On 5/20/2012 4:39 PM, meekerdb wrote:
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 possible 4-manifolds.
Because otherwise the amazing precision of the mathematical models
based on the assumption of, among other things, that physical systems
exist in space-time that is equivalent to a 4-manifold. The mathematical
reasoning involved is much like a hugeJenga tower
<http://en.wikipedia.org/wiki/Jenga#Tallest_tower>; pull the wrong piece
out and it collapses.
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
I agree with your point that Markov's theorem does not disallow the
existence of some particular algorithm that can compute the relation
between some particular pair of 4-manifolds. Please understand that this
moves us out of considering universal algorithms and into specific
algorithms. This difference is very important. It is the difference
between the class of universal algorithms and a particular algorithm
that is the computation of some particular function. The non-existence
of the general algorithm implies the non-existence of an a priori
structure of relations between the possible 4-manifolds.
I am making an ontological argument against the idea that there
exists an a priori given structure that *is* the computation of the
Universe. This is my argument against Platonism.
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,
No, it cannot. If there does not exist a general algorithm that can
compute the homomorphy relations between all 4-manifolds then what is
the result of such cannot exit either. We cannot talk coherently within
computational methods about "a topology" when such cannot be specified
in advance. Algorithms are recursively enumerable functions. That means
that you must specify their code in advance, otherwise your are not
really talking about computations; you are talking about some imaginary
things created by imaginary entities in imaginary places that do
imaginary acts; hence my previous references to Pink Unicorns.
Let me put this in other words. If you cannot build the equipment
needed to mix, bake and decorate the cake then you cannot eat it. We
cannot have a coherent ontological theory that assumes something that
can only exist as the result of some process and that same ontological
theory prohibits the process from occurring.
or it could evolve only through topologies that were computable from
one another? Where does it say our universe must have all possible
The alternative is to consider that the computation of the
homomorphies is an ongoing process, not one that is "already existing in
Platonia as a string of numbers" or anything equivalent. I would even
say that time_is_ the computation of the homomorphies. Time exists
because everything cannot happen simultaneously.
We must say that the universe has all possible topologies unless we
can specify reasons why it does not. That is what goes into defining
meaningfulness. When you define that X is Y, you are also defining all
not-X to equal not-Y, no? When you start talking about a collection then
you have to define what are its members. Absent the specification or
ability to specify the members of a collection, what can you say of the
What is the a priori constraint on the Universe? Why this one and
not some other? Is the limit of all computations not a computation? How
did this happen?
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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