On 11/2/07, Sko-D <[EMAIL PROTECTED]> wrote:
> 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?

That is an interesting thought.  Perhaps a simple way to demonstrate it
would be to say if this universe contains a finite amount of information
then there exist axiomatic systems, proofs, mathematical structures and
numbers that require more information to describe than could be accurately
represented in said finite universe.  These concepts will forever be
inaccessible to us in a universe if we are limited in our ability to build a
computer which can store an infinite amount of information.

Wei Dai made a post some time ago (
http://groups.google.com/group/everything-list/msg/20c8a685bef59597 ) which
says that a computer with unbounded memory can in theory be made in a
universe with finite energy if spread over an unbounded area.


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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