[From Bill Powers (2006.07.12.0857 MDT)]
Marc Abrams (2006.07.12.1041) --
Bill, you intimated that the block diagram, in principle, could be used for _any_ control process and not just a tracking task.
Yes
My questions had to do with using the diagram at the upper levels of the hierarchy and what those numbers might represent at a higher level of abstraction in the block diagram
The key to analyzing any control task is to identify a controlled variable -- that is, some perception that can vary, and which one tries to keep in a particular state.
This is most difficult to do when the variable seems to be of a kind that either exists or doesn't exist, like "success." Either you succeed in doing something, or you don't. How can that be tied to a variable number?
There's an obvious answer, but let's consider the most direct one first. There is one number scale on which a variable is either true or false: the binary scale. The number 0 means one perceives no success, and 1 means one perceives success. The reference condition for this perception is normally 1, though if you're playing chess with a grandchild it could conceivably be 0. The functions in the control-system diagram would all be binary functions: if the perception is 0 and the reference is 1, then the error is 1 and the output sent to a lower system is 1. This is a crude on-off control system like a home thermostat.
The obvious answer, and a more realistic one, is that we actually perceive degrees of success other than total failure and complete triumph. There is a continuum of states between these limits and we can set the reference value anywhere between those limits, depending on how important success is to us. Given that continuum, we can use the model pretty much as in the block diagram program -- though of course some of the details of the functions may well have to be different.
The most important question is one I can't answer: what kind of perceptual input functions can create higher-order perceptual signals? The way we handle that now is just to propose that there is a perceptual signal that corresponds to what we, the experimenters and observers, see being controlled by the other system. It's like the "distance" between cursor and target that we see being controlled in a tracking task. We don't propose an input function that takes the light distribution on the retina and from it calculates that distance (though I actually did that in the Little Man, after a fashion). We just say that there is an internal signal corresponding to the external state of whatever variable we think is being controlled, and we take the external measure of that variable to be a measure of the perceptual signal as well. That's why I went through all that stuff about the change of units and the scaling factor in the input function.
Not only that, but what would a change in value signify? I might also add, how could I show a change in either "goal" or "perception" _during_ a run?
The short answer is that a change in value of a perceptual signal signifies a change in the magnitude of the variable being controlled. A change in the reference signal's value signifies that the control system is to keep the same perceptual signal at a new value, matching the new value of the reference signal.
A longer answer concerns how we might try to measure changes in the reference signal's magnitude. Basically we have to match the model to the behavior while the reference signal is (we hope) being held constant, and then look at the difference when the reference signal, on request, varies. Look in Wayne Hershberger's book -- the title is something about purposive behavior and "conation and control". My library is all in boxes right now, and 375 miles away (I'm writing measurement of purpose for that book.
The basic experiment consisted of a tracking task divided into three parts. In the first and third parts, marked by beeps, the participant kept the cursor aligned between two stationary target line-segments. In the middle third, the person made the cursor move in a staircase pattern first upward and then downward again relative to the target.
The analysis program first matched a simple control model with a constant reference signal to the behavior in the first and last thirds of the run (marked by beeps during the data-taking run). Then the behavior of the model with a constant reference signal was compared with the real behavior in the middle third, when the supposed reference signal was increasing and then decreasing in steps. On the basis of the difference between the model and real mouse positions, the model's equations were solved for the reference signal. The result was a deduced reference signal, and it went up and then back down again in steps. I should add that the disturbances being applied all through the experimental run almost completely masked any stairstep patterns in the data . But by smoothing the deduce reference signal pattern, the program made the steps stand out very clearly.
That's as close as I have come to measuring voluntary changes in a reference signal's magnitude, in a pretty simple experiment with controlling a simple variable, the distance between a cursor line and a target line. In principle the same strategy could be used to measure the reference signal in higher-order systems, but it will be a long time before we know enough to do that.
Best,
Bill P.
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from my daughter Allie's house). I wrote a paper on experimental