I do not think we have an answer to the first question. At the end it does not really matter whether our universe runs on an actual computer or is simply equiva

I do not think we have an answer to the first question. At the end it does not really matter whether our universe runs on an actual computer or is simply equivalent to a computable process (as opposed to an uncomputable one). However, for aesthetic reasons some scientists guide their work in theoretical physics by studying specifically only physical laws that are, in principle, computable. Said in other words, some scientist take the "Extended Church-Turing Thesis"[1] as an axiom of physics and work from there. To the side question, yes, that is a typical definition of "computable" (usually what a CS theorist means by the word). The reason we believe it is a useful practical definition is that (1) such a definition ends up equivalent to a number of other interesting definitions and such a net of equivalences usually ends up being interesting and empowering (2) Turing machines form a "universal" modality of computation because we have proofs that they can "efficiently" simulate other theoretical models of computation (3) We simply do not know of other modalities of computation that can exist in our universe (which is a bit of a circular statement in the context of this conversation) (4) It simply seems to be a useful formalism that enabled us to prove a ton of useful results, so even if it was not as elegant as I claim, it definitely ended up being a productive and practical way of thinking. Side note: Quantum computing muddles the water a bit in terms of what is efficiently computable, but if something is not computable for a Turing machine it is still not computable for a quantum computer (however there are a few things that seem to take exponential time on a Turing machine while taking only polynomial time on quantum computer). [1]: https://www.scottaaronson.com/papers/npcomplete.pdf https://www.scottaaronson.com/papers/npcomplete.pdf