On Wed, Dec 27, 2000 at 04:50:42PM +0100, [EMAIL PROTECTED] wrote: > None of the quantum effects we observe forces us to give up the simple > idea that our universe can be simulated on a classic TM, just like > there is no evidence that forces us to assume the existence of complex > and incomputable things such as uncountable sets.
I think we understand each other sufficiently on the other issues, so I'll only follow up on this one. I agree that our universe can be simulated on a classic TM. What I don't agree with is that our universe can be simulated quickly on a classic TM, which is what a speed prior based on a classic TM would predict. In other words, the speed prior predicts that we will never observe any quantum effects that can't be simulated quickly on a classic TM. I suggest that you talk about this prediction more explicitly in your paper since it would have major consequences. Many people are busy trying to build quantum computers, which would be a waste of effort if this prediction is correct. Even within classic models of computation, there seem to be significant variations in speed. As far as I can tell from my theory of computation book, moving from a multi-tape TM to a single-tape TM can cause a squaring of running time for some problems, which would translate to a squaring of the speed prior for some strings. So a similar question is, how do you pick which classic TM to base S on?