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.
Or just your regular 8/9th grade Algebra course where you should have learned systems of equations. That's where I first encountered using matrices for systems of equations at least. (maybe it was Algebra 2+ but it was definitely before taking Linear Algebra in college).
I'm not sure how to interpret this comment, it could easily be read in multiple ways. (Depends on priors)
Regardless, it's a shockingly common occurrence. I'd agree it's not the right way, but it is also a common way. That perspective might define those priors
When growing up, I'm sure my fellow students and I were not the only ones get responses to questions like "Why can't one divide by zero?" or "Why is Pi necessary to compute to area of a circle?" answered like "because that's just how things work" or "because it just is."
I'm not going to sit here and act like I was a star student or anything. I was more of a class clown type. I absolutely hate math and all things math. That was, until I went to college. A switch flipped when I was in a Calculus II class.
Our professor asked, "What is a 100 divided by 0?" People in the class responded with, "You can't divide by 0 because it's undefined." To which our professor responded with, "Why?" Then a student took out a calculator and showed the professor that the answer as indeed undefined. To which he responded with, "Ok, how do you that calculator is correct? Do you just believe it because people told you that dividing by zero is undefined? Ok, the answer is undefined... but why?"
Right then and there, a switch flipped in my brain. I realized that I was basically institutionalized to just not question math and to just accept that things work a certain way "just because." It was at that point I actually started to become interested in math, and it completely changed my outlook on math in a positive manner. I love math now (despite being horrible at it).
This reminds me of a lot of what I see in grad school and academia. Something akin to what Tom Wolf talks about here[0]
> I’ve always been a straight-A student.
> if something was not written in a book I could not invent it unless it was a rather useless variation of a known theory. More annoyingly, I found it very hard to challenge the status-quo, to question what I had learned.
I don't think this part is isolated to math, but there's a lot of acceptance for "because" being an answer. Being in an authoritative position and being challenged can be frustrating, but I think a lot of that frustration is self-generated. We stifle creativity when young and it should be no surprise that frequently when people challenge, they don't have the tools to do so (or be receptive) effectively. Truthfully, "I don't know"[1] still shuts down the conversation.
But I think people themselves are uncomfortable with not knowing. I know I am! But that isn't a feeling of shame, it is a feeling that creates drive.
[1] Alternatively, variations like: "That's a good question, I don't know" or "Great question, but we don't have the tools to address that yet". The last one need not undermine your authority either. Truthfully, the common responses resulted in me becoming strongly anti-authoritarian. Which, also has greatly benefited my career as a researcher. So, thanks lol
I remember my high school math teacher responding "that's an interesting question, I don't know" and then coming back with an answer the next lesson after researching the subject.
Yeah, I was worried it might come off as sarcastic or something. Hopefully the original commenter doesn’t take it that way, or reads this follow up. Unfortunately, adding stuff like “honestly” often makes a comment look even more sarcastic. It is a real pain.
But yes, I am expressing honest admiration—it was a bad move on the part of the teacher I think, which the poster seems to have overcome!
Well I appreciate clarifying! I originally took it as sarcastic but second guessed myself. I figured math is pedantic, so maybe being a little pedantic here could help haha.
I went through the same thing, it really isn't easy. But it is also why I don't blame others for not seeing it. It would be hypocritical to do so. I'm just not sure what's the best way to share, I'm open to ideas. Unfortunately we have to contend with priors that we see here, though I'm happy if my efforts even make one more person able to share in this beauty.
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.
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.”
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.
> 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.
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)
It has nothing to do with the definition of math. If you put people in an MRI and give them random problems then you’ll notice a distribution in the patterns of brain activity that are distinct. Some of these groupings we’ll call “math like” because the problems are more like mathematics than linguistics. And in the other distribution we’ll call them “word like” because the problems fall into the category we associate with word problems.
The fact that we see separate patterns of brain activity is the interesting part not any semantic argument about what you or mathematicians feel should be defined as being math or not.
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.
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.
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.
> 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)
I'm not disagreeing, but just wanted to point out that this phrasing is commonly used by bad faith actors. I'm not saying you're using it this way and I legitimately do not think you are. But I wanted to point it out because I think your comment could be interpreted another way and this phrase might be evidence for someone to make that conclusion.
The classic example is conspiracy theorists. But lots of bad faith actors also use it to create leading questions that generally ignore or lead away from important context. Again, I do not think you're doing this. The rest of your comment makes me think you're acting in good faith.
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.
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?
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.
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).
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.
> I mean is it any surprise kids get bored in math?
Indeed. Kids did not evolve to learn things because they would be useful years down the road. But they did evolve to inhale knowledge at very high rates wherever it extends their capabilities in the moment.
My take on this is that math should be tied to kids crafting, experimenting, and learned directly in the context of its fun and creative uses.
Geometry screams out to be developed within a context of design, crafting, art and physical puzzles. Algebra, trigonometry, calculus ... they all have direct (and fun) uses, especially at the introduction stage.
The availability for graphics software, sim worlds, 3D printing, etc. should make math, from the simplest to most advanced, more fun and immediately applicable than ever.
Boredom with math is a failure to design education for human beings.
(Then there is the worst crime of all - moving kids through math in cohorts, pushing individuals both faster and slower than they are able to absorb it. Profound failure by design.)
> Indeed. Kids did not evolve to learn things because they would be useful years down the road. But they did evolve to inhale knowledge at very high rates wherever it extends their capabilities in the moment.
I strongly disagree with this. Children play. Most animals play. It is not hard to see how the skills learned through play lead to future utility despite potentially none at the time. We invent new games, new rules, and constantly imagine new worlds. The skills gained from these often have no utility beyond that that is self-constructed. Though many do have future rewards. I think we often miss those though because that path is through generalization. Learning how to throw a ball can help with learning physics, writing, driving, and much more. They don't perfectly transfer but it'd be naive to conclude that there aren't overlaps.
I think the truth is that as long as we are unable to predict the future, we really can't predict what skills will be useful and what specific knowledge should be pursued. We can do this in a more abstract sense as we can better predict the near future than far but that also means we should learn creativity and abstraction, as these allow us to adapt to changes. And that is why I believe we evolved these methods, and why you see things like play in most creatures.
> I strongly disagree with this. Children play. Most animals play.
I am not arguing against this. On the contrary, I agree with this completely.
Pairing the opportunity to learn and use highly general long term knowledge, toward progression in their own intrinsic interests (crafting, whatever) is the point I am making.
The alternative, a long line of math for math's sake, which neglects to harness and support each child's need and motivation to continually advance their own natural interests in all kinds of idiosyncratic directions.
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
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.
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.
Math major here. 'is' is a reflexive relationship. If math is language, therefore language is math. I believe clearly language is not math, therefore math is not language. Math is described with language, Math itself is not language. It is a 'has-a' relationship vs a 'is-a' relationship.
Forgive me if I doubt, but your comment would strongly suggest otherwise, along with this one[0].
The reason for doubt is a failure in fairly basic logic. Your claim is:
¬(A ↦ B) ⟹ ¬(B ↦ A)
I'd expect anyone willing to claim the title of "math major" is aware of structures other than bijections and isomorphisms. The mapping operator doesn't form an abelian group.
The word "is", typically refers to the logical equals operator (written as "="). Let A = Math, and let B = Language, the phrase "Math is Language" is therefore "A = B". My claim is that "B != A", which implies "A != B" because "!=" is reflexive. "A != B" then contradicts the claim "A = B". In words: because "language is not math", therefore it cannot be true that "math is language".
This is not number theory, not set theory, just logic. I don't see how the properties of Abelian groups applies. I do suspect that non-abelian groups is a case where "¬(A ↦ B) ⟹ ¬(B ↦ A)" is false, and would be a contadiction to my counter claim if "¬(A ↦ B) ⟹ ¬(B ↦ A)" was my counter-claim. No, my counter claim is simply that because "B != A" therefore "A != B"
The statement "¬(A ↦ B) ⟹ ¬(B ↦ A)" is quite different, and I'm not 100% sure whether you are mixing set and logic notations? [0][1] It does seem you are bringing in number theory concepts, or we are misunderstanding one another?
I assume "↦" is the set mapping operator and "⟹" is logical implies, and "¬" is logical not. "¬(A ↦ B) ⟹ ¬(B ↦ A)" could potentially be phrased as: "If the element A cannot be mapped to B, then the element B cannot be mapped to A". I would agree that statement is not 'generally' true. Could you please clarify so we are not talking past each other.
[0] Per google: The symbol "↦" is a mapping symbol, typically used to indicate a function or relationship where one element maps to another. It's not a standard logical operator in the same way that symbols like &&, ||, or ¬ are. Instead, it represents a directional relationship between sets or elements, often seen in set theory and mathematical notations
As I said elsewhere (here for others), I'm not going to play this game of *willful misinterpretation.* Your very words do not hold up to the same bar your are attempting to hold mine to. I know you are upset you got caught in a lie, but fuck around and find out. ¯\_(ツ)_/¯ Domain experts can recognize other domain experts pretty easily
> No, my counter claim is simply that because "B != A" therefore "A != B"
We all know that this is not always true. It may be true in certain cases, in certain fields (pun intended), but you know that this is such a basic logical fallacy that it is taught to children.
Here's a counterexample so we can lay this to rest.
Let "A" be "a square"
Let "B" be "a rectangle"
B != A -> "A rectangle is not a square" (True)
A != B -> "A square is not a rectangle" (False)
Stop cosplaying, stop trolling, stop acting in bad faith.
Did you even look at my name? There's 2 people that should come to mind. Certainly any logician would notice.
The equality relationship is symmetric, "For every a and b, if a = b, then b = a" [1]. This holds for the negation as well.
Or, "Properties of Equality... The [equality] relation must also be symmetric. If two terms refer to the same thing, it does not matter which one we write first in an equation. ∀x.∀y.(x=y ⇒ y=x)" [2]
The 'is' relationship in logic is understood to be equality. The 'is a' relationship in logic is subset. Colloquially, the word "is" can be either one though.
I notice in your counter example you swapped the "is" relationship with "is a". Keeping the "is" relationship: "A rectangle is not square" (true generally, but false for specific cases for rectangles). That is really the distinction, the sometimes true vs always true.
Let's stick to the precise definition of "is" to mean a logical equality from here on please, and be precise when we use "is" vs "is a" and never infer "is" to actually mean "is a".
So, with "Math is a language" vs "Math is language". Which do you mean?
> That's only in your head. Inventing claims so that you can pretend other people are wrong isn't a good move.
I'm not the only one that interprets a statement as "Math is Language" to be of the form "A = B" where "math" is A, "language" is B, and "is" is the equals operator, see: https://news.ycombinator.com/item?id=43874322
Seems kinda simple.. You're engaging in a almost pure personal attacks. Care to address the substance of how the 3 word long statement is not of the form "A = B", but is of some other different form? In which case, perhaps you can guide the conversation for why it is an interesting statement or not? If you want to change all the givens and use your own definitions, please provide those. Without common ground, this remains uninteresting.
> I'm not the only one that interprets a statement as "Math is Language" to be of the form "A = B" where "math" is A, "language" is B, and "is" is the equals operator, see: https://news.ycombinator.com/item?id=43874322
This appears to be a link that contains zero support for your sentence. Neither the comment you linked nor the response below it features such an interpretation.
> Seems kinda simple.. You're engaging in a almost pure personal attacks. Care to address the substance of how the 3 word long statement is not of the form "A = B", but is of some other different form?
You're in luck! I've already provided that material, and you responded to it. For further discussion, you'd need to have a better working understanding of English.
Very cool how the last sentence you leave off with always has to be a personal attack. It's breaking the rules of the discussion, irrelevant. Stop trying to win points. Let's focus on the substance.
> This appears to be a link that contains zero support for your sentence. Neither the comment you linked nor the response below it features such an interpretation.
It's interesting, because there is a disagreement about whether there is a paradox or not. There is a paradox if you take my perspective (that an equals relationship is being expressed), but none if an implication relationship is assumed.
These two sentences:
- "By that same logic you could also say that language is math"
- "Not quite, but the inverse is true."
The "not quite" says that "language is math" is not true. So we have "A = B", but "B != A", which is a paradox. OTOH it's not a paradox if what is actually being said is "A => B" but "B !=> A"
> You're in luck! I've already provided that material, and you responded to it.
Hello bad faith! I hope you are doing well today. Let's end the conversation here.
You're not making it look good. A common use of be is to express set membership rather than identity. For example, "two is an even number" or "tigers are cats".
We may hope that one day you'll come to realize that set membership is not reflexive, and - more to the point - also not symmetric.
> A common use of be is to express set membership rather than identity
Google for "logical "is a" vs logical "is"".
Google AI answers this:
> "is" typically represents an equality relation
Rest is from the AI response:
In logic, "is" typically represents an equality relation, while "is a" (or "is of the type") represents an inclusion relation. "Is" indicates that two things are the same or identical, while "is a" indicates that one thing is a member of a larger class or set of things.
Logical "is" (equality):
Meaning:
"A is B" means that A and B are the same thing, or have the same properties.
Example:
"The Eiffel Tower is in Paris" (the Eiffel Tower and the thing in Paris are the same thing).
Logical "is a" (inclusion or type):
Meaning: "A is a B" means that A belongs to the category or class of things that are B.
Example: "A dog is an animal" (dogs are a type of animal).
"silk is cloth" is not true except for the colloquial interpretation that infers "silk can sometimes be a cloth". Given the clarifications, it seems the OP is intending to say it's an exact equality and not a colloquial definition that actually means "subset".
I'll note, I have not asked any questions other than (paraphrasing): "what do you mean precisely?" To which, I have not gotten any answers other than trolling and flaming; and examples that all conveniently swap "is" with "is a".
You're saying that "Math" and "Language" are 'sets'? And that the phrase "Math is Language" should be interpreted as expressing the relationship between sets?
If we do want to talk sets, that seems far more interesting.
The statements like "Math is a language", or "Math has equivalence classes within languages", or "Mathematics are a Language" are slightly more interesting to consider IMO.
>> Math major here.
> You say that like you think it's a qualification?
Agree, appeal to authority fallacy. I take that over mis-framing any day though.
Any old-timers might appreciate that we're arguing over the meaning of the word "is" =D
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.
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.
> 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.
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.
> 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.
The word "is", maps to the logical "equals" operator. I agree with the example, but I don't agree it is relevant. There is no implies operator.
The statement "Math is Language", where A is Math and B is Language, maps to the logical assertion: "A = B".
If we are going to really be kinda twisty and non-standard, we could interpret the english "is" to be "is an equivalence class of". Which would map to your example pretty well: language is indeed an equivalence class of math, but math is not an equivalence class of language. Though, nobody is talking about implies operator or equivalence class here.. It's a "is" relationship, logical *equals*
You point out the "is a" relationship, not the "is" relationship, they are different. [0]
Find examples with two singular nouns and just the word 'is'.
The phrase in question: 'Math is language' is an example, or something like 'food is love' is too. I concede you could interpret those last few sentences with poetic license to be read more like: "A is a form of B", or "A is a B" - though that is not what was written and this is not a place to expect that much poetic license.
*edit*: a minute later, thought of a good example. "ice is water". True that "ice is a form of water", but strictly speaking no, "ice is not water". I'll concede there could exist an implied "is a", or an implied "is a form of", but that is poetic license IMO.
[0] Google AI summarized it pretty well: google "logical "is a" vs logical "is"
> In logic, "is" typically represents an equality relation, while "is a" (or "is of the type") represents an inclusion relation. "Is" indicates that two things are the same or identical, while "is a" indicates that one thing is a member of a larger class or set of things
> You point out the "is a" relationship, not the "is" relationship, they are different.
Well, what you reacted to was, let me copy'n'paste, "Math is a language". It was you who insisted that "is" in this sentence maps to "equals" relation, so thanks for agreeing that you were wrong.
I'm reacting to: "Math is language. 'Everything' is language. Language is the image of reality."
There are other discussions which say:
- Math is a subset of language, surely
- It's easily argued that languages are subsets of math.
Given that context, the distinction seems to be very important.
I find the following idea (paraphrasing) to be very interesting: "not only is math a subset of language, but the language and math are equal sets." I also think it's not true, but am curious how a person would support this assertion. So, my challenge is, because the logical "is" relationship is reflexive and the reflexive property does not hold here - how can this be true? The most satisfying answer has been (paraphrasing) "cause I'm using non-precise language and you should just infer what I meant." Which is fine I guess..
I literally copied "Math is a language." from your quote that started this subthread. Nobody here has typed "Math is language" - except you. Just open https://news.ycombinator.com/item?id=43873113, press CTRL+F and see for yourself. I can't fathom how can you still deny being so obviously wrong.
Honestly I don't think his point even stands. We were using English to communicate and English doesn't have the strict rules of mathematics. That's literally why we created math (which I'll gladly call "a class of languages"). He's right, "is" maps to "equivalent" but he's also wrong because "is" also maps to "subset" and several other things. "Is" is a surjection.
The problem here all comes down to seadan83 acting in bad faith and using an intentional misinterpretation of my words in order to fit them to their conclusion. I'm not going to entertain them more because I won't play such a pointless game. The ambiguity of written and spoken language always allows for such abuse. So either they are a bad faith actor "having fun" (trolling) finding intentional misinterpretations to frustrate those who wish to act in good faith or they are dumb. Personally, I don't think they're dumb.
> We were using English to communicate and English doesn't have the strict rules of mathematics.
Agree.
> He's right, "is" maps to "equivalent" but he's also wrong because "is" also maps to "subset" and several other things. "Is" is a surjection.
I agree. So, why can't either interpretation be valid? Perhaps, because one is obviously not true? Yet, it seemed like there was a clarification that the obviously not true relationship was the intended one!!!
Godelski previously wrote: "Coding IS math. Not "coding uses math".
I interpreted that clarification to mean you intended "is" to be a strict "is". Particularly given the other context and discussion of "is a" in other threads. I suspect now you were perhaps emphasizing "uses a" vs "is a", rather than "uses a" vs "is". Not a satisfying conclusion here. It would be a lot more interesting if the precision could have been there and had we been able to instead talk about whether all coding languages form an abstract algebra or not. Or perhaps use that line of reasoning to explain why all coding is a form of math. That would have been far more interesting..
Thinking about this a bit more.. I think I can refute your statement that "coding is math" and not "coding uses math".
I'm sorry the conversation got so caught up on pedantics.
Previously I would have quite readily agreed that at least "coding is a subset of math" - now I'd only agree in the sense that coding is an applied math, just like Physics is applied Math.
So, it does seem to be clearly a 'uses' relationship, and I'll support the assertion. To explain, coding is the act of creating a series of boolean expression (governed by boolean algebra) to create a desired output from a given input. To really explain, code is translated to assembly, which is then translated to binary, which then directly maps to how electrical signals flow out of CPU registers into a series of logical circuits. Assuming no faulty circuits, that flow is completely governed by boolean algebra. We therefore use boolean algebra to create our programs, we define a series of boolean operations to achieve a certain goal. We are _using_ boolean algebra to arrange a series of operations that maps a given set of inputs to a desired output. In the colloquial sense, coding is applied math, it is not pure math though. We use boolean algebra to create our programs, the programs are not boolean algebra themselves, but an application of boolean algebra.
Now, tying it all back to the article and implications. The data collected stated that the language parts of the brain are more responsible for whether we are able to learn programming. That seems to imply that the math part of programming is so far abstracted, that the parts of the brain which are used for math are no longer the most salient.
I wonder how the experiments and results in the article would have gone had the topic been electrical circuits and electrical engineering, which is far closer to the underlying math than coding.
It's such an absurd thing to argue about that I just assumed that some massive brainfart happened there. It happens to everyone, not everyone doubles down on it though.
But then again, isn't a good portion of this thread non-mathematicians arguing about what math is? I really thought ndriscoll put it succinctly[0]
> It's like trying to argue about the distinction between U(1), the complex numbers with magnitude 1, and the unit circle, and getting upset when the mathematicians say "those are 3 names for the same thing".
I fear the day some of these people learn about Topology.
> But then again, isn't a good portion of this thread non-mathematicians arguing about what math is?
No, a good chunk is clarification of "WTF do you mean?"
The abstract arguing I suspect we all find to not be interesting and absurd. Let's go to substance here..
The article has stated there is evidence that the math related regions of the brain are not nearly as heavily used when coding as compared to the language regions. The "mathematicians" seem to be arguing that this can't be true because coding and math are so closely related.
This is why the article and evidence are interesting. Coding and math are clearly and very closely related in many ways. Yet, the way the brain handles and interprets coding is more akin to pure language, than it is to pure math.
Which I suppose makes it all the more interesting that Math, Language, and coding are so related, yet (per the evidence and the article) - the brain does not see it that way.
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.
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.
> 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.
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).
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
Your response opened with addressing the headline, which anyone who had "RTFM" (RTFA) would have realized was unrelated to the body of the article. You then veered off into a tangent about the nature of math which again was not addressing the content of the article.
The underlying nature article, linked from the posted story, makes it even more clear what is being discussed, with the abstract stating:
> This experiment employed an individual differences approach to test the hypothesis that learning modern programming languages resembles second “natural” language learning in adulthood.
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?
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...