Re: poly: Infinite calculations in an open universe?

From: Hal Finney <>
Date: Wed Dec 10 1997 - 12:23:11 PST

Obviously these are highly abstract philosophical considerations.
Whether any of us will be around to care about computation at the end
of the universe is questionable at best.

Still I find it interesting to consider the question of whether there
is a limit on the amount of computation which can be done, given our
understanding of the laws of physics. A universe which allows only a
finite possible amount of computation (as ours seems to, based on the best
cosmological evidence) is one which is limited in a very fundamental way.
Philosophically it would be more satisfying for there to be at least
the theoretical possibility of unlimited calculations.

Frank Tipler looks at this in theological terms, seeing prospects for
resurrection, and in some sense identifying the infinite computation
with God. This is a very personal view which is particular to him,
but the question of whether computation is limited is interesting in
its own right.

As to the question of whether an infinite computation could simulate all
universes, or solve all problems, I think the answer is that it could
do so, to any desired level of precision. It could not enumerate all
the real numbers. But it could enumerate all the rationals, which are
everywhere dense.

It is an interesting question whether there could be an uncountable
infinity of interesting problems. Countable infinity is hard enough to
grasp. Uncountable is much harder.

Received on Wed Dec 10 20:32:46 1997

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