AM: Still back on square one.
RM: Not really. I think we are just talking past each other. This is all lovely work in this post. It shows that when you know the controlled variable you know what is most important about the behavior.
AM: A researcher has two drawings of Venus from the same rubber band experiment, made by two different subjects who had different gains for position control. No amount of looking at the drawing will show how it was made, if the researcher does not know the controlled variable. The exact pattern was irrelevant to the subjects, all they saw was a knot staying in one position because they moved their hand to keep it there.
RM: Yes. Exactly.
AM: The Venus drawings are definitely a side effect of control of position, and they are not identical. Two different subjects produced two different drawings. Why are there any differences? Because the drawing fidelity reflects subject’s gain.
RM: Probably. But it could also reflect differences in the feedback functions in the two cases. The lower fidelity drawing might have been drawn underwater, for example.
AM: The side effects of control of position are irrelevant to the subject, but are very relevant to the researcher. He can fit two models to two drawings of Venus, providing them with the same disturbance he gave to subjects, and he can find out the gains of the subjects for position control.
RM: It’s not really the side effects per se that are relevant to the researcher. The side effect of S’s behavior (controlling) in your example is the shape of the squiggle produced by variations in S’s output, qo. In this case E is not trying to evaluate the relative gain of 2 S’s by comparing how well the outputs of each S match a particular squiggle shape;. Rather, E is evaluating relative gain by looking at the correlation between variations in qo and variations in qd (or by measuring rms deviation between these two variables). The actual shape of the pattern traced out by qo and qd – the side effect of variations in qo and qd – is irrelevant.
AM: This was fun.
RM: It was indeed! You do such nice work!
AM: Maybe you can point to which variable is the side effect and which variable is not the side effect. I just see one qo per model.
RM: Again, it’s the squiggly shape traced out by variations in qo that is the side effect of S’s controlling; this side effect is irrelevant to both S and E. What is relevant to E in this analysis is the correlation between variations in qo and variations qd (or the rms deviation of qo from qd).
AM: As for your quote, you are mistaking what is irrelevant to the subject with what is irrelevant to the researcher. If you look in that comment on A&H, you will find ‘the invariants are interesting as a check on the model’.
RM: What Bill is saying here is that these invariants are interesting in the same way that the observed behavior of a real subject doing the tracking tasks in your demo are a check on your model of that behavior. Your model should (and will) produce the same squiggle in response to the squiggly disturbance as does the real subject. Indeed, I did exactly this analysis in the “Control Blindness” paper.
RM: Here is a shot of an S controlling the position of the knot in the rubber band game:
RM: It shows the trace of S’s variations in qo (upper left) that compensate for E’s variations in qd (lower right). Most observer’s of a video if this task didn’t notice that S was controlling the position of the knot. Many thought that S was tracing out a kangaroo. Others thought S was tracing out something else. The shape of S’s trace is a side-effect of S’s controlling the perceived position of the knot. Indeed, it’s clear that the pattern traced out by S’s movements are an irrelevant side effect of S’s controlling because what that pattern was was in the eye of the beholder.
RM: I converted the time course of these traces to numbers that could be used in a contorl model and fitted thel model to the data. The results are here:
RM: The correlation between the output of the model (red dots) and the actual movements made by S (green dots) was .98. Since the model fit the pattern traced out by S quite well you could say that the pattern – a side effect of controlling – provided an interesting check on the model. But it’s not really the pattern per se that provided the check on the model; it was the fit of the model’s variations in qo – variations that made the movement pattern as a side effect – to S’s variations in qo that was the actual check on the model.
AM: I’ve asked where did you get the silly idea that side effects of control don’t reflect properties of the control system? The discussion of velocity profiles in A&H does not address this question. If you would put different gains to the arm, you would get different velocity profiles. Side effects, such as the Venus drawings, or the exact shape of the velocity profile, do reflect properties of the system that made them.
RM: The invariant velocity profiles that Bill referred to as “an interesting check on the model” are a check on the model in the same way that S’s output traces are a check on the model of behavior in the rubber band demo. The check was to see whether the Little Man model doing the same tasks as the Ss in the A-H experiment would produce outputs (qo) that are the same as those produced by the real Ss. The only thing about the outputs that is known to us is that they could be converted to invariant velocity profiles. So the fact that the Little Man outputs could be converted to invariant velocity profiles was one way to check on whether the model fit the data – whether the model was controlling in the same way as the real subjects. This check was evidence that the model was controlling the same perceptual variables in the same way as the real subjects.
RM: It is in this sense that the invariant velocity profiles are an “interesting as a check on the model”. The fit of the model to those profiles tells you that the model is controlling the right perceptions in the right way. Of course, there would be some parameter fitting to get a best fit of model to data. And the parameter values that give you the best fit will certainly tell you something about how the controlling works. But what is most important is that in the case of the A-H data we found that a model controlling a hierarchy of certain perceptions will produce outputs that, as a side effect, result in invariant velocity profiles.
RM: The model was evaluated in terms of those side effects because that’s the only measures of performance that were available. We would have gotten the same result – a successful fit of model to data – if the model were fitted to the raw movement data – the data from which the invariant velocity profiles were derived.
RM: PCT modeling is all about finding the right perceptions to control – “right” in the sense that when the model controls these perceptions it behaves just like the real organism.