Arcane details

[Martin Taylor 980307 16:45]

Recent comments about the amount of CSGnet space wasted on arcane details
of PCT set me to thinking--in fact, going up a level.

Why am I, personally, wasting so much time trying to be accurate and
resisting disturbances to perceptions related to the accuracy of
statements about control?

I think it comes from having realized some years ago (after joining CSGnet)
that I had made a big mistake about 20 years earlier. At that time, I
had developed and published a hierarchic control model to explain the
different kinds of experience we have when touching or feeling objects.
And obviously, around that time I had read Bill Powers paper in Science,
because years later (after joining CSGnet) I came across the copy I had
torn out to keep as a permanent reference. (As I write this, I don't
remember the publication date of either paper, but I think it must have
been around 1970, because it was in the late 60s that I was working on

Now, I _saw_ Bill's paper, I read it, and obviously I thought it important
enough to keep. I had been developing a hierarchic control approach to
one aspect of perception. I had had undergraduate training as an
engineer, and nearly specialized in control theory for graduate work.
Why did I not realize the implications of what Bill wrote? If any
psychologist should have been in a good position to understand what
he was saying, I should have been. But I didn't. (So I empathize with
all those "conventional psychologists" who "just don't get it." If I
didn't, with that background, how could I expect them to get it?).

It took another 20 years, and a quite independent encounter with Bill
through being pointed at CSGnet (because "it might interest you") for
me to realize what PCT was all about, and how all-encompassing it is. I
consider those 20 years wasted, when I could have been investigating the
implications of the simple statement: "All behaviour is the control of

Now, better late than never, I want to investigate the implications of
the basic statement. As a one-time student of control, I tend to take an
engineering viewpoint. From that viewpoint, I know how critical some
points are in the behaviour of a control system--whether it is in a human
or in a set of simultaneous equations. I also know that some things are
not critical, but often it is hard to see what those things are.

To analyze a single elementary control system, with lags and so forth, is
easy if the functions are linear. You just write down the Laplace transforms
and multiply them around the loop, and then rearrange until you find
the variable that interests you in terms of other variables. But when
the functions are non-linear, you can't do that. Sometimes you can't do
it even as an approximation. Then you have problems.

One of the ways you deal with problems of this kind is to look for
boundary statements, statements that limit what must be true of all systems
of the kind you are discussing. When you can't analyze exactly the effects
of one variable on another, sometimes you can determine the maximum or
minimum possible effect. That is what I tried to do, starting around 1991
(at least before March 1992, which is when I started archiving messages)
with the information-theoretic approach. Bill P is quite correct in saying
that I did not succeed in doing the analysis fully, but the attempt was
to be able to say things that are _at least_ true of all control systems,
linear or nonlinear, with single-valued or multiple-valued functions,
provided that they operate as perceptual control systems acting on a
continuously (or sporadically) observed environment.

The current set of technical hassles comes from the same source, I think.
If one is to say anything sensible about the interactions of many control
systems, one has to be clear about the behaviour, or at least the
characteristics of the behaviour, of individual control systems. One
must know what kinds of variation lead a control system to be susceptible
to oscillation, for example. If part of the control system's output
disturbs another control system, whose output (delayed) disturbs the
first, under what conditions will the loop(s) oscillate, and under
what conditions can one treat them as effectively independent? That is
the kind of question that leads to statements about robust and unstable
structures of many control systems.

I think that what one control system does is interesting. Some behaviours
of even the most elementary control loop are not obvious at first glance,
and many people (including, I'm sure, myself) make misleading statements
about them from time to time. The mathematics is non-trivial except when
the whole loop is linear. Simulations can help, but there are distinct
problems (not always avoided) about discrete-time simulations of
systems that vary continuously in continuous time.

What I am interested in primarily is the extended implications of assuming
that PCT is absolutely correct. (Parenthetic note: This is not the same
as assuming Bill Powers is absolutely correct about PCT, even if he
did invent/discover it). I can do this only by taking the engineering
view to see what can happen or what must happen (two limiting kinds of
statement) in certain configurations or with certain parameter values.
Under what conditions, if any, do qualitatively different phenomena
show up? What are they?

To follow this interest requires a certain precision, which often shows
up on CSGnet as, shall we say, tedious scholasticism, talking about
arcane points of no general interest. Some of these points, however,
are bifurcations. If they are not understood, they imply behaviours
quite different from what actually will happen. That's OK in fiction,
but not in what I believe to be a fundamental science of behaviour.