On 09 Oct 2014, at 21:03, John Clark wrote:
On Thu, Oct 9, 2014 , Bruno Marchal <[email protected]> wrote:
>> If nature can do it then there is no reason humans can't harness
nature to do it for us, but there is ZERO evidence that nature can
solve NP complete problems (much less non computable problems!) in
polynomial time.
> I agree for the NP complete. But quantum computation suggest some
NP hard, but not complete
For once we agree, although nobody can yet prove it most think there
is a class of problems that is harder than the polynomial time
problems that existing conventional computers can solve efficiently
but not as hard as NP complete problems, and this is the class of
problems that Quantum Computers would be good at; factoring large
number is probably of this class and so is calculating what a
particle will do quantum mechanically.
>>> The point, I thought, was theoretical at the start.
>> You theory predicted that soap films could solve NP-complete
problems.
> I never said that. I read that mathematicians have proved this for
some NP hard (not NP complete) problem.
Mathematicians have proven that soap films can solve a NP complete
problem, but when the experiment is actually performed it is found
that soap films can NOT solve that NP complete problem.
That conforms to the theory according to which in theory practice
obeys to the theory, but in practice it does not :)
Of course one of the implicit assumptions those mathematicians made
was that real numbers were, well... real. I'll let you draw a
conclusion from that.
I would need to (re)study that paper to be sure. I don't think they
made the mistake of using explicit decimal of non computable real, in
which case even a ruler do non computable things, if the classical
theory of ruler is taken seriously.
I think we agree that beyond the apparent collapse (explainable with
the quantum FPI in Everett) nothing seems non computable in nature.
Nor do anyone known how to realizer a system with physical equations
having non computable solutions. Obviously it is easy to build an ad
hoc non computable solution to the SWE, like Ae^iH, with H an
hamiltonian depending ona non computable numbers. If that exists in
Nature, we could not recognize it as such, unless it is an easy non
computable numbers capable of being computed in the limit. Note that
evolution does that in some sense. We know that the program "dinosaur"
terminated (in our local branch), we don't know that for bees, but we
may know it (hopefully not).
OK.
Now, once we agree that 2+2=4 is true independently of us, we must
agree that all programs executions are emulated, in the Turing
mathematical sense independently of us.
Then, as you said yourself, your consciousness is not localized, and
in this case the continuation possible are determined by the
distribution of the relevant relative states in arithmetic.
Why does it seems that above our substitution level we sum the
probabilities, and below we sum amplitudes of probability? It
eliminates the white rabbits indeed, by randomization of the phases
(as Feynman showed), but we have to extracts this from the internal
views of the self-aware (Löbian) observers.
That must be true too, independently of us. Then the translation in
arithmetic explains the role and presence of a sort of solispist/
intuitonist knower, with no name, not being a machine from his points
of view, and it explains the shadow of the necessary orthogonality
relations, on the possible sigma_1 sentences. That it leads to the
correct phase randomization is just an open (and of course not easy)
problem.
>> A good experiment ALWAYS outranks theory, any theory.
> Not always.
ALWAYS.
PLEASE TALK LOUDER, I HAVE A BANANA IN THE EAR.
I guess you meant by "theory" a physical, or philosophical, or
theological, theory. Then OK.
But I can argue that some theory cannot be outranked by an experiment.
Two possible examples: the theory that I (you) are conscious here and
now (may be hallucinated, just conscious). The other example:
elementary arithmetic. It has not changed since the Babylonians, I
think, more than eight millennia ago.
The theory, that is the idea we suggest we can agree on is:
0 ≠ s(x)
s(x) = s(y) -> x = y
x+0 = x
x+s(y) = s(x+y)
x*0=0
x*s(y)=(x*y)+x
I am sure you agree that this cannot be experimentally falsified. Of
course we can find many case in which it might be misapplied, like the
with the bottle having some hole.
> QM remains undefeated,
It remains undefeated because up to now every exparament ever
performed conforms beautifully with what Quantum Mechanics predicted
would happen however strange that outcome may seem to us.
The quantum principle, using probabilities defined by the Pythagorean
theorem, the cosinus, instead of volumes, seems to me a very solid
principle.
We might hesitate still about the right hamiltonian though.
But with comp, we inherit the problem of justifying it from inside
arithmetic.
On the day that a exparament does not come out as predicted by
Quantum Mechanics is the day
Quantum Mechanics dies, but I wouldn't hold my breath.
Yes. Just replace the derivative in the SWE (i*h_bar dpsi/ dt = Hpsi)
by the fractional derivative d^r psi/dt^r, with r a correction to make
away the Mysterious Matter, they need it apparently to explain the
early 10^-23 second of the Big Bang. r is Ring constant, very close to
one. Ring is a chinese mathematician who got a prize in 2725).
This would delinearize enough to make the parallel universe visitable,
but it will take more than ten millennia to get the technology. This
violates also the cherished principles of thermodynamic, but they can
survive, just a bit q-deformed.
I am dreaming aloud. QM false?
It is of course also an open problem in arithmetic, in the
computationalist setting. We can compare the logic of the observable
defined in arithmetic with the logic of the observable of what we
infer from number measurements.
It is the question of the linearity of the bottom "reality". It is
where the nothingness get populated with infinite energies and the
like. It is where the white rabbits can take refuge. Sometimes we have
to renormalize so that the white rabbit can get a job. It is in the eye.
Bruno
John K Clark
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