Emil wrote:

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>There is classical mechanics, and there are classical >computers, which can search an unordered set of n items in >O(n) time. > >There is quantum mechanics, and there are (in theory) quantum >computers, which can do the same in O(n^(1/2)) time. > >Is it conceivable that there is yet another level of extrapolation -- >that someday we might discover a "doubly-quantum mechanics" >which allows for a doubly-quantum computer to be built, which >can do this task in, say, O(n^(1/4)) time? > >The question is probably ill-posed, as anything is conceivable (in >the trivial sense). Thus, I will break the question down a bit: > >First, could there be a mathematical model for a computational >device that is to the Quantum Turing Machine what the Quantum >Turing Machine is to the Turing Machine, and that has interesting >computational properties that exceed the QTM in an analogous >way? (Note that this question is independent of whether anything >in the physical world actually behaves like a such an object.) If >the answer to this is no, then I guess nothing more needs to be >said. Otherwise: > >What are the most immediate objections in physics to such a >thing existing, above and beyond the fact that no data showing >such effects have turned up? Part of what I mean by "above and >beyond" is that perhaps the requisite experiments have not been >done yet, or are not yet possible with current experimental >technology, or existing data has not been analyzed in >such-and-such a way. However, I do not wish to propose >invisible pink unicorns* which exist only when we don't look at >them. I am looking for an *explanation* (in the FoR sense). > >- Emil You raise a very interesting and fundamental question. I have provided an *explanation*, argueably in the FoR sense, that IF we are willing to accept some hypothesis H in the "philosophy of mind" then the mind-body problem can be reduced partially into a justification of the "real" laws of physics from the some mean discourse by Universal (Turing) machines. That is: H entails physics is a branch of machine psychology. And I have begin to extract the logic of "probability one on the consistent extensions" defined on any consistent states of sound universal turing machine, and I get results giving evidence that such logic is a quantum logic, with relative linearisation of (computational histories) quite similar to the quantum multiverse. Unfortunately most basic elementary question are still unsolved. For exemple Bell's inequality, even orthomodularity are still open problems. Still it looks like the logic of elementary observations is a quantum logic (I got also a logic of qualia, which is also quantump like, ...). But it is still possible I get something else. Keeping the hypothesis H, it would mean the quantum is wrong and that something else is true. H would then gives a light on the next physics. Well, if H is true H gives light on the *last* physics, because H gives the necessary shapes of any form of reliable observability. Observability = machine's observability, because H is the computationalist hypothesis in the philosophy of mind (the hypothesis that there is a level such that I can survive (= I experience nothing) through a digital functional substitution made at that level) + (to be complete) the Post-Church-Turing thesis, and a sort of minimal amount of arithmetical platonism. More in my URL (below) and in the everything-list (+ the FOR list). Bruno http://iridia.ulb.ac.be/~marchal