Dear CMR,

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Interleaving. ----- Original Message ----- From: "CMR" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Wednesday, January 21, 2004 1:07 AM Subject: Re: Is the universe computable? > > > Think of it this way, what is the cardinality of the equivalence class > > of representations R of, say, a 1972 Jaguar XKE, varying over *all > > possible languages* and *symbol systems*? > > I think it is at least equal to the Reals. > > Is this correct? If R has more than one member, how can we coherently > > argue that "information is physical" in the material monist sense? > > > [CMR] > Assuming you mean R is countably infinite(?), then a solution would be a > finite universe of underlying discrete structure, ala Fredkin, I imagine. > [SPK] If Fredkin is proposing a Cellular Automata based model that would be the case, but CA based models have a problem of their own: how to show that the global synchrony of the shift function can obtain. It is puzzleling to me why it is hard to find a discussion of this in the literature. > >[SPK] > > What if the "informing" and "constraining" (?) is done, inter alia, > > by the systems that "use up" the universal resources? > > > > What if, instead of thinking in terms of a priori existing solutions, > > ala Platonia, if we entertain the idea that the *solutions are being > > computation in an ongoing way* and that what we experience is just one (of > > many)stream(s) of this computation. Such a computation would require > > potentially infinite "physical resources"... > > Would it be to much to assume that all we need to assume is that the > > "resources" (for Qcomputations, these are Hilbert space dimensions) are > > all that we have to assume exists a priori? > > Does not Quantum Mechanics already have such build in? > [CMR] > Yes, this would indeed follow. But what of a view of QM itself emerging form > qubits? > as, for instance, expressed in the so-called Bekenstein bound: the entropy > of any region > of space cannot exceed a fixed constant times the surface area of the > region. [SPK] Maybe I am mistaken but does not QM enter into the very definition of a qubit? As the to idea of Bekenstein's bound, that is, IMHO, more of a problem than a solution and leads in the wrong direction. It has been shown (http://tph.tuwien.ac.at/~svozil/publ/embed.htm) that it is impossible to completely "embed" the logical equivalent of a QM system (with Hilbert space dimensions greater than 2) into the logical equivalent of a classical system. I take this to explicitly rule out considerations that space-time can be treated as just a Minkowskian (or, more generally, one would consider the Poincare' group) space and expect to be able to treat it as the background or "support" for the necessary machinery of a QM system. >[CMR] > This suggests > that the complete state space of any spatially finite quantum system is > finite, so > that it would contain only a finite number of independent qubits. > [SPK] Again, that does not work because we can not take space-time (ala GR) to be "big enough" to allow us to fit QM into it. On the other hand, it has been shown that a QM system, considered as a quantum computational system, can simulate, with arbitrary accurasy, any classical system, given sufficient "Hilbert space" dimensions - which play the role of "physical resources" for QM systems. See: http://arxiv.org/abs/quant-ph/0204157 This leads me to the idea that maybe space-time itself is something that is secondary. It and all of its contents (including our physical bodies) might just be a simulation being generated in some sufficiently large Hilbert space. This idea, of course, requires us to give Hilbert space (and L^2 spaces in general?) the same ontological status that we usually only confer to space-time. ;-) Kindest regards, Stephen