2012/5/21 Stephen P. King <stephe...@charter.net>
> 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.
> Hi Brent,
> 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 huge Jenga
> 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 *every pair*.
> 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 topologies?
> 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?
No it's not a computation, it arises because at every step, computations
diverge into new sets of infinite computations, giving rise to the 1p
> How did this happen?
> "Nature, to be commanded, must be obeyed."
> ~ Francis Bacon
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