alt Hacker NewsIt can be the case that both:
- The physics of the universe can be completely modeled as computation, and
- It's possible to pose undecidable problems about the way the universe unfolds
This is intrinsic to the idea of undecidability even for Turing machines, e.g. "we equate computation with the functioning of Turing machines, but there are real processes executable in Turing machines that are undecidable".
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sgt101 • today at 5:41 PM
Of course, if our universe is undecidable it must be the case that computable processes can be executed within it, and it might be the case that all of the processes that are ever executed within it are computable... but it might be that some of the processes that are executed are not computable... because the machine may.. or may not?
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A key thing about the undecidability problem wrt physics is preparation of the initial state. In math and computer science it is relatively straightforward to prepare such problems now (though this represented an enormous leap conceptually), but the "undecidability" of all physical problems relies on construction of materials that are clearly unconstructable - systems of infinite negentropy (eg Turing machines), infinite mass (the lattice), bespoke local interactions etc. Problems standing in the way of physics decidability are typically chaos, far from equilibrium mechanics, elementary SNR considerations and so forth, not problems of logic.