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!
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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