On 23 Oct 2012, at 08:03, 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. 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.
Good point.
Bruno
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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