At 16:39 06/05/04 -0400, Stephen Paul King wrote:
Daer Bruno and George,

    At the risk of being massively naive, does this idea seem to be related
to the infamous problem of Boltzmann's Stosszahlansatz?

    My reasoning is that in order to figure out how do define a universal
prior (or probability measure for the initiona conditions that led
inevitably to our common world of experience) we need to understand how to
define a ration of worlds like ours to all possible worlds, or the
computational equivalent: algorithms that generate worlds like ours as a
subset of the collection of all possible algorithms.

I do believe that worlds generated by an algorithm have a null measure (it is
a reason for not believing in "Classical mechanics" or any singular reality).
What I would call "worlds" are emergent psychological constructs linked to an
infinite set of running algorithm.
I would not use the expression "universal prior" in this context (unless
you really talk about Schmidhuber like prior, but then I refer you to older post,
where I show that if such prior exists they should be derived from comp, not
imposed at the start).
Boltzmann's Stosszahlansatz ? I don't know yet. A priori I would say that
classical form of indeterminacy (like deterministic chaos) is based (with comp)
to algorithmic complexity. Quantum indeterminacy is based on
consistent self-multiplication. They are quite different form of uncertainty.
And you know my (pedagogical) problem: to say more we should go through
that logical barrier just to interpret correctly what the machine (G) and its guardian
angel (G*) *can* tell us ...


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