Re: poly: Infinite calculations in an open universe?

Another factor which may help is reversible computing; the bounds
calculated by Tipler are actually lower bounds since we can do
reversible calculations beside the dissipating calculations (needed
for error correction, secure storage etc). In the Dyson scenario
things look even better, since thermal noise gets weaker and weaker
all the time, enabling more and more reversible calculations.

Hal Finney <hal@rain.org> writes:

> 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.

I think the later is possible. The problem is the Bekenstein Bound,
which limits the amount of information (including quantum information?
I think so) in a given volume with mass. But if you enlarge the
volume, the information can grow with no increase in mass (you simply
enlarge the spatial dimensions of phase space). This suggests that you
can have at least t^2 growth of available states.

> 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?

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Anders Sandberg                                      Towards Ascension!
asa@nada.kth.se                            http://www.nada.kth.se/~asa/
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