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A comment on Non-computability of solutions of certain equations on digital computers (2022). Parent comment

Re:Non-computability of solutions of certain equations on di... by NegativeK on Saturday August 03, 2024 @09:02PM (#41150420)
Is it specifically the fact that it's a physical process that makes it earth shattering?

Physical models of computers ( https://en.wikipedia.org/wiki/Billiard-ball_computer ) have been around for a long time, which means that noncomputability has been tangible for a long time.

I might be numb, though, to the fact that much of what want to understand can't be. If the universe isn't discrete, then it seems like noncomputability is the default.

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Re:Non-computability of solutions of certain equations on di... by vinnyvichy on Sunday August 04, 2024 @01:26AM (#41151315)
Hey, I feel you, my first thought was that continuously differentiable functions aren't physical :)
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Re:Non-computability of solutions of certain equations on di... by jpt4 on Sunday August 04, 2024 @02:46AM (#41151552)
The first order theories of the real numbers using addition and multiplication are decidable [0], while FO theories of the integers under the same operations are not.

[0] https://en.wikipedia.org/wiki/Decidability_of_first-order_th...

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Re:Non-computability of solutions of certain equations on di... by vinnyvichy on Sunday August 04, 2024 @03:55AM (#41151833)
Wikipedia can be confusing..

https://mathoverflow.net/questions/134259/is-the-first-order...

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Re:Non-computability of solutions of certain equations on di... by 082349872349872 on Sunday August 04, 2024 @05:23AM (#41152179)
> it seems like noncomputability is the default

compare https://en.wikipedia.org/wiki/Weierstrass_function#Density_o... (1872 et seq)?

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