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. 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.
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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