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Well no. It doesn't say how to progress from one state to another. It just tells us how numbers relate to each other. This isn't perfect but something like, ma
by john567 5y ago
Well no. It doesn't say how to progress from one state to another. It just tells us how numbers relate to each other.
This isn't perfect but something like, math express things while computation progresses things.
You could argue that a particular mathematical framework is computational but I'm just trying to exemplify a distinction.
- adastra22 5y agoI don't think this is an accurate take on math. Beyond the fact that a lot of math fields deal explicitly with state updates (e.g. discrete math), there is also the constructionist framework for mathematical foundations which removes "non-computational" theorems like that law of the excluded middle. When you do this you get a form of math where all proofs are necessarily computational and there is a viable direct translation into code. It is not generally why many constructivist mathematicians are interested in that framework, but it is a nice side-effect. I think your intuitions about how math works is an unfortunate side effect of how math is often taught, and not so much reflected in mathematics itself. https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_mathematics) https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_...