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From: kp@uts.amdahl.com (Ken Presting)
Newsgroups: comp.ai,sci.physics
Subject: Re: Quasicrystals and hidden variables (Chaos and AI)
Summary: Penrose cites Deutch
Keywords: finite discrete systems, periodicity, quasicrystals, QM
Message-ID: <965p02gf9cNw01@amdahl.uts.amdahl.com>
Date: 13 Apr 90 18:53:18 GMT
References: <6925@cps3xx.UUCP> <3142@usceast.UUCP> <54tJ025u963u01@amdahl.uts.amdahl.com> <3161@usceast.UUCP> <39oH02W8981q01@amdahl.uts.amdahl.com> <5328@ucrmath.UCR.EDU>
Reply-To: kp@amdahl.uts.amdahl.com (Ken Presting)
Organization: Amdahl Corporation, Sunnyvale CA
Lines: 63

In article <5328@ucrmath.UCR.EDU> baez@x.UUCP (john baez) writes:
>In article <39oH02W8981q01@amdahl.uts.amdahl.com> kp@amdahl.uts.amdahl.com (Ken Presting) writes:
>
>I haven't managed to get ahold of it - does Penrose's
>book really suggest that the growth of quasicrystals,
>which seems to require "forethought" or nonlocal correlations
>to make the quasicrystal come out exactly right, indicates
>that there are nonlocal hidden variables, or that 
>quantum computers can exceed the powers of Turing machines?

(Penrose' book, _The Emperor's New Mind_, is terrific.  I recommend it
highly for anyone interested in computation, physics, or AI, especially
for anyone who has formal training in one or two of those subjects, and
is curious about applications to the others)

Penrose does not say much about the growth of quasicrystals.  He does
pay some attention to the problem of deciding whether a given set of
tiles will non-periodically cover the plane.  I have seen (but not read)
a book called _The Mathematics of Quasicrystals_, so there may be some
serious attention being paid to the issues.

Penrose does cite David Deutch, "Quantum thoery, the Church-Turing
pinciple, and the universal quantum computer", Proc. Roy. Soc. (1985)
A400, 97-117.  Apparently, a quantum device can exhibit some of the
*speed* properties of a non-deterministic TM.  As far as I know, there
is no (well-founded) suggestion that non-recursive functions can be
computed by these devices.

>
>What does he say about this?  I've heard rumors... in 
>my opinion, the obvious way out would be that real-world
>quasicrystals are not perfect but have defects when they
>get "stuck" in "solving the jigsaw puzzle".  

That is probably the most reasonable position to take at the moment.  The
Sci. Am. note, "Quasicrystal Clear" (Jan 1990) supports it.

It reports the hypothesis that quasicrystal growth is guided by entropic
phenomena (the hypothesis is not explained in detail).  This does not
sound like a good idea to me.  Thermodynamic variables are defined non-
locally themselves.  Furthermore, a thermodynamic explanation of a
phenomenon ought to have an underlying mechanical explanation.

Whether Brownian motion will do the job depends on the strength of the
evidence for perfect tiling in quasicrystal structure.

>
>As for quantum mechanics and chaos, it's worth remarking that
>quantum systems in a *bounded* region of space almost
>always (i.e. except for cooked-up pathological mathematical
>examples) have discrete spectrum hence evolve almost 
>periodically.  This is the famous "absence of quantum chaos."

This is very interesting.  Discreteness in the spectrum of energy states
is not by itself sufficient - there is no problem in having a denumerable
infinity of discrete states within a finite interval.

If a real system can depend in a macroscopically observable way on
how close it gets to (eg) an ionization energy, then chaotic behavior
might be observable in QM.  How are the mathematical examples constructed?


Ken Presting  ("Clap your hands if you believe in hidden variables")