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"Writing software" = "writing down math". Consider: * "Writing software" means arranging symbols (bits in a machine language, UTF or ASCII characters in a hig

by cs702 4y ago

"Writing software" = "writing down math". Consider: * "Writing software" means arranging symbols (bits in a machine language, UTF or ASCII characters in a high-level language) in certain permitted ways, to transform an input sequence of symbols (e.g., a stream of byte values representing user actions from a video game controller) into an output sequence of symbols (e.g., byte values representing pixel RGB colors for display on a screen). * "Writing down math" (e.g., to prove something, or to solve a problem) means arranging symbols ('x', '2', '+', etc.) in certain permitted ways, to transform an input sequence of symbols (representing mathematical notions) into an output sequence of symbols (representing other mathematical notions). Turing, Church, Curry, Gödel, and many others realized this in the 1920's and 1930's. That said, most self-described "software developers" are typically working to solve relatively simple problems for immediate practical application, whereas most self-described "mathematicians" are typically working to solve highly complex problems, often highly abstract in nature, without regard for practical application.

petemir 4y ago
I fear that's a very narrow view of mathematics. Nevertheless, most of the time you can see the output of what you created while programming, check if it's the correct result, etc. I don't think it's like that in math, where you deal in a much more abstract realm.
- cs702 4y ago
  "Mathematics" is not the same as "writing down math."
  - petemir 4y ago
    I stand by what I said, applicable even to proofs, but I take your point.
    - cs702 4y ago
      :-)
constantcrying 4y ago
Mathematics is not about computation. Certain means of arranging computation are entirely irrelevant to mathematics, computation is a mathematical tool, not an end.
- cs702 4y ago
  I never said that mathematics "is about computation." What I did say is that writing down mathematics is equivalent to writing software. Both require the use of a formal system.
  - constantcrying 4y ago
    >I never said that mathematics "is about computation." But programming is about computation. If mathematics isn't about computation as well, then they are not alike. >What I did say is that writing down mathematics is equivalent to writing software. It is not. That is plainly false. E.g. mathematics considers objects which are not computable and makes non-computable calculations with those objects. I am aware that you can encode certain formal mathematics into certain software, but that is like saying cooking is like programming because you can encode recipes as a program. >Both require the use of a formal system. So what?
    - epgui 4y ago
      >> What I did say is that writing down mathematics is equivalent to writing software. > It is not. That is plainly false. Whether the two look the same or not, maths and computer programs are in fact fundamentally isomorphic. [1] [1] https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspon...
      - constantcrying 4y ago
        >isomorphic Certainly not every computation is a proof. What statement does: void f(){ printf("?"); } prove?

by cs702 4y ago

petemir 4y ago

I fear that's a very narrow view of mathematics. Nevertheless, most of the time you can see the output of what you created while programming, check if it's the correct result, etc. I don't think it's like that in math, where you deal in a much more abstract realm.

cs702 4y ago
"Mathematics" is not the same as "writing down math."
- petemir 4y ago
  I stand by what I said, applicable even to proofs, but I take your point.
  - cs702 4y ago
    :-)

constantcrying 4y ago

Mathematics is not about computation. Certain means of arranging computation are entirely irrelevant to mathematics, computation is a mathematical tool, not an end.

cs702 4y ago
I never said that mathematics "is about computation." What I did say is that writing down mathematics is equivalent to writing software. Both require the use of a formal system.
- constantcrying 4y ago
  >I never said that mathematics "is about computation." But programming is about computation. If mathematics isn't about computation as well, then they are not alike. >What I did say is that writing down mathematics is equivalent to writing software. It is not. That is plainly false. E.g. mathematics considers objects which are not computable and makes non-computable calculations with those objects. I am aware that you can encode certain formal mathematics into certain software, but that is like saying cooking is like programming because you can encode recipes as a program. >Both require the use of a formal system. So what?
  - epgui 4y ago
    >> What I did say is that writing down mathematics is equivalent to writing software. > It is not. That is plainly false. Whether the two look the same or not, maths and computer programs are in fact fundamentally isomorphic. [1] [1] https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspon...
    - constantcrying 4y ago
      >isomorphic Certainly not every computation is a proof. What statement does: void f(){ printf("?"); } prove?