A quick thought experiment with Tegmarks mathematical universe raises
the issue of the observers relation to the "platonic" world of math. I
also introduce MiT professor Seth Lloyd's ideas on the universe.

Imagine that one of the many universes is a very small one, say so
small it can only contain a few thousand bits of information. This
would limit the mathematical concepts, proofs and such that could in
any way be "contained" in this universe. An "observer" in this
universe would have access to a small distorted "mathematical reality"
and deduce a different multiverse from what we would. Size isn't the
only imaginable spanner in the works. Others could be physical laws
that make the universe equivalent to a non-turing-complete computer,
etc.
Seeing as all observers are inside a universe, could one use this
thought experiment to argue for an "observer dependence" for the
mathematical reality?

At the very least, if we see the "mathematical reality" of the
multiverse as more real, we would have to concede that the (outside)
mathematical reality is not accessible to us, because we can't prove
that mathematical reasoning inside our universe is not similarly
restricted. (You may spot a catch 22 for an attempt at a proof :-)

Somewhat related is Seth Lloyd's work at MiT, which might be of
interest to readers of this mailing list:

Lloyd argue that if the universe contains everything, it must also
somehow contain its laws of physics and the universe itself must
calculate their effects. Lloyd found that our universe, in the
first split second after the big bang, had only calculated 10^20 bits
of information. This should in turn give an "imprecision" in the laws
of physics right after the big bang. Today's universe has had time to
calculate 10^120 bits of information and while this is vast, Lloyd has
found that the physics of a set of 400 entangled particles blows this
limit. Entangled particles are important components in quantum
computers and experiments with a dozen entangled particles have
already been accomplished. Lloyd therefore predict that as work
progresses on quantum computers, we will hit a computational barrier
in the universe itself.

Lloyd and Tegmark dosn't seem to contradict each other as Lloyd only
places the laws of physics inside the universe, not the "mathematical
reality".


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