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 
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 
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.

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 
considerations. The Big Bang theory (considered in classical terms) has a 
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

Why not? NP-hard problems have solutions ex hypothesi; it's part of their defintion. What would a "prior" computation mean? 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. 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.


    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 
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
    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 
solutions to NP-Hard problems, but not in any Platonic sense.

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