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I think this article misses a crucial point with it's phrasing, or construction of the "design vs mathematics" tradeoff. Mathematics is superior for underpinnin

by 14113 9y ago

I think this article misses a crucial point with it's phrasing, or construction of the "design vs mathematics" tradeoff. Mathematics is superior for underpinning programming languages because it is universal. Design, like art, relies on a shared view on the world to be appeasing. Design from the 70's, or 80's is often unappealing to modern viewers because of the lack of shared experience with the designer, for example. Mathematics solves this by appealing to a shared underlying "truth", that allows not only programmers with different backgrounds, but also computers to understand and process a programming language.

taeric 9y ago
See my post regarding Knuth's studies of languages for programming pre 1950. Simply put, mathematics had very little to help in the way of describing iterative processes. Arguably, we are still debating the mathematics of iterative processes to this day.
zokier 9y ago
What do you think programming languages are standing upon if not math? And I don't think math really "solves" any of the issues that are on debate here. You still need language and notation to express your precious maths, and that falls to the very same pitfalls as what is seen in PL design.
- kd0amg 9y ago
  What do you think programming languages are standing upon if not math? Many do, especially in academia, but quite a few seem to be standing on a combination of "this looks like it'll do what I want" and "this interpreter is the spec."
  - marktangotango 9y ago
    Indeed, It's almost as if the gp has never seen cobol or early fortran. Zero theoretical basis for either of those very popular languages (for their time).
tpetricek 9y ago
Mathematics is very good at maintaining the impression that it is universal and superior, but that's pretty questionable once you start looking at how it actually works. For two nice references, see: * https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From * https://en.wikipedia.org/wiki/Proofs_and_Refutations https://en.wikipedia.org/wiki/Proofs_and_Refutations As for mathematics being superior for underpinning programming languages - that's certainly how some people make it look, but nobody really tries to explain what exactly is the link between mathematical foundations of programming and actual programming. (I did this for my PhD and I'm still not sure how it's supposed to work.) Everyone just hand-wavy assumes it's somehow there. The best account for how this might looks is perhaps this: https://plato.stanford.edu/entries/computer-science/ https://plato.stanford.edu/entries/computer-science/

by 14113 9y ago

taeric 9y ago

See my post regarding Knuth's studies of languages for programming pre 1950. Simply put, mathematics had very little to help in the way of describing iterative processes. Arguably, we are still debating the mathematics of iterative processes to this day.

zokier 9y ago

What do you think programming languages are standing upon if not math? And I don't think math really "solves" any of the issues that are on debate here. You still need language and notation to express your precious maths, and that falls to the very same pitfalls as what is seen in PL design.

kd0amg 9y ago
What do you think programming languages are standing upon if not math? Many do, especially in academia, but quite a few seem to be standing on a combination of "this looks like it'll do what I want" and "this interpreter is the spec."
- marktangotango 9y ago
  Indeed, It's almost as if the gp has never seen cobol or early fortran. Zero theoretical basis for either of those very popular languages (for their time).

tpetricek 9y ago

Mathematics is very good at maintaining the impression that it is universal and superior, but that's pretty questionable once you start looking at how it actually works. For two nice references, see: * https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From * https://en.wikipedia.org/wiki/Proofs_and_Refutations https://en.wikipedia.org/wiki/Proofs_and_Refutations As for mathematics being superior for underpinning programming languages - that's certainly how some people make it look, but nobody really tries to explain what exactly is the link between mathematical foundations of programming and actual programming. (I did this for my PhD and I'm still not sure how it's supposed to work.) Everyone just hand-wavy assumes it's somehow there. The best account for how this might looks is perhaps this: https://plato.stanford.edu/entries/computer-science/ https://plato.stanford.edu/entries/computer-science/