more Wolfram thoughts
Rajarshi Ray
I'm a little puzzled by this piece (Wolfram, Cellular Automata, 1983):
"While mathematical systems with computational power beyond that of
universal computers may be imagined, it seems likely that no such
systems could be built with physical components. This conjecture could
in principle be proved by showing that all physical systems could be
simulated by a universal computer. The main obstruction to such a proof
involves quantum mechanics."
How does quantum mechanics obstruct proving that any physical system may
be simulated by a universal computer? Can't you simulate QM systems on
computer? Well, maybe not in terms of computational complexity but
surely you can on disregarding such matters? After all, physicists did
hand calculations for QM long before computers were used.
TIA
-Rajarshi
--
"Intuition is not something that is given. I've trained my intuition
to accept as obvious shapes which were intially rejected as absurd,
and I find everyone else can do the same."
- Benoit Mandelbrot, on Fractals
Roland Franzius
Rajarshi Ray schrieb:
>
> Hi,
>
> I'm a little puzzled by this piece (Wolfram, Cellular Automata, 1983):
>
> "While mathematical systems with computational power beyond that of
> universal computers may be imagined, it seems likely that no such
> systems could be built with physical components. This conjecture could
> in principle be proved by showing that all physical systems could be
> simulated by a universal computer. The main obstruction to such a proof
> involves quantum mechanics."
>
> How does quantum mechanics obstruct proving that any physical system may
> be simulated by a universal computer? Can't you simulate QM systems on
> computer? Well, maybe not in terms of computational complexity but
> surely you can on disregarding such matters? After all, physicists did
> hand calculations for QM long before computers were used.
- Benoit Mandelbrot, on Fractals
Quantum mechanical systems can be computational simulated only with
respect to the time evolution of their statistical behaviour as parts of
a statistical ensemble of identical prepared undistinguishable systems.
To simulate a single quantum system say a hydrogen atom by a non quantum
computer contradicts the 0th axiom of quantum theory: There is now way
to get the systems information without disturbing it in such a way that
your knowlegde is useless for the exeact evolution in the future after
the measurement. If we neclect complexity questions (computer to large
to conserve its current state) standard computers are able to conserve
and multiply their internal state. So the real quantum game of chance is
absent.
--
Roland Franzius
+++ exactly <<n>> lines of this message have value <<FALSE>> +++
ROGER BAGULA
referring to. Some problems are theoretically undecidable, even if you can
write a program for them, the computer will never reach a halting point.
The example is:
The cat in a box paradox. Is the cat alive or dead?
Until you open the box and observe, there is no answer.
Just probability wave functions...
I once had a cat who lived
trapped in my garage for several weeks without food or water.
When I discovered her, she was almost dead. If I had known she was
there, I would have let her out.
She lived almost a year longer, after recovering.
Rajarshi Ray wrote:
> Hi,
>
> I'm a little puzzled by this piece (Wolfram, Cellular Automata, 1983):
>
> "While mathematical systems with computational power beyond that of
> universal computers may be imagined, it seems likely that no such
> systems could be built with physical components. This conjecture could
> in principle be proved by showing that all physical systems could be
> simulated by a universal computer. The main obstruction to such a proof
> involves quantum mechanics."
>
> How does quantum mechanics obstruct proving that any physical system may
> be simulated by a universal computer? Can't you simulate QM systems on
> computer? Well, maybe not in terms of computational complexity but
> surely you can on disregarding such matters? After all, physicists did
> hand calculations for QM long before computers were used.
>
> TIA
>
> -Rajarshi
>
> --
> "Intuition is not something that is given. I've trained my intuition
> to accept as obvious shapes which were intially rejected as absurd,
> and I find everyone else can do the same."
>
> - Benoit Mandelbrot, on Fractals
--
Respectfully,
Roger L. Bagula
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david_...@my-deja.com
tf...@earthlink.net wrote:
> The "Halting Problem" in complexity is probably what he was
> referring to. Some problems are theoretically undecidable, even if you
can
> write a program for them, the computer will never reach a halting
point.
> The example is:
> The cat in a box paradox. Is the cat alive or dead?
> Until you open the box and observe, there is no answer.
> Just probability wave functions...
The famous cat and related issues probably does have
something to do with the problem Isaac mentions below.
But this has nothing whatever to do with the halting
problem.
Really, they're totally different things. The halting
problem is the problem of writing a program to determine
whether an arbitrary other program will terminate. It's
impossible to write a computer program to determine this
in general, but nonetheless a given program either does
or does not halt - nothing spooky about it, we just
can't tell which. Otoh (at least according to standard
QM) the cat in that box is _neither_ alive nor dead.
Not just that we don't know which - neither one is true.
Sent via Deja.com http://www.deja.com/
Before you buy.
Clark
david_...@my-deja.com wrote:
>
> Really, they're totally different things. The halting
> problem is the problem of writing a program to determine
> whether an arbitrary other program will terminate. It's
> impossible to write a computer program to determine this
> in general, but nonetheless a given program either does
> or does not halt - nothing spooky about it, we just
> can't tell which. Otoh (at least according to standard
> QM) the cat in that box is _neither_ alive nor dead.
> Not just that we don't know which - neither one is true.
>
Yes, they're totally different things, although often confused. I'm
interested, though, in why you think that excluded middle (or bivalence,
whatever) applies to undecidable problems in maths, while not in
physics. Is it something to do with the difference between the
underlying (both non-standard) logics you need to adopt in each of the
cases?
Bob
Steven B. Harris
> Otoh (at least according to standard
>> QM) the cat in that box is _neither_ alive nor dead.
>> Not just that we don't know which - neither one is true.
I don't think "standard QM" has anything much say about this issue.
QM is empirical, and more than that is mostly add-on philosophical
window dressing which is a matter of taste and religion. The "kernal"
of QM is a set of equations which tell you the probabilities of what
you'll find WHEN you make a measurement. This stuff does NOT tell you
much about the possible kinds of physical "machinery" (i.e.
decoherance, pilot waves, particles sniffing out paths, baby universes
splitting, etc, etc) which determine those probabilities. The
"machinery" in QM is the math rules, and all we know about the physical
machinery behind the math, is that the physical interactions can't be
both deterministic and local. But this is not much of a constraint.
The math rules for physical interactions themselves do not address the
philosophical problem of what exists before you take the measurement,
or what continues to exist if you don't, except that we know that if
there is hidden machinery, it can't all be there in front of you, but
is distributed over space (non local-- outside your light cone), where
you can't get at it. But, OTOH< there might not be any such machinery
at all.
So-- the rules do NOT say the cat is alive or dead, or both, or
neither, before you look. It could be either way. The rules tell you
the probabilities for what you'll find when you open the box-- yes.
They ALSO tell you that IF what you find is determined before you look
(the cat IS really alive or dead) THEN whatever deterministic machinery
which decides that (decoheres the cat or puts you into a dead or live
cat universe) is part of larger bunch of stuff some of which is outside
your light cone. Forget about predicting it. BUT the same rules just
as well allow a random world in which the cat has no existence in any
way at all, before you look. So it could be either way. Pick whatever
makes you least nauseus. Deciding which way it "really" is, is
speculation, but it's not (at this point) science.
David C. Ullrich
>
>
>david_...@my-deja.com wrote:
>
>>
>> Really, they're totally different things. The halting
>> problem is the problem of writing a program to determine
>> whether an arbitrary other program will terminate. It's
>> impossible to write a computer program to determine this
>> in general, but nonetheless a given program either does
>> or does not halt - nothing spooky about it, we just
>> can't tell which. Otoh (at least according to standard
>> QM) the cat in that box is _neither_ alive nor dead.
>> Not just that we don't know which - neither one is true.
>>
>Yes, they're totally different things, although often confused. I'm
>interested, though, in why you think that excluded middle (or bivalence,
>whatever) applies to undecidable problems in maths, while not in
>physics. Is it something to do with the difference between the
>underlying (both non-standard) logics you need to adopt in each of the
>cases?
On the one hand I didn't say anything about excluded
middle applying to undecidable problems in general - I was
talking about something much more specific: A given computer
program either halts or it doesn't. I'd have a hard time explaining
why I think that, sorry. Seems clear.
Otoh I didn't say that the cat was neither alive
nor dead, I said that that was what QM said (and of
course it appears that perhaps I should have phrased
it a little differently). I'd have an even harder time
explaining why excluded middle does not apply here
than why I think it does apply above - this is because
I don't understand it any better than you do. I was
just quoting what I've been told (tried to make it
clear that's all I was doing). Sorry.
All I was really trying to say was that the
undecidability of the halting problem really has
nothing to do with the purported indeterminate
status of that cat - they're totally different sorts
of uncertainty.
>Bob
David C. Ullrich
wrote:
>In <396CBC04...@brutele.be> Clark <cl...@brutele.be> writes:
>
>> Otoh (at least according to standard
>>> QM) the cat in that box is _neither_ alive nor dead.
>>> Not just that we don't know which - neither one is true.
>
>
Well fine - I certainly didn't mean to imply anything that
contradicts the above, probably I should have said something
about one standard interpretation of QM.
All I was really trying to say was that whatever
mysteries are associated with the status of that cat have
no relation to the unsolvability of the halting problem.
Edward Green
>In <396CBC04...@brutele.be> Clark <cl...@brutele.be> writes:
>
>> Otoh (at least according to standard
>>> QM) the cat in that box is _neither_ alive nor dead.
>>> Not just that we don't know which - neither one is true.
>
>
> I don't think "standard QM" has anything much say about this issue.
>QM is empirical, and more than that is mostly add-on philosophical
>window dressing which is a matter of taste and religion. The "kernal"
>of QM is a set of equations which tell you the probabilities of what
>you'll find WHEN you make a measurement. This stuff does NOT tell you
>much about the possible kinds of physical "machinery" (i.e.
>decoherance, pilot waves, particles sniffing out paths, baby universes
>splitting, etc, etc) which determine those probabilities. The
>"machinery" in QM is the math rules,
Amen to that, brother. Well said...
>and all we know about the physical
>machinery behind the math, is that the physical interactions can't be
>both deterministic and local.
But I do not agree with that. If that is the right hand side of
the syllogism "Bell + experimental verification => ___" then I
think your conclusion is misleading unless we have some twisted
definitions of terms. The conclusion is "not local" for a
well defined sense of "local"; determinism or chance simply does
not enter into it except in the arena of historical confusion.
The machinery cannot be local in this given sense, whether or not
it is also "deterministic".
I don't know much, but I know a few simple things well, and that is
one of them.
>But this is not much of a constraint.
>The math rules for physical interactions themselves do not address the
>philosophical problem of what exists before you take the measurement,
>or what continues to exist if you don't, except that we know that if
>there is hidden machinery, it can't all be there in front of you, but
>is distributed over space (non local-- outside your light cone), where
>you can't get at it. But, OTOH< there might not be any such machinery
>at all.
>
> So-- the rules do NOT say the cat is alive or dead, or both, or
>neither, before you look. It could be either way. The rules tell you
>the probabilities for what you'll find when you open the box-- yes.
>They ALSO tell you that IF what you find is determined before you look
>(the cat IS really alive or dead) THEN whatever deterministic machinery
>which decides that (decoheres the cat or puts you into a dead or live
>cat universe) is part of larger bunch of stuff some of which is outside
>your light cone. Forget about predicting it. BUT the same rules just
>as well allow a random world in which the cat has no existence in any
>way at all, before you look. So it could be either way. Pick whatever
>makes you least nauseus. Deciding which way it "really" is, is
>speculation, but it's not (at this point) science.
I am almost swayed by your rhetoric, but not quite! You seem to imply
that a kind of pure randomness can rescue locality from Bell. It
cannot. I am aware there is also a school of thought that "quantum
locality" is rescued from Bell, but I think this is merely a
confusingly labeled version of "non-locality" by any other name;
a rose is a rose, and etc. The locality defeated by Bell is an
extremely abstract and puissant beast, merely a formalization of
the idea that "stuff nearby" may have an influence on local outcomes,
regardless of whether or not it has that old-time-religion
"deterministic" influence, and stuff over there may not... that
is, if stuff over there is beyond a radar range during a duration of
an outcome. Any other labeling or "new" sort of locality reminds
me of Animal Farm, and the pigs' "new" equality; if you catch my
drift.
But as any child knows, if we are not limited to stuff within
radar range of the events immediately preparatory to an outcome,
viz., if there is in fact a preferred rest frame in which we can
send superluminal signals to coordinate "non-local" events, then
we can forget all this angst about "non-locality", cry Bell as he
may. Things can thn be local in a sense your sainted grandma would
understand, just not Einstein local. (The only reason I threw
in "preferred rest frame" was that this allows us to practice this
kind of locality, in concept, consistent with no deviations yet
observed from Lorentz invariance, without playing any shell games
to avoid paradoxical causal loops. No, we can play up front an in
the open, and not worry about "Sure it communicated backwards in
time, but it couldn't send any useful information!!! Bwa, ha,
ha!!" Jeesh.)
Before you give this last a 5% Bayesian prior, you may recall that
many well trained people may have given a similar prior to parity
violation, before Chu's (?) experiment. I am not saying that
because parity was violated Lorentz invariance must be violated
also, or that I "believe" Lorentz invariance is violated, but I am
defending my judgment that it is reasonable to harbor some reasonable
non-zero prior that it _may_ be violated, and not dismiss it out
of hand as the ranting of a madman. After all, parity was a damn
fine symmetry also, almost "obvious" in its ubiquity, verifiable
AFAIK to many decimal places in many kinds of experiments -- except
some crucial kind of experiment. I give eventual violation of
Lorentz symmetry about a 50% prior.. if you care... a sophisticated
way I saying "I don't know".
I "believe", i.e. give a very high prior to, the universe has _some_
kind of underlying topology... well, obviously it does, the topology,
the neighborhoods, of space time. But if it also has another "deeper"
topology, where stuff can influence other stuff apparently completely
off in left field according to the manifest topology, I still very
much doubt the universe is topologically equivalent to a point; i.e.,
that all the stuff out there affects all the other stuff out there all
the time; that would be too stupid, and a hell of a way to run a
railroad. I would first assume, and look for, if Kant was right, and
the manifest metric of spacetime is somehow not fundamental, a deeper
fundamental metric and topology, rather than the idiot topology (is
that the correct technical term? :) where all events that ever are or
were, anywhere, are tripping over each other's feet.
This last rantlet is complementary to, not to be confused with, the
superluminal possibility.
Hokay? :-)
Ed