**Stephen P. King** (*stephenk1@home.com*)

*Fri, 23 Jul 1999 12:12:15 -0400*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Stephen P. King: "[time 473] Re: [time 469] Re: [time 464] Parallel transport, etc....Part 1"**Previous message:**Matti Pitkanen: "[time 471] Noncomputability"

Dear Matti,

I am working on my responce to [time 469], my computer lockedup and I

have had to start over...

Matti Pitkanen wrote:

*>
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*> Part of Roger Penrose's hypothesis regarding the form
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*> of a final theory is that its dynamics should be
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*> noncomputable. Recall that this simply means that no
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*> Turing machine could reproduce this dynamics in the
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*> output of a calculation. Mathematics already offers
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*> examples of noncomputable sequences whose first few
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*> elements we know, but only because we have hit upon
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*> methods that suffice to identify those particular
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*> elements.
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*>
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*> [MP] I read Shadows of the Mind and Penrose's comments
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*> on it on some homepage. He left open whether
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*> quantum theory os genuinely non-deterministic or
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*> whether noncomputality gives rise to effective nondeterminism.
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*>
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*> I think the basic problem is that
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*> quantum nondeterminism is *not* random! On the
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*> contrary: in quantum jump only states belonging to discrete
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*> set of states are possible. It is extremely difficult to
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*> see how this kind of non-randomness could result from
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*> deterministic but non-calculable dynamics.
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*> In addition one should understand the reduction
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*> probabilities. And the prize for all these feats
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*> would be mystery: we we experience of having free will
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*> despite that free will is not actual!
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*> ***********
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*>
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*> When looking for noncomputability in physics, Penrose
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*> suggests that quantum gravity with topology change
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*> might be noncomputable, since four-manifolds are
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*> not classifiable, and four-manifolds would interpolate
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*> between the spacelike hypersurfaces at either end
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*> of a sum over histories. This would give us
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*> noncomputable amplitudes, and so noncomputable
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*> transition probabilities.
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*>
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*> [MP]
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*> I have seen this kind of argument somewhere.
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*> One could however consider quite well the possibility
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*> that amplitude is calculable after all. Calculation
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*> need not be done by numerical computing by taking
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*> actually the sum over all histories.
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*>
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*> On basis of frustrating personal experiences I do not
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*> believe on the summation over histories:
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*> a purely formal generalization of
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*> Feynmanns sum over histories approach is in question. There
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*> is not guarantee that resulting amplitudes are unitary.
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*> I spend more than seven years trying to make some sense
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*> about summation over spacetime surface idea until I realized
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*> that configuration space geometry is the only possibility
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*> to achieve manifestly unitary theory.
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*> **************
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*>
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*> This might be suitable for a noncomputable stochastic
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*> theory, but I wonder if we could go further and have
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*> a deterministic noncomputable theory. In this regard
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*> I find Chaitin's number interesting. Chaitin's number
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*> is the halting probability for a Turing machine,
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*> given certain weightings on initial conditions.
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*> Not only is Chaitin's number noncomputable, it is a
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*> random real, which means that it is statistically
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*> indistinguishable from a random series.
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*>
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*> Could the apparent randomness of quantum behavior,
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*> rather than resulting from real (albeit structured)
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*> randomness, be the result of a pseudorandom,
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*> deterministic noncomputable dynamic?
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*>
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*> Best,
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*> MP
*

Umm, I think that Peter's idea that the appearence of randomness is due

to "secondary observer interactions" is the best quess so far! In other

words, yes!, I agree with you! ;-) But "non-computable", to me, means

"not computable by a Turing Machine" It is "computable" by an

Interaction Machine, as Peter defines it!

Later,

Stephen

**Next message:**Stephen P. King: "[time 473] Re: [time 469] Re: [time 464] Parallel transport, etc....Part 1"**Previous message:**Matti Pitkanen: "[time 471] Noncomputability"

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