# Behavioral Illusions: The Basis of a Scientific Revolution

Great. Let’s stick to this.

First order of business if finding the controlled variable. For drawing the Venus, we can say that the controlled variable is knot position, because the example was just doing the rubber band test.

You’re saying that if the drawing of Venus looks exactly like the Venus contour this tells you NOTHING about the system that produced it? If the drawing looks like a potato, this tells you NOTHING about the system that made the drawing as a side effect of controlling knot position?

RM: Yes. The fact that S draws Venus or a Potato (or is it Potatoe;-) tells you nothing about the nature of the system that produced it. But if you know that S is controlling the knot while opposing E’s disturbance, then you know that the system that produced the drawing is a control system, it was Venus (or a Potato) because that is what had to be drawn to oppose E’s disturbance and how accurately Venus mirrors E’s Venus can be taken to reflect characteristic of the output function of the system.

Nonono. E is always disturbing the knot position with a drawing of Venus, in both cases. The subject does not know this and does not care.

The controlled variable is knot position.

Subject A:
Experimenter’s disturbance is a contour of Venus. Subject’s behavior is exact contour of Venus.

Subject B:
Experimenter’s disturbance is a contour of Venus. Subject’s behavior is a potato, potatoe or tomato looking curve.

This tells you nothing about the subject A’s properties nor about subject B’s properties?

RM: and how accurately Venus mirrors E’s Venus can be taken to reflect characteristic of the output function of the system.

How does this fit with the previous statements? The output function is not a part of the organism?? What if the feedback function has higher gain in A than in B? What if the input function has higher gain in A than in B?

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Nonono. E is always disturbing the knot position with a drawing of Venus, in both cases. The subject does not know this and does not care.

The controlled variable is knot position.

Subject A:

Experimenter’s disturbance is a contour of Venus. Subject’s behavior is exact contour of Venus.

Subject B:

Experimenter’s disturbance is a contour of Venus. Subject’s behavior is a potato, potatoe or tomato looking curve.

This tells you nothing about the subject A’s properties nor about subject B’s properties?

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AM: Nonono. E is always disturbing the knot position with a drawing of Venus, in both cases. The subject does not know this and does not care.

RM: Ah, that’s a horse of a different color.

AM: The controlled variable is knot position.

RM: You mean both subjects A and B are known to be controlling knot position?

AM: Subject A:

Experimenter’s disturbance is a contour of Venus. Subject’s behavior is exact contour of Venus.

Subject B:

Experimenter’s disturbance is a contour of Venus. Subject’s behavior is a potato, potatoe or tomato looking curve.

This tells you nothing about the subject A’s properties nor about subject B’s properties?

RM: No, it tells you that you were wrong about subject B controlling knot position

RM: No, it tells you that you were wrong about subject B controlling knot position

Both subjects are definitely controlling position.
Give the rubber band to a person with Parkinson’s disease. What do you think you’ll get?

Try a model with low gain and a model with high gain.

Side effects, that is properties of action in this case, can tell you a lot about the organism, after you’ve found out the controlled variable, and you know this.

RM: But if you know that S is controlling the knot while opposing E’s disturbance, then you know that the system that produced the drawing is a control system, it was Venus (or a Potato) because that is what had to be drawn to oppose E’s disturbance and how accurately Venus mirrors E’s Venus can be taken to reflect characteristic of the output function of the system.

Is the output function not a property of the organism?

RM: No, it tells you that you were wrong about subject B controlling knot position

AM: Both subjects are definitely controlling position.
Give the rubber band to a person with Parkinson’s disease. What do you think you’ll get?

RM: A much noisier version of the Venus but not a potato.

AM: Side effects, that is properties of action in this case, can tell you a lot about the organism, after you’ve found out the controlled variable, and you know this.

RM: No, I don’t know this. S’s drawing of the Venus is a side effect. S’s movements that make this drawing are NOT side effects; they are outputs that compensate for E’s disturbance to the controlled variable. How closely S’s movements mirror E’s disturbances does tell you something about the characteristics of S’s ability to control.You are getting seduced by the fact that the pattern of E’s disturbances are in the form of Botticelli’s Venus. Just as you are seduced by the fact that there is typically something close to a beautiful 1/3 or 2/3 power relationship between movement velocity and curvature.

RM: But both Venus and the power law are irrelevant side effects of control; they tell you nothing about the controlling done by the organism. If E’s disturbances were a random pattern instead of Venus, the pattern S draws would still be a mirror image of E’s pattern because it has to be in order to keep the knot under control. And you would learn just as much about S’s controlling from the random pattern as from Venus. All that matters is that output continuously compensate for disturbance to the controlled variable; what you learn about S’s controlling comes from analyzing how well output mirrors disturbances.

RM: Same is true for the power law, although for somewhat different reasons; in that case both velocity and curvature are properties of a variable (such as the position of the cursor) that is being controlled relative to a variable reference. And it turns out that almost any pattern of variation of the reference will produce movement where velocity and curvature are related by something close to the 1/3 or 2/3 power law.

RM: So if you must look upon these lovely sirens that are the side-effect of control, do so while strapped to the mast of PCT;-)

RM: But if you know that S is controlling the knot while opposing E’s disturbance, then you know that the system that produced the drawing is a control system, it was Venus (or a Potato) because that is what had to be drawn to oppose E’s disturbance and how accurately Venus mirrors E’s Venus can be taken to reflect characteristic of the output function of the system.

AM: Is the output function not a property of the organism?

RM: Yes, indeed. And you can tell something about it by how well S’s movements mirror E’s disturbances. It doesn’t matter whether E’s disturbances race out Venus or a random squiggle. All that matters is how well S’s output mirrors E’s disturbance. Venus (and the random squiggle) are irrelevant side effects of the controlling done by S. Indeed, S knows nothing of what he is drawing, Venus, random squiggle or whatever. It’s irrelevant to control of the position of the knot.

In case you get these things by mail you will see that I sent the previous post by accident before completing it. Go to the topic if you want to read the completed post. I think it would be worth it; it’s truly Joycean in the richness of it’s literary allusions;-)

RM: No, I don’t know this. S’s drawing of the Venus is a side effect. S’s movements that make this drawing are NOT side effects; they are outputs that compensate for E’s disturbance to the controlled variable.

You say “drawing of the Venus is a side effect”, and “movements that make the drawing are not side effects”

But you are talking about the same variable. That is both qo, movement output. How is qo at the same time a side effect and not a side effect?

RM How closely S’s movements mirror E’s disturbances does tell you something about the characteristics of S’s ability to control.

The subject did not intend to closely mirror E’s disturbance. He is just intending to keep the knot on the center position. His movements, and all the properties of those movements, are side effects of controlling position, and importantly - they depend on the properties of the subject, such as gain.

RM: And you would learn just as much about S’s controlling from the random pattern as from Venus.

Sure. You would learn just as much, because the properties of qo depend on the properties of the subject. For high gain - you get a nice mirror image of the disturbance. For low gain, you get a less nice mirror image of the disturbance, whatever the image was.

From what I can see, properties of action do tell you important things about the control system. The actions are a side effect of control of perception, they are irrelevant to the subject, but they are certainly not irrelevant to the experimenter, because they can reveal subject’s properties.

Behavioral illusions are interesting phenomena. Generally, they are based on taking the open-loop model of behavior, and then studying the properties and relationships between inputs and outputs. In open loop, this works great, you get the open loop function by relating inputs to outputs.

In closed loop, this also works great, but you don’t get the of the organism function, you get the environment function (inverted), if the total loop gain is high enough. If you don’t know you’re dealing with a closed loop system, you might attribute the input-output function to the organism instead of to the environment. That is the behavioral illusion, the 1978 definition.

A bit wider definition of the behavioral illusion is simply taking the open loop model as model of organism behavior, or rather - taking an open loop model might lead to a behavioral illusion.

One redefinition is: “the appearance of a causal relationship between behavioral variables when such a relationship does not, in fact, exist” (M&S 2017). This is not the nor a behavioral illusion. Errors in causality attribution don’t really have anything to do with the behavioral illusion.

Another redefinition is “a behavioral illusion, where an observed relationship between variables is seen as revealing something about the mechanisms that produce a behavior when, in fact, it does not” (M&S, 2018)

(Why is there no acknowledgement of using two different versions of the behavioral illusion definition in the two papers? The first about causality, second about ‘revealing something about mechanisms’’?).

The second redefinition is also nonsense and has nothing to do with PCT. Any observed relationship between variables in a control loop depends on all the elements of the loop - changing the gain in the output will change the input-output relationship. Changing the environment feedback gain will also change the input-output relationship, and it will change the stability of qi, and so on.

In other words - any observed relationship between variables in the control loop always reveals something about the mechanisms that produce behavior, it always depends on the all elements of the loop and in changes in their properties.

I’m putting aside all the other criticisms of the two papers, and sticking to the definition of the behavioral illusion, or a behavioral illusion, you seem to think they are the basis for a revolution, but all I see are several different and incompatible definitions of behavioral illusions. Can’t base a revolution on incompatible definitions.

The problem with some mainstream approaches is taking actions as the main thing to study. The mistake is a consequence of taking the open loop model of behavior, or loosely, a consequence of the behavioral illusion.
However, even if we take the closed loop model of behavior, we still have to study actions, as they are another important variable in the control loop. Any changes in action, without changes in the experimental setup or the feedback function, or the disturbance, might reflect some changes in the organism.

RM: No, I don’t know this. S’s drawing of the Venus is a side effect. S’s movements that make this drawing are NOT side effects; they are outputs that compensate for E’s disturbance to the controlled variable.

AM: You say “drawing of the Venus is a side effect”, and “movements that make the drawing are not side effects”

AM: But you are talking about the same variable. That is both qo, movement output. How is qo at the same time a side effect and not a side effect?

RM: No, they are definitely not the same variable. S’s finger movements that compensate for E’s disturbances (call them q1o) are definitely not the same as the patterns (Venus or random squiggle, say) that are a result of those movements (call them q2o). The outputs q1o are part of the control loop involved in keeping on target; the outputs q2o are a side effect of that controlling; they, like the power law, are the beautiful sirens that are calling to you with the song of an important scientific finding which will lull you to them and have you crashing onto the rocks of mainstream psychology. Beware!

RM How closely S’s movements mirror E’s disturbances does tell you something about the characteristics of S’s ability to control.

AM: The subject did not intend to closely mirror E’s disturbance. He is just intending to keep the knot on the center position. His movements, and all the properties of those movements, are side effects of controlling position, and importantly - they depend on the properties of the subject, such as gain.

RM: Correct! So the pattern of those movements – Venus or squiggle – per se, tells you nothing about the properties of the subject. What tells you about the subject’s properties is how well the subject keeps the controlled variable in the reference state (which may be variable, making things a bit more interesting). But the essential component in determining the properties of the subject is determining the variable(s) the subject is controlling. That’s the central fact to be determined about behavior in order to produce a PCT explanation of it; you must determine what variable(s) the subject is controlling. And you can’t do it by looking at side effects because you don’t even know they are side effects until you know what variable(s) are being controlled.

Best Regards

Homer…er. Rick

RM: No, they are definitely not the same variable. S’s finger movements that compensate for E’s disturbances (call them q1o) are definitely not the same as the patterns (Venus or random squiggle, say) that are a result of those movements (call them q2o). The outputs q1o are part of the control loop involved in keeping on target; the outputs q2o are a side effect of that controlling;

Sorry, I need a drawing or a simulation or something. Qo1 are finger movements, finger being attached to the rubber band. Qo2 is the pattern drawn by the finger movements? Qo2 are a result of the movements? I don’t see it.

RM: But the essential component in determining the properties of the subject is determining the variable(s) the subject is controlling.

We already know they are both controlling position.

Hi Adam

RM: No, they are definitely not the same variable. S’s finger movements that compensate for E’s disturbances (call them q1o) are definitely not the same as the patterns (Venus or random squiggle, say) that are a result of those movements (call them q2o). The outputs q1o are part of the control loop involved in keeping on target; the outputs q2o are a side effect of that controlling;

AM: Sorry, I need a drawing or a simulation or something. Qo1 are finger movements, finger being attached to the rubber band. Qo2 is the pattern drawn by the finger movements? Qo2 are a result of the movements? I don’t see it.

RM: Think of it in terms of the model of S’s behavior. The model just produces output, Qo1, as a function of error, e, the difference between a reference signal (presumably = 0) and the controlled variable – the distance between knot and dot: Qo1 = f(e). The value of Qo2 – be it Venus or any of an infinite number of other two dimensional squiggles – is a side effect of the fact that Qo1 is opposed to disturbances to the controlled variable: Qo1 = - d. So if d = Venus the Qo2 will be the negative of Venus; if d = some other 2 D squiggle the Qo2 will be the negative of that squiggle.

RM: Powers showed how eye-catching the side effects of control can be in several demonstrations, the most relevant ones being the “squared circle” demo – where S traces out a square (Qo2) while controlling (using Qo1) for keeping a cursor moving in a circle – and the other being "the “writing hello” demo – where S is seen to be writing “hello” (Qo2) while controlling (using Qo1) a cursor in 2 space relative to a fixed target.

RM: The power law and invariant velocity profiles are irrelevant (though seemingly important) side effects of control just like the square movements in the squared circle demo and the written word “hello” in the writing hello demo are irrelevant (but seemingly important) side effects of control. These side effects seem like they should tell us something important about behavior but, in fact, they tell us nothing about how the behavior was produced.

RM: But the essential component in determining the properties of the subject is determining the variable(s) the subject is controlling.

AM: We already know they are both controlling position.

RM; If the word “both” refers to E and S then we know that E is not just controlling the position of her finger; E is also controlling for making a pattern by varying those positions appropriately – the pattern of Venus or some other 2 D line drawing. So Qo2 is not an irrelevant side effect of E’s controlling; it is the main thing E is controlling for – and she is doing it in order to demonstrate how seductive the side effects of controlling can be.

Best

Rick

RM: Think of it in terms of the model of S’s behavior. The model just produces output, Qo1, as a function of error, e, the difference between a reference signal (presumably = 0) and the controlled variable – the distance between knot and dot: Qo1 = f(e).

OK. The model is controlling position.

RM: The value of Qo2 – be it Venus or any of an infinite number of other two dimensional squiggles – is a side effect of the fact that Qo1 is opposed to disturbances to the controlled variable: Qo1 = - d. So if d = Venus the Qo2 will be the negative of Venus; if d = some other 2 D squiggle the Qo2 will be the negative of that squiggle.

qo1 = qo2 ?

I really don’t see a difference between qo1 and qo2. In a control model, there is just qo to me. The movement of the finger is going to be the mirror image of the disturbance. The movement of the finger is qo. What is this other variable “effect of qo” ? I think they are really the same variable. The finger movement will be the the mirror of d.

RM: Powers showed how eye-catching the side effects of control can be in several demonstrations, the most relevant ones being the “squared circle” demo – where S traces out a square (Qo2) while controlling (using Qo1) for keeping a cursor moving in a circle – and the other being "the “writing hello” demo – where S is seen to be writing “hello” (Qo2) while controlling (using Qo1) a cursor in 2 space relative to a fixed target.

In the square-circle demo you can either draw the circle or the square, and the disturbances and mapping are different in each case. There are no qo1 and qo2. In one case the qi is a circle, in other it is a square, and qo changes appropriately.

RM; If the word “both” refers to E and S then we know that E is not just controlling the position of her finger; E is also controlling for making a pattern by varying those positions appropriately – the pattern of Venus or some other 2 D line drawing. So Qo2 is not an irrelevant side effect of E’s controlling; it is the main thing E is controlling for – and she is doing it in order to demonstrate how seductive the side effects of controlling can be.

No, “both” refers to two systems. The the point of the Venus example is to compare two systems with different gains in their performance in keeping the knot at the center position.
One system is drawing an almost perfect Venus, without trying to do that, just by opposing the disturbance. The drawing is a side effect of the control of position and some properties of the drawing depend on the properties of the system.

The other system drew a less accurate mirror image of Venus, while controlling the same variable, the position of the knot.

The accuracy of drawing (from the point of view of the experimenter) is simply a side effect of control of position.

When you compare the two drawings side by side, one made by a high gain control system, other by a low gain control system, you can see which one is high gain, and which one is low gain.

The drawing of the Venus is in both cases a side effect of control, and in both cases DEPENDS on the properties of the system.

The same thing would happen if you would compare two subjects doing the square-circle demo, or writing “hello”.

Comparing mere side effects of control of position tells you which system is high gain, and which system is low gain.

I think I’ve asked this before - where exactly do you get this silly idea that side effects of control don’t reflect properties of the control system?

AM: I really don’t see a difference between qo1 and qo2.

RM: Then guess I can’t help you.

AM: When you compare the two drawings side by side, one made by a high gain control system, other by a low gain control system, you can see which one is high gain, and which one is low gain.

RM: Yes, of course. As long as you know that the disturbance to the controlled variable was the same in both cases.

AM: The drawing of the Venus is in both cases a side effect of control, and in both cases DEPENDS on the properties of the system.

AM: The same thing would happen if you would compare two subjects doing the square-circle demo, or writing “hello”.

RM: Yes, exactly. As long as you know the disturbance is the same in both cases it doesn’t matter whether the disturbance is Venus, a square or hello. The pattern of the disturbance – and thus the side effect of control (whether S makes Venus, a square or hello) is irrelevant; In all cases you are just seeing how well the two systems compensate for the disturbance to the controlled variable.

AM: Comparing mere side effects of control of position tells you which system is high gain, and which system is low gain.

RM: But you are not comparing the side effects. You are not comparing the relative ability of the systems to control for a pattern that looks like Venus, square or hello. You are comparing the relative ability of the systems to resist disturbances to a controlled variable, disturbances that happen to vary over time in the shape of Venus, a square or hello.

AM: I think I’ve asked this before - where exactly do you get this silly idea that side effects of control don’t reflect properties of the control system?

RM: From Bill Powers and my own studies of PCT. But I re-post here a quote from Bill regarding the Atkeson, Hollerbach velocity profiles – a side effect of controlling perceptions of limb position – that, hopefully, will help you understand where I got that silly idea.

BP: The path which Atkeson, Hollerbach (and many others at MIT and elsewhere) are treading is a blind alley, because no matter how the observations are made and the invariances are calculated, there will be no hint of the control-system organization, the SIMPLE control-system organization, that (I claim) is actually creating the observed trajectories. (RM – emphasis now added for emphasis;-)

Best

Rick

Still back on square one.

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.

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.

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.

EDIT:

This was fun. Here is the disturbance template, not sure who is the author of the contour, found it online:

Then there are two models keeping the knot (qi) at position (0,0):

We know the controlled variables. Comparing two models and the template can reveal something about the mechanisms doing the behavior, even though the behavior of the system, the movements of the hand were not the intended effect.

RM: Think of it in terms of the model of S’s behavior. The model just produces output, Qo1, as a function of error, e, the difference between a reference signal (presumably = 0) and the controlled variable – the distance between knot and dot: Qo1 = f(e). The value of Qo2 – be it Venus or any of an infinite number of other two dimensional squiggles – is a side effect of the fact that Qo1 is opposed to disturbances to the controlled variable: Qo1 = - d. So if d = Venus the Qo2 will be the negative of Venus; if d = some other 2 D squiggle the Qo2 will be the negative of that squiggle.

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.

python code of the model

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’.

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.

Any other sources?

link to code

Here are some velocity profiles. Two position control systems get a step disturbance at t=2s. The high gain control system has a Ko of 100, for low gain it is 20. The velocity profiles are both calculated as dqo / dt, velocity of output.

The exact shape of the velocity profile is not controlled, the system is only controlling position. The shape of the velocity profile is a side effect of position control and reflects the gain of the position control system, and really reflects many other properties of the system - such as the fact that it is a simulated system that can have instantaneous jumps in velocity, though small. A more realistic simulation system would have an object with mass being moved, maybe some friction etc, and then the velocity profile would resemble a bell. But this one does not simulate mass, and it is visible in the velocity profile.

To spell it out - the exact shape of the velocity profile is not relevant for the control system, it is a side effect of position control but it absolutely reflects system properties.

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.

Best regards

Rick