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From: Hal Ruhl <hjr.domain.name.hidden>

Date: Fri, 04 May 2001 18:20:00 -0700

Dear Juergen:

I am not so much interested in provability as I am in whether or not the

"noise" in a universes history is pseudorandom or random and forging an .

At 5/4/01, you wrote:

*>Which are the logically possible universes? Max Tegmark mentioned
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*>a somewhat vaguely defined set of ``self-consistent mathematical
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*>structures,'' implying provability of some sort. The postings of Bruno
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*>Marchal and George Levy and Hal Ruhl also focus on what's provable and
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*>what's not.
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*>
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*>Is provability really relevant? Philosophers and physicists find
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*>it sexy for its Goedelian limits. But what does this have to do with
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*>the set of possible universes?
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*>
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*>I believe the provability discussion distracts a bit from the
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*>real issue. If we limit ourselves to universes corresponding to
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*>traditionally provable theorems then we will miss out on many formally
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*>and constructively describable universes that are computable in the
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*>limit yet in a certain sense soaked with unprovable aspects.
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*>
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*>Example: a never ending universe history h is computed by a finite
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*>nonhalting program p. To simulate randomness and noise etc, p invokes a
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*>short pseudorandom generator subroutine q which also never halts. The
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*>n-th pseudorandom event of history h is based on q's n-th output bit
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*>q(n) which is initialized by 0 and set to 1 as soon as the n-th element
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*>of an ordered list of all possible program prefixes halts. Whenever q
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*>modifies some q(n) that was already used in the previous computation of
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*>h, p appropriately recomputes h since the n-th pseudorandom event.
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*>
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*>Such a virtual reality or universe is perfectly well-defined. At some
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*>point each history prefix will remain stable forever. Even if we know p
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*>and q, however, in general we will never know for sure whether some q(n)
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*>that is still zero won't flip to 1 at some point, because of Goedel etc.
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*>So this universe features lots of unprovable aspects.
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*>
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*>But why should this lack of provability matter? It does not do any harm.
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*>
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*>Note also that observers evolving within the universe may write
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*>books about all kinds of unprovable things; they may also write down
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*>inconsistent axioms; etc. All of this is computable though, since the
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*>entire universe history is. So again, why should provability matter?
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*>
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*>Juergen Schmidhuber http://www.idsia.ch/~juergen/toesv2/
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Received on Fri May 04 2001 - 15:25:50 PDT

Date: Fri, 04 May 2001 18:20:00 -0700

Dear Juergen:

I am not so much interested in provability as I am in whether or not the

"noise" in a universes history is pseudorandom or random and forging an .

At 5/4/01, you wrote:

Received on Fri May 04 2001 - 15:25:50 PDT

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