we'll eventually find that the language brain matters more for math than the math brain.
The language brain matters more for programming than the math brain? (2020)
351–360 of 465 posts
Re: The language brain matters more for programming than the math brain? (2020)
#352Earlier quoted context omitted.
> Is a DAG traversal algo "math", or is it more computer-sciencey? Firstly, computer science is math. Secondly, I remember covering graphs in a discrete math course back when I was in college. > What if you do it in SQL? SQL is more-or-less a poor implementation of relational algebra. Ie, math.
Computer science is math in the same way that physics is philosophy, in that computer science certainly started as math, just like the natural sciences used to be subdisciplines of philosophy. But it's hardly a useful grouping any more. You can study and do well in computer science with minimal knowledge of most of the core mathematical subjects. While graph theory certainly crosses over into math, you can cover most…
> You can study and do well in computer science with minimal knowledge of most of the core mathematical subjects.
You will fail at Theoretical Computer Science without mathematical proficiency. Go read some textbooks and papers in theoretical CS. It is a subfield of mathematics. Theorems and proofs. Rigorous and difficult mathematics.
Re: The language brain matters more for programming than the math brain? (2020)
#353Earlier quoted context omitted.
> 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, b…
> Coding IS math. Programming is an expression of logic, which is absolutely mathematics. But then we also have to think about naming variables and classes, structuring our code so that it is more readable by other developers, and so on. That's less about formal reasoning and more about communication. There is an engineering aspect to programming (prototyping, architecture, optimization, etc). It's a combination of m…
> Coding IS math.
The murky world of software patents would like a word about that.
For me, coding also feels artistic at times. But we see artistic beauty in mathematics all the time, so no wonder. But often I look at ugly code, and maybe that is subjective, but fixing that code makes it also feel prettier.
It is clear all developers have their owm artistic style, and probably that is why there is so much disagreement in the industry. Maybe we are lacking the pure mathemetical language to describe our intent in a more beutiful and precise way that is more clearly the-right-way. As in how we find beauty in simple physics equations.
Re: The language brain matters more for programming than the math brain? (2020)
#354Earlier quoted context omitted.
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 mat…
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 t…
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.
I guess I've been lucky with my math teachers.
Re: The language brain matters more for programming than the math brain? (2020)
#355There 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 re…
I figure the programming brain matters the most for programming.
Re: The language brain matters more for programming than the math brain? (2020)
#356Although 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 a…
> 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.
Re: The language brain matters more for programming than the math brain? (2020)
#357It 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 the…
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 sca…
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.
Re: The language brain matters more for programming than the math brain? (2020)
#358Earlier quoted context omitted.
Logic doesn't follow. There is no problem with A -> B ∧ B -/-> A Here's an example. "I live in San Francisco" would imply "I live in the US". But "I live in the US" does not mean "I live in San Francisco". Here's a more formal representation of this: https://en.wikipedia.org/wiki/Bijection,_injection_and_surje...
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 pre…
> The word "is", maps to the logical "equals" operator.
It very obviously doesn't. A square is a rectangle. seadan83 is (probably) a mammal. Math is a language.
Re: The language brain matters more for programming than the math brain? (2020)
#359Earlier quoted context omitted.
Interpreting a CRUD apps (or fragments of them) as theorems is interesting (given a programming language and culture that doesn't suck)! e.g. if you have a function `A => ZIO[Any,Nothing,B]`, then you have reasonable certainty that barring catastrophic events like the machine going OOM or encountering a hardware failure (essentially, things that happen outside of the programming model), that given an A, you can run s…
> It's not the type of thing that gets mathematicians excited Says who? I've certainly seen mathematicians get excited about these kinds of things. Frequently they study Programming Languages and will talk your ear off about Category Theory. > You can often blindly code your way through things by just following the type signatures and having a vague sense of what you want to accomplish. Sounds like math to me. A simp…
I think we're in agreement. My comment about the halting problem was meant to refer to Rice's theorem (the name was slipping my mind), which I occasionally see people use to justify the idea that you can't prove interesting facts about real-world programs. In practice, real-world programming involves constantly proving small, useful theorems. Your useful theorem (e.g. `Map[User,Seq[Account]] => Map[User,NetWorth]`) is probably not that interesting to even the category theorists, but that's fine, and there's plenty you can learn from the theorists about how to factor the proof well (e.g. as _.map(_.map(_.balance).sum)).
Re: The language brain matters more for programming than the math brain? (2020)
#360Although 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 a…
> 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…
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.