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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-
by NegativeK 2y ago
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 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.
- vinnyvichy 2y agoHey, I feel you, my first thought was that continuously differentiable functions aren't physical :)
- jpt4 2y agoThe 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_theories_of_the_real_numbers https://en.wikipedia.org/wiki/Decidability_of_first-order_th...
- vinnyvichy 2y agoWikipedia can be confusing.. https://mathoverflow.net/questions/134259/is-the-first-order-theory-with-of-real-numbers-with-addition-and-multiplicat https://mathoverflow.net/questions/134259/is-the-first-order...
- 082349872349872 2y ago> it seems like noncomputability is the default compare https://en.wikipedia.org/wiki/Weierstrass_function#Density_of_nowhere-differentiable_functions https://en.wikipedia.org/wiki/Weierstrass_function#Density_o... (1872 et seq)?