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 is
equivalent our universe there must exist a computation of the homomorphies between all
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
therefore our universe cannot be considered to be the result of a computation in the
Turing 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?
It is well known that the act of defining an exact "time slice" is a computationally
intractable problem, the Cauchy surface problem
Physicists use approximations and cheats to get around this intractability.
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