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 ofnumbers that is equivalent our universe there must exist acomputation of the homomorphies between all possible 4-manifolds.## Advertising

Why?Hi Brent,Because otherwise the amazing precision of the mathematicalmodels based on the assumption of, among other things, that physicalsystems exist in space-time that is equivalent to a 4-manifold. Themathematical reasoning involved is much like a hugeJenga 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 all possible 4-manifolds*. If our universe-now hasa particular topology and our universe-next has a particulartopology, there in nothing in Markov's theorem that says that analgorithm can't determine that. It just says that same algorithmcan't work for *every pair*.I agree with your point that Markov's theorem does not disallowthe existence of some particular algorithm that can compute therelation between some particular pair of 4-manifolds. Pleaseunderstand that this moves us out of considering universal algorithmsand into specific algorithms. This difference is very important. Itis the difference between the class of universal algorithms and aparticular algorithm that is the computation of some particularfunction. The non-existence of the general algorithm implies thenon-existence of an a priori structure of relations between thepossible 4-manifolds.I am making an ontological argument against the idea that thereexists an a priori given structure that *is* the computation of theUniverse. This is my argument against Platonism.therefore our universe cannot be considered to be the result of acomputation in the Turing universal sense.Sure it can. Even if your interpretation of Markov's theorem werecorrect our universe could, for example, always have the same topology,No, it cannot. If there does not exist a general algorithm thatcan compute the homomorphy relations between all 4-manifolds thenwhat is the result of such cannot exit either.The result is an exhaustive classification of compact 4-mainifolds.The absence of such a classification neither prevents nor entails theexistence of the manifolds.

`But you fail to see that without the means to define the manifolds,`

`there is nothing to distinguish a manifold from a fruitloop from a pink`

`unicorn from a ..... Absent the means to distinguish properties there is`

`no such thing as definite properties.`

We cannot talk coherently within computational methods about "atopology" when such cannot be specified in advance. Algorithms arerecursively enumerable functions. That means that you must specifytheir code in advance, otherwise your are not really talking aboutcomputations; you are talking about some imaginary things created byimaginary entities in imaginary places that do imaginary acts; hencemy previous references to Pink Unicorns.Let me put this in other words. If you cannot build the equipmentneeded to mix, bake and decorate the cake then you cannot eat it.You can have the equipment mix, bake, decorate and eat a cake withouthaving the equipment to mix, bake, decorate, and eat all possible cakes.

`My analogy failed to demonstrate its intended idea, it seems. Let me`

`rephrase. Do cakes exist as cakes if it is impossible to mix, bake and`

`decorate them? Do they just magically appear out of nothing? No. Neither`

`does meaningfulness and the definiteness of properties.`

We cannot have a coherent ontological theory that assumes somethingthat can only exist as the result of some process and that sameontological theory prohibits the process from occurring.or it could evolve only through topologies that were computable fromone another? Where does it say our universe must have all possibletopologies?The alternative is to consider that the computation of thehomomorphies is an ongoing process, not one that is "already existingin Platonia as a string of numbers" or anything equivalent. I wouldeven say that time_is_ the computation of the homomorphies. Timeexists because everything cannot happen simultaneously.We must say that the universe has all possible topologies unlesswe can specify reasons why it does not.I don't fee any compulsion to say that. In any case, this universedoes not have all possible topologies.

`Why do not see that as surprising? We experience one particular`

`universe, having one particular set of properties. How does this happen?`

`What picked it out of the hat?`

If you want to hypothesize a multiverse that includes universes withall possible topologies then there will be no *single* algorithm thatcan classify all of them. But this is just the same as there is noalgorithm which can tell you which of the UD programs will halt.

`Indeed! It is exactly the same! The point is that since there is`

`nothing that can computationally "pick the winner out of the hat" then`

`how is it that we experience precisely that winner? Maybe the selection`

`process is not a computation in the Platonic sense at all. Maybe it is a`

`real computation running on all possible physical systems in all`

`possible universes for all time.`

`I am trying to get you to see the difference between structures`

`that are assumed to exist by fiat and structures that are the result of`

`ongoing processes. 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 guess what ontology I am championing?`

That is what goes into defining meaningfulness. When you define thatX is Y, you are also defining all not-X to equal not-Y, no?No. Unless your simply defining X to be identical with Y, a meresemantic renaming, then a definition is something like X:=Y|Zx. Andit is not the case that ~X=~Y.

OK.

When you start talking about a collection then you have to definewhat are its members. Absent the specification or ability to specifythe members of a collection, what can you 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`

`the representations or appearances have meaningful content. Who plays`

`that role in your thinking?`

BrentWhat is the a priori constraint on the Universe? Why this one andnot some other? Is the limit of all computations not a computation?How did this happen?

No attempts to even comment on these? -- 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.