poly: Infinite calculations in an open universe?

While we are on these eschatological subjects, I have a question based
on a discussion on another mailing list.

Frank Tipler's book, The Physics of Immortality, takes as its premise that
an infinite amount of computation will be possible, and explores what
the cosmological implications will be. Whether you believe the premise
or not, it is a question with implications for the possible future of life.

Tipler concludes that only a closed, collapsing universe allows for infinite
computations. Even with this cosmology it is still a hard trick to reach
infinity, requiring massive and unstable deformations of the shape of
space-time during collapse. Tipler concludes that not only must life
survive, but that it must take control over the entire universe and guide
its shape during the collapse phase. It's going to be an exciting ride
if he's right.

Tipler rejects earlier arguments that open universes will allow infinite
computations (I think Freeman Dyson had suggested this). While Dyson
showed that you can theoretically continue calculating forever, Tipler
says that the number of states your computer can fall into is finite.
The decreasing density of matter and the limits of the speed of light
prevent communication over ever-larger distances and this limits the
total state space of your computer, and so you can't really do infinite
computations.

I believe Tipler also rejects another method occasionally suggested, which
is the formation of "basement universes" which bud off our own, and which
could conceivably form the basis for new calculations. As I recall the
argument, there is only a limited amount of information which can be
passed into the new universes, preventing them from being used to do
an infinite amount of calculation.

What I was wondering is whether the new ideas in quantum computing
could provide a way around this. Quantum computers can be thought of as
spanning multiple parallel universes, in the many worlds interpretation.
In a sense, these multiple universes work together to produce a useful
result in each component universe which could not have been done within
that amount of time using just that universe's resources. With n quantum
bits you can perform two to the n calculations (although combining the
results can not typically be done with perfect efficiency).

I wonder whether this multiplicative factor could counter Tipler's
pessimistic conclusions about the possibilities for an open universe.
Obviously multiplying computation efficiency by a constant factor would
not help. I think it would be necessary over time to include larger and
larger numbers of universes within the scope of the quantum computer.
Would this require more and more matter to be available? That won't
work well in a Dyson universe where matter is decreasing in density.
Maybe you could do increasingly subtle (and time consuming?) measurements
on a limited amount of matter in order to get the same effect.

Going from n to two-to-the-n is a very powerful step in counting theory.
It raises you from one level of infinity to another. Could it conceivably
be enough in this context to allow the total number of states to diverge
and get you over the infinity barrier?

Hal
Received on Mon Dec 8 17:53:31 1997