[From Bill Powers (931222.1125 MST)]
Bill Silvert (931222.1311 AST) --
In your field, ecosystems, control theory would come into the
picture only for analyzing the behavior of individual
organisms.
A bit puzzling, since organisms often function cooperatively.
I spent many productive years applying control theory to
populations, only now to discover I was doing the impossible!
No, just an application that violates my generalization. How dare
you.
If you have two identical control systems working in parallel to
accomplish control of the same variable with the same reference
level, then you can do a control-system analysis of the
combination. Non-control-theoretic analysis comes into the
picture when the two systems are not identical, when they are not
controlling exactly the same variable, and when the reference
signals differ. As the differences increase, you begin to get
interactions (such as conflict) that can't be seen as control
relationships, but have a different meaning. If you have a good
description of each system separately, as control systems, those
descriptions then become part of a larger system in which the
interactions are not those that hold inside one control system.
For example, if one system is organized to emphasize control of
cumulative error, and the other is organized to emphasize control
of rate of change of error, each system by itself may be quite
stable, but if you put the two systems together in a cooperative
task, the pair of systems may be unstable, going into spontaneous
oscillations. So the system consisting of two interacting control
systems has properties that are not properties of either
individual control system, or of any control system. I observed
this sort of instability in a two-person tracking task with a
married couple, about 20 years ago. They got divorced a year
later, although considering the divorce rate that probably
doesn't prove anything.
As to your applications to populations, I can't comment sensibly
without seeing the work. Got any relevant reprints or preprints?
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Martin Taylor (931222.1100)--
One class of stable control systems conforms to this
description, but only in the sense that its behavior would be
a particular subset of all the behaviors that fit the
description.
I'm not sure what you intend to imply by "only in the sense
that ..."
I meant only in the sense that one can say that planetary orbits
are conic sections, but not all conic sections are planetary
orbits. Among all the orbits in phase-space that one can imagine,
only a small subset would describe the behavior of a stable
control system.
However, what you say is true: "there are non-control
systems that look the same". One can always hand-propel (i.e.,
control by use of arbitrary forces) a system through behaviors
that match any given trajectory, making it appear to have certain
dynamical characteristics that it doesn't actually have. This is
the problem I raised with respect to limit cycles.
Your generalized knobby phase space doesn't apply to the question
of limit cycles (closed or almost-closed orbits), does it?
The "irreducible system noise" is the limited information-
gathering rate of the perceptual system of the control system.
I was thinking more in terms of thermal-like noise, present even
when there is no input.
OK on the rest. I'm glad I understood, or that you understood me
to have understood, or whatever.
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Chuck Tucker (931223) (Have you been past the International Date
Line recently?)
I think that generalizations like
Scientific facts and theories do <<not>> describe reality.
.. are more provocative than informative. Scientific facts and
theories certainly describe _observations_. There is considerable
evidence that we can affect the observations by our actions, and
that between action and observation there is SOMETHING that works
in a regular way. Sometimes, too, our observations suddenly
depart from their usual pattern, even though we have not acted;
there certainly seems to be SOMETHING capable of acting on our
observations aside from ourselves.
We cast our scientific theories, like control theory, in a form
that proposes what some details of the external something might
be, that would account for what we observe. Rather more often
than one would rationally predict, advances in techniques permit
us to discover ways of generating observations that correspond to
details of these models (as we can now visualize the spiral
structure of DNA in modern microscopes). This creates a distinct
impression that our guesses about the SOMETHING were pretty good.
Of course we have no way to check on that impression except
through observation. On the other hand, if I hear your voice
coming from the next room, it is not an unreasonable guess to say
that you are at least in the house (although I could be hearing
your voice from a tape recorder, a possibility I can check by
looking).
What I find off-putting about these generalizations is that they
come out like saying "Science is just a big waste of time; it
doesn't tell us anything real, and it's all just a big illusion.
The only thing it's good for is solving the problems I happen to
be interested in solving, and if it's not good for that it's not
good for anything."
Maybe that sour judgment isn't quite what you intended to convey,
but that's what came out of my receiver.
Anyway, Happy Christmas and New Year, Scrooge.
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And the same to everyone to whom it matters.
Bill P.