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
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