### Control of Size

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#### What to Do

This demonstration illustrates the use of the Test for the Controlled Variable (TCV) to determine which of two perceptual aspects of the same physical situation is actually under control. Start the demonstration by pressing the "Run" button. You will see a solid circle in the upper left and a rectangle of varying height in the center of the display. Your job is to keep the size of the rectangle equal to the size of the filled circle. You do this by moving the mouse to the left -- to decrease the width of the rectangle-- or right -- to increase its width -- in order to compensate for the variations in the height of the rectangle.

A trial lasts for one minute. At the end of a trial you will see a graph of your results as well as measures of how well you did at controlling the size of the rectangle, keeping it equal to the size of the filled circle. These measures are used to determine which aspect of the figures you were controlling when you were controlling the ôsizeö of the rectangle.

There are (at least) two possible aspects of the figures that could correspond to the perception of size that you were controlling. One possibility is area, which, for the rectangle is width (w) times height (h). The other possibility is perimeter, which is 2*(w + h). If the ôsizeö of the rectangle that you are controlling is area then you have to vary the width of the rectangle to compensate for variations in its height in order to keep the perceived area of the rectangle equal to the perceived area of the circle. If the ôsizeö of the rectangle that you are controlling is perimeter then you have to vary the width of the rectangle to compensate for variations in its height in order to keep the perceived area of the rectangle equal to the perceived area of the circle.

This demo uses the TCV to determine which perceptual aspect of the rectangle you are controlling as itĺs ôsizeö. If the area of the circle is called A, then if you are controlling the area of the rectangle, keeping it equal to the area of the circle, then you have to vary w so that w * h = A, where A is constant. If the perimeter of the circle (actually, the circumference) is called P then if you are controlling the perimeter of the rectangle, keeping it equal to the circumference of the circle, then you have to vary w so that 2*(w + h) = P, where P is constant. In other words, if you are controlling the area of the rectangle then the perception you are controlling is proportional to w * h; if you are controlling the perimeter of the rectangle then the perception you are controlling is proportional to w+ h.

The TCV determines which perception your are controlling as ôsizeö by computing a quantity called the stability factor, S, which is defined as

S = 1 ľ Vobs/Vexp

where Vobs is the observed variance of the possible controlled perception and Vexp is the expected variance of this variable is it were not under control. The idea is that if a variable is under control then its observed variance, Vobs, will be much less than itĺs expected variance, Vexp. When this is the case, the ratio Vobs/Vexp will approach 0 and the stability factor, S will be close to 1.0. If the variable is not under control then Vobs will be about the same as Vexp, the ratio Vobs/Vexp will be close to 1.0 and S will be close to 0.0. So the closer S is to 1.0 the more likely it is that the variable is under control.

The computer does the TCV by computing S for the two possible perceptions -- area (w*h) and perimeter (2*(w+h)) -- that might be the variables that are controlled as the ôsizeö of the rectangle. These two stability factors are reported at the end of each one minute session. If you were controlling area, then the Area Stability value should be larger (and closer to 1.0) then the Perimeter Stability value, and vice versa if you were controlling perimeter.

Besides the stability values, the program also displays a graph of the relationship between variations in the height of the rectangle (which is a disturbance to the possible controlled variables, area and perimeter) and variations in the width of the rectangle (which is proportional to your mouse movements (outputs) that compensate for this disturbance. If you are controlling area, the relationship between disturbance (h) and output (w) will be non-linear because, in order to keep area, A, constant w must be reciprocally related to h. So the graph of w versus h should look like h = 1/w. If, on the other hand, you are controlling perimeter, the relationship between disturbance (h) and output (w) will be linear because, in order to keep area, A, constant w must be negatively related to h. So the graph of w versus h should look like h = - w. So both the stability values and the graph of the disturbance-output relationship can be used to determine which perception is being controlled as ôsizeö.

This demonstration works best when you are able to control the perception of area or perimeter skillfully. It takes some practice to be able to do this; I find it particularly difficult to control perimeter. But once you are able to control these variables well you will see that the stability value for the aspect of the display you are controlling as ôsizeö will be much closer to 1.0 than is the stability value for the aspect of the display that you were not controlling. Also, the graph of the disturbance-output relationship will be clearly non-linear when you are controlling area and much more linear when you are controlling perimeter. So I recommend trying this task several times, sometimes controlling area and sometimes controlling perimeter, to see how the stability factor and the disturbance-output graph can be used to test to determine which perceptual aspect of the display you are controlling as ôsizeö.

This demonstration illustrates some important aspects of control theory based research. First, verbal descriptions of possible controlled variables are not a sufficient basis for research aimed at determining the perceptions around which an organismĺs behavior is organized. ôSizeö is an ambiguous description of a controlled perception. In order to determine what perception(s) an organism is controlling it is necessary to develop quantitative descriptions of these perceptions. In this case the possible perceptions under control were quantitatively defined (in terms of the physical variables in the display) as h*w and 2(h+w). Second, itĺs difficult to tell what perception is being controlled if control of that perception is not very good. Third, possible controlled perceptions are often highly correlated, as area and perimeter. When this is the case, the stability measure of control can be quite high for a variable even when it is not the variable under control. For example, the stability measure for perimeter can be quite high even when one is controlling area. A complete version of the TCV involves finding a definition of the controlled perception that gives the highest value of the stability measure of control. That is, the aim of research on the controlling done by living organisms is to find the best definition of the perceptual variables around which their behavior is organized.