On 10/23/2012 7:16 PM, meekerdb wrote:
On 10/23/2012 3:35 PM, Stephen P. King wrote:
On 10/23/2012 1:29 PM, meekerdb wrote:
On 10/23/2012 3:40 AM, Stephen P. King wrote:
snip
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,
I don't see that they are even similar. Existence of the aforesaid
prime number just means it satisfies a certain formula within an axiom
system. The pink unicorn fails existence of a quite different kind,
namely an ability to locate it in spacetime. It may still satisfy
some propositions, such as, "The animal that is pink, has one horn,
and loses it's power in the presence of a virgin is obviously
metaphorical."; just not ones we think of as axiomatic.
Hi Brent,
Why are they so different in your thinking? If the aforesaid prime
number is such that there does not exist a physical symbol to represent
it, how is it different from the pink unicorn? Why the insistence on a
Pink Unicorn being a "real' creature?
I am using the case of the unicorn to force discussion of an
important issue. We seem to have no problem believing that some
mathematical object that cannot be physically constructed and yet balk
at the idea of some cartoon creature. As I see it, the physical paper
with a drawing of a pink horse with a horn protruding from its forehead
or the brain activity of the little girl that is busy dreaming of riding
a pink unicorn is just as physical as the mathematician crawling out an
elaborate abstract proof on her chalkboard. A physical process is
involved. So why the prejudice against the Unicorn? Both exists in our
minds and, if my thesis is correct, then there is a physical process
involved somewhere. No minds without bodies and no bodies without minds,
or so the expression goes...
once we drop the pretense that existence is dependent or contingent
on physicality.
It's not a pretense; it's a rejection of Platonism, or at least a
distinction between different meanings of 'exists'.
Right, I am questioning Platonism and trying to clear up the
ambiguity in the word 'exists'.
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
But do the 1p have to exist? Can they be Sherlock Holmes and Dr. Watson?
1p is the one thing that we cannot doubt, at least about our own
1p. Descartes did a good job discussing that in his /Meditations/...
That something other than ourselves has a 1p, well, that is part of the
hard problem! BTW, my definition of physicality is not so different from
Bruno's, neither of us assumes that it is ontologically primitive and
both of us, AFAIK, consider it as emergent or something from that which
is sharable between a plurality of 1p. Do you have a problem with his
concept of it?
(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?
That's already assuming the universe is just computation, which I
think is begging the question. It's the same as saying, "Why this and
not that."
No, I am trying to nail down whether the universe is computable or
not. If it is computable, then it is natural to ask if something is
computing it. If it is not computable, well.. that's a different can of
worms! I am testing a hypothesis that requires the universe (at least
the part that we can observe and talk about) to be representable as a
particular kind of topological space that is dual to a Boolean algebra;
therefore it must be computable in some sense.
There has to be something that cannot be changed merely by changing
one's point of view.
So long as you think other 1p viewpoints exist then intersubjective
agreement defines the 'real' 3p world.
My thinking is that it exists as a necessary possibility in some a
priori sense and it actually existing in a 'real 3p' sense are not the
same thing. Is this a problem? The latter implies that it is accessible
in some way. The former, well, there is some debate...
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.
So the universe solves that problem. So what? We knew it was a
soluble problem. Knowing it was NP-hard didn't make it insoluble.
I am assuming computability and thus solubility. The point is the
question of available resources, this is where the Kolmogorov stuff
comes in... My thesis is that if resources are not available for a given
computation then it cannot be run, not complicated...
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?
They refer to something abstract (e.g. number of nodes in a graph),
but they may have application by giving them a concrete interpretation
- just like any mathematics.
What difference does what they refer to matter? Eventually there
has to be some physical process or we would be incapable of even
thinking about them! The resources to perform the computation are either
available or they are not. Seriously, why are you over complicating the
idea?
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.
snip.
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.
That problem assumes GR. But thanks to QM the future is not computed
just from the past, i.e. the past does not have to have enough
information to determine the future. So the idea that computing the
next foliation in GR is 'too hard' may be an artifact of ignoring QM.
If the universe is QM then it can be considered as a quantum
computer and its resource requirements are different from those of a
classical machine. I think... I'm trying to get this right...
Also it's not clear what resources the universe has available with
which to compute.
I am trying to figure the answer to that question.
If you consider every Planck volume as capable of encoding a bit,
and observe the holographic bound on the information to be computed I
think there's more than enough.
Yes, that is my hypothesis. The point is that the number of Planck
voxels in our observable universe is a large but finite number. It is
not infinite. This tells us that there is something strange about the
Platonic idea of computation, as it assumes the availability infinite
resources for a Universal Turing Machine in its complete neglect of the
question of resources. One way to escape this is to allow for the
universe to actually be infinite or that there actually exist an
infinite number of finite physical universes.
--
Onward!
Stephen
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