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In article <2953@dciem.dciem.dnd.ca> mmt@dretor.dciem.dnd.ca (Martin Taylor) writes:
>>virtually all chaotic dynamical systems have the characteristic of a
>>computational horizon beyond which any particular computer cannot keep
>>up with the physical system in doing the simulation.
>
>The problem is not whether a process is computable, or if computable is
>chaotic, but that there is no way that the *actual* behaviour of any
>small part of the universe can be described by deterministic laws, even
>though the entire universe may be.  For the behaviour of a part of the
>universe to be detemined, that part would have to be isolated from the
>rest of the universe, and thus be unobservable.

Pardon my philosophisms, but unobserved does not imply undetermined.
Sure, we couldn't tell what was happening between observations, but what
that shows is that we don't know whether our descriptions are true.  It
does not show that the descriptions are false.  Of course, the usual
strategy is to take some system which can be reset to some more-or-less
known state (say, a ball at the top of a ramp), let it run for a while,
and observe it at the end.  If the outcome is reproducible, then the
system is deterministic.  Pace Hume, this is a pretty reliable form of
argument.

>                                                 If it were not isolated,
>the part whose behaviour is supposedly described would be affected by
>"surprising" events (events from other parts of the universe not subsumed
>in the description of the boundary conditions and/or descriptive laws.

But part of setting up a measurement is controlling as many outside
influences as possible, so that the act of measurement is the only
perturbation.  What makes measurements different from other other
perturbations is that there is a theoretical account of how the
measuring device interacts with the system to be measured.  For
example, a galvanometer in a circuit changes the resistance and
inductance of the circuit, but the theory of electromagnetism has
very specific predictions about the magnitude of those changes.
And of course the theory also explains the degree of deflection of
the needle.

It is very simplistic to simply read a meter and suppose that the
reading describes the state of the system.  For convenience in the
lab, measuring devices are designed to perturb as little as possible.
But the most sensitive measurements must take the perturbations into
account, and correct for them, using a theoretical analysis (and
experience with the devices, of course).

>Often, these outside influences do not matter, because the observed system
>is in a dynamic state near an attractor, or some similar insensitive
>condition.

If we consider the system under observation to include the perturbations
of the measuring device, as in the case of a circuit with a galvanometer,
then we can let photons fall on the meter (violating the controlled
interaction objective), for exactly the rason you state.  The meter
is highly insensitive to photon impact.

I always thought that the whole point of designing measuring devices
was to achieve this effect - known perturbation on the measured system,
coupled to a macroscopically observable indicator.  This applies to
every measurement from Litmus paper to bubble chambers.

>            But it might be near a repellor across which the unexpected
>event pushes it, into a quite different basin of attraction.

This is of course what digital hardware designers try to avoid.

>                                                              I don't
>think it much matters about the system being chaotic, provided that the
>chaos is expressed in the form of a strange attractor, because it is
>likely that most of th trajectories in the attractor have behaviourally
>similar consequences.

If you could elaborate on "strange attractors", I would appreciate it.
This is outside my (very limited) familiarity with chaos theory.

>What this points out is that there is *NO* physical system that can
>be guaranteed to compute according to any algorithm.

I suppose you mean that unless the outside influences are restricted,
any system can be pushed out of any attractor basin (eg by holding an
RF radiator near the bus traces on a CPU board).  But it's not that
big a deal to isolate a system for practical purposes.  After all,
computers do work pretty well.

>                                                      If the algorithmic
>nature of computation is what causes Penrose to require new physics,
>he need not bother.  All he needs is to note that brains and computers
>are sub-parts of the universe, and therefor are non-deterministic.

For the reasons above, I don't think this follows.  I'm not sure whether
you're making a metaphysical, epistemological, or practical argument.
You seem to me to have a very intriguing idea, which is why I tried to
make my objections very explicit.  I may well be missing something.

>-- 
>Martin Taylor (mmt@zorac.dciem.dnd.ca ...!uunet!dciem!mmt) (416) 635-2048
>"Viola, the man in the room
>doesn't UNDERSTAND Chinese. Q.E.D."  (R. Kohout)

(Love the .sig :-)