On 29 Apr 2011, at 02:42, Stephen Paul King wrote:

Please allow me to ask another question. Is the notion of an “observer moment” corresponding to “the smallest possible conscious experience” related to Bruno’s concept of substitution level? ISTM that both act like the idea of a coarse graining on an ensemble that is used to define the entropy of a system in that all of the members of the ensemble that are indistinguishable from a macroscopic point of view.

You can easily relate them.

Let us distinguish the 1-OMs from the 3-OMs. The 1-OM are experiences of an individual when his brain is in some computational state S. We assume comp, of course, so we can attribute a 1-OM to some such state. The 3-OMs are given by all the equivalent computational states S, S', S'', ... obtained in the universal dovetailing. For example the state of your brain emulated by a program computing the Heisenberg evolution of the Milky Way at the level of strings, or the state of your brain obtained by another program simulating the quantum fluctuation of the void, or the state of your brain obtained by a fortran program emulating a lisp program emulating a prolog program emulating ... emulating the search of the solution of some universal diophantine polynomial, etc. All those programs are emulated by the universal dovetailer, and all the finite pieces of computations obtained by such emulation can be proved to exist in a tiny part of arithmetic. There are aleph_0 such finite piece of computations, and they are all "run" by the UD. The first person glue them into a priori 2^aleph_0 infinite computations. For each of them, you can always find in arithmetic a computation which is more fine grained. But you, by the first person indeterminacy, cannot know in which computation you are. Actually you can be said belonging to all of them, and your physical laws are determined by the measure on your continuations of such computations. From this you can see that the highest level of substitution defines the measure on the possible lowest one, which you cannot distinguish, by definition. That is why, if we look at ourselves below that level, we have to be confronted with a strong form of indeterminacy. Boltzman's idea cannot be used at this stage, though, without having a measure on the relative computations, and this prevents a direct use of the notion of entropy. We need more physics for that, but, as I have already explained we have to derive that physics from the numbers and self-reference if we don't want to miss the relationship between the quanta and the qualia offered by the splitting between provable self-reference and true self-reference (G and G* and their intensional variants).



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