I was mainly trying to point out that the mathematical term "computation" is not limited to deterministic computers. Since the GP was mentioning computable func

I was mainly trying to point out that the mathematical term "computation" is not limited to deterministic computers. Since the GP was mentioning computable functions as something requiring determinism, I believe they were also talking more about the mathematical notion of computation rather than physical computers. I should also note that our computers can very much solve NP-complete problems. They can't implement NP-complete algorithms to solve them, but all NP problems can be solved by a deterministic computer or a quantum computer - it just takes [much] more compute time (assuming P != NP, otherwise it may even take the same time). This is very relevant to this discussion, because in fact it is well known and proven that the non-determinism in the NP model does not give any amount of extra computational power beyond a Turing machine. That is, a non-determinstic Turing machine can solve exactly the same set of problems as a deterministic Turing machine (but, as far as it is known today, faster). The same is true of Quantum computers. Hyper-computation refers to even more fanciful mathematical models which are actually able to solve problems that a Turing machine can't solve, even with infinite time. They involve things like performing an infinite amount of Turing machine steps in one Hyper-Turing machine step, or having access to an oracle which tells you if a computation halts etc.