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.
The language brain matters more for programming than the math brain? (2020)
261–270 of 465 posts
Re: The language brain matters more for programming than the math brain? (2020)
#262Earlier 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…
>Programming is an expression of logic, which is absolutely mathematics.
and also philosophy.
Re: The language brain matters more for programming than the math brain? (2020)
#263Earlier quoted context omitted.
By that same logic you could also say that language is math. In fact I think your quote kind of disproves your point because the content/state of a program is super important in coding more than the form. Coding used to be very close to pure math (many early computer science classes were taught in the Math Department in universities) but it has been so far abstracted from that to the point that it is its own thing an…
> By that same logic you could also say that language is math Not quite, but the inverse is true. The language to math direction doesn't work because a lack of formalism. I can state incomprehensible sentences or words. (There's an advantage to that in some cases!) but when you do that with code you get errors and even you do it with math its just that there's no compiler or interpreter that tells at you
>I can state incomprehensible sentences or words.
since you can express paradoxes with match, perhaps not that different.
Re: The language brain matters more for programming than the math brain? (2020)
#264Good 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 proo…
>Good code
"Good code" is very subjective. Even readability and modularity can be taken too far.
Re: The language brain matters more for programming than the math brain? (2020)
#265Good 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 proo…
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.
Re: The language brain matters more for programming than the math brain? (2020)
#266Earlier quoted context omitted.
I don't think that quote really supports coding and math being equivalent. To me, the quote provides an abstraction of math through a structuralist perspective. Language can also be viewed through this abstraction. I think coding could share the abstraction, but that doesn't make the three of these fields equivalent.
> coding and math being equivalent Please see lambda calculus. I mean equivalent in the way mathematicians do: that we can uniquely map everything from one set to another
This seems like the setup to a joke about how mathematicians don't know how to communicate to ordinary folks
Re: The language brain matters more for programming than the math brain? (2020)
#267Earlier quoted context omitted.
> 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
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.
> Math major here
The reason for doubt is a failure in fairly basic logic. Your claim is:
¬(A ↦ B) ⟹ ¬(B ↦ A)
Re: The language brain matters more for programming than the math brain? (2020)
#268Earlier quoted context omitted.
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.
> 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.
No, not always. Quite a lot of high-level code doesn't require any math at all. It doesn't take math to perform CRUD operations, which account for a lot of programming work. Sure, the underlying machine code is all based on math, but the higher level programming doesn't need to involve a single math equation for it to be useful. Let's see where the goalposts move now...
Re: The language brain matters more for programming than the math brain? (2020)
#269Earlier quoted context omitted.
math != calculation. It's an actively stupid fiction for people who don't understand what math is.
> 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?
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.
Re: The language brain matters more for programming than the math brain? (2020)
#270Earlier quoted context omitted.
> 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…
Do you think mathematicians don’t have to think about naming variables and structuring proofs?
The presumably-mathematicians who wrote my Algorithms textbook (CLRS) didn't seem to think giving the variables in their algorithms useful names. They just use i, x, etc. all over the place and don't even consider giving things actual names. This makes the book much less accessible than it would be if they treated it more like most people write code.