On Mon, 2 Sep 1996 Eric Watt Forste <arkuat@factory.net> Wrote:
>>Clark:
>>Tipler argues, correctly I think, that IF true
>>immortality is possible, and not just living an
>>astronomically long time, THEN the universe must
>>re-collapse. Immortality is defined as the ability
>>to have an infinite number of thoughts.
>What about Dyson's work on the infinite survivability of
>sophontic life in an indefinitely expanding, cooling
>universe? [...] In the Heat Death scenario, computation
>would gradually but inexorably slow down, but it would have
>a future that is, for all practical purposes, infinite.
Dyson showed that if the universe is open there would always be a time when
life could exist, but that's not immortality because it would not be possible
for the universe to perform an infinite number of calculations, and so there
would not be an infinite amount of subjective time, even if objectively
there is an infinite amount of it. If the universe is open there would an
infinite amount of space, but there would be an upper bound on the amount of
energy and on the amount of momentum in the universe.
You can't describe a system just by specifying it's configuration space,
saying where all the particles in it are, you must also specify what the
momentum of each particle is, this is the Phase Space and is a measure of the
complexity of a system. According to General Relativity, the size of the
universe's Phase Space is proportional to the velocity it is expanding or
contracting at, gravity gets stronger when things get closer together and
it's always attractive, so in the Big Crunch the velocity of the collapse
will keep getting faster and faster without limit.
In the Big Crunch, space goes to zero but Phase Space does not, it goes to
infinity, and thus complexity can increase without limit in a closed universe
but not in an open one. Of course, to have any confidence that all this
really does go to infinity and not just to a very large number we need to
have a much better understanding of quantum gravity.
John K Clark johnkc@well.com
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