From: Eliezer S. Yudkowsky (email@example.com)
Date: Tue Jun 24 2003 - 21:55:42 MDT
Lee Corbin wrote:
> In our universe, in our bubble, there exist infinitely many
> regions the size of our Hubble volume. Within our universe,
> the laws of physics are the same everywhere, and thus Tegmark
> and many others assume there exist other regions, also about
> 80 billion light years wide, that are completely identical
> to ours. After all, QM dictates that there are only so many
> states that can obtain in a volume of definite size. The
> number of possible states is so vast, however, that it's
> safe to say that there is probably no volume identical to
> ours closer than 10^10^118 away.
Actually, 10^10^118 is the upper bound, not the lower bound. There could
be an identical bubble much closer, and given that our universe is not in
a maxentropy state, there probably is.
In separate calculations I have seen 10^120 given as the number of bits of
entropy in our universe, of which we have used only 10^80, i.e., none.
That is, our universe has 10^10^120 possible states (megamathematically
speaking), and our present state, by its low entropy, falls within a tiny
fraction of that volume; a mere 10^10^80 possibilities. So if other Level
I worlds are low-entropy I should expect to see a duplicate of our
hubblebubble... pardon me; if many Level I hubblebubbles are low-entropy,
I should expect the spacing of our Informational Hubblebubble's many
instantiations to be no more than 10^10^80 lightyears apart from each
other on the average.
Though it is noteworthy that at least some of me are so close that they
will eventually see the light rays from each other... at least one in
10^10^29 of me, anyway.
-- Eliezer S. Yudkowsky http://intelligence.org/ Research Fellow, Singularity Institute for Artificial Intelligence
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