# Behavioral illusion, based on Powers (1978)

It seems that main cause of our disagreement have been your repeated mistakes in identifying and defining functions in the control loop. You also have non-standard notation for functions, like f[] or g[], and also for the function inverse you write g-1, and you often mistake solutions of systems of functions.

The organism function in PCT is always defined as the function that takes qi as input, and gives qo as output. The feedback function is not always defined, because it often assumed it doesn’t change the organism output qo, but in the 1978 paper it is defined as the function that takes qo as input, and gives “contribution” to qi as output, which I’ve named qf.

Your first reaction was that giving the output of the feedback function a name is somehow wrong and misleading. Your second reaction was to claim that the output of the feedback function was not “a real entity”. Your third reaction was to define the feedback function as qi = G(qo), and for the rest of the topic you keep writing that the feedback function relates qi to qo. This is not only misleading but also very wrong.

Take a look here, for example: https://www.mathsisfun.com/sets/function.html , or some other math source that describes what are functions and what are relationships, etc.

Relating
A function relates an input to an output.

### Formal Definition of a Function

A function relates each element of a set with exactly one element of another set (possibly the same set).
The Two Important Things!
1."…each element…" means that every element in X is related to some element in Y.
2. “…exactly one…” means that a function is single valued. It will not give back 2 or more results for the same input. “One-to-many” is not allowed, but “many-to-one” is allowed:

When a relationship does not follow those two rules then it is not a function … it is still a relationship, just not a function.

AM: The feedback function does not relate qi to qo, it relates qo to qf.

Or take a look again at the source of your conviction that functions correspond to causal paths.

RM My impression was that the relationship between o and d is a side effect of the system acting to to keep error at zero. Indeed, I thought that was one way of looking at the “behavioral illusion”; the illusion being that the relationship between d and o appears to reflect the causal path from stimulus (disturbance) to response (output) when, in fact, no such causal path exists. Do I have that wrong?

BP: Yes . There is clearly a causal path from d to qi (the disturbance function), another from qi to e (perceptual function and comparator with an input from r), another from e to o (output function), and finally another from o to qi (environmental feedback function). All but the last work in the “forward” direction.
Nothing mysterious happens when the loop is closed. The forward functions do not disappear. They are still there and are always working.

You were saying that the possible explanation of the behavioral illusion is that the causal path does not exist at all. The causal path does exist, Bill replied, and it goes trough all those function in a loop. Nothing about “causal functions”, and certainly nothing about functions corresponding to causal paths.

RM: Conventional psychologists can’t be looking at qo = G^-1(qe) or qo = F(qe) because they can’t see qe !

AM: Sure they can, qe is H(qd), by definition. You claim explicitly “RM: experimental psychologists assume that h() is a multiplier of 1.”, so qe = qd, and all the equations hold, and the experimental psychologists are really seeing qo = G^-1(qd), while they think they are seeing qo = F(qd).

RM: Assuming h() is a multiplier of 1 doesn’t make h() a multiplier of 1. Bill’s analysis is based on the fact that the independent variable in an experiment, qd, is what the experimenter sees as the cause of the behavior. So you correctly state that what psychologists think they are seeing is qo = F(qd), since experimental psychologists implicitly assume that h() is a multiplier of 1.0. But what that are really seeing (if the system under study is a control system) is qo = G^-1 [h(qd)] not qo = G^-1(qd).

AM: If the H is not really the multiplier with 1, but some other function, they will absolutely see qo = G^-1(qe), or equivalently qo = G^-1( H(qd)), while they might think qo = F(qd).

RM: And that fact is captured by writing what they actually see as qo = G^-1 [h(qd)] . Your introduction of the variable qe just confuses things.

AM: But you’ve missed the point:
They are looking at qo = G^-1 ( H (qd)).
They think they are looking at qo = F(H(qd)).

RM: I think it’s better to say that they think the are looking at qo = f(qd) since scientific psychologists have no notion that qd is a disturbance to a controlled variable, which is what H(qd) implies.

AM: There, now with H. The only difference between these two equations is that the F is replaced by G^-1.

RM: Yes, it is the behavioral illusion experienced by psychologists doing conventional psychological experiments.

AM: That is the behavioral illusion. Taking a wrong model, a zero feedback system, as the model of organism behavior. That is the point of the whole section of the 1978 paper that talks about the behavioral illusion, although not the general point of the paper.

RM: Yes, indeed.

AM: The preceding part is complete nonsense:

RM You can’t tell anything about the behavior of a living control system – an N-System – by studying relationships between independent (stimulus) and dependent (response) variables.

RM: I take it that you mean the “succeeding part” that you quoted as what is complete nonsense. Would it be less nonsensical if I had said: When the organism under study is an N-System the form of the dependence of qo (DV) on qd (IV), which appears to reveal something about the organism under study, actually reflects only properties of the local environment. Maybe it sounds less nonsensical when Bill says it;-)

AM: Qd and qo are stimuli and responses. The tracking task is a careful examination of the relationship between a continuous stimulus and continuous response. Any test for the controlled variable is going to be conducted by applying a stimulus that possibly disturbs the controlled variable and examining the relationship between the stimulus and the response, and other variables we can calculate from the stimulus, the response and our model of the system, including the hypothetical controlled variable qi. If the response ‘cancels’ the stimulus, and qi is near zero, that is a good hint we found the controlled variable, for example. But we are still doing stimulus-response experiments. The difference is that stimuli and responses are continuous, so we allow feedback from the behavior to the controlled variable, and we study individuals and their behavior, and not averages of stimuli and responses in groups.

RM: I don’t think it’s helpful to call experiments based on an understanding of organisms as control systems stimulus-response experiments. The main goal of PCT-based experiments is to identify controlled variables. You do this by manipulating IVs (S) which could be called stimuli. But what you are looking for as the DV ® is lack of effect S on the hypothetical controlled variable. If S has an effect then you try a new hypothesis about the controlled variable, testing it using different Ss. It’s an iterative process. Of course, when you have identified a controlled variable there will be S-R relationships between disturbances to that variable and system outputs that compensate for those disturbances. But these S-R relationships are only of incidental interest. Once you know what variable(s) the system is controlling you know how the system will respond ® to any disturbances (S) to those variables.

AM: You need to find a better way of saying the sentence I quoted. Maybe: “You can’t find the organism function by looking at the S-R plot”. or “S-R experiments focused at finding controlled variables can reveal important things about the organism”

RM: I think I’ll just stick with describing the research as testing for controlled variables and leave the S-R out of it.

RM: The behavioral illusion doesn’t result from an error in system identification; it reveals an error in system identification. And it shows that this error in system identification results from failure to see that the system is a control system

AM: “System identification” in this context means identifying the system, organism, as a Z or N system. so your second sentence is “And it shows that this error in system identification results from a failure of system identification.”

RM: You’re right. The way I said it could be rephrased as a tautology. It would have been better to say: the behavioral illusion shows that the error in system identification that you are making – taking an N-system for a Z system – results from failure to notice the existence of controlled variables: the fact of control.

RM: I did that on purpose because I was well aware of the fact that the power law is not an example of the S-R illusion that Powers describes in the 1978 paper.

AM: Then you redefine behavioral illusion to be different from the 1978 definition. Instead of the “organism function” you put “something about the mechanisms that produce behavior”.
Why the redefinition while still quoting the 1978 paper? Why even call it “a” behavioral illusion, instead of just “statistical artifact”. This way is sounds like the the 1978 behavioral illusion is just some statistical artifact.

RM: So you’re complaint is about me calling the power law a behavioral illusion? What do you think it is?

AM: I don’t know where you get this silly idea that side effects don’t tell you anything about the system. They don’t tell you what is the controlled variable, and that is the main thing to discover, I agree, but the various side effects can certainly be useful in finding other parameters of the system. After finding the controlled variable, you can look at responses at different frequencies, examine delays, speeds, amplitudes… All reveal something about the system, while not being the main effect.

RM: Some of these are not side effects, from my point of view. A side effect is an observed aspect of the behavior of a control system that has nothing to do with its operation; it’s something you don’t have to put into a model of the control system in order to produce the observed behavior. Behavioral illusions are side effects of control in that sense. The fact that the observed relationship between qd and qo is the inverse of the feedback function (the S-R behavioral illusion described in the 1978 paper) is a side effect of control in this sense. Same for the power law;you don’t have to put anything into the control model to make the power law appear.

RM: Assuming h() is a multiplier of 1 doesn’t make h() a multiplier of 1. Bill’s analysis is based on the fact that the independent variable in an experiment, qd, is what the experimenter sees as the cause of the behavior. So you correctly state that what psychologists think they are seeing is qo = F(qd), since experimental psychologists implicitly assume that h() is a multiplier of 1.0. But what that are really seeing (if the system under study is a control system) is qo = G^-1 [h(qd)] not qo = G^-1(qd).

Agreed.

RM: And that fact is captured by writing what they actually see as qo = G^-1 [h(qd)] . Your introduction of the variable qe just confuses things.

It might be confusing to some people, but it is still correct to just replace the output of a function with a name. The only reason for introducing it was to simplify the equations describing the solution for Z and N systems, and to show how there is only one difference.

Those equations in the paper contained also the qi* and H, so “hiding” them really simplifies things and makes the comparison easier.

RM: I take it that you mean the “succeeding part” that you quoted as what is complete nonsense. Would it be less nonsensical if I had said: When the organism under study is an N-System the form of the dependence of qo (DV) on qd (IV), which appears to reveal something about the organism under study , actually reflects only properties of the local environment . Maybe it sounds less nonsensical when Bill says it;-)
[…]
Of course, when you have identified a controlled variable there will be S-R relationships between disturbances to that variable and system outputs that compensate for those disturbances. But these S-R relationships are only of incidental interest

The nonsensical part is saying or implying that in PCT we are not observing stimulus-response relationships. We are. A lack of effect is a relationship. A zero correlation. There will always be an SR relationship whenever you measure it, but it will not always be a function. I agree with your logic here, just not with the expressions.

RM: I think I’ll just stick with describing the research as testing for controlled variables and leave the S-R out of it.

Great.

RM: So you’re complaint is about me calling the power law a behavioral illusion? What do you think it is?

My complaint (in this thread, anyway) is that you did not define the behavioral illusion as the 1978 paper defines it, and for some reason still quoted the 1978 paper as reference for the term. You have redefined the term into a very different phenomenon, not consistent with the original definition.

RM: Some of these are not side effects, from my point of view. A side effect is an observed aspect of the behavior of a control system that has nothing to do with its operation; it’s something you don’t have to put into a model of the control system in order to produce the observed behavior. Behavioral illusions are side effects of control in that sense. The fact that the observed relationship between qd and qo is the inverse of the feedback function (the S-R behavioral illusion described in the 1978 paper) is a side effect of control in this sense. Same for the power law;you don’t have to put anything into the control model to make the power law appear.

I don’t see it. More examples of your definition of side effects, please.

Observed relationship between qd and qo being determined by the G^-1 is - I think - the main effect of feedback, it is the same effect that makes qd and qf equal, and the same effect that makes qi equal to qi* or zero.

I think that before finding the controlled variable, all effects are hypothetically main effects or side effects. My hypothesis is that the power law is a side effect of controlling something like the shape of drawing and the rhythm or average velocity, and also depends on the properties of the system, because different systems will show the power law at different speeds. Also depends on the shape drawn, as different shapes will show different exponents.

The important part being - to classify something as a side effect, first the main effect needs to be found, the controlled variable. If there is no controlled variable found, you can’t claim something is a behavioral illusion, by my definition of side-effects.

But in a way, I do agree with you, the power law does not tell you anything definite about the system until you find the controlled variables. It might be that it is an intended effect, it might be it is not. Proof and demonstration only by models and experiments.

AM: It seems that main cause of our disagreement have been your repeated mistakes in identifying and defining functions in the control loop.

RM: I don’t think so.

AM: Or take a look again at the source of your conviction that functions correspond to causal paths.

RM … the illusion being that the relationship between d and o appears to reflect the causal path from stimulus (disturbance) to response (output) when, in fact, no such causal path exists. Do I have that wrong?

BP: Yes . There is clearly a causal path from d to qi (the disturbance function), another from qi to e (perceptual function and comparator with an input from r), another from e to o (output function), and finally another from o to qi (environmental feedback function). All but the last work in the “forward” direction.
Nothing mysterious happens when the loop is closed. The forward functions do not disappear. They are still there and are always working.

AM: You were saying that the possible explanation of the behavioral illusion is that the causal path does not exist at all. The causal path does exist,

RM: That’s right. I was wrong and Bill corrected me. Thanks to his correction and this discussion with you I now understand the behavioral illusion much better than I did. As Bill notes, the forward causal path from qd to qo (defined by the disturbance, perceptual, comparator and output functions), still exist in a closed loop. But in a closed loop system we can’t see this path (that is, we can’t see the forward function that relates qd to qo). What we see is the inverse of the feedback function, g, that relates qo to qi (or, if you prefer, that relates qo to an effect on qi).

So while there is a forward function connecting qd to qo in a closed loop, the experimental psychologist can’t see it ***or it’s inverse ***! That is, the experimental psychologist can see neither f nor f-1. The experimenter can see only the inverse of the feedback function, g-1, and takes it to be f (or f-1 if he thinks Powers demonstrated something other than what he demonstrated in the 1978 paper). That’s the behavioral illusion; the illusion is that when you see a relationship between qd and qo you are seeing f (or f-1) when what you are actually seeing is g-1.

Best

Rick

RM: Some of these are not side effects, from my point of view. A side effect is an observed aspect of the behavior of a control system that has nothing to do with its operation; it’s something you don’t have to put into a model of the control system in order to produce the observed behavior.

AM: I don’t see it. More examples of your definition of side effects, please.

RM: In the rubber band demo if you, as E, apply disturbances to the position of the knot so that S has to move her end of the rubber band in a way that traces out a perfect rendering of Botticelli’s Venus on the Half Shell, then that picture is a side effect of S controlling the position of the knot.

AM: I think that before finding the controlled variable, all effects are hypothetically main effects or side effects. My hypothesis is that the power law is a side effect of controlling something like the shape of drawing and the rhythm or average velocity, and also depends on the properties of the system, because different systems will show the power law at different speeds. Also depends on the shape drawn, as different shapes will show different exponents.

RM: Great! So start testing! I think you could do an exceptionally good job if it.

AM: The important part being - to classify something as a side effect, first the main effect needs to be found, the controlled variable. If there is no controlled variable found, you can’t claim something is a behavioral illusion, by my definition of side-effects.

RM: Absolutely. So start testing!

AM: But in a way, I do agree with you, the power law does not tell you anything definite about the system until you find the controlled variables. It might be that it is an intended effect, it might be it is not. Proof and demonstration only by models and experiments.

RM: Amen.

Best

Rick

AM: I don’t see it. More examples of your definition of side effects, please.
RM: In the rubber band demo if you, as E, apply disturbances to the position of the knot so that S has to move her end of the rubber band in a way that traces out a perfect rendering of Botticelli’s Venus on the Half Shell , then that picture is a side effect of S controlling the position of the knot.

Ok, makes sense. Any properties of qo, the final trajectory are a side effect of keeping qi stable.

The problem is that this definition of side effects is in conflict with your definition of a behavioral illusion. If the contour of Venus look exactly like the template you wanted to get, this tells you something very important about the control system that made it. For one, it is a high-gain control system, at the speeds that you gave it. If the contour of Venus looks somewhat distorted, the gain was not so high, the errors were not well compensated.

AM: But in a way, I do agree with you, the power law does not tell you anything definite about the system until you find the controlled variables. It might be that it is an intended effect, it might be it is not. Proof and demonstration only by models and experiments.

RM: Amen.

No so fast.

The same thing goes for “a behavioral illusion” in your power law papers. If it turns out that the power law is the main effect, that the trajectory is the controlled variable, or the instantaneous affine velocity is the controlled variable, both of which you suggested might be controlled; then the power law is not a side effect, it is the main effect, intended and achieved.

On the other hand, if some other variable is controlled, then the power law is a side effect, but it does tell you something about the control system. The exact speeds where the power law appears tell you something about, for example, force production constraints of the organism, or something about the interaction of the body and the environment in the loop, things like friction, inertia. etc.

Either way, really, the definition of “a behavioral illusion” is not self consistent.

AM: I don’t see it. More examples of your definition of side effects, please.
RM: In the rubber band demo if you, as E, apply disturbances to the position of the knot so that S has to move her end of the rubber band in a way that traces out a perfect rendering of Botticelli’s Venus on the Half Shell , then that picture is a side effect of S controlling the position of the knot.

AM: Ok, makes sense. Any properties of qo, the final trajectory are a side effect of keeping qi stable.

AM: The problem is that this definition of side effects is in conflict with your definition of a behavioral illusion. If the contour of Venus look exactly like the template you wanted to get, this tells you something very important about the control system that made it. For one, it is a high-gain control system, at the speeds that you gave it. If the contour of Venus looks somewhat distorted, the gain was not so high, the errors were not well compensated.

RM: Yes, but you know all that (or can know it, using modeling) because you know what the controlled variable is: the position of the knot. These are the kinds of things manual control theorists have been able to find out because they study control in situations where they know what the controlled variables are (or should be).

RM: What is unique about PCT Is that it posits that ALL behavior is the control of perceptual variables. This hypothesis is explicit in the hierarchical PCT model of purposive behavior. The hypothesis is that organisms control a hierarchy of different TYPES of perceptual variables. This hypothesis has been subjected to very little testing and yet it is treated as though it is a known fact. I’m trying to move PCT research in the direction of testing Powers’ hypothesis about the control hierarchy, a hypothesis (and a description of some of the evidence supporting it) that takes up at least 60% of B:CP.

AM: But in a way, I do agree with you, the power law does not tell you anything definite about the system until you find the controlled variables. It might be that it is an intended effect, it might be it is not. Proof and demonstration only by models and experiments.

RM: Amen.

AM: No so fast.

AM: The same thing goes for “a behavioral illusion” in your power law papers. If it turns out that the power law is the main effect, that the trajectory is the controlled variable, or the instantaneous affine velocity is the controlled variable, both of which you suggested might be controlled; then the power law is not a side effect, it is the main effect, intended and achieved.

RM: I agree. But I consider it very unlikely that the power law itself is a controlled variable; a person would have to be continuously perceiving whether the velocity and curvature of their movements had the appropriate power relationship. But if you could figure out a way to test that hypothesis (or the more plausible one about control of affine velicity) that would be great.

AM: On the other hand, if some other variable is controlled, then the power law is a side effect, but it does tell you something about the control system. The exact speeds where the power law appears tell you something about, for example, force production constraints of the organism, or something about the interaction of the body and the environment in the loop, things like friction, inertia. etc.

RM: I don’t think so but if you do figure out a way to test for the variables being controlled when organisms move their limbs then that in itself would be a wonderful discovery, from my perspective anyway.

RM: Perhaps now is the appropriate time for me to confess that I don’t consider myself to be a PCT research maven. I’m pushing research based on testing for controlled variables because I know that’s the right way to study the behavior of living control systems and I know that’s the kind of research Bill Powers was hoping researchers would start doing. I haven’t done a lot of this kind of research myself but I have some some (the best example, I think, is my object interception research where the test for controlled variable was used to choose the best of three different hypotheses about the variable controlled when intercepting moving objects).

RM: I’m mainly pushing testing for controlled variables because I would like some help doing this kind of research from people, like you Adam, are a lot smarter than I am. This is a very new approach to studying the behavior of living systems and it will take some ingenuity to figure out how to do it properly since it has never really been done before.

Best

Rick

I feel like you’ve missed my main point: side effects, as you define them, do tell you something about the system you’re testing. If you define a behavioral illusion as taking the side effects to tell you something about the system you’re testing, then that definition is wrong. It is not an illusion, side effects CAN tell you something about the organism or the control loop in general, after you find the controlled variable.

M&S: " …a behavioral illusion occurs when an observed relationship between variables is seen as revealing something about the mechanisms that produce a behavior when, in fact, it does not"

RM: In the rubber band demo if you, as E, apply disturbances to the position of the knot so that S has to move her end of the rubber band in a way that traces out a perfect rendering of Botticelli’s Venus on the Half Shell , then that picture is a side effect of S controlling the position of the knot.

AM: The problem is that this definition of side effects is in conflict with your definition of a behavioral illusion. If the contour of Venus look exactly like the template you wanted to get, this tells you something very important about the control system that made it. For one, it is a high-gain control system, at the speeds that you gave it. If the contour of Venus looks somewhat distorted, the gain was not so high, the errors were not well compensated.

RM: You can only have found – let alone even known about the existence of – the controlled variable if you had approached understanding the behavior from a PCT perspective. And in that case you would know which aspects of the behavior are side-effects (which are irrelevant to understanding the behavior) and which are not (which are relevant to understanding the behavior.

M&S: " …a behavioral illusion occurs when an observed relationship between variables is seen as revealing something about the mechanisms that produce a behavior when, in fact, it does not"

RM: In the rubber band demo if you, as E, apply disturbances to the position of the knot so that S has to move her end of the rubber band in a way that traces out a perfect rendering of Botticelli’s Venus on the Half Shell , then that picture is a side effect of S controlling the position of the knot.

AM: The problem is that this definition of side effects is in conflict with your definition of a behavioral illusion. If the contour of Venus look exactly like the template you wanted to get, this tells you something very important about the control system that made it. For one, it is a high-gain control system, at the speeds that you gave it. If the contour of Venus looks somewhat distorted, the gain was not so high, the errors were not well compensated.

RM: The side-effect is the observation that S is drawing a perfect rendering of Venus on the Half Shell. That observation tells you nothing about the mechanism that produced that behavior. But once you know that S is controlling the position of the knot (the controlled variable) then you know that how closely S’s drawing motions mirror the disturbance produced by E tells you something about the mechanism that produced that behavior; how closely S’s drawing motions mirror the disturbance produced by E is not a side-effect of control; it is a characteristic of control. But you can only know that once you know what S is controlling and, thus, that E’s movements are a disturbance to that variable.

Best

Rick

RM: You can only have found – let alone even known about the existence of – the controlled variable if you had approached understanding the behavior from a PCT perspective. And in that case you would know which aspects of the behavior are side-effects (which are irrelevant to understanding the behavior) and which are not (which are relevant to understanding the behavior.

A “controlled variable” is standard jargon of control theory, including perceptual control theory.

And yes - when you find the controlled variable, you know that maintaining the controlled variable is the main effect of the control system. All other effects are side effects. You cannot know what is a side effect and what is a controlled variable without at least a few TCVs.

You don’t know what is the main effect or what is the side effect until you find the controlled variable.

And here we come back to “a behavioral illusion”. You cannot claim something is a side effect if you haven’t found the controlled variable.

RM: The side-effect is the observation that S is drawing a perfect rendering of Venus on the Half Shell *. That observation tells you nothing about the mechanism that produced that behavior. But once you know that S is controlling the position of the knot (the controlled variable) then you know that how closely S’s drawing motions mirror the disturbance produced by E tells you something about the mechanism that produced that behavior; how closely S’s drawing motions mirror the disturbance produced by E is not a side-effect of control; it is a characteristic of control. But you can only know that once you know what S is controlling and, thus, that E’s movements are a disturbance to that variable.

Bold is demonstrably wrong. If the drawing is a perfect rendering of the Venus, this tells you that the mechanism is a high gain control system. That is the property of the mechanism, a characteristic of control.

Now, you claim that the power law is an example of a behavioral illusion, but you haven’t done a single test for the controlled variable. You don’t know what is the main effect and what is a side effect.

AM: when you find the controlled variable, you know that maintaining the controlled variable is the main effect of the control system. All other effects are side effects.

RM: Not true. For example,the effects of output and disturbances on the controlled variable are not side effects.

AM: And here we come back to “a behavioral illusion”. You cannot claim something is a side effect if you haven’t found the controlled variable.

RM: True, you have to have demonstrated that the observed behavior could be a side-effect of controlling some variable. And I have.

RM: The side-effect is the observation that S is drawing a perfect rendering of Venus on the Half Shell *. That observation tells you nothing about the mechanism that produced that behavior. …

AM: Bold is demonstrably wrong. If the drawing is a perfect rendering of the Venus, this tells you that the mechanism is a high gain control system. That is the property of the mechanism, a characteristic of control.

RM: As I said before, that is true only if you know that E’s disturbance movements were a mirror image of the Venus – so that S’s compensatory movements would be the non-mirror image of the Venus. The perfect rendering of the Venus in itself tells you nothing about the mechanism that produced S’s behavior.

AM: Now, you claim that the power law is an example of a behavioral illusion, but you haven’t done a single test for the controlled variable. You don’t know what is the main effect and what is a side effect.

RM: I have done such a test and I know that the power law could definitely be a side-effect of control. I described this test in my reply to your reply to my power law paper and in a previous post. But here it is again. Here are the data that demonstrate that the power law can be a side effect of controlling cursor position:

RM: Here are cursor movements made with a mouse.The controlled variable is the position of the cursor. It is controlled relative to a variable reference while it is also being disturbed by the computer. The cursor movements follow the power law; the mouse movements that produced the cursor movements don’t. The power coefficient for cursor movement is .3 (for R versus V) and .7 (for C versus A). The power coefficient for mouse movement is .05 (for R versus V) and .98 (for C versus A). The controlled result of mouse movement follows a power law but the mouse movements that produce that result don’t. So the power law fits a movement that was not the movement the subject was making (the mouse movement) but the one the subject was intending.

RM: The power law that characterizes cursor movement is a side effect of a control process that had nothing to do with producing a power law, as evidenced by the completely non-power law mouse movements that produced those cursor movements. The power law seen here is, therefore, a side effect of the operation of a control system that is intending to produce a particular cursor movement trajectory.

Best regards

Rick

AM: And here we come back to “a behavioral illusion”. You cannot claim something is a side effect if you haven’t found the controlled variable.

RM: True, you have to have demonstrated that the observed behavior could be a side-effect of controlling some variable.

Could be? That is not enough. The power law can be observed in pure noise. It also is perfectly possible to not get a power law when controlling position for slow targets. On the other hand, it is not possible for humans to make a non-power law trajectory when they are drawing ellipses fast. After some speed, all the exponents are 2/3.

For that behavior, fast drawing, relevant for the phenomenon of the power law, you did not do a test for the controlled variable. Position control fails for high speeds, you need to control a different variable.

To show that the power law is a side effect of controlling some variable, you need to find - well, I need to find - one variable or a set of variables that are stable when a person draws fast ellipses (or other shapes) despite disturbances to those variables; and a model that controls those variables and shows the power law in the same situations as the person - and does not show the power law in the same situations as the person.

But this is a topic on the behavioral illusion, and we already agreed that the power law is not an example of the behavioral illusion.

AM: And here we come back to “a behavioral illusion”. You cannot claim something is a side effect if you haven’t found the controlled variable.

RM: True, you have to have demonstrated that the observed behavior could be a side-effect of controlling some variable.

AM: Could be? That is not enough.

RM: I said “could be” in order to leave the door open to the very slight possibility that the power law is a controlled variable. But there is considerable evidence against that possibility: 1) the variability of the power law coefficient is more than what would be expected if it were controlled 2) most randomly generated movements correspond to a 2/3 power law coefficient, varying around it by about the same amount as organism-produced limb movements and 3) if none-power law movements are required to compensate for disturbances to a controlled variable – as was the case for the mouse movements in the tracking task I described in the previous post – then those non-power law movements will made; no problem. So I believe it has been conclusively demonstrated that the power law IS a side effect of control.

AM: For that behavior, fast drawing, relevant for the phenomenon of the power law, you did not do a test for the controlled variable. Position control fails for high speeds, you need to control a different variable.

RM: Perhaps. But I think it has been shown pretty clearly that the power law is a side effect of control, whatever variable(s) is (are) being controlled.

AM: To show that the power law is a side effect of controlling some variable, you need to find - well, I need to find - one variable or a set of variables that are stable when a person draws fast ellipses (or other shapes) despite disturbances to those variables; and a model that controls those variables and shows the power law in the same situations as the person - and does not show the power law in the same situations as the person.

RM: Why waste your time on showing that the power law is a side effect of control? I only did it to encourage those who are studying how people produce movements to stop wasting time studying this behavior from the mainstream perspective and start studying it from a control theory – specifically perceptual control theory – perspective. In other words, why not start figuring out the variables organisms control when they move their limbs.

AM: But this is a topic on the behavioral illusion, and we already agreed that the power law is not an example of the behavioral illusion.

RM: I suppose we agreed that it is not an example of “the” S-R illusion described in Powers 1978. But since it is an irrelevant side effect of control, having nothing to do with how movement is produced, it is certainly “a” behavioral illusion.

Best

Rick

RM: Why waste your time on showing that the power law is a side effect of control? I only did it to encourage those who are studying how people produce movements to stop wasting time studying this behavior from the mainstream perspective and start studying it from a control theory – specifically perceptual control theory – perspective. In other words, why not start figuring out the variables organisms control when they move their limbs.

The problem always was - and still is - how do people move their limbs. Any side effect - properties of the action that appear in human behavior - MUST appear in the behavior of the model doing the same task in the same conditions, if we are to consider the model explaining the behavior.

RM: Why waste your time on showing that the power law is a side effect of control? I only did it to encourage those who are studying how people produce movements to stop wasting time studying this behavior from the mainstream perspective and start studying it from a control theory – specifically perceptual control theory – perspective. In other words, why not start figuring out the variables organisms control when they move their limbs.

AM: The problem always was - and still is - how do people move their limbs. Any side effect - properties of the action that appear in human behavior - MUST appear in the behavior of the model doing the same task in the same conditions, if we are to consider the model explaining the behavior.

RM: You know that they are side effects only if you have already got the correct model of the behavior. A correct model of the behavior will be organized around the control of the perceptual variables that are the ones controlled by the organism being modeled. This model will automatically produce the same “side effects” as does the organism in the same circumstances.

RM: The goal of modeling behavior from a PCT perspective isn’t to develop a model that produces the same side-effects of control; it’s to develop a model that accounts for the observed controlling that is being done by the organism. Side effects are simply the aspects of behavior that behavioral scientists pay attention to when they don’t know that behavior is control. Behavioral scientists want to account for these side effects because they are consistent with their mainstream view of how behavior “works”. Side effects of control are the “red herring” you hear tell of in Bill’s 1978 paper. If you don’t know that behavior is control then you really have no need for PCT, which is a theory of control, not of irrelevant side effect of control.

RM: With PCT it’s phenomena phirst. If you don’t know that the phenomenon you are dealing with is control – the production of consistent results in a disturbance prone environment – then applying PCT to behavior is putting the cart way before the horse.

Best

Rick

RM: You know that they are side effects only if you have already got the correct model of the behavior. A correct model of the behavior will be organized around the control of the perceptual variables that are the ones controlled by the organism being modeled. This model will automatically produce the same “side effects” as does the organism in the same circumstances.

Nope. Demonstrably false.

In the tracking task, the controlled variable is the cursor-target distance. When you make a model with the correct controlled variable, you have to fit the model to each individual subject. Only then will you get a lot of the properties of subject behavior reproduced in the model.
The subject in a tracking task does not intent to have any particular accuracy, or any particular speed, for example. Simply using the correct controlled variable is the first step, but only when you tune the gains, delays, etc, the behavior of the model, will you get the model reproducing subject behavior for many different disturbances. Same speeds, same accuracy, same delays…

RM: The goal of modeling behavior from a PCT perspective isn’t to develop a model that produces the same side-effects of control; it’s to develop a model that accounts for the observed controlling that is being done by the organism. Side effects are simply the aspects of behavior that behavioral scientists pay attention to when they don’t know that behavior is control.

Again, demonstrably incorrect.

Look at Bill’s paper on arm control - he reproduced bell-shaped velocity curves and acceleration curves in arm movement, at the same time claiming that they are side effects of control of position and the properties of muscles and really the whole control hierarchy.

RM: Behavioral scientists want to account for these side effects because they are consistent with their mainstream view of how behavior “works”. Side effects of control are the “red herring” you hear tell of in Bill’s 1978 paper. If you don’t know that behavior is control then you really have no need for PCT, which is a theory of control, not of irrelevant side effect of control.

No, not at all. Behavioral scientists have observed some invariants and laws in behavior, and a correct model of behavior in question must reproduce those side effects.

The red herring (not in 1978 paper, I think) is simply assuming that the invariants and laws themselves are the controlled variable, the intended result. If there is a bell-shaped velocity, the red herring is assuming that the subject intended to produce the bell-shaped velocity, and then creating an elaborate control architecture that can produce such a velocity profile.

In the power law business, the produced trajectory has specific speed-curvature relationships. The red herring is assuming that the trajectory itself is intended and controlled.

RM: With PCT it’s phenomena phirst. If you don’t know that the phenomenon you are dealing with is control – the production of consistent results in a disturbance prone environment – then applying PCT to behavior is putting the cart way before the horse.

Yeah, ok, that doesn’t sound so bad.

I like these paragraphs on modelling from LCS:

RM: You know that they are side effects only if you have already got the correct model of the behavior. A correct model of the behavior will be organized around the control of the perceptual variables that are the ones controlled by the organism being modeled. This model will automatically produce the same “side effects” as does the organism in the same circumstances.

AM: Nope. Demonstrably false.

RM: I’d say it demonstrably took too much for granted so you got your signals crossed.

AM: In the tracking task, the controlled variable is the cursor-target distance. When you make a model with the correct controlled variable, you have to fit the model to each individual subject.

RM: Of course. I took that for granted. But I accept your correction. I should have said: A model controlling the correct variables with the appropriately selected control parameters will automatically produce the same “side effects” as does the organism in the same circumstances. How’s that?

RM: The goal of modeling behavior from a PCT perspective isn’t to develop a model that produces the same side-effects of control; it’s to develop a model that accounts for the observed controlling that is being done by the organism. Side effects are simply the aspects of behavior that behavioral scientists pay attention to when they don’t know that behavior is control.

AM: Again, demonstrably incorrect.

RM: Well, to quote a politician a dearly dislike: There you go again;-) In fact, it’s exactly right. And I"ll say it again to prove it: The goal of modeling behavior from a PCT perspective isn’t to develop a model that produces the same side-effects of control.

AM: Look at Bill’s paper on arm control - he reproduced bell-shaped velocity curves and acceleration curves in arm movement, at the same time claiming that they are side effects of control of position and the properties of muscles and really the whole control hierarchy.

RM: Oy vey! He didn’t do this to show how PCT research is done! He did it to show why mainstream research is bankrupt. That is, he did it for the same reason I produced my control model of movement control: to show that the folks who are studying invariant movement trajectories and power laws of movement are completely off base in their research; they are studying irrelevant side effects of control thinking they things tell them something important about behavior when they don’t.

RM: Behavioral scientists want to account for these side effects because they are consistent with their mainstream view of how behavior “works”. Side effects of control are the “red herring” you hear tell of in Bill’s 1978 paper. If you don’t know that behavior is control then you really have no need for PCT, which is a theory of control, not of irrelevant side effect of control.

AM: No, not at all. Behavioral scientists have observed some invariants and laws in behavior, and a correct model of behavior in question must reproduce those side effects.

RM: That’s your conclusion. It’s certainly not mine or Bill’s. Indeed, it’s precisely the opposite of what one would conclude based on an understanding of PCT. What behavioral scientists who understand PCT should do is ignore these things!! They are red herrings, sirens calling you from the rocks of ignorance. Just drop it and start doing research based on an understanding of organisms as perceptual control systems.

AM: The red herring (not in 1978 paper, I think) is simply assuming that the invariants and laws themselves are the controlled variable, the intended result.

RM: “… if one’s purposes [in doing behavioral research]concern objectivized side effects of control behavior, the man-machine blunder amounts to nothing worse than a few mislabelings having no practical consequences. If one’s interest is in the properties of persons, however, the man-machine blunder pulls a red herring across the path of progress” (Powers, 1978).

RM: It doesn’t sound to me like Bill was saying what you take him to be saying. The power law, invariant trajectory profiles, etc are objectivized side effects of control behavior. They are red herrings because they are irrelevant to understanding the behavior of living control systems.

RM: The only way you could know that the power law, invariant trajectory profiles, etc are objectivized side effects of control behavior is because you know what the actor is controlling. So you’ve already explained these side effects once you have explained the behavior in terms of the variables under control.

AM: If there is a bell-shaped velocity, the red herring is assuming that the subject intended to produce the bell-shaped velocity, and then creating an elaborate control architecture that can produce such a velocity profile.

AM: In the power law business, the produced trajectory has specific speed-curvature relationships. The red herring is assuming that the trajectory itself is intended and controlled.

RM: If a researcher assumed that the subject intended (in the PCT sense) to produce the invariant velocity profile or power law then that researcher would know that these are hypotheses about the variables the actor is controlling. So this researcher would would test to see whether the invariant velocity profile or power law are, indeed, controlled variables. And she would find that they are not and would move on to other hypotheses about the variables controlled when people make movements in space.

RM: In fact, the researcher who study these things are mistakenly taking them for intended results. They can’t tell an intended from an unintended result because they are looking at organisms are output generators. What is going on with research on what we know (but the researchers don’t know) are objectivized side effects of control is that researchers think these invariants reveal something important about how people work. So they will keep chasing these red herrings by doing experiments to see how variables affect them in the vague hope that this will reveal something about the mechanisms that produced these phenomena – and they won’t find what they are looking for because the actual explanation is just not what they want to hear: that these are irrelevant side effects of control – boy do they not want to hear that!

RM: Once you understand that organisms are control systems you no longer get seduced by randomly noticed characteristics of behavior – such as velocity profiles or power laws – no matter how invariant or mathematically attractive they are. You just ignore them and start looking for the variables around which the behavior of interest is organized.

RM: With PCT it’s phenomena phirst. If you don’t know that the phenomenon you are dealing with is control – the production of consistent results in a disturbance prone environment – then applying PCT to behavior is putting the cart way before the horse.

AM: Yeah, ok, that doesn’t sound so bad.

RM: Good.

Best

Rick

RM: Me too!

RM I should have said: A model controlling the correct variables with the appropriately selected control parameters will automatically produce the same “side effects” as does the organism in the same circumstances. How’s that?

That is good. The point of it being - the side effects of control of position in the tracking task are also side effects of the control parameters, including properties of the organism - input gain, output gain, etc.

If side effects depend on the parameters, that means you can learn a lot about the system just from the side effect (again with the disclaimer that you know the controlled variable).

RM: The goal of modeling behavior from a PCT perspective isn’t to develop a model that produces the same side-effects of control .

Nonsense.

If the model does not reproduce behavior of the subject, it does not deserve to be called a model of the behavior of the subject. Behavior of the subject includes all the main effects and side effects.

Take the tracking task - it reproduces all the main effects and most of the side effects of controlling position in a situation with a random disturbance.

RM: Oy vey! He didn’t do this to show how PCT research is done! He did it to show why mainstream research is bankrupt. That is, he did it for the same reason I produced my control model of movement control: to show that the folks who are studying invariant movement trajectories and power laws of movement are completely off base in their research; they are studying irrelevant side effects of control thinking they things tell them something important about behavior when they don’t.

He built a model of human arm control. He showed how the velocity profiles emerge from the properties of the system and control of position, without explicit trajectory control. Sure, there are other reasons for building the model, but the model DID reproduce the laws found in human behavior.

RM: That’s your conclusion. It’s certainly not mine or Bill’s. Indeed, it’s precisely the opposite of what one would conclude based on an understanding of PCT. What behavioral scientists who understand PCT should do is ignore these things!! They are red herrings, sirens calling you from the rocks of ignorance. Just drop it and start doing research based on an understanding of organisms as perceptual control systems.

Nonsense. Why did Bill show velocity profiles of the arm? He certainly did not ignore them.

RM: Once you understand that organisms are control systems you no longer get seduced by randomly noticed characteristics of behavior – such as velocity profiles or power laws – no matter how invariant or mathematically attractive they are. You just ignore them and start looking for the variables around which the behavior of interest is organized.

Let’s just focus on this part. Bill certainly did not ignore the velocity profiles. If his arm produced trapezoidal profiles, it would have to go back to the drawing table.

Side effects of control are ALSO side effects of organism properties and also side effects of disturbance properties and so on. If there are regular side effects, they must be explained by the model.

A PCT model of behavior must first identify the controlled variable, and second, all the properties of behavior must be reproduced, including any laws and mathematical regularities (if they are indeed regularities and not illusions), in the same conditions that they appear in experiments in humans.