On 10/23/2012 7:16 PM, meekerdb wrote:

On 10/23/2012 3:35 PM, Stephen P. King wrote:On 10/23/2012 1:29 PM, meekerdb wrote:On 10/23/2012 3:40 AM, Stephen P. King wrote:## Advertising

snip

But you wrote, "Both require the prior existence of a solution to aNP-Hard problem." An existence that is guaranteed by the definition.Hi Brent,OH! Well, I thank you for helping me clean up my language! Let metry again. ;--) First I need to address the word "existence". I havetried to argue that "to exists" is to be "necessarily possible" butthat attempt has fallen on deaf ears, well, it has until now for youare using it exactly how I am arguing that it should be used, as in"An existence that is guaranteed by the definition." DO you see thatexistence does nothing for the issue of properties? The existence ofa pink unicorn and the existence of the 1234345465475766th primenumber are the same kind of existence,I don't see that they are even similar. Existence of the aforesaidprime number just means it satisfies a certain formula within an axiomsystem. The pink unicorn fails existence of a quite different kind,namely an ability to locate it in spacetime. It may still satisfysome propositions, such as, "The animal that is pink, has one horn,and loses it's power in the presence of a virgin is obviouslymetaphorical."; just not ones we think of as axiomatic.

Hi Brent,

`Why are they so different in your thinking? If the aforesaid prime`

`number is such that there does not exist a physical symbol to represent`

`it, how is it different from the pink unicorn? Why the insistence on a`

`Pink Unicorn being a "real' creature?`

`I am using the case of the unicorn to force discussion of an`

`important issue. We seem to have no problem believing that some`

`mathematical object that cannot be physically constructed and yet balk`

`at the idea of some cartoon creature. As I see it, the physical paper`

`with a drawing of a pink horse with a horn protruding from its forehead`

`or the brain activity of the little girl that is busy dreaming of riding`

`a pink unicorn is just as physical as the mathematician crawling out an`

`elaborate abstract proof on her chalkboard. A physical process is`

`involved. So why the prejudice against the Unicorn? Both exists in our`

`minds and, if my thesis is correct, then there is a physical process`

`involved somewhere. No minds without bodies and no bodies without minds,`

`or so the expression goes...`

once we drop the pretense that existence is dependent or contingenton physicality.It's not a pretense; it's a rejection of Platonism, or at least adistinction between different meanings of 'exists'.

`Right, I am questioning Platonism and trying to clear up the`

`ambiguity in the word 'exists'.`

Is it possible to define Physicality can be considered solely interms of bundles of particular properties, kinda like Bruno's bundlesof computations that define any given 1p. My thinking is that what isphysical is exactly what some quantity of separable 1p have asmutually consistentBut do the 1p have to exist? Can they be Sherlock Holmes and Dr. Watson?

`1p is the one thing that we cannot doubt, at least about our own`

`1p. Descartes did a good job discussing that in his /Meditations/...`

`That something other than ourselves has a 1p, well, that is part of the`

`hard problem! BTW, my definition of physicality is not so different from`

`Bruno's, neither of us assumes that it is ontologically primitive and`

`both of us, AFAIK, consider it as emergent or something from that which`

`is sharable between a plurality of 1p. Do you have a problem with his`

`concept of it?`

(or representable as a Boolean Algebra) but this consideration seemsto run independent of anything physical. What could reasonablyconstrain the computations so that there is some thing "real" to aphysical universe?That's already assuming the universe is just computation, which Ithink is begging the question. It's the same as saying, "Why this andnot that."

`No, I am trying to nail down whether the universe is computable or`

`not. If it is computable, then it is natural to ask if something is`

`computing it. If it is not computable, well.. that's a different can of`

`worms! I am testing a hypothesis that requires the universe (at least`

`the part that we can observe and talk about) to be representable as a`

`particular kind of topological space that is dual to a Boolean algebra;`

`therefore it must be computable in some sense.`

There has to be something that cannot be changed merely by changingone's point of view.So long as you think other 1p viewpoints exist then intersubjectiveagreement defines the 'real' 3p world.

`My thinking is that it exists as a necessary possibility in some a`

`priori sense and it actually existing in a 'real 3p' sense are not the`

`same thing. Is this a problem? The latter implies that it is accessible`

`in some way. The former, well, there is some debate...`

When you refer to the universe computing itself as an NP-hardproblem, you are assuming that "computing the universe" is member ofa class of problems.Yes. It can be shown that computing a universe that containssomething consistent with Einstein's GR is NP-Hard, as the problem ofdeciding whether or not there exists a smooth diffeomorphism betweena pair of 3,1 manifolds has been proven (by Markov) to be so. Thistells me that if we are going to consider the evolution of theuniverse to be something that can be a simulation running on somepowerful computer (or an abstract computation in Platonia) then thatsimulation has to at least the equivalent to solving an NP-Hardproblem. The prior existence, per se, of a solution is no differentthan the non-constructable proof that Diffeo_3,1 /subset NP-Hard thatMarkov found.So the universe solves that problem. So what? We knew it was asoluble problem. Knowing it was NP-hard didn't make it insoluble.

`I am assuming computability and thus solubility. The point is the`

`question of available resources, this is where the Kolmogorov stuff`

`comes in... My thesis is that if resources are not available for a given`

`computation then it cannot be run, not complicated...`

It actually doesn't make any sense to refer to a single problem asNP-hard, since the "hard" refers to how the difficulty scales withdifferent problems of increasing size.These terms, "Scale" and "Size", do they refer to some thingabstract or something physical or, perhaps, both in some sense?They refer to something abstract (e.g. number of nodes in a graph),but they may have application by giving them a concrete interpretation- just like any mathematics.

`What difference does what they refer to matter? Eventually there`

`has to be some physical process or we would be incapable of even`

`thinking about them! The resources to perform the computation are either`

`available or they are not. Seriously, why are you over complicating the`

`idea?`

I'm not clear on what this class is.It is an equivalence class of computationally soluble problems.http://cs.joensuu.fi/pages/whamalai/daa/npsession.pdf There are manyof them.Are you thinking of something like computing Feynman path integralsfor the universe?Not exactly, but that is one example of a computational problem.snip.

No, I am trying to explain something that is taken for granted;it is more obvious for the Pre-established harmony of Leibniz, but Iam arguing that this is also the case in Big Bang theory: the initialcondition problem (also known as the foliation problem) is a problemof computing the universe ahead of time.That problem assumes GR. But thanks to QM the future is not computedjust from the past, i.e. the past does not have to have enoughinformation to determine the future. So the idea that computing thenext foliation in GR is 'too hard' may be an artifact of ignoring QM.

`If the universe is QM then it can be considered as a quantum`

`computer and its resource requirements are different from those of a`

`classical machine. I think... I'm trying to get this right...`

Also it's not clear what resources the universe has available withwhich to compute.

I am trying to figure the answer to that question.

If you consider every Planck volume as capable of encoding a bit,and observe the holographic bound on the information to be computed Ithink there's more than enough.

`Yes, that is my hypothesis. The point is that the number of Planck`

`voxels in our observable universe is a large but finite number. It is`

`not infinite. This tells us that there is something strange about the`

`Platonic idea of computation, as it assumes the availability infinite`

`resources for a Universal Turing Machine in its complete neglect of the`

`question of resources. One way to escape this is to allow for the`

`universe to actually be infinite or that there actually exist an`

`infinite number of finite physical universes.`

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