CS) and it helps with certain stuff (understanding graphics programming, ML and LLMs, plus knowing maths on its own is useful), but I still don't feel it was strictly necessary. Language and basic logic is enough IMO.

Ygg2• 1 year ago

Whenever encountering such sensationalist headline, it's good to remind ourselves of "[Replication needed]" tag.

rconti• 1 year ago

The most obvious way in which I think "math" and "programming" are related is the way they're taught; by repetitive performance of problem sets. I got frustrated in math for this reason; it takes a lot of energy to sit and focus on a whole bunch of hard problems that all "look the same". It was too easy to do 1 or 2 and think "okay, I got it" and then move on, not realizing the repetition was the key to memorization.

I feel the same way about starting learning programming. Repetition, repetition, repetition, until you "get good".

literallyroy• 1 year ago

Is 42 participants statically significant?

mrinterweb• 1 year ago

Personally, I find ruby one of the most readable languages because of the language and its DSLs. To be fair, the DSLs are very readable, but the lines can blur between what is ruby and what is a DSL.

sota_pop2• 1 year ago

I have really come to enjoy using LINQ queries (specifically with lambda syntax) in the C# language. Although I’m a little biased because I work mostly in C#.

jackcosgrove• 1 year ago

I had to scroll through most of the paper to find this.

All participants were right-handed native English speakers with no exposure to a second natural language before the age of 6 years

Which removes a confounder that Python mimics English syntax.

Still if this is a typical study recruiting thirty-some undergrads as subjects it's probably not generalizable, or even replicable given the same experimental setup.

vlovich123• 1 year ago

Counter example: I can pick up any new programming language within 3-6 months and be proficient but it takes a year to pick up some minor fluency in a human language and I still have yet to obtain full fluency in any other language as an adult.

nielsbot• 1 year ago

I suspect, however, that a programming language is a much more limited domain than a human language.

I often tell people it's not that learning a language is hard, is learning that language's software library... and learning a software library doesn't feel like learning a language. More like learning a set of tools.

kjellsbells• 1 year ago

It's funny that this popsci article instantly succeeded in dividing the HN commenters into math/not-math camps. Porque no los dos?

Programming is the manifestation of thought through the medium of a keyboard and screen. If you are a clear thinker, if you can hold multiple things in your head at once, if you can reason about things and their relations, well, you can be a strong programmer.

It seems wholly unremarkable to me that someone new to Python would not be fazed by it, given it's fundamental basis in words (print, if, etc.) Someone with a background in languages, who can think well enough to explicitly or implicitly pick up the structure of the language, is gonna do just fine. "Oh, so when I see a while, I need to end with a colon" isnt so different from "when I shout, I need to add a ! at the end"

(Java gets a special place in hell for forcing "public static void main" on every beginner.)

Math only really comes into it when you want to reason about things that have a history of being manipulated mathematically, typically for reasons of convenience. You could probably invert a matrix in SNOBOL, but its a lot easier to pull out lists and arrays and linear algebra.

In other words, lets see the follow up paper to this where Python newbies are asked to model the trajectory of a bead on a wire and see how they do.

rerdavies• 1 year ago

The language brain is more important than the math brain for reading the first lesson on how to program in Python. Fixed that for you.

Does answering a quiz on the contents of the first lesson on how to program in Python really encapsulate anything concrete about who will and will not be able to actually program in Python?

I've always been disturbed by the disconnect between "first lessons" on programming languages and how I personally actually learn programming languages. I can't help thinking that the researchers have measured something else other than whether people have learned to program.

FilosofumRex2• 1 year ago

You can make any subject "mathy", because there are relations, ratios, correlation and patterns in everything. My favorite example, is how Chomsky mathified linguistics, and made it esoteric, undecipherable, uncomputable and thereby linguists unemployable, even in research labs.

But as a matter of practice, teaching programming to engineers/scientists, even to mathematicians, is an order of magnitude easier than teaching math to CS folks. Simply quiz job candidates on fp arithmetics, and see how many fail miserably.

kevin_thibedeau• 1 year ago

I'd posit that this is part of why Pascal lost. Making and/or the same precedence as */+ only appeals to mathematicians and gets in the way of ordinary uses for Boolean expressions where you want them lower than the sub-expressions they concatenate in a language-like manner.

twodave2• 1 year ago

In my experience, language skill may or may not matter for programming, but it certainly matters for understanding a problem space. You can be a great programmer, building the wrong thing because you didn’t understand the requirements or see the gap in them and know to ask the right clarifying question, etc.

Lately I’ve also felt language skills matter when writing concise, specific AI prompts. This has become a useful part of my programming workflow in, I suppose, the last year or so. Before that it was knowing “how to Google” well, but that’s less language-dependent in my opinion.

PicassoCTs• 1 year ago

I guess its the ability to tell long, forking stories, traversing several abstraction layers. Dante Alighieri would be loving this! Its the ability to walk through a mental palace, room for room again.

ChrisMarshallNY• 1 year ago

That makes sense.

Probably the most valuable math classes for me, were ones that had me use algebra to solve word problems.

And, fundamentally, all languages describe the same stuff, using different tokens. That is pretty much in line with programming languages.

w10-1• 1 year ago

Not sure why the title left out the essential term: it matters more for learning programming

I believe the goal is to encourage those (young people) allergic to math but good in languages to realize they could be good at programming. That's worthy and important (though ironic to use a scientific study to do so).

As for the larger question commenters are raising, I notice often programmers reducing programming to problem-solving, and that to modeling, thence to math writ large; then they prove their point by noting that the most significant algorithms have strong and deep roots in math. The argument is: if the pinnacle of programming is math, then the more math-like programming is (in people and style), the better. (Hence: functional programming and provable algorithms are the epitome)

This argument is invariably made only by math experts, and does have the effect of reducing competition and selecting for like-minded persons, so there's at least the possibility of infection with self-interest and bias to the familiar.

I think the real distinction lies in this: with math, once you have a model, you fit things into that, and exclude other things. You do perfectly, but only in your domain. With language, any differance (any difference that makes a difference) starts to be named and tracked and dealt with somehow. It may grow in confusing ways, but it turns out (like architecture) it actually makes much more sense to adapt the structure to the use and relevance than vice-versa.

Sure, some subset of architecture is engineering by necessity, and it's probably even the hardest subset. But that's also the most portable knowledge and practice, and I would argue, thus easier to find and deploy once you've isolated such a need, particularly since mathy stuff fits nicely in a reusable library.

So math is an important but relatively isolated part of programming, and thinking it's ideal for everything is missing the point that programming matters for some purpose.

"attention is all you need" is but one example of the priority of relevance over structure in systems.

blobcode• 1 year ago

the requirements for advanced math classes for every computer science major seem unnecessary

Computer science is much more than programming - and I think that most of the value derived is from being able to think about problems, which largely require the abstract type of thinking encouraged by more advanced math. Code is just a tool.

anacrolix• 1 year ago

I would agree. Linguistics and literature have always been a strong interest of mine, and many computer scientists. Moreso, I find weaker programmers struggle with spelling, grammar, various dyslexias and torrent-of-thought code organisation.

dublin• 1 year ago

Of course it does. Math is not programming - it's almost entirely irrelevant to programming and certainly to software and architecture development. Most modern programming only involves math for trivial things like counting.

This classic article explains the real issue - like Mike Gancarz' classic on the Unix Philosophy, this is something all younger hackers should read, but few have, since these are the fundamental ideas that have created our modern world of computers: https://web.archive.org/web/20000529125023/http://www.wenet....

banq• 1 year ago

If we distinguish between form and content: Mathematics = form; language = content. However, mathematics is only one type of form, and subject-predicate-object grammar also belongs to form, yet grammar falls under language.

For example: "Matter determines consciousness." If we apply first-principles thinking—where does matter come from? This statement then becomes: "XXX created matter, and matter determines consciousness." At this point, our interest shifts to the first-principle subject "XXX," focusing our attention on it. Who is XXX? God?

In this thought process, we use the subject-predicate-object grammatical structure to trace back the original subject "matter" in "matter determines consciousness"—where does matter come from? Although this formal reasoning does not involve specific mathematical formulas, it indeed employs formal logic to uncover a flaw and opens the door to deeper rabbit-hole

voidhorse2• 1 year ago

Abstraction is a huge factor in this too. Language may be dominant because we are at a stage in which the vast majority of programming is little more than hooking together tidy abstractions that are already highly optimized and predominantly organized linguistically.

It you ever need to get into the guts of a system or need to solve bleeding edge problems for which good abstractions don't yet exist, the "math brain" becomes significantly more relevant.

I say this as someone who studied literature and philosophy. The majority of what I know about programming and software engineering I either taught myself or learned from the tutelage of others on the job. Early on in my career, a solid mathematics background was, indeed, not that relevant. These days, though, I'd be lost without it. Whether you like it or not, when it comes to doing real engineering you necessarily need to establish bounds and prove things about those bounds and typically you'll need to do this numerically or at the very least using inductive structures. Linguistic aptitude is still relevant, but it helps less in these cases.

sota_pop2• 1 year ago

As others have commented, I believe strongly that to define “language brain” and “math brain” is a false dichotomy and bunk neuroscience. Mathematics IS a language in itself; a collection of symbols created to express concepts. This study works really hard to make a statement that most people already know: anyone can be a good programmer, mathematician, “whatever” if they have the interest, drive, and opportunity to do it.

An interesting book that illustrates the evolving societal perception of mathematicians (and by extension, computer scientists) over time is “Duel at Dawn”. The modern (sic recent) notion is the reclusive genius (maybe even suggestion of autism) who possesses the alien, superhuman, unattainable, too-cool-for-you ability to process numbers and information that you can only be born with. (Those familiar with the TV show “the big bang theory” would recognize the trope of the “Sheldon Cooper” character.) This is False.

The reality is that no one is born with the super-human ability to do anything - anyone who is very good at something has worked very hard to get good at that thing regardless of the perception.

edit: my initial criticism of “the study” was based upon the article. On a skim of the actual cited paper, I revised my specific criticism, but the actual paper still comes off as no more than a mild eugenics argument dressed in psychology and statistics jargon.

concordDance2• 1 year ago

Can't see any eugenics there, can you quote?

albertoCaroM• 1 year ago

Although the study by Prat et al. (2020) suggests that linguistic aptitude is a better predictor than numeracy for learning programming in Python, it should be read carefully, as it can easily be oversimplified.

To begin with, the study measures functional numeracy: the ability to solve everyday numerical problems. This is quite different from the kind of advanced mathematics often associated with programming, such as formal logic, symbolic abstraction, or the use of formal languages (as found in denotational semantics or type theory).

These more abstract skills—not basic arithmetic—are essential for understanding recursion, type inference, or algorithm design. That functional numeracy has low predictive power in this study does not imply that deep mathematical reasoning is irrelevant to programming.

Moreover, the language used in the study is Python, which was explicitly designed to be readable and semantically close to natural language. This may give an advantage to individuals with strong verbal skills, but the results don’t necessarily generalize to languages like C, Lisp, or Haskell, where symbolic and logical density is much higher.

Finally, language and mathematics are not opposing domains. They share cognitive underpinnings, such as working memory, executive attention, and hierarchical structure processing. The key is not which one "wins," but how they interact and complement each other in different programming contexts.

mmaunder• 1 year ago

These more abstract skills—not basic arithmetic—are essential for understanding recursion, type inference, or algorithm design.

No they're not. Academia has spent decades trying to formalize many aspects of programming and continues to be confused by the lack of correlation between comp sci grads and innovative programmers. Why is it that the drop-outs are succeeding so wildly?

Recursion, for example, is learned by most of us real world achievers when we hit a brick wall in programming that other methods won't solve, and we have that aha moment of "this is why this exists". Not because we studied advanced math with symbolic abstraction, denotational semantics and type theory.

The uncomfortable truth is that almost all of professional programming and innovative programming (creating useful stuff never before seen) never uses any of the advanced math skills that are prerequisites in every degree program. I think much of the sadism around teaching this is perpetuated by "I did it so you have to" and academic gatekeeping.

When you get really really good at programming and hit the most productive zone in your life, it feels like language. That you have the ability to just say it.

ndriscoll6• 1 year ago

When you get good at math, it also feels like language. Mathematicians see expressions like `|x-y|` and the read it as synonymous with "distance" just as they would "distancia". Physicists pick out fragments of large equations and say "this term acts sort of like an 'effective' mass", etc. There is a sort of vocabulary to mathematical patterns.

Picking up a skill without intentional study is great, but you still learned the skill. Programming languages are formal languages. Most mathematicians don't study foundations either.

Professional programming doesn't often make use of specific advanced mathematical knowledge, but I find it makes everyday use of the skills.

TheOtherHobbes• 1 year ago

The drop-outs are "succeeding wildly" because people like Turing, Church, and Hilbert invented the sand pit they're playing in.

Knuth created LaTeX. Pandoc is written in Haskell, famous for being a completely useless academic language with no real purpose beyond torturing undergraduates (it says here.) Efficient search and data compression algorithms aren't hacked together in late night hobby coding sessions.

Cryptography, digital signal processing for images, sound, and video, and ML core algorithms are all mathematical inventions. The digital world literally runs on them.

"Real world achievers" might want to try being a little less parochial and a little more educated about the originators of the concepts and environments they take for granted.

Vibe coding "Social AI chatbot network with ads = $$profit$$" or "Cat videos as a service" is only possible because the entire field stands on the shoulders of mathematical giants.

notnullorvoid• 1 year ago

You are making a rather wild assumption that dropouts don't have the abstract math skills that correlate with programming skill.

I'd argue that if they can figure out recursion after hitting a brick wall like you describe, then that's a good indication they did have abstract math aptitude to begin with.

In my personal experience the hardest part of mathematics is it's grammar and language. It's very different from natural language, whereas programming is much closer. You can take nearly any math problem and convert it to pseudo code and it'll be much more understandable for those programmers who never studied (or struggled with) advanced math.

Programming requires a base level of natural language aptitude that nearly all adults have, there's diminishing returns for anything approaching the levels of a poet or novelist for example.

Shorel4• 1 year ago

My own definition of mathematics for the sake of this comparison: - If you can write a formal proof, starting from some assumptions and proving some result, it is mathematics. The assumptions are the axioms. Then you use logic, which is the same programming logic, and then you get to some result.

It can be an invariant in a programming function, it can be a more general result, if you can write a proof, it is mathematics. Most algorithms involve proofs, so they are mathematics.

It has nothing to do with it being "sadism" or academic gatekeeping.

These people are doing mathematics without knowing it is mathematics. That's all.

Why is it that the drop-outs are succeeding so wildly?

Here is where you can learn about confirmation bias and educate yourself.

bitzun• 1 year ago

This reads like an LLM wrote it.

nurettin• 1 year ago

It does! Who structures their posts like a platonic rhetorical piece??

CjHuber• 1 year ago

There is even the em dash in it

_1tem• 1 year ago

This tracks with my experience perfectly. Hated the math at my Computer Science program in university, barely passed the math courses while excelling at the programming courses, loved taking linguistics, foreign languages, and literature as electives. To this day, programming, foreign languages, and literature is what I do all day every day.

blueboo• 1 year ago

we'll eventually find that the language brain matters more for math than the math brain.

dmos62• 1 year ago

My take on skills related to programming is that it's a dance between writing skills and working memory. I've measurably bad working memory, which had led to compensation with writing skills, which led to a programming style that's fairly disciplined and focused on "wholesome" readability. A downside is that I still struggle interacting with code that's written by the working-memory-oriented programmers.

I've recently taken up a daily practice to improve my cognitive skills. Currently I'm using NeuroNation, and it is quite great. The stimulus to start the practice was getting my memory tested (clinically) and learning that it's below norm.

john-h-k3• 1 year ago

Has anyone here actually read the paper? Heavily clickbait headline, completely exaggerating the study results, which themselves are not very rigorous (to be generous)

Tiny sample size - 36 people completed

Numeracy has R^2 = .27 Language has R^2 = .31

They then run stepwise regression to determine variance contributions, seemingly ignoring their earlier results, and this leads to almost no contribution from numeracy. Why? Because they have ~10% shared variance and stepwise regression is greedy - will just take whatever you give it first.

I can't mention this part enough. If you got a second, very similar language test, and added it to the model, you would _also_ find it has almost no unique variance added.

Every thing they measure is incredibly noisy and they do not once attempt to deal with this. Human based reviewers, time-to-completion, etc.

p-value for "language learning is more significant than numeracy" on the values they give (Steiger test) gives 0.772. Utterly insignificant.

Also, to beat the point home, just think about the argument here: * Numeracy contributes 27% of variance

* Language skills contribute 31% of variance

* After regression step, numeracy contributes only 2% of unique variance. Because you added a correlated variable!

SanjayMehta• 1 year ago

It reads like an ad for something.

hansvm• 1 year ago

To be somewhat fair, their numeracy scatter plot visually looks more like a dart board than any real process. The fact that you got a positive-sloping line out at all from the regression has to do more with the positions of the outliers than anything else. You're at least able to visually examine the language aptitude plot and see an up-and-to-the right connection between the two variables.

john-h-k3• 1 year ago

I agree, but also via some napkin math, the chance of getting those different results is something like 40%.

(Ie, if you sample the same signal twice for the numbers they did in the study, there’s a 40% chance it’ll be >0.04 away from the original sample, as numeracy was from language)

gitroom• 1 year ago

Honestly, all this "math brain" vs "language brain" stuff just feels off to me - I've always been more of a pattern and abstraction person anyway. Makes me wonderif schools focused more on teaching real abstract thinking early, would way more kids just "get" programming without even stressing over math class?

whatagreatboy• 1 year ago

Not treating math as just another language for expressing your thoughts is a weird position to take. I cannot take this position seriously.

jalopy• 1 year ago

Interesting tidbit:

>> In this study, high levels of these beta oscillations were associated with faster learning and more programming knowledge

This makes me think those binaural beat programs attuned to beta wave frequency might help with heavy coding sessions?

Can anyone point to studies that confirm/reject this?

yawboakye• 1 year ago

tautological. math is language.

mathgradthrow• 1 year ago

the language brain matters for math much more than the math brain.

g_host56• 1 year ago

I could have told you this for free :)

but really it just depends: - web or app information software: logic and language matters more here - doing what Donald Knuth does: math matters more here

Shorel4• 1 year ago

My own definition of mathematics for the sake of this comparison:

- If you can write a formal proof, starting from some assumptions and proving some result, it is mathematics. The assumptions are the axioms. Then you use logic, which is the same programming logic, and then you get to some result.

It can be an invariant in a programming function, it can be a more general result, if you can write a proof, it is mathematics. Most algorithms involve proofs, so they are mathematics.

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

Related Stories