Dynbamic system analysis; PCT and tetrahedrons

[From Bill Powers (931202.0750 MST)]

Oded Maler (931202) --

Dynamics is the mathematical theory of things that change with
time according to some laws. Control systems (with or without
their environment) *are* dynamical systems of certain sort.


I think a-priori that a PCTer might benefit from the study of
dynamical systems in the same sense that he will benefit from
studying arithmetic or linear algebra.

Right on, Oded. There are, however, some other considerations.

My impression is that many psychologists (and even some
mathematicians) who talk about "dynamic systems" think they are
talking about some new invention. They identify the whole field
of dynamic systems analysis with a certain type of dynamic
system, a certain kind of model, not realizing that the model
that has taken their fancy by no means exhausts the
possibilities. It's a form of synecdoche: referring to a whole in
terms of one of its parts.

A great many of the arguments that PCTers have had with
psychologists arise because certain psychologists who are just
beginning to learn how to do systems analysis don't understand
that they are re-inventing methods that have been taught as an
integral part of physics and engineering for a century or more.
In physical science and engineering these methods are simply
taken for granted as one tool used in analyzing physical systems.
For an old-timer who has been using these methods, in however
limited a way, since shortly after getting out of diapers,
learning about modern dynamic systems analysis is like being told
that one has been speaking prose all of one's life.

There are two aspects to system analysis. One is defining the
system: the dreaded "word problem." This requires having an
acquaintance with real physical systems, understanding how they
can be organized and how to break them down into parts suitable
for analysis. The other part is to represent variables and
relationships by mathematical forms, and solve the resulting
mathematical expressions. The first aspect requires what is known
as physical intuition -- the ability to visualize a system and
know what is likely to be involved in its operation,
qualitatively. This ability can be acquired only by playing
around with real systems, learning their properties and quirks
and getting a feel for how things actually work. The second
aspect requires mathematical training, the more the better. This,
unfortunately for me, requires not only the availability of good
mathematical training, but the capacity to absorb it, which is
not given to all of us in equal measure. I absorb mathematics a
little better than the average person does, but compared to what
others can do with mathematics, I am a Neanderthaler.

Good system analysis requires both aspects. Great mathematicians
often have lousy physical intuition. Great intuitionists often
detest and distrust mathematics. But most of us are neither kind
of greats, so our best bet is to find a balance within our

This leaves most psychologists in an uncomfortable position,
because electing to pursue psychology (and of course similar
fields) is, in our traditional educational system, also normally
an election NOT to enter either the grubby world of engineering
or the abstract world of mathematics. As a result, when
psychologists have tried to get into the field of system
analysis, they (naming no names) tend to do both parts of it
poorly. Their physical models are full of holes that are obvious
to anyone with physical intuition, and their mathematical
analyses are both error-prone and insufficiently connected to the
world of real things. They lack experience with system analysis,
and so commit elementary procedural errors like presenting the
same equation in two forms and thinking that they have a system
of equations (e.g., a certain paper on which I have commented).
Or they represent an organism-environment relationship with a
single equation, when it obviously requires at least two
independent equations for complete definition (e.g., the
"matching law"). Or they propose a mathematical explanation for
some kind of behavior, under the impression that the mathematical
expressions themselves, with no physical help, can bring about
the result that is described (e.g., "equations of constraint").

It's just as bad, I think, to overemphasize the mathematical
side. Many system analysts are superb mathematicians, but they
waste their talents on analyzing systems that have very little
likelihood of actually existing. Abstract mathematical systems
can have very interesting properties, but when they're brought
into the real world they may turn out to have few applications,
or none at all. Even when, as sometimes happens, these
mathematical properties of abstract systems prove to be very
important in the real world, there's a tendency for their
proponents to start seeing everything in the same terms,
forgetting about all the phenomena to which the mathematics just
doesn't apply. And there's a tendency to warp the real world to
fit the wonderful new mathematical discovery, as in the claim
that coastlines are fractals, having the same form at all scales,
which is not true (have you ever picked up a rock from a beach? A
fractal beach doesn't have any loose rocks). From the pure
mathematician's enthusiastic point of view, however, little
deviations from the theorem don't count. And so the actual
workings of the world tend to be shunted aside in favor of an
imagined, and simpler, world.

I agree with you, Oded, even though I think there are some other
sides to the current discussion that can't be dismissed. However,
I find no fault in your concluding statement:


Knowledge of sophisticated math is not necessary for the basic
PCT insight, and is certainly not sufficient for it, but I
cannot see how the possesion of a general conceptual framework
for analyzing systems that change with time, is not an
advantage for a PCTer.

Hal Pepinsky (931202)

Thanks for your agreement with my ideas about dealing with

Before you draw any general conclusions about PCT, you should
really give yourself more time to understand how it is put
together. The following, for example, shows that you have only an
approximate idea of what is meant by various terms used in PCT,
or else you have not learned how to express yourself in these
terms in a way that would make sense to a PCTer.

But I still think we can propose and test our guesses as to
whether your control disturbances or mine will be amplified or
dampened by choosing one course of behavior rather than another.
I keep being told I don't get it, but let me try again: I'm
thinking that organization in this instance refers to the nature
of the comparators we select.

"Control disturbances" is not an expression that has meaning in
PCT. A disturbance is some event in your environment that has an
influence on what you are perceiving and controlling. Normally,
your actions automatically change when such a disturbance acts,
cancelling most of the effect that the disturbing event would
have had if you had not acted. So even though a potentially
disturbing event has occurred, it ends up having no significant
effect on the perception it would otherwise influence. Perhaps
this is how you understand it, but in that case your words are
less than precise.

In an adult person, there is ordinarily no question of "choosing"
one behavior over another. Control theory applies to people who
are already organized to behave automatically. Even what appear
to be choices are made on the basis of learned reasoning, in a
way that permits of no outcome but the one implied by learned

The comparator is simply part of a learned control system, and
control is defined as the way such a system acts. Consciousness
is not necessarily involved, although it is usually involved in
at least part of the whole system. Even complex intellectual
behaviors covered by PCT run automatically, according to whatever
fixed organization they have.

You must "choose" a behavior when no automatic system is able to
counteract disturbances. This often occurs when a situation
arises in which two control systems inside one person come into
action at the same time, in a way such that only one of them at a
time can actually succeed in controlling. This is "conflict."
When this happens, it is possible that no learned system can
resolve the problem. Now, indeed, consciousness gets involved,
and a new process called reorganization comes into play. This
process is involved in most of the things you talk about as
deviations from PCT. The process of reorganization is neither
learned nor rational. It is creative, inventive, experimental,
apparently random. It is the most powerful process in the person,
and also the most stupid. Reorganization is brought into play by
deviations of the organism itself from a state of viability, and
ends only when that state is restored (or the organism dies --
reorganization, being random, does not always have a happy
ending). Reorganization is probably always going on to some

Conflict can also arise between individuals, a case even more
pertinent to your interests. In that case, one person's automatic
control systems require a state of the environment (or of a
relationship to another person) that is incompatible with another
person's automatic control systems. The two systems quite
automatically begin to oppose their efforts. This occurs without
thought or planning; it is simply the natural and automatic
outcome of pursuing incompatible goals. It is the root cause of

Conflicts, either intrapersonal or interpersonal, are important
to an organism because they nullify the ability to control in
some regard. This upsets the internal ecology of the system as a
whole, and in the normal course of affairs leads to
reorganization. Thus most conflicts are resolved without any
fanfare, by mechanisms that are built into all higher organisms.
The resolution involves, usually, a change in higher levels of
organization such that the next time the same situation arises, a
modified set of subgoals or perceptions is used that avoids
creating the conflict. Perhaps this is what you meant by
"choosing different comparators." The change is not in the
comparators, but in the system that chooses lower-level means of

When conflicts become complex and multiple, however,
reorganization may not succeed, or it may lead to a repeating
cycle of unsatisfactory solutions. Resolving such conflicts, I
think, depends largely on intervention from an independent agency
-- like a therapist or an ombudsman, someone who is not part of
the conflict. And for a person to become a successful negotiator
between conflicting parties or points of view, that person must
have found, through reorganization, a method for dealing with
conflicts that can be taught.

This is how I interpret your "tetrahedronal" approach. It is a
learnable attitude one can take toward conflict, that avoids
taking either side and promotes awareness of the conflict that
can open the door to a successful (although unpredictable)
resolution of the conflict. You discovered this approach, this
attitude, through a series of reorganizations of your own when
you were in Norway.

I feel threatened by someone whose series of responses to others
indicate that they have a set position and course of treatment
of others in mind. I refer to this as an unchanging or
unresponsive motive for behavior. The motive or intentionality
can no more be directly observed than can a quark, but it can be
inferred from a course of interaction, as when someone persists
in confirming that someone else is one of your typical paranoid

Yes. This threat comes from the very automaticity of the other's
control systems: from the if-then logic that prescribes a set
treatment from a conventionalized classification of symptoms. It
is basically a conflict between someone else's concept of how to
treat problems and your concept of how to treat them. It is a
conflict between their automatic control systems and your
automatic control systems.

The difference in your tetrahedronic approach is that you don't
subscribe to the conventional if-then logic. In fact, it appears
to me that you have learned how to leave room for reorganization,
the random element. This is learnable, although it is more common
for people to learn to detect signs of reorganization in
themselves and take immediate steps to stop it, because they
don't understand what is going on. When you come across a
conflict situation, your automatic response is not to classify it
and look up the appropriate treatment in a book, but to follow a
different strategy, the one you call tetrahedronic. When you see
reorganization happening, you do not back away, but allow it to
happen. Instead of fearing it, you value it.

This is just as much a control process as the one you reject. You
have a concept of how an interaction should be shaped, and you
vary your actions to bring the actual interaction into that
shape, the shape you call tetrahedronic. In order to do this, you
must be able to perceive the actual shape of the interaction, to
compare that with the desired shape, and to turn the discrepancy
into a change in your actions that will erase the discrepancy and
make the interaction truly tetrahedronic. That is exactly how a
control system works. With continual practice, you have acquired
skill at doing this; you have made this way of dealing with
people automatic. This does not mean unconscious; it just means
that you have worked out the bugs. You have also worked out ways
to show others, by metaphor and example, how to perceive
situations in this same way, and thus go on dealing with new
conflicts in a new and more effective way after you are gone.

The interesting part to me is that Martin's protests, like mine,
that he finds PCT true albeit not the whole truth, falls on deaf
ears: he, like me, is treated as trying to destroy or dismiss
PCT. I think instead each of us is in his own way trying to
RELATE to it.

It takes time to understand the logic and the details of PCT, and
thus to see all that it has to say about human experience. It has
more to say than any person realizes on first acquaintance. I
think Martin would agree that his present understanding of PCT is
very different from the one he had after a month or two of
exploring it. The more you learn about it, the more you can see
that it explains.

I don't mean by this that it explains everything; PCT is a theory
under development, not a finished product. One day it may prove
to be an appendage to another and more comprehensive theory of
behavior. But that's beside the point here.

What I ask is simply that people study PCT until they begin to
see the simplicity and power of the interlocking details of the
theory. That takes a long time. I don't know anyone who has done
it in less than two years, and that includes people smarter than
me or you. I am cautioning against drawing premature conclusions.
Much of what you see as going beyond PCT seems that way to you
because you have not found out for yourself all that PCT can
explain. Not all of what you see -- I'm sure that every
intelligent person like you who comes to PCT, after mastering
what there is to be known, will find that there is still
something to contribute to it that was not realized before. Many
of the changes in the theory that have come about over recent
years arose because after some people had gone through all their
"yes-buts" and found the answers to their own objections, they
came up with a "yes-but" that the theory genuinely couldn't
handle. Many discussions on this network over the past three
years have been concerned with working out explanations of
phenomena that I had never considered and couldn't explain. Some
of them have led to modifications of the theory -- very exciting
moments. The key factors in these explanations were often worked
out by people other than me -- for example, Martin Taylor's
recent careful analysis of how to handle psychophysical
experiments in which the control processes are not obvious. Even
the name "perceptual control theory" was invented on the net --
was it Gary Cziko, or Kent McClelland? Sorry, I should remember.

I think that much about PCT will become clear to you when you put
it in its proper place. Your dealings with people are practical,
not theoretical. Your tetrahedronic approach is a practical
method, not a theoretical method. What PCT attempts to do is not
to prescribe a best way of dealing with people, but to explain
how it is that people can do ANYTHING that we find them doing,
whether good or bad. If you were to describe your tetrahedronic
approach in complete detail, the PCTer would accept it as
something that a person can do, and try to understand what is
involved in doing it. In just the same way, if we can describe
exactly what an if-then therapist is doing, we can try to explain
how behaving in that way is possible, using PCT as the framework.
When you can bring ALL that people do into a common framework of
understanding, you will understand far better what is good about
the good, and bad about the bad, in terms of compatibility with
human nature. You will have a better understanding of what you
are already doing and you might even see ways of doing it better.

Keep up the effort, Hal. Your ability to take flak is admirable,
and I perceive that you are capable of learning from experience.
All will be well in the end.
Best to all,

Bill P.

[From Cliff Joslyn (931203.2300 EST), Yow!]

[From Bill Powers (931202.0750 MST)]

Oded Maler (931202) --

>Dynamics is the mathematical theory of things that change with
>time according to some laws. Control systems (with or without
>their environment) *are* dynamical systems of certain sort.

Right on, Oded. There are, however, some other considerations.

Right, now, everybody repeat after me: all control systems are
dynamical systems; not all dynamical systems are control systems.
Therefore things that are true about a restricted class of dynamical
systems (like complex chaotic Prigoginean systems which nevertheless
lack control) need not be true about control systems; but everything
that is true about ALL dynamical systems (like state determinism) is
also true for ALL control system.


Cliff Joslyn, Cybernetician at Large, 327 Spring St #2 Portland ME 04102 USA
Systems Science, SUNY Binghamton NASA Goddard Space Flight Center
cjoslyn@bingsuns.cc.binghamton.edu joslyn@kong.gsfc.nasa.gov

V All the world is biscuit shaped. . .