Re: Is the universe computable?

From: Hal Finney <hal.domain.name.hidden>
Date: Tue, 13 Jan 2004 10:06:04 -0800

Georges Quenot writes:
> I do not believe in either case that a simulation with this level
> of detail can be conducted on any computer that can be built in
> our universe (I mean a computer able to simulate a universe
> containing a smaller computer doing the calculation you considered
> with a level of accuracy sufficient to ensure that the simulation
> of the behavior of the smaller computer would be meaningful).
> This is only a theoretical speculation.

What about the idea of simulating a universe with simpler laws using such
a technique? For example, consider a 2-D or 1-D cellular automaton (CA)
system like Conway's "Life" or the various systems considered by Wolfram.

Suppose we sought to construct a consistent history of such a CA system
by first starting with purely random values at each point in space and
time. Now, obviously this arrangement will not satisfy the CA rules.
But then we go through and start modifying things locally so as to
satisfy the rules. We move around through the mesh in some pattern,
repeatedly making small modifications so as to provide local obedience
to the rules. Eventually, if we take enough time, we ought to reach a
point where the entire system satisfies the specified rules.

Now, I'm not sure how to combine this process with Georges' proposal to
maximize some criterion such as the gradient of orderliness. I suppose
you could simply repeat this process many times, saving or remembering
the best solution found so far. But it would be nice if you could
combine the two steps somehow, looking for valid solutions which also
scored highly in the desired optimization property.

Among simple CA models are ones which have been shown to be universal,
meaning that you can set up systems which do computation within the CA
"universe", and those systems could do various sorts of sequential
calculations. Let's suppose, as Georges' ideas might suggest, that
some optimization principle can implicitly promote the formation of such
sequential computational systems within the simulated universe.

To get back to Wei's question, it would seem that when we do manage to
create such a universe using non-sequential optimization as described
above, there would be no particular need for the early steps of the
simulated computation to be stabilized before the later steps. The order
in which stabilization occurs in any given run could be essentially
arbitrary or random.

Hal
Received on Tue Jan 13 2004 - 13:08:29 PST