[Martin Taylor 2004.03.26.1017]
[From Bill Powers (2004.03.26.0609 MST)]
Peter Small (2004.03.26) --
Bill has said quite a lot of what I had intended to say in response
to Peter, so I will deal with other matters.
Before you characterize
PCT, I think it would be a good idea to understand it. So far you haven't
shown very strong indications of that.
It may be helpful to relate my own experience. I once considered
doing graduate work in control theory, but instead moved into
psychology, particularly perception, by way of Operations Research.
During my official working life I alternated between computer
development and psychology research, and in the 80's and 90's
developed a "Layered Protocol" theory of interpersonal and
person-to-computer communication. Before that, I had co-authored a
book chapter on haptic touch, which argued that the perceptions
available through touch were in large part determined by a mult-level
feedback process. In the early 90's I was pointed toward PCT by a
person who read my postings on the system dynamics mailing list. It
took a year or two, but eventually I realized that my LP Theory was
just a special case of PCT.
Now, despite that background, which should have made me an ideal
candidate for quickly understanding PCT, it took at least a year,
maybe longer, of getting into arguments on the predecessor of CSGnet
(mostly with Rick), before I really began to understand PCT to the
extent where I felt I could make a substantive contribution.
The point I'm trying to get across is that it isn't really a very
good idea to criticise PCT on short acquaintance, unles that
criticism is done for the purpose of discovering in what ways one's
understanding of "conventional" PCT differs from how it is normally
understood.
Enhancements and illumination of PCT from other disciplines are
always to be welcomed. PCT is a _functional_ description of what may
be happening when people perceive and act. If PCT is basically
correct (and I think elementary physics says it must be), then it
will have experiential consequences that are worthy of study. And it
must have physical/physiological mechanisms that support it, and that
might help to argue for one or other particular implementation of the
basic idea of PCT--that behaviour is the control of perception, where
"perception" is taken to mean the state of some variable inside the
organism, and "control" means maintaining the state of that variable
near some reference value in the face of influences external to the
organism that might otherwise change it.
If you have noticed these phenomena you will see why PCT is constructed as
it is, and you will understand what PCT is about. I don't know what the
"chaotic oscillators" model is about -- there don't seem to be any
phenomena that relate to it at an observable level (without the aid of a
lot of imagination).
Here, I'm on Peter's side. I do (I think) understand what he is
talking about, though he uses a bit of shorthand. Here's a slightly
more longhand version.
In reasonably simple terms, whenever you have a feedback
process--meaning a situation in which a change in a variable in some
way influences the state of that variable at a later time--you have a
"dynamic". "Dynamic" is just a fancy term for describing all the
different ways that system might behave, given any prescribed
starting state.
If you look at a system with a dynamic, and find it in a particular
starting state, you can trace its future evolution in the absence of
external influences. That state evolution is called an "orbit."
Orbits can behave in one of three ways: (1) An orbit might spiral in
toward some fixed point, (2) it might spiral toward some path that
repeats endlessly, or (3) it might follow some more complex path in
which very slight differences in the starting conditions eventually
result in very different traces for the orbit.
The three possibilities for the eventual destination of an orbit are
called "attractors". They are called: (1) fixed point, (2)
oscillator, and (3) strange. When Peter talks about "Chaotic
oscillators" he is talking about a particular kind of "strange
attractor", which has the property that for a long time, if you look
at the system state, its orbit looks quite like that of a simple
oscillator, but at some unpredictable moment it takes off in some
other direction, quite probably coming to look again as if it is a
simple oscillator, but a different one.
All of this may seem very abstract, but I think it is essential for
any serious analysis of PCT, because PCT is essentially based around
the idea of feedback, and feedback systems with nonlinearities that
are greater than a square law, or that are transcendental, are very
likely to have attractors that are "strange" for lare ranges of
values of their internal parameter settings.
The "classic" HPCT hierarchy is as liable to exhibiting strange
attractors as is any other complex feedback structure. The different
stages in the development of complex perceptions are necessarily
non-linear, not only because of the impossibility of creating
physical devices with infinite range, but also because there would be
no value of having more than one level if the perceptual functions
were linear. However, HPCT simulations always are done with parameter
settings that result in fixed point attractors. Set the parameters a
bit wrong, and the hierarchy goes wild.
The fact that the system dynamic is parameterized to give fixed point
attractors is what allows (in fact almost defines) control. What I
mean is that an influence from outside will move the system state to
a new place in the dynamic, and if the dynamic has a fixed point
attractor, the orbit will lead the system state back to that
attractor--unless the disturbance was sufficient to move the system
state into a completely different attractor basin. The new basin
might even have an oscillator as an attractor rather than a fixed
point.
But the ability to control is not limited to dunamics with fixed
point attractors. Oscillators also can be controlled. A disturbance
simply moves the system state to a new point on the dynamic, and its
orbit returns the system back to its original oscillator attractor.
Here we are dealing with what in HPCT is a higher-level control
system, one in which time matters.
When the attractor is "strange", however, things are a little
different. Control is still possible, if the strange attractor has a
quasi-oscillatory form, since orbits do then converge in at least
some regions of the attractor basin. But control is not guaranteed in
the presence of arbitrary disturbances, because the new system state
may be at a point on the dynamic at which the orbit leads directly to
a new quasi-oscillator part of the strange attractor. Might this
sound like reorganization? Might it relate to the shifting ways in
which ambiguous perceptions or perceptions of over-stabilized inputs
are resolved?
I'm not going to pursue this further, here, but non-linear dynamics
does seem to me to offer a fruitful way to view PCT. However fruitful
or fruitless that view may turn out to be, it is certainly not wrong.
Moreover, I think that the chaotic (strange attractor) possibilities
afforded by the interactions of control systems are a very plausible
way of generating not only new perceptions, but new kinds of
perceptions. Parameter refinement, or the introduction of prescribed
disturbances, can shift quasi-oscillator strange attractors into
acting like true oscillators, while allowing the possibilities of
rapid change (of, for example perception) when the occasion arises.
Bottom line: I think both Peter and Bill are right, and I think they
are both wrong, in different ways.
Martin