On 10/23/2012 1:29 PM, meekerdb wrote:
On 10/23/2012 3:40 AM, Stephen P. King wrote:
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!
But you wrote, "Both require the prior existence of a solution to a
NP-Hard problem." An existence that is guaranteed by the definition.
Hi Brent,
OH! Well, I thank you for helping me clean up my language! Let me
try again. ;--) First I need to address the word "existence". I have
tried to argue that "to exists" is to be "necessarily possible" but that
attempt has fallen on deaf ears, well, it has until now for you are
using it exactly how I am arguing that it should be used, as in "An
existence that is guaranteed by the definition." DO you see that
existence does nothing for the issue of properties? The existence of a
pink unicorn and the existence of the 1234345465475766th prime number
are the same kind of existence, once we drop the pretense that existence
is dependent or contingent on physicality.
Is it possible to define Physicality can be considered solely in
terms of bundles of particular properties, kinda like Bruno's bundles of
computations that define any given 1p. My thinking is that what is
physical is exactly what some quantity of separable 1p have as mutually
consistent (or representable as a Boolean Algebra) but this
consideration seems to run independent of anything physical. What could
reasonably constrain the computations so that there is some thing "real"
to a physical universe? There has to be something that cannot be changed
merely by changing one's point of view.
When you refer to the universe computing itself as an NP-hard problem,
you are assuming that "computing the universe" is member of a class of
problems.
Yes. It can be shown that computing a universe that contains
something consistent with Einstein's GR is NP-Hard, as the problem of
deciding whether or not there exists a smooth diffeomorphism between a
pair of 3,1 manifolds has been proven (by Markov) to be so. This tells
me that if we are going to consider the evolution of the universe to be
something that can be a simulation running on some powerful computer (or
an abstract computation in Platonia) then that simulation has to at
least the equivalent to solving an NP-Hard problem. The prior existence,
per se, of a solution is no different than the non-constructable proof
that Diffeo_3,1 /subset NP-Hard that Markov found.
It actually doesn't make any sense to refer to a single problem as
NP-hard, since the "hard" refers to how the difficulty scales with
different problems of increasing size.
These terms, "Scale" and "Size", do they refer to some thing
abstract or something physical or, perhaps, both in some sense?
I'm not clear on what this class is.
It is an equivalence class of computationally soluble problems.
http://cs.joensuu.fi/pages/whamalai/daa/npsession.pdf There are many of
them.
Are you thinking of something like computing Feynman path integrals
for the universe?
Not exactly, but that is one example of a computational problem.
What would a "prior" computation mean?
Where did you get that cluster of words?
From you, below, in the next to last paragraph (just because I quit
writing doesn't mean I quit reading at the same point).
Ah, I wrote "...if the prior computation idea is true. " I was
trying to contrast two different ideas: one where all of the
computations are somehow performed "ahead of time" (literally!) and the
other is where the computations occur as they need to subject to
restrictions such as only those computations that have resources
available can occur.
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!
But no one but you has ever suggested the universe is computed and
then implemented to a two-step process. So it seems to be a muddle of
your invention.
No, I am trying to explain something that is taken for granted; it
is more obvious for the Pre-established harmony of Leibniz, but I am
arguing that this is also the case in Big Bang theory: the initial
condition problem (also known as the foliation problem) is a problem of
computing the universe ahead of time.
Brent
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!
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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