On Mon, May 03, 2010 at 02:08:44PM -0400, Jesse Mazer wrote:
> If this notion of considering the frequency of different finite sequences in
> an infinite sequence is a well-defined one, perhaps something similar could
> also be applied to an infinite spacetime and the frequency of Boltzmann
> brains vs. ordinary observers, although the mathematical definition would
> presumably be more tricky. You could consider finite-sized chunks of
> spacetime, or finite-sized spin networks or something in quantum gravity,
> and then look at the relative frequency of all the ones of a given "size"
> large enough to contain macroscopic observers. Suppose you knew the
> frequency F1 of "chunks" that appeared to be part of the early history of a
> baby universe, with entropy proceeding from lower on one end to higher on
> the other end, vs. the frequency F2 of "chunks" that seem to be part of a de
> Sitter space that had high entropy on both ends. Then if you could also
> estimate the average number N1 of ordinary observers that would be found in
> a chunk of the first type, and the average number N2 of Boltzmann brains
> that would be found spontaneously arising in a chunk of the second type,
> then if F1*N1 was much greater than F2*N2 you'd have a justification for
> saying that a typical observer is much more likely to be an ordinary one
> than a Boltzmann brain.
>
> Jesse
>

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It is far more likely that the distribution of Boltzmann brains
follows a Solomonoff-Levin distribution, which arises from a uniform
distribution over descriptions, and considering equivalences between
those descriptions.
I'm sure you've read my book, so you would be aquainted with the idea.
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