the Universe, Computability, and the Singularity
EDIT at Karma −5: Could the next “good citizen” to vote this down leave me a comment as to why it is getting voted down, and if other “good citizens” to pile on after that, either upvote that comment or put another comment giving your different reason?
Questions about the computability of various physical laws recently had me thinking: “well of course every real physical law is computable or else the universe couldn’t function.” That is to say that in order of the time-evolution of anything in the universe to proceed “correctly,” the physical processes themselves must be able to, and in real-time, keep up with the complexity of their actual evolution. This seems to me a proof that every real physical process is computable by SOME sort of real computer, in the degenerate case that real computer is simply an actual physical model of the process itself, create that model, observe whichever features of its time-evolution you are trying to compute, and there you have your computer.
Then if we have a physical law whose use in predicting time evolution is provably uncomputable, either we know that this physical law is NOT the only law that might be formulated to describe what it is purporting to describe, or that our theory of computation is incomplete. In some sense what I am saying is consistent with the idea that quantum computing can quickly collapse down to plausibly tractable levels the time it takes to compute some things which, as classical computation problems, blow up. This would be a good indication that quantum is an important theory about the universe, that it not only explains a bunch of things that happen in the universe, but also explains how the universe can have those things happen in real-time without making mistakes.
What I am wondering is, where does this kind of consideration break with traditional computability theory? Is traditional computability theory limited to what Turing machines can do, while perhaps it is straightforward to prove that the operation of this Universe requires computation beyond what Turing machines can do? Is traditional computability theory limited to digital representations whereas the degenerate build-it-and-measure-it computer is what has been known as an analog computer? Is there somehow a level or measure of artificiality which must be present to call something a computer, which rules out such brute-force approaches as build-it-and-measure-it?
At least one imagining of the singularity is absorbing all the resources of the universe into some maximal intelligence, the (possibly asymptotic) endpoint of intelligences desiging greater intelligences until something makes them stop. But the universe is already just humming along like clockwork, with quantum and possibly even subtler-than-quantum gears turning in real time. What does the singularity add to this picture that isn’t already there?