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> because programming is really really simple Millions of programmers that work hard and for a long time to master their trade are just dumb for not learning i

> because programming is really really simple Millions of programmers that work hard and for a long time to master their trade are just dumb for not learning it instantly, like you. Poor bastards, deluding themselves they do somehow advance the field, while in reality programmers are just doing "tabs vs spaces" over and over again, and any kind of advancement is given to them by our benevolent mathematical overlords. No. We've worked for decades to make programming this simple. You're driving an obviously overpowered car in a race, but choose to conveniently forget about its specs once you win. > Mathematicians have written plenty of such cheat sheets, you can find them everywhere just by Googling. Here is one for physics Sure they were created. I never said they weren't, so please stop insinuating that. I (not GGP) said specifically: > It has literally nothing to do with explaining the syntax *close to where it's used*. And that is not being done, so I really don't understand how the rest of the paragraph has anything to do with me. > say that nobody cares about your woes because that python documentation was in fact not easy enough for you to read! So? What's wrong with that? Are you telling me I'm dumb? Is it really all you can do? Well, it's either that I'm simply an uneducated idiot, or that the documentation indeed could be better. You seem to default to the former. Well, I feel differently about that.

Jensson 5y ago
> So? What's wrong with that? Are you telling me I'm dumb? Is it really all you can do? No, I am saying that people take a long time to understand this. Programmers expects things to have a simple explanation behind it since in programming everything does have a simple explanation, since computers can only do very few things. But in math you quickly expand to concepts beyond, even as early as calculus you add infinities and continuous quantities and how to work with those, you can't ever program those things since those operations cannot be expressed using finite instructions. There is no "this function performs an integral on this other thing and is expressed using these steps of operations". For example, lets say you want to sum 1/N^2 for N from 1 to infinity. How would you express that? You can't do it in a loop, since the loop never ends. You can stop at an arbitrary point, but how do you know that stopping there results in a good value? You can't, unless you do the math, calculus is a good tool to solve that. With it we can show that summing 1/N results in an infinite result, while 1/N^2 settles on a value and creates a way for you to calculate that value with error bars.
- klibertp 5y ago
  > you can't ever program those things since those operations cannot be expressed using finite instructions. And now you're telling me that Mathematica, Maple and the like don't exist. Yeah, we can't express the concepts directly, but if we're very good at one thing, it would be emulation. > How would you express that? Like this: >>> from sympy import * >>> i, n, m = symbols('i n m', integer=True) >>> # For example, lets say you want to sum 1/N^2 for N from 1 to infinity. >>> Sum(1 / n ** 2, (n, 1, oo)) ∞ ____ ╲ ╲ 1 ╲ ── ╱ 2 ╱ n ╱ ‾‾‾‾ n = 1 Would do the same with the integral. There's even that strange elongated S and everything...
  - Jensson 5y ago
    You didn't program the sum, you just created a program that looks like the math symbols.
    - klibertp 5y ago
      I said: emulation. You don't actually need to stretch your mind to infinity to reason about it, right? I mean, you're not a matrioshka brain the size of a star, right? (Just making sure) So if your mind can cope with infinities by using just the very finite storage accessible to you, what prevents computers from doing the same? Like this: >>> summation(1 / n ** 2, (n, 1, oo)) 2 π ── 6 Dunno, seems legit? How come it appeared, even though my computer has only 32gb of ram, waaaay too little to hold infinity? EDIT: obviously, I still didn't program it myself! I'm dumb, after all. But someone apparently did. EDIT2: and that person also made sure that even the dumber coders (like me) can use, and benefit from, the tool they wrote.
      - Jensson 5y ago
        A computer understands instructions. You can give it instructs to loop and sum values. Those aren't instructions telling the computer what an infinite sum is. Math is about making humans understand such concepts, we have yet to be able to program those concepts. For example, when you write a sum in python then the computer will sum the values and do the work for you. But when you write an infinite sum like that, you the human still has to do all the math work figuring out what to do with it, so you didn't circumvent the need to do math at all. The computer doesn't understand the sum. You can program simple simple rules for it to try to simplify it, but it still isn't nearly as versatile as a skilled human. For example this problem is a basic problem from a first year course, it makes sense that someone programmed in the human derived solution for it, but they haven't actually programmed the logic for infinite sums into the computer.

Jensson 5y ago

> So? What's wrong with that? Are you telling me I'm dumb? Is it really all you can do? No, I am saying that people take a long time to understand this. Programmers expects things to have a simple explanation behind it since in programming everything does have a simple explanation, since computers can only do very few things. But in math you quickly expand to concepts beyond, even as early as calculus you add infinities and continuous quantities and how to work with those, you can't ever program those things since those operations cannot be expressed using finite instructions. There is no "this function performs an integral on this other thing and is expressed using these steps of operations". For example, lets say you want to sum 1/N^2 for N from 1 to infinity. How would you express that? You can't do it in a loop, since the loop never ends. You can stop at an arbitrary point, but how do you know that stopping there results in a good value? You can't, unless you do the math, calculus is a good tool to solve that. With it we can show that summing 1/N results in an infinite result, while 1/N^2 settles on a value and creates a way for you to calculate that value with error bars.

klibertp 5y ago
> you can't ever program those things since those operations cannot be expressed using finite instructions. And now you're telling me that Mathematica, Maple and the like don't exist. Yeah, we can't express the concepts directly, but if we're very good at one thing, it would be emulation. > How would you express that? Like this: >>> from sympy import * >>> i, n, m = symbols('i n m', integer=True) >>> # For example, lets say you want to sum 1/N^2 for N from 1 to infinity. >>> Sum(1 / n ** 2, (n, 1, oo)) ∞ ____ ╲ ╲ 1 ╲ ── ╱ 2 ╱ n ╱ ‾‾‾‾ n = 1 Would do the same with the integral. There's even that strange elongated S and everything...
- Jensson 5y ago
  You didn't program the sum, you just created a program that looks like the math symbols.
  - klibertp 5y ago
    I said: emulation. You don't actually need to stretch your mind to infinity to reason about it, right? I mean, you're not a matrioshka brain the size of a star, right? (Just making sure) So if your mind can cope with infinities by using just the very finite storage accessible to you, what prevents computers from doing the same? Like this: >>> summation(1 / n ** 2, (n, 1, oo)) 2 π ── 6 Dunno, seems legit? How come it appeared, even though my computer has only 32gb of ram, waaaay too little to hold infinity? EDIT: obviously, I still didn't program it myself! I'm dumb, after all. But someone apparently did. EDIT2: and that person also made sure that even the dumber coders (like me) can use, and benefit from, the tool they wrote.
    - Jensson 5y ago
      A computer understands instructions. You can give it instructs to loop and sum values. Those aren't instructions telling the computer what an infinite sum is. Math is about making humans understand such concepts, we have yet to be able to program those concepts. For example, when you write a sum in python then the computer will sum the values and do the work for you. But when you write an infinite sum like that, you the human still has to do all the math work figuring out what to do with it, so you didn't circumvent the need to do math at all. The computer doesn't understand the sum. You can program simple simple rules for it to try to simplify it, but it still isn't nearly as versatile as a skilled human. For example this problem is a basic problem from a first year course, it makes sense that someone programmed in the human derived solution for it, but they haven't actually programmed the logic for infinite sums into the computer.