Is the universe computable?

From: Georges Quenot <Georges.Quenot.domain.name.hidden>
Date: Tue, 06 Jan 2004 17:32:05 +0100

I start from a part of this post from David Barrett-Lennard (Mon,
3 Nov 2003 19:48:49) but I could probably hev selected several
similar other ones:

> Given the "source code" for the simulation of our universe, it would
> seem to be possible to add some extra instructions that test for a
> certain condition to be met in order to tamper with the simulation.
> It would seem likely that there will exist simulations that match our
> own up to a certain point in time, but then diverge. Eg it is
> possible for a simulation to have a rule that an object will suddenly
> manifestitself at a particular time and place. The simulated conscious
> beings in such a universe would be surprised to find that induction
> fails at the moment the simulation diverges.

It seems to me that there is a very strong assupmtion here which
is that there should be some synchronicity between the "time" in the
postulated computer into which the universe would be simulated and
the time inside that simulated universe (as this is typically the
case when an electronic device is simulated).

But such an assumption not only does not seem necessary in any way
but it also does not seem possibly consistent (or it would be very
arbitrary at least) with a universe like ours for what we know of
the implications of general relativity (it does not seem possible
to define any global time in any consistent way in our universe).

Many other way of simulating the universe could be considered like
for instance a 4D mesh (if we simplify by considering only general
relativity; there is no reason for the approach not being possible in
an even more general way) representing a universe taken as a whole
in its spatio-temporal aspect. The mesh would be refined at each
iteration. The relation between the time in the computer and the time
in the universe would not be a synchrony but a refinement of the
resolution of the time (and space) in the simulated universe as the
time in the computer increases.

Alternatively (though both views are not necessarily exclusive), one
could use a variational formulation instead of a partial derivative
formulation in order to describe/build the universe leading again to
a construction in which the time in the computer is not related at
all to the time in the simulated universe.

It seems to me finally that the simulations in which there is a
synchrony between the time in this universe and the time in the
computer simulating it are very specific (if even existing) among
all other possible simulations of the same universe (at least
for the kind of relativistic universe we live in). I would even
conjecture that the measure of the set of synchronous simulations
is null within the set of all possible simulations of a given (not
so trivial) universe (if one can give a sound sense to this).

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 ?

Georges.
Received on Tue Jan 06 2004 - 11:34:34 PST