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:
On 10/23/2012 2:03 AM, meekerdb wrote:
On 10/22/2012 11:35 AM, Stephen P. King wrote:
On 10/22/2012 6:05 AM, Quentin Anciaux wrote:
I don't understand why you're focusing on NP-hard problems... NP-hard problems 
are
solvable algorithmically... but not efficiently. When I read you (I'm surely
misinterpreting), it seems like you're saying you can't solve NP-hard 
problems... it's
not the case,... but as your input grows, the time to solve the problem may be 
bigger
than the time ellapsed since the bigbang. You could say that the NP-hard 
problems for
most input are not technically/practically sovable but they are in theories 
(you have
the algorithm) unlike undecidable problems like the halting problem.

Quentin
Hi Quentin,

    Yes, they are solved algorithmically. I am trying to get some focus on the
requirement of resources for computations to be said to be solvable. This is my
criticism of the Platonic treatment of computer theory, it completely ignores 
these
considerations. The Big Bang theory (considered in classical terms) has a 
related
problem in its stipulation of initial conditions, just as the Pre-Established Harmony of
Leibniz' Monadology. Both require the prior existence of a solution to a NP-Hard
problem. We cannot consider the solution to be "accessible" prior to its actual
computation!

Why not?  NP-hard problems have solutions ex hypothesi; it's part of their 
defintion.

"Having a solution" in the abstract sense, is different from actual access to the solution. You cannot do any work with the abstract fact that a NP-Hard problem has a solution, you must actually compute a solution! The truth that there exists a minimum path for a traveling salesman to follow given N cities does not guide her anywhere. This should not be so unobvious!

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.

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'.

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?

(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."

There has to be something that cannot be changed merely by changing one's point 
of view.

So long as you thing other 1p viewpoints exist then intersubjective agreement defines the 'real' 3p world.



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.


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.


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.



What would a "prior" computation mean?

    Where did you get that cluster of words?
From you, below, in the next to last paragraph (just because I quit writing doesn't mean I quit reading at the same point).

Ah, I wrote "...if the prior computation idea is true. " I was trying to contrast two different ideas: one where all of the computations are somehow performed "ahead of time" (literally!) and the other is where the computations occur as they need to subject to restrictions such as only those computations that have resources available can occur.



Are you supposing that there is a computation and *then* there is an implementation (in matter) that somehow realizes the computation that was formerly abstract. That would seem muddled.

    Right! It would be, at least, muddled. That is my point!

But no one but you has ever suggested the universe is computed and then implemented to a two-step process. So it seems to be a muddle of your invention.

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

Brent



Brent


If the universe is to be explained as a computation then it must be realized by the computation - not by some later (in what time measure?) events.

    Exactly. The computation cannot occur before the universe!


Brent

    The calculation of the minimum action configuration of the universe such 
that there
is a universe that we observe now is in the state that it is and such is consistent with
our existence in it must be explained either as being the result of some 
fortuitous
accident or, as some claim, some "intelligent design" or some process working 
in some
super-universe where our universe was somehow selected, if the prior computation idea is
true.
I am trying to find an alternative that does not require computations to occur prior
to the universe's existence! Several people, such as Lee Smolin, Stuart 
Kaufmann and
David Deutsch have advanced the idea that the universe is, literally, computing its next
state in an ongoing fashion, so my conjecture is not new. The universe is 
computing
solutions to NP-Hard problems, but not in any Platonic sense.








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