> Remember the "dust theory" - Permutation City was not run on any specific
> physical computer, but on the general substrate of reality. So if this
> substrate is finite (the Bekenstein Bound for the entire spacetime is
> finite), then Permutation City will eventually stop growing, while if it
> is infinite (like in an open universe) then it can (and will) run
> forever.
I passed this thought along to Greg Egan, who commented as follows (I quote
with his permission):
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I thought about the "quantity of dust" issue a bit more after I finished
the book, and I can't see how (if the "dust theory" is true at
all) you could tell the difference between a universe ultimately made of
just two distinguishable "pieces of dust" called "1" and "0", which are
"recycled" (i.e. perceived to be arranged in patterns like 1001001110, when
there's really only one of each "in existence") ... and a universe with a
certain larger but finite quantity of "1"s and "0"s. To be finite or not
is a property of the way you *use* the dust -- of the upper-level laws of
physics. So our universe could be a closed, finite universe, and the
Permutation City universe could grow forever ... and *both* could simply be
different rearrangements of the same two pieces of dust.
I suppose that's really just Platonic materialism -- but I don't think
there's a choice between that, and a finite supply of dust you can run out of
(against your own laws of physics). I think the dust theory implies
arbitrary freedom to recycle, so the notion of "quantity of dust" is
meaningless, so for economy's sake we should say there's just a single "0"
and a single "1".
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Damien Broderick