# Dynbamic system analysis; PCT and tetrahedrons

**URL:** <http://discourse.iapct.org/t/dynbamic-system-analysis-pct-and-tetrahedrons/3677>\
**Category:** CSG1993\
**Created:** [December 2, 1993, 6:39pm UTC](http://discourse.iapct.org/t/dynbamic-system-analysis-pct-and-tetrahedrons/3677 "1993-12-02T18:39:14Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![William\_T\_Powers2](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/w/c67d28/32.png) [@William\_T\_Powers2](http://discourse.iapct.org/u/William_T_Powers2)\
**Post date:** [December 2, 1993, 6:39pm UTC](http://discourse.iapct.org/t/dynbamic-system-analysis-pct-and-tetrahedrons/3677/1 "1993-12-02T18:39:14Z")

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[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  
capabilities.

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  
> individuals.
> 
> 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  
> reasoning.
> 
> 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  
> degree.
> 
> 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  
> violence.
> 
> 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  
> action.
> 
> 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  
> > schizophrenics.
> 
> 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.

---

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**Author:** ![\_Cliff\_Joslyn](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/_/7993a0/32.png) [@\_Cliff\_Joslyn](http://discourse.iapct.org/u/_Cliff_Joslyn)\
**Post date:** [December 5, 1993, 4:06am UTC](http://discourse.iapct.org/t/dynbamic-system-analysis-pct-and-tetrahedrons/3677/2 "1993-12-05T04:06:57Z")

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[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.

O-----------------------------------------------------------------------------\>

> 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. . .