The main goal of research based on Perceptual Control Theory (PCT) – and what distinguishes such research from all other behavioral research based on Control Theory – is to find out what perceptual variables organisms are controlling when they are behaving. The main theoretical proposition of PCT is that the behavior of organisms in general, and humans in particular, involves the control a hierarchy of different *types* of perceptual variables. The hypothetical types are described in Powers’ book “Behavior: The control of perception” (B:CP).

In order to test this hypothesis it is necessary to start collecting many different examples of the variables organisms control using some version of the test for the *controlled variable* (TCV). The result would be a database of controlled variables that might look something like Table 8.1 in my book “The Study of Living Control Systems”. In order for such a database to be useful, controlled variables should be described in a way that makes it possible to objectively determine their type – objectively in the sense that the description provides a rational basis for agreement that different controlled variables are of the same type.

All the controlled variables in Table 8.1 are described verbally. Such descriptions are unlikely to provide a good basis for an objective classification of these variables by type. A mathematical description of controlled variables would probably provide the best basis for an objective classification. But there are very few examples of research aimed at providing accurate mathematical descriptions of controlled variables. I’ve done some of this research but the variables described were pretty simple, such as position (x), distance (x1-x2), angle (arcsin[x1-x2)/(y1-y2)]), area (x*y), perimeter (2*[x+y]), and optical velocity (d[angle]/dt).

I think it’s important to figure out how more complex controlled variables can be described precisely – mathematically if possible; for example, how to give a precise definition of a variable like “Employment Status” at the bottom of Table 8.1. But in thinking about this problem I realized that it is unnecessary to define a controlled variable in terms of the physical “reality” to which it corresponds. A precise, mathematical description of a controlled variable need only describe that variable in terms of the variables of which it is composed. And both the controlled variable and the variables of which it is composed will be perceptual variables.

We do this already with some of the simplest controlled variables that we have studied. For example, the controlled variable in the compensatory tracking task is a perceptual variable that is defined mathematically as a *difference* between variables: target position - cursor position. We can think of target and cursor position as being physical variables but, in fact, they are perceptual variables themselves.

So I think the solution to finding mathematical descriptions of complex controlled variables is to develop mathematical descriptions of those variables in terms of the perceptual variables of which they are composed, variables that are themselves expressed mathematically in terms of the perceptual variables of which they are composed.

Because we can describe controlled variables solely in terms of perceptual variables, we can understand the perceptual basis of behavior without knowing how controlled perceptual variables relate

to reality. This means that the question of how well controlled perceptions correspond to reality is really irrelevant to a PCT understanding of behavior. In particular, it means that when we observe poor control it is never because there is a poor correspondence between between the variable being controlled – which is always a perception – and the reality represented by that perception. From a PCT perspective, when we observe poor control it is because the agent is not controlling or is unable to control the perceptual variable we think they are (or should be) controlling. This fact is illustrated in my “Just Following Instructions” demo.

Anyway, I would appreciate any ideas people have about how to usefully describe controlled variables so that these descriptions could be used as a basis for classifying controlled variables by type, the goal being to see if the types found correspond to those hypothesized by Powers in B:CP and other places.