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. > > > Why? > > 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 > 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 *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 > collection? > > 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 indeterminacy. Quentin > How did this happen? > > > > -- > Onward! > > Stephen > > "Nature, to be commanded, must be obeyed." > ~ Francis Bacon > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to everything-list@googlegroups.com. > To unsubscribe from this group, send email to > everything-list+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > -- All those moments will be lost in time, like tears in rain. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
