On 5/20/2012 1:31 PM, Stephen P. King wrote:

My point is that for there to exist an a priori given string of numbers that isequivalent our universe there must exist a computation of the homomorphies between allpossible 4-manifolds.

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Why?

Markov theorem tells us that no such homomorphy exists,

`No, it tells there is no algorithm for deciding such homomorphy *that works for all`

`possible 4-manifolds*. If our universe-now has a particular topology and our`

`universe-next has a particular topology, there in nothing in Markov's theorem that says`

`that an algorithm can't determine that. It just says that same algorithm can't work for`

`*every pair*.`

therefore our universe cannot be considered to be the result of a computation in theTuring universal sense.

`Sure it can. Even if your interpretation of Markov's theorem were correct our universe`

`could, for example, always have the same topology, or it could evolve only through`

`topologies that were computable from one another? Where does it say our universe must`

`have all possible topologies?`

Brent

It is well known that the act of defining an exact "time slice" is a computationallyintractable problem, the Cauchy surface problem<http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&sqi=2&ved=0CE8QFjAB&url=http%3A%2F%2Fwww.tapir.caltech.edu%2F%7Elindblom%2FPublications%2F10_CommMathPhys.61.87.pdf&ei=G1O5T9y1NYG69QT036GoCg&usg=AFQjCNGQxEJa9DEFbyKnXiub-nS7zvPksw&sig2=9za6duwSbfQp-yZ_Cj6vzA>.Physicists use approximations and cheats to get around this intractability.

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