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From: baez@x.ucr.edu (john baez)
Newsgroups: comp.ai,sci.physics
Subject: Quasicrystals and hidden variables (Chaos and AI)
Keywords: finite discrete systems, periodicity, quasicrystals, QM
Message-ID: <5328@ucrmath.UCR.EDU>
Date: 8 Apr 90 06:04:46 GMT
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In article <39oH02W8981q01@amdahl.uts.amdahl.com> kp@amdahl.uts.amdahl.com (Ken Presting) writes:
>Any real quasicrystal must of
>course be finite, and except for growth, is a static structure.  But
>the existence of objects which can be non-periodic over arbitrary spatial
>scales suggests the possiblity of processes which are non-periodic over
>arbitrarily long intervals of time.  The growth of a quasicrystal itself
>might serve as an example, but it is not clear that quasicrystals can be
>grown to large sizes.  It is also non-standard(!) to suppose that atomic
>processes can be deterministic, but in the context of quasicrystals the
>non-local hidden variable theories are more appealing than usual.

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?

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".  

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."