Georges Quenot writes:
> I would be interested in reading the opinions of the participants
> about that point and about the sense that could be given to the
> question of what "happens" (in the simulated universe) in any non-
> synchronous simulation "when" the simulation diverges ?

I'll make two points.  First, you're right that there are other ways of
computing a universe than simply starting with some initial conditions
and evolving "time" forward step by step, computing the state of the
universe at each subsequent instant.  You list several ways this might
happen and I agree that this concept makes sense.  We might call this
"non-sequential" or "non-temporal" simulation.

But, given the specific temporal structures that exist in our universe,
there are limitations to how this computation can be done.  Specifically,
we are able to construct physical computers in this universe which perform
complex calculations.  And among these calculations are those which are
believed to be inherently sequential and lengthy, calculations for which
the answer cannot be computed without spending a great deal of time from
the initial values.

Given that our universe contains systems like this, it constrains the
amount of computation which must be done in any kind of non-sequential
simulation.  Specifically, the non-sequential simulation must do at
least as much computation in order to produce our universe as the more
traditional kind of sequential simulation.  This demonstrates a limit
on the power of non-sequential simulation.

My second point is with regard to your specific question, what would
happen if we tried to simulate a universe which diverged in some
space-time region from the conventional physical laws?  This is our
often-discussed "flying rabbit" paradox (we have other names as well),
where it seems that if all universes exist, we might as well be living
in a universe which was lawful everywhere except in some small region,
or up until a certain time, as in one where the laws are truly universal.

Your question is whether this concept makes sense in a non-sequential
simulation, or whether it assumes sequential simulation.

I think it makes just as much sense in the context of non-sequential
simulation.  The non-sequential simulator is trying to find or create a
universe which satisfies certain physical laws.  It may be iteratively
solving a differential equation or using some other non-temporal method,
but that is its goal, its mechanism.  The case at hand is simply
a matter of defining the physical laws to be different in different
regions of space-time.

We could define the physical laws which the non-sequential simulator is
trying to solve in some such terms.  We'd say, observe these laws in this
region, but these other laws in that region.  For example, we might say
to observe the true laws of our universe (whatever they turn out to be)
up to simulated time T, and then to observe other laws after time T.
Or similarly we could have one set of laws up to spatial coordiate X,
and another set of laws on the other side of X.

The non-sequential simulator would have no more difficulty in creating
a universe which satisfied such non-uniform physical laws than in one
where the laws were the same everywhere.  So I'd say that the issue of
sequential vs non-sequential simulation is irrelevant to the question
of the existence of "flying rabbit" universes and does not shed light
on the issue.

Hal Finney

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