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:


But you wrote, "Both require the prior existence of a solution to a NP-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 me try again. ;--) First I need to address the word "existence". I have tried to argue that "to exists" is to be "necessarily possible" but that attempt has fallen on deaf ears, well, it has until now for you are 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 that existence does nothing for the issue of properties? The existence of a pink unicorn and the existence of the 1234345465475766th prime number are the same kind of existence,

I don't see that they are even similar. Existence of the aforesaid prime number just means it satisfies a certain formula within an axiom system. The pink unicorn fails existence of a quite different kind, namely an ability to locate it in spacetime. It may still satisfy some propositions, such as, "The animal that is pink, has one horn, and loses it's power in the presence of a virgin is obviously metaphorical."; 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 contingent on physicality.

It's not a pretense; it's a rejection of Platonism, or at least a distinction 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 in terms of bundles of particular properties, kinda like Bruno's bundles of computations that define any given 1p. My thinking is that what is physical is exactly what some quantity of separable 1p have as mutually consistent

But 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 seems to run independent of anything physical. What could reasonably constrain the computations so that there is some thing "real" to a physical universe?

That's already assuming the universe is just computation, which I think is begging the question. It's the same as saying, "Why this and not 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 changing one's point of view.

So long as you think other 1p viewpoints exist then intersubjective agreement 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-hard problem, you are assuming that "computing the universe" is member of a class of problems.

Yes. It can be shown that computing a universe that contains something consistent with Einstein's GR is NP-Hard, as the problem of deciding whether or not there exists a smooth diffeomorphism between a pair of 3,1 manifolds has been proven (by Markov) to be so. This tells me that if we are going to consider the evolution of the universe to be something that can be a simulation running on some powerful computer (or an abstract computation in Platonia) then that simulation has to at least the equivalent to solving an NP-Hard problem. The prior existence, per se, of a solution is no different than the non-constructable proof that Diffeo_3,1 /subset NP-Hard that Markov found.

So the universe solves that problem. So what? We knew it was a soluble 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 as NP-hard, since the "hard" refers to how the difficulty scales with different problems of increasing size.

These terms, "Scale" and "Size", do they refer to some thing abstract 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 many of them.

Are you thinking of something like computing Feynman path integrals for the universe?

    Not exactly, but that is one example of a computational problem.


No, I am trying to explain something that is taken for granted; it is more obvious for the Pre-established harmony of Leibniz, but I am arguing that this is also the case in Big Bang theory: the initial condition problem (also known as the foliation problem) is a problem of computing the universe ahead of time.

That problem assumes GR. But thanks to QM the future is not computed just from the past, i.e. the past does not have to have enough information to determine the future. So the idea that computing the next 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 with which 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 I think 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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