Comment by feoren | Hacker News Reader

Comment by feoren | Hacker News Reader

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> it's a pretty common joke how virtually inapplicable calc is to us

If you think calculus is not important to software development than you are not bothering to look. Just a few examples:

- Calculus was the first math class I took that gave a clear definition of what a "function" really is. Do you use functions?

- Analyzing the properties of functions to see what operations made sense to do or not (e.g. continuous vs discontinuous).

- The concept of taking a function at various points and adding a small value to it to see how it changes is extremely important in sensitivity analysis and optimization.

- Anything involving non-uniform probability distributions, like sampling a random number from various distributions, requires understanding the relationship of PDFs and CDFs, which is one of derivative/definite integral. This means any form of realistic simulation, any estimations of time to failure, performance of anything, etc.

- Gradient descent and backpropagation in neural networks are completely opaque if you don't understand derivatives.

- Most games or simulations deal with rates of change.

- The concept of infinitesimals applies to finding tangents to curves, showing up in vector graphics all the time.

- Anything involving elevation in GIS, analysis of water flow, even topographic maps

I'm honestly sick and tired of seeing these crazy anti-learning comments like "I'm in software development and I literally never use calculus / linear algebra / type theory / lambda calculus / algorithms and data structures / boolean logic / binary trees / linked lists / stacks / queues / geometry / algebra / arithmetic" <-- then you're artificially limiting yourself and you're a much worse software developer than the ones who actually do use those things. What do you do all day, copy code from StackOverflow and hope it works? Don't discourage other people from learning just because you were too lazy: in fact that's literally what this entire post is about. You're part of the problem.

> Do you use functions?

Unless you're using Haskell or something similar, mathematical functions and what most programming languages call "functions" are very different and are better referred to as procedures. Mathematical functions don't have any concept of some basic constructs like variables (state in general), I/O, or even sequential computation. Pure functional languages have to use things like monads to model procedures.

Sure, but you know what has state? ODEs and their discrete-time analogue, recurrence relations. You first meet ODEs in calculus. Even if you say “who cares about continuous time, my computer is fundamentally discrete!” you won’t have a concept of limiting behaviors without calculus.

> I'm honestly sick and tired of seeing these crazy anti-learning comments

I don't know why you're mad at me, I _literally said_ "I'm still happy I learned it", along with saying we should be teaching more advanced math. I said it was a common _joke_, not that we literally never use it. I went on to say it was "less useful" than other math you'll learn, not "not useful at all". Perhaps you should read the whole comment before getting so angry.

And no, just because I don't use calculus all day doesn't mean I "copy code from StackOverflow", I honestly don't know how you could come to such a silly conclusion (or how you think knowledge of calculus is necessary to understand most data structures). Do you think self-taught developers who never learned calculus are just incapable of learning or using data structures and algorithms, and don't know what functions are? I can tell you quite confidently that they can and do, because I know many of them.

> If you think calculus is not important to software development than you are not bothering to look. Just a few examples:

Half of what you listed isn't really Calculus at all: for comparison my highschool taught functions, continuous vs discontinuous, rates of change, and topographic maps in Math classes which happened years before taking Calculus. Then the Calc class was like 70% memorizing "whats the integral of cosecant?", was which I think we should be able to agree is absurdly useless even for people who actively work in a math-heavy field.

I suspect this form of calculus is what people are responding to when they say calc is useless; they should be teaching the things you're saying (including how to think about functions) and e.g. introducing Euler's method getting into what happens when your step size become arbitrarily small are all useful things to a broader set of people, but the actual implementation of Calculus classes in practice is instead entirely useless trivia that provides almost no insights if you wanted to do any of the things in your comment.

I definitely benefit from knowing calculus. But I always disliked it, it was taught in such a mechanical fashion.

I only really started to get math when I learned about linear algebra, combinatorics, proofs, A&D, algebraic structures, mathematical logic etc. And quite frankly those topics helped me much, much more than calculus.

I think learning other areas of math would better serve most people. I think logic and probability then maybe combinatorics and statistics would be much better than calculus and especially trigonometry.

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