Tom Bourbon

3 March 2001

This is an introduction to the simplest model we use in perceptual control theory (PCT) to explain how living things control parts of their worlds.  William T. Powers  developed PCT to apply to all living things, but I will only talk about people.

Think about how a person controls perceptions when he drives a car. First, there must be an automobile, with a steering mechanism, so that the person’s actions affect the direction the car moves. The person must have some idea of where he wants to see the front of the car, relative to his view of the road: he must have an idea of where the car ought to be, from his point of view. He must also see where the car is, relative to where he wants to see it. If his perceptions of where the car "is," and where he thinks it "ought to be," are a match, then his actions do not change.

If the place where a person thinks the car "ought to be" and where she sees it "is," do not match, her actions change. Her changed actions change the state of the steering device, which changes the direction the front wheels point, which changes the position of the car on the road, which changes her perception of where the car is, relative to the road. When all of those changes create a perceived match between "ought to be" and "is," her actions stop changing. All the while, many other things affect the relationship between where the car "ought to be" and where it "is." Among those influences are (a) things in the environment -- the changing path of the road, wind, water on the road, holes and stones, other drivers, stray animals, and so on, and (b) things in the driver -- fatigue, effects of drugs or alcohol, aching muscles, temporary blindness due to sunlight or headlights shining in the eyes, and so on. When something happens that would disturb the car’s position and cause it to vary, the person acts and cancels out the effects of the disturbance.

In PCT, when we use the phrase, "the fact of control," we refer to this process in which a person acts and creates a desired perception that is often reflected in what we see from the outside as a controlled state of the world. Then the person acts to defend that perception against disturbances. We see the person's defense of her perception as her defense of a state of the world. In PCT, we say that the control we see from outside a person is a consequence (a byproduct) that occurs when she acts to control many of her own perceptions. If we are correct, then the only kind of theoretical system that can explain the phenomenon of control is a perceptual control system. I show the simplest model of a perceptual control system in a diagram named, " Basic Loop." The words a person uses to label the parts of the PCT model shown in the Basic Loop are not terribly important, but only so long as the person accurately describes the basic functional organization of the model.

The PCT equations and diagrams show relationships among variables and physical effects in the environment, and functions and signals inside the control system. Don't think that only a mathematician or engineer can understand PCT. I am neither of those. A little effort following what I am about to say can yield immense gains in understanding why we present the PCT model in a particular way. A deeper understanding of basic PCT might help you appreciate how some people  use ideas from PCT to explain social interactions.

Be sure to follow the diagram while you read what follows. It shows every signal and function that I describe below. We will start at an arbitrary place on the diagram and systematically work our way around the entire model.

A theoretical model that explains how a person controls his perceptions, for example when he drives a car, must include certain features. They are not options. Remove any one of them, and the system cannot control its perceptions. Here are the essential features in such a model.

 (1) The system must have an input function,  i, that is affected by the physical state of some environmental variable. In creatures like us, many input functions are called sensory receptors.

 (2) When the state of the environmental variable changes, something about the input function must change in an analogous way. In turn, changes in the input function must lead to changes further along in the system, changes like the activity in certain neurons, or the concentrations of certain chemicals at various places in the body. In PCT, we call an internal change that originates in the input function a  perceptual signal,  p, or a perception, for short.

 (3) If the environmental variable that affects the perceptual signal,    p, is a  controlled variable,   cv, then inside the system, something must specify the magnitude of the perceptual signal,    p, that "ought to" come out of the input function. In PCT, we call the "something" a   reference signal,   r, and we think that, like perceptual signals, many reference signals are also activity in certain neurons, or concentrations of certain chemicals.

 (4) There must be a  comparator function,  c, that compares the magnitudes of the perceptual signal,    p, and the reference signal,  r. A comparator is a place where, in effect, one physiological signal is subtracted from the other, as in the equation,   p - r. In creatures like us, comparators are often cell bodies of neurons, where opposite physiological effects converge from other neurons, some of which function as reference signals, and others as perceptual signals.

 (5) The comparator,  c, produces a  perceptual error signal,  e, which is the difference between   p and   r , such that   e = p - r.  The error signal can range from "zero" (no discrepancy between   p and  r  ( p - r = 0)), to positive ( p > r, or "p is larger than the value specified by  r"), to negative ( p < r, or "p is smaller than the value specified by r").

 (6) A perceptual error signal,  e, is a very weak neural or chemical event inside a control system. It must act on an output function,  o, that takes in a very weak  e and gives out a much stronger quantity of "output"-- an output quantity,  qo. In creatures like us, output functions are often things like glands and muscles that are affected by neural or chemical error signals, and that give out   qo, in the form of  secreted juices, or of forceful muscle contractions that pull on parts of our skeletons. In the case of muscles,  qo is force generated by biochemical and biomechanical events in muscle filaments, and the sum of such forces affects the acceleration of the parts of our skeleton attached to a particular muscle.

 (7) From outside a person, we see some of his glandular secretions, or his muscular pulls, and we call those his actions,  a.

 (8) There must be a way for actions to affect a controlled variable in the environment. In PCT, we account for that path by way of a  feedback function,  f, that physically links the person’s actions,  a, to the controlled variable,   cv.

 (9) We have arrived again at the controlled variable,  cv .  We first encountered the  cv  when we defined the reference signal,   r, in step 3. At every moment, the physical state of the  cv is determined jointly by the control system's actions,  a, as they affect the  cv through the feedback function,   f, and by any disturbances. A disturbance,  d , is a physical event, other than the control system’s own actions, that affects the physical state of the   cv .

(10) The present state of the controlled variable,   cv, must act on the control system’s input function,  i, by way of input quantities of energy,  qi, like light, sound, mechanical pressure, and chemical concentrations, that physically connect the  cv to the input function. The   qi affects the input function,  i, which gives out a perceptual signal,   p.

(11) We have come full circle in our description of the simplest PCT model. It is a model of circular causality. In this kind of circular causal system, things do not happen sequentially. Every function I described works at the same time as every other function. Every signal has some magnitude, all of the time. The functions do not work in a sequence, with one producing a signal then stopping, followed by the next function that suddenly begins to work, and so on. The perceptual signal always has some magnitude. It does not go away after it affects the comparator. The error signal always has some magnitude. It does not go away after it affects the output function. No lineal model of cause and effect can describe or explain what we have just described here. No lineal model of cause and effect, no matter whether it is behavioristic, or neurocognitive,  can explain the phenomenon of perceptual control. That is  another story, for another time.

(12) All the while that the things in steps 1 through10 occur, other things happen in the environment. For example, the system’s actions,  a, affect more than just the controlled variable,   cv. Actions always affect many other variables, perhaps an infinite number of them. Usually, but not always, those other effects are unintended or incidental side effects when a person acts. It is impossible for a person to prevent or avoid all of them. In the diagram, I illustrate one incidentally affected variable and give it the highly original name,  incidentally affected variable ,  iv. Also, the system can sense variables other than the ones it affects or controls. In the diagram I illustrate one sensed, but unaffected and uncontrolled, variable, and call it,  unaffected variable ,  uv. 

(13) Together,  controlled variables and  incidentally affected variables  make up the consequences of behavior.

Now the model is complete.

All that I just said is summed up in two simple algebraic equations. At any given moment, the equation for what happens inside the control system is:

(1)  e = p - r.

In words, the error signal is equal to the perceptual signal minus the reference signal. The biological "calculation" of  e occurs continuously in the comparator function,   c.

The error signal,  e, affects the output function,  o, which produces the system’s actions,  a.

At every moment, the state of the controlled variable,  cv, in the environment is represented by:

(2)  cv = a + d.

In words, at any moment, the state of the controlled variable is determined by the sum of (1) the effects of the control system’s actions,  a, as they affect the  cv through the feedback function,   f, and (2) the present value of any disturbance,  d, that acts on the  cv.

The  cv affects the input function,  i, which produces the present state of the perceptual signal,   p.

That is it. These two elegant and simple simultaneous equations explain the controlled state of a little part of the world, at a moment in time. They explain the phenomenon of control -- the fact of control.

There are no words or names in the PCT equations. We believe every symbol in the equations is analogous to something inside ourselves, or in the environment, but no words can unambiguously represent the "things" to which the the symbols refer. Every word has many meanings to many people, but  a is always  a, and  r  is always  r.

Let's simply replace the symbols in one of the equations with words I used to describe the model:

error signal = perceptual signal - reference signal.

Immediately, some people dislike the word "error." Others say, "I can't understand what you mean by ‘signal.’ It’s too complicated for me." Many people want to call the reference signal a "goal," but others become outraged whenever someone uses the word "goal" in a discussion about living things; they argue for a phrase like, "strange attractor." And on it goes.

But  e is always  e, and  cv is always  cv.

When we talk to people about the PCT model, we must use ambiguous words to tell them about something that is not word-like. For one thing, we must arrange the words linearly, in the proper sequences to form phrases, sentences, and so on; but all the parts of a control system work simultaneously in a circle. The organization and functioning of the model are all that count, not any particular words we use to label its parts, or to explain what it does.

This introduction, along with the diagram "Simple Loop," is enough for now. If you already understand this material, keep the diagram handy and go to the next lesson, which is about   simple examples  of control. On the other hand, if all of this still seems new to you, go back over the discussion, with the diagram in hand, until everything makes sense. If you still have problems after several attempts to understand the material,  contact me.