> Then question then becomes, I suppose, if in fact our universe is a digital
> one (if not strictly a CA) havng self-consistent emergent physics, then
> might it not follow that it is "implemented" (run?) via some extra-universal
> physical processes that only indirectly correspond to ours?
This is a good point, and in fact we could sharpen the situation as
Suppose multiverse theory is bunk and none of Tegmark's four levels work.
The universe isn't infinite in size; there is no inflation; the MWI is
false; and all that stuff about Platonic existence is so much hot air.
There is, in fact, only one universe.
However, that universe isn't ours. It's a specific version of Conway's
2D Life universe, large but finite in size, with periodic edge conditions.
Against all odds, life has evolved in Life and produced Self
Aware Subsystems, i.e. observers. These beings have developed a
civilization and built computers. See the link I supplied earlier,
http://rendell.server.org.uk/gol/tm.htm for a sample of such a computer.
On their computers they run simulations of other universes, and one
of the universes they have simulated is our own. Due to a triumph
of advanced mathematics, they have invented a set of physical laws of
tremendous complexity compared to their own, and these laws allow for
atoms, chemistry, biology and life of a form very different from theirs.
They follow our universe's evolution from Big Bang to Heat Death with
Unbeknown to us, this is the basis for our existence. We are a simulation
being run in a 2D CA universe with Conway's Life rules.
Now, is this story inconceivable? Logically contradictory? I don't
see how. The idea that only one "real" universe might exist, but that it
could create any number of "simulated" ones, is pretty common. Of course
it's more common to suppose that it's our universe which is the "real"
one, but that's just parochialism.
And what does it say about the physical properties which are necessary
for computation? We have energy; Life has "blinkiness" (the degree to
which cells are blinking on and off within a structure); neither property
has a good analog in the other universe. Does the "real" universe win,
in terms of deciding what properties are really needed for computation?
I don't think so, because we could reverse the roles of the two universes
and it wouldn't make any fundamental difference.