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This is slightly off topic, but is an honest question: Would physics and math benefit from a reworking of flat mathematical expressions into something that look

This is slightly off topic, but is an honest question: Would physics and math benefit from a reworking of flat mathematical expressions into something that looks more like code? Additionally, I wonder why more functions aren't given names like sin and cos so that it's all more like an API than constant rewriting the same equation. For example, Black-Scholes is complete nonsense [1], but the C implementation is pretty easy to parse [2]. Yes, the code is 100 lines longer, but just like in programming, you'd just use it by name. 1. https://wikimedia.org/api/rest_v1/media/math/render/svg/d85601f6192ee85748c2deef28240275510d634e https://wikimedia.org/api/rest_v1/media/math/render/svg/d856... 2. https://gist.github.com/codeslinger/472083/0acc95f745def15a3677b021742b27416a78bcf3 https://gist.github.com/codeslinger/472083/0acc95f745def15a3...

a9h74j 5y ago
Haven't read it, but you might look for the Structure and Interpretation of Classical Mechanics[1] [1] https://mitpress.mit.edu/books/structure-and-interpretation-classical-mechanics-second-edition https://mitpress.mit.edu/books/structure-and-interpretation-...
cinntaile 5y ago
They're not really the same thing anymore though, the second is only an approximation of the first?
throwaway81523 5y ago
Not really. If you look at the C code there are a bunch of executable steps that are straightforward to carry out, but it gives no clue at all about why they do what they do. A human after reading them doesn't come out any smarter than a compiler. The equation on the other hand makes reasonable sense if you know something about stochastic PDE's. Of course just looking at the symbols without any context won't help much, but you can read the article: https://en.wikipedia.org/wiki/Black-Scholes_equation https://en.wikipedia.org/wiki/Black-Scholes_equation That in turn might not be easily understandable either, but it's written in terms of well-known concepts that they teach in math classes. You can get textbooks about that stuff and all that sort of thing. At the end of the day, making sense of it will take a level of mental effort comparable (not by coincidence) to taking a couple of years of math classes (starting from basic calculus) and doing all the assignments. Making the equations look more like code won't help with that. It's about developing understanding and facility with the mathematical ideas.

a9h74j 5y ago

Haven't read it, but you might look for the Structure and Interpretation of Classical Mechanics[1] [1] https://mitpress.mit.edu/books/structure-and-interpretation-classical-mechanics-second-edition https://mitpress.mit.edu/books/structure-and-interpretation-...

cinntaile 5y ago

They're not really the same thing anymore though, the second is only an approximation of the first?

throwaway81523 5y ago

Not really. If you look at the C code there are a bunch of executable steps that are straightforward to carry out, but it gives no clue at all about why they do what they do. A human after reading them doesn't come out any smarter than a compiler. The equation on the other hand makes reasonable sense if you know something about stochastic PDE's. Of course just looking at the symbols without any context won't help much, but you can read the article: https://en.wikipedia.org/wiki/Black-Scholes_equation https://en.wikipedia.org/wiki/Black-Scholes_equation That in turn might not be easily understandable either, but it's written in terms of well-known concepts that they teach in math classes. You can get textbooks about that stuff and all that sort of thing. At the end of the day, making sense of it will take a level of mental effort comparable (not by coincidence) to taking a couple of years of math classes (starting from basic calculus) and doing all the assignments. Making the equations look more like code won't help with that. It's about developing understanding and facility with the mathematical ideas.