On 5/20/2012 6:53 PM, Stephen P. King wrote:

On 5/20/2012 8:08 PM, meekerdb wrote:On 5/20/2012 4:13 PM, Stephen P. King wrote: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 isequivalent our universe there must exist a computation of the homomorphies betweenall possible 4-manifolds.## Advertising

Why?Hi Brent,Because otherwise the amazing precision of the mathematical models based on theassumption of, among other things, that physical systems exist in space-time that isequivalent to a 4-manifold. The mathematical reasoning involved is much like ahugeJenga tower <http://en.wikipedia.org/wiki/Jenga#Tallest_tower>; pull the wrongpiece 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 allpossible 4-manifolds*. If our universe-now has a particular topology and ouruniverse-next has a particular topology, there in nothing in Markov's theorem thatsays that an algorithm can't determine that. It just says that same algorithm can'twork for *every pair*.I agree with your point that Markov's theorem does not disallow the existence ofsome particular algorithm that can compute the relation between some particular pairof 4-manifolds. Please understand that this moves us out of considering universalalgorithms and into specific algorithms. This difference is very important. It is thedifference between the class of universal algorithms and a particular algorithm thatis the computation of some particular function. The non-existence of the generalalgorithm implies the non-existence of an a priori structure of relations between thepossible 4-manifolds.I am making an ontological argument against the idea that there exists an a priorigiven structure that *is* the computation of the Universe. This is my argument againstPlatonism.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 ouruniverse could, for example, always have the same topology,No, it cannot. If there does not exist a general algorithm that can compute thehomomorphy relations between all 4-manifolds then what is the result of such cannotexit either.The result is an exhaustive classification of compact 4-mainifolds. The absence ofsuch a classification neither prevents nor entails the existence of the manifolds.But you fail to see that without the means to define the manifolds, there is nothing todistinguish a manifold from a fruitloop from a pink unicorn from a ..... Absent themeans to distinguish properties there is no such thing as definite properties.We cannot talk coherently within computational methods about "a topology" when suchcannot be specified in advance. Algorithms are recursively enumerable functions. Thatmeans that you must specify their code in advance, otherwise your are not reallytalking about computations; you are talking about some imaginary things created byimaginary entities in imaginary places that do imaginary acts; hence my previousreferences 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.You can have the equipment mix, bake, decorate and eat a cake without having theequipment to mix, bake, decorate, and eat all possible cakes.My analogy failed to demonstrate its intended idea, it seems. Let me rephrase. Docakes exist as cakes if it is impossible to mix, bake and decorate them? Do they justmagically appear out of nothing? No. Neither does meaningfulness and the definiteness ofproperties.

Because I can bake a cake, does it follow that all possible cakes exist?

We cannot have a coherent ontological theory that assumes something that can onlyexist as the result of some process and that same ontological theory prohibits theprocess 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 anongoing 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 thehomomorphies. Time exists because everything cannot happen simultaneously.We must say that the universe has all possible topologies unless we can specifyreasons why it does not.I don't fee any compulsion to say that. In any case, this universe does not have allpossible topologies.Why do not see that as surprising? We experience one particular universe, having oneparticular set of properties. How does this happen? What picked it out of the hat?If you want to hypothesize a multiverse that includes universes with all possibletopologies then there will be no *single* algorithm that can classify all of them. Butthis is just the same as there is no algorithm which can tell you which of the UDprograms will halt.Indeed! It is exactly the same! The point is that since there is nothing that cancomputationally "pick the winner out of the hat" then how is it that we experienceprecisely that winner? Maybe the selection process is not a computation in the Platonicsense at all. Maybe it is a real computation running on all possible physical systems inall possible universes for all time.I am trying to get you to see the difference between structures that are assumed toexist by fiat and structures that are the result of ongoing processes.

You mean like the integers, the multiverse, Turing machines,...?

This is debate that has been going on since Democritus<http://plato.stanford.edu/entries/democritus/> and Heraclitus<http://plato.stanford.edu/entries/heraclitus/> stepped into the Academy. Can you guesswhat ontology I am championing?That is what goes into defining meaningfulness. When you define that X is Y, you arealso defining all not-X to equal not-Y, no?No. Unless your simply defining X to be identical with Y, a mere semantic renaming,then a definition is something like X:=Y|Zx. And it is not the case that ~X=~Y.OK.When you start talking about a collection then you have to define what are its members.

`I'm not talking about a collection. You're the one assuming that all 4-manifolds exist`

`and that everything existing must be computed BY THE SAME ALGORITHM. That's two more`

`assumptions than I'm willing to make.`

Absent the specification or ability to specify the members of a collection, what canyou say of the collection?This universe is defined ostensively.Interesting word: Ostensively <http://www.thefreedictionary.com/ostensibly>."Represented or appearing as such..." It implies a subject to whom therepresentations or appearances have meaningful content. Who plays that role in yourthinking?

You do. When I write "this" you know what I mean.

BrentWhat 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?No attempts to even comment on these?

`As Mark Twain said, "I'm pleased to be able to answer all your questions directly. I`

`don't know."`

Brent

-- Onward! Stephen "Nature, to be commanded, must be obeyed." ~ Francis Bacon --You received this message because you are subscribed to the Google Groups "EverythingList" 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.

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