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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-overlappin

by jll29 1y 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.

reverendsteveii 1y 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.
- danielmarkbruce 1y ago
  math != calculation. It's an actively stupid fiction for people who don't understand what math is.
  - radlad 1y ago
    > It's an actively stupid fiction for people who don't understand what math is. This comes off quite judgmental, and doesn't help me understand your actual point. Could you elaborate on the differences, as you see them?
    - tylerhou 1y ago
      In higher math (typically 2nd year and onwards at US universities) there is fairly little explicit calculation, and math is more about studying the (formal) relationships between mathematical objects. For example, we can abstractly define topological spaces and abstractly define algebraic “groups,” and algebraic topology studies the relationships between topological spaces and algebraic groups. This is somewhat like having a “data type” defined by some library, examining ways it can be transformed into data types defined by some other library, and studying what invariants hold under those transformations. In some sense, an undergraduate math education is akin to learning the “standard library” (in the software engineering sense) of higher mathematics. Most courses start with basic abstractions of some mathematical object and repeatedly construct more and more abstractions on top of those. The structure of those abstractions is similar to how you might build a library. A professional mathematician is expected to be fluent in the mathematical standard library, just like how you might expect an experienced software engineer to be fluent in Python’s standard library. If this analogy is true, people who can learn Python relatively quickly might be able to also learn higher mathematics relatively quickly under the right pedagogical environment.
      - ndriscoll 1y ago
        One personal project I'd love to find the time for is to try to write out a sequence of math notes that essentially builds up a Lean repository, intentionally "refactoring" as it goes along. So you do some explicit coordinate vector or system-of-equation calculations with both real and complex numbers, eventually define interfaces for fields and vectors, do your linear algebra proofs, realize that linear endomorphisms are almost-but-not-quite a field, so define rings and go back and refactor your field proofs to use them, realize vector spaces are "K[T] not-quite vector spaces", define modules, refactor your vector space code, etc. This was kind of how math classes worked, but without that explicit phrasing. It would certainly make the analogy between the two activities more obvious. I also wonder whether people would have less trouble with quantifiers if they were phrased in programming terms: a proof of "forall x, p(x)" is a function x=>p(x), and a proof of "there exists x such that p(x)" is a pair (x, p(x)). e.g. Continuity: (epsilon: R, h: epsilon>0, x_0: R) => (delta: R, h2: (x: R, h3: d(x,x_0) < delta) => d(f(x),f(x_0)) < epsilon) Uniform continuity: (epsilon: R, h: epsilon>0) => (delta: R, h2: (x: R, x_0: R, h3: d(x,x_0) < delta => d(f(x),f(x_0)) < epsilon)) proof of UC => C = (epsilon, h, x_0) => let delta, h2 = UC(epsilon,h) in (delta, h2(_,x_0,_)) So when you're trying to figure out how to do the proof, it's clear what kind of type you need to return and your IDE could help you with autocomplete based on type inference.
    - danielmarkbruce 1y ago
      It is hugely judgmental of people making claims and doing studies who don't understand that elementary arithmetic is a tiny part of math. I judge them. It's ok to be ignorant of a topic, but they shouldn't discuss it or make suggestions. The comment below/above sort of explains it, except I'd argue covering it starts/can start/should start much earlier than at university. Basically, the vast majority of most branches of math, especially pure math, involves very little in the way of calculation. And the way math gets taught (and stupid claims about "math brain") means that many kids who aren't in the top few % of "doing calculation" never get to do the classes where it's less important. LLMs, trained on words/tokens and symbols and logical combinations of them, are proving to be good at math, and bad at calculation/arithmetic. If an LLM went to school we'd never let it train on real math tokens. It would get shoved in the corner as a "model bad at math" because it was a "model bad at arithmetic".
    - owlbite 1y ago
      Most math is more about definition, proof and structuring/relationships than about numbers. It is a bit of a joke among math students that numbers above 5 are effectively infinity, they crop up that rarely.
  - voidhorse 1y ago
    This. And we do a huge disservice to tons of people by basically instilling the opposite idea. So many of the people I know that either claim they are "not math people" or who claim they "dislike math" say this because they were subject to nothing but tedious calculation in school and were never show the logical, conceptual, and actually interesting parts of mathematics. I despised math until I read Frege's foundations of arithmetic in college since it was the first time I ever had someone actually show the point and make it interesting.
karmakaze 1y 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.
- pier25 1y ago
  "naming things" is really about "recognizing things" and/or "understanding things". It much deeper than just language.
  - FilosofumRex 1y ago
    Yes, exactly, just watch how little babies recognize and communicate about hundreds of objects, emotions and situations before they're able to utter momma or dadda.
- hirvi74 1y 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 1y 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 1y 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.
- danielmarkbruce 1y 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 1y 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 1y 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.
pier25 1y 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.
twodave 1y 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 1y 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 1y 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 1y ago
I figure the programming brain matters the most for programming.

by jll29 1y ago

reverendsteveii 1y 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.

danielmarkbruce 1y ago
math != calculation. It's an actively stupid fiction for people who don't understand what math is.
- radlad 1y ago
  > It's an actively stupid fiction for people who don't understand what math is. This comes off quite judgmental, and doesn't help me understand your actual point. Could you elaborate on the differences, as you see them?
  - tylerhou 1y ago
    In higher math (typically 2nd year and onwards at US universities) there is fairly little explicit calculation, and math is more about studying the (formal) relationships between mathematical objects. For example, we can abstractly define topological spaces and abstractly define algebraic “groups,” and algebraic topology studies the relationships between topological spaces and algebraic groups. This is somewhat like having a “data type” defined by some library, examining ways it can be transformed into data types defined by some other library, and studying what invariants hold under those transformations. In some sense, an undergraduate math education is akin to learning the “standard library” (in the software engineering sense) of higher mathematics. Most courses start with basic abstractions of some mathematical object and repeatedly construct more and more abstractions on top of those. The structure of those abstractions is similar to how you might build a library. A professional mathematician is expected to be fluent in the mathematical standard library, just like how you might expect an experienced software engineer to be fluent in Python’s standard library. If this analogy is true, people who can learn Python relatively quickly might be able to also learn higher mathematics relatively quickly under the right pedagogical environment.
    - ndriscoll 1y ago
      One personal project I'd love to find the time for is to try to write out a sequence of math notes that essentially builds up a Lean repository, intentionally "refactoring" as it goes along. So you do some explicit coordinate vector or system-of-equation calculations with both real and complex numbers, eventually define interfaces for fields and vectors, do your linear algebra proofs, realize that linear endomorphisms are almost-but-not-quite a field, so define rings and go back and refactor your field proofs to use them, realize vector spaces are "K[T] not-quite vector spaces", define modules, refactor your vector space code, etc. This was kind of how math classes worked, but without that explicit phrasing. It would certainly make the analogy between the two activities more obvious. I also wonder whether people would have less trouble with quantifiers if they were phrased in programming terms: a proof of "forall x, p(x)" is a function x=>p(x), and a proof of "there exists x such that p(x)" is a pair (x, p(x)). e.g. Continuity: (epsilon: R, h: epsilon>0, x_0: R) => (delta: R, h2: (x: R, h3: d(x,x_0) < delta) => d(f(x),f(x_0)) < epsilon) Uniform continuity: (epsilon: R, h: epsilon>0) => (delta: R, h2: (x: R, x_0: R, h3: d(x,x_0) < delta => d(f(x),f(x_0)) < epsilon)) proof of UC => C = (epsilon, h, x_0) => let delta, h2 = UC(epsilon,h) in (delta, h2(_,x_0,_)) So when you're trying to figure out how to do the proof, it's clear what kind of type you need to return and your IDE could help you with autocomplete based on type inference.
  - danielmarkbruce 1y ago
    It is hugely judgmental of people making claims and doing studies who don't understand that elementary arithmetic is a tiny part of math. I judge them. It's ok to be ignorant of a topic, but they shouldn't discuss it or make suggestions. The comment below/above sort of explains it, except I'd argue covering it starts/can start/should start much earlier than at university. Basically, the vast majority of most branches of math, especially pure math, involves very little in the way of calculation. And the way math gets taught (and stupid claims about "math brain") means that many kids who aren't in the top few % of "doing calculation" never get to do the classes where it's less important. LLMs, trained on words/tokens and symbols and logical combinations of them, are proving to be good at math, and bad at calculation/arithmetic. If an LLM went to school we'd never let it train on real math tokens. It would get shoved in the corner as a "model bad at math" because it was a "model bad at arithmetic".
  - owlbite 1y ago
    Most math is more about definition, proof and structuring/relationships than about numbers. It is a bit of a joke among math students that numbers above 5 are effectively infinity, they crop up that rarely.
- voidhorse 1y ago
  This. And we do a huge disservice to tons of people by basically instilling the opposite idea. So many of the people I know that either claim they are "not math people" or who claim they "dislike math" say this because they were subject to nothing but tedious calculation in school and were never show the logical, conceptual, and actually interesting parts of mathematics. I despised math until I read Frege's foundations of arithmetic in college since it was the first time I ever had someone actually show the point and make it interesting.

karmakaze 1y 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.

pier25 1y ago
"naming things" is really about "recognizing things" and/or "understanding things". It much deeper than just language.
- FilosofumRex 1y ago
  Yes, exactly, just watch how little babies recognize and communicate about hundreds of objects, emotions and situations before they're able to utter momma or dadda.
hirvi74 1y 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 1y 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 1y 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.
danielmarkbruce 1y 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 1y 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 1y 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.

pier25 1y 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.

twodave 1y 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 1y 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 1y 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 1y ago

I figure the programming brain matters the most for programming.