Chaos & Determinism

[from Gary Cziko 920521.1615]

Bill Powers (920521.0800) writes:

I think we can now distinguish between closed-loop determinism and open-
loop determinism.

Open-loop determinism is the kind physicists think about. Open-loop
determinism can't be demonstrated without introducing multiple chains of
integrations that have to remain accurate for long periods of time, and in
which the system may encounter chaos-type bifurcations.

Closed-loop determinism is forgiving of changes in initial conditions and
in at least some parameters. It can work in the presence of Chaos. . . .

I find this distinction very helpful. But aren't there open-loop
deterministic systems that are able to fend off chaos, at least to some
degree? I'm thinking of things like planetary motion. I understand that
to some extent there are chaotic things happening there, but nonetheless
the planets stay in their "intended" orbits. How are these open-loop
systems able to maintain this consistence of behavior? I realize, of
course, that if the planets DIDN'T have just the right position and
velocity and direction they wouldn't be there for us to marvel about (and
we wouldn't be here on earth marvelling). But given that they are there,
how do they manage to hang in there for so long in spite of the
unpredictable buffeting they encounter from the passage of neighboring
planets, comets, solar wind, etc. Is it just simply that the disturbances
are not great enough, like wind on a heavy pendulum which may move
chaotically to some degree but on the average contiues to point downward?

We can
predict that a normal driver can keep the car within 2 feet of the intended
path and 2 degrees of the intended direction, and that the errors at the
end of the trip will be comparable to those at the beginning (that is, if
the position is in error by two feet and the direction by two degrees one
minute after a trip starts, an hour later the position will still be in
error by no more than about two feet and the direction by no more than
about two degrees). The systems that determine future conditions the most
reliably are closed-loop deterministic systems, systems containing purposes
and the means of implementing them.

This may impress the car driver, but may have less impact on the railroad
engineer. He can bail out of a moving train and the train will no be more
than a couple inches (if that much) in error after many hours.

Illinois has been warm and sunny. When are you and Mary moving back here?

--Gary

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Gary A. Cziko Telephone: (217) 333-4382
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