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!

What would a "prior" computation mean?

    Where did you get that cluster of words?

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!

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! Did you stop reading at this point?


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.




--
Onward!

Stephen


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