From: Hal Finney <hal@rain.org>

Date: Mon Dec 08 1997 - 09:45:23 PST

Date: Mon Dec 08 1997 - 09:45:23 PST

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

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