# Behavioral illusion, based on Powers (1978)

Adding the H function that converts a disturbance to the disturbance effect on qi is definitely a thing to explore. The solution for the qo-qo in an ideal negative feedback system is:

qo = G^-1 [ H (qd) ]

The interesting phenomenon is when the disturbance function is the same as the feedback function, G=H. The inverse of G cancels out the inner G, and the equation simplifies to just

qo = qd

If H and G are nonlinear, the nonlinearities cancel out, we get a linear relationship.

AM: You also wrote in the previous post (twice) that the organism function is relating qd and qo, that is not correct. The organism function is relating qi and qo.
RM: Actually, we are both correct.

Nice damage control. You were referring to some other organism function.

Also, correct for the qo varying as derivative of qd.

Let me get back to this:

RM: Maybe this is the source of our apparently irreconcilable differences. This is an invention of yours; it has nothing to do with Bill’s 1978 paper. What you are saying is that qo and qi are not related by a function because there are other causal paths ending in qi. In Bill’s analysis in the 1978 paper the only other causal path ending in qi besides the one from qo is the one from qd. So you are saying that because qi = h(qd) + g(qo), qo and qi are not related by the function g(). Nothing like that shows up in Bill’ analysis probably because it is not true; qd and qo have independent effects (via independent functions) on qi so the functional relationship between qo and qi – the feedback effect of qo on qi – can be treated – indeed, must be treated – independently from the effect of qd on qi.

I’m saying that because qi = h(qd) + g(qo), it is not correct to say “qi and qo are related by function G”, because it is misleading. It implies that you can write qi = G(qo), but that is not correct, because that is not what the plots are going to show.

If you make a plot for an ideal negative feedback system, qi is going to be just one constant value (emphasize - in IDEAL negative feedback systems, in real systems it is going to be some low correlation cloud). So, qi is really not related (correlated) to any other variable in the ideal negative feedback system, even though there are at least two causal paths ending in qi.
(edited the upper two paragraphs a few times, not yet sure it is too clear. Qi is related to qo by an integral, which is a function too…)

Which brings me to the answer to what happens if the type of the controlled variable is different - nothing much. For good control, qi is always going to be more stable (have less variance) than some disturbing quantity, because behavior will vary to oppose the disturbance and keep qi near the reference value. To the extent any real system is well approximated by an ideal negative feedback system, the relationships hold. For low gain control, or difficult disturbances, or very nonlinear input functions, many things are possible, like your demo area vs perimeter shows.

RM: It seems to me that discussing the behavioral illusion without discussing controlled variables is like discussing the bent stick illusion without discussing the differential refraction of light in air and water.

Not at all. Qi represents all possible controlled variables. All the same to math or simulation. Just trying to stay on topic.

RM: And I also wonder why you are fixated on the S-R behavioral illusion described in Powers (1978).

I think it is a very interesting phenomenon, not just as the possible illusion in behavior research, but as a general property of negative feedback systems. It was used in analog computers to build inverse functions, and it is still used in control engineering and in designing amplifier circuits, etc, etc. Wherever there are feedback systems, there is input-output determined by the function in the feedback path, and mostly independent of the amplifier gain in the forward path. It is important to understand it right, can be useful for research.

RM: It doesn’t seem relevant to your power law of movement research. It’s only relevant to research where an environmental variable (qd) is manipulated under controlled conditions to determine whether there is concomitant variation in a behavioral variable (qo). In the power law research both variables involved in the power law – curvature and speed of movement – are behavioral variables. So there is no controlled variable being disturbed by one of those variables and protected from that disturbance by the other.

That sounds like something I would say (almost). Highly suspicious to hear it from you.

Ok, I’ll bite. What brings you to that conclusion after your previous conviction that the power law is an example of the behavioral illusion?

AM: The interesting phenomenon is when the disturbance function is the same as the feedback function, G=H. The inverse of G cancels out the inner G, and the equation simplifies to just

qo = qd

RM: Yes, this is the situation in most of the tracking tasks we use in demos since G and H are typically multipliers of 1.0. That’s why we see the nice “mirror image” relationship between qo and qd.

AM: If H and G are nonlinear, the nonlinearities cancel out, we get a linear relationship.

RM: Yes!.

AM: You also wrote in the previous post (twice) that the organism function is relating qd and qo, that is not correct. The organism function is relating qi and qo.

RM: Actually, we are both correct.

AM: Nice damage control. You were referring to some other organism function.

RM: It wasn’t “damage control”. It was simply pointing out an essential fact about what Powers was referring to as the “organism function” in the article we have been discussing. You were right that qo = f(qi) is the “organism function” in a control diagram. But because Powers paper was about how scientific psychologists go about trying to determine the organism function, he wrote the organism function as qo = f[h(qd)]. This is because experimental psychologists implicitly assume that the proximal cause of behavior – what we call qi – is directly proportional to the distal cause – qd – which is the independent variable in conventional psychology experiments. That is, experimental psychologists have assumed tha h(qd) is essentially a multiplier of 1 so that qi = qd. So while conventional psychologists are actually looking at the relationship qo = f[h(qd)] they assume they are looking directly at the system function qo = f(qi).

RM: It is not “damage control” to point out that Powers considered qo = f[h(qd)] --rather than qo = f(qi) – to be the relevant organism function because seeing the organism function as qo = f[h(qd)] is crucial to understanding the behavioral illusion, as can be seen in this except from Powers (1978):

RM: I highlighted “organism function” to make it clear that Bill is referring to the second equation – qo = f[h(qd)] – as the organism function, the one for a Z- system.

AM: Let me get back to this:

RM: Maybe this is the source of our apparently irreconcilable differences…What you are saying is that qo and qi are not related by a function because there are other causal paths ending in qi…

AM: I’m saying that because qi = h(qd) + g(qo), it is not correct to say “qi and qo are related by function G”, because it is misleading. It implies that you can write qi = G(qo), because that is not what the plot are going to show.

RM: Well, I don’t think it is misleading. But I no longer think this is the reason for our disagreement.

RM: It seems to me that discussing the behavioral illusion without discussing controlled variables is like discussing the bent stick illusion without discussing the differential refraction of light in air and water.

AM: Not at all. Qi represents all possible controlled variables. All the same to math or simulation. Just trying to stay on topic.

RM: I meant that when the topic of discussion is the behavioral illusion as described in Powers (1978) – an illusion that results from failure to take into account the fact that qd and qo have opposing effects on a controlled variable, Qi, whatever that variable may be – it seems like the discussion should always focus on the fact that the illusion occurs because the existence of controlled variables is being ignored or missed.

RM: And I also wonder why you are fixated on the S-R behavioral illusion described in Powers (1978)…
RM: It doesn’t seem relevant to your power law of movement research…

AM: That sounds like something I would say (almost). Highly suspicious to hear it from you.

AM: Ok, I’ll bite. What brings you to that conclusion after your previous conviction that the power law is an example of the behavioral illusion?

RM: I never thought the power law was an example of the behavioral illusion described in Powers (1978). It was obvious from the get go that the power law was not that kind of illusion; there was no independent variable that could be the qd causing a qo via the organism. But it is an illusion in the same way that the observed relationship between qd and qo is an illusion; it is an observed side effect of control that is taken to reflect something about how the organism works – about the organism function – when it doesn’t. I explained this in both of my papers on the power law. You (and almost everyone else involved in that debate) didn’t care much for my explanation, to say the least. So let’s just leave it at our agreeing that the power law is not an example of the behavioral illusion described in Powers (1978).

Best

Rick

RM: It wasn’t “damage control”. It was simply pointing out an essential fact about what Powers was referring to as the “organism function” in the article we have been discussing. You were right that qo = f(qi) is the “organism function” in a control diagram. But because Powers paper was about how scientific psychologists go about trying to determine the organism function, he wrote the organism function as qo = f[h(qd)].

Sorry, I thought it was damage control.

To me, it seems like “the organism function” is always F, defined in equation (1) qo = F(qi). Bill is very consistent about it in the paper. The equation qo = f(h(qd)) is not the organism function, and he doesn’t refer to it as the organism function. It is the solution for a zero-feedback system for qo, meaning “how will qo depend on other variables in the system”.

In the text you highlighted, he is saying that the organism function F is replaced by the feedback function G’s inverse in the solutions. He is comparing to equations, solution for qo for an N system, and solution for qo for a Z system. He is also saying that qi* can be taken as zero. Let’s also put a name to H(qd), to simplify the expressions:

(1) qi* = 0
(2) qe = H(qd)

(3) qo = G^-1 [ qi* - H(qd) ]
(4) qo = G^-1 [ H (qd) ]
(5) qo = G^-1 ( qe )

Equation (3) is a solution for qo for a negative feedback system taken from the paper, and equation (5) is a slightly simplified form.

(6) qo = F [ H (qd) ], using (2):
(7) qo = F ( qe )

Equation (6) is a solution for qo for a zero feedback system taken from the paper, and equation (7) is a slightly simplified form.

Specifically in the sentence where you highlighted “organism function”, he is referring to these two equations:

N-system equation: (5) qo = G^-1 ( qe )
Z-system equation: (7) qo = F ( qe )

In the N-system equation, qo is determined by the feedback function’s inverse of qe. In the Z-system equation, the qo is determined by the F function of qe. That is why he says “the organism function F in the z-system equation is replaced by the feedback function g^-1 in the N system equation”.

RM: So while conventional psychologists are actually looking at the relationship qo = f[h(qd)] they assume they are looking directly at the system function qo = f(qi).

If they are looking at an N system, they are looking at qo = G^-1 ( H (qd) ], or simplified (5) qo = G^-1(qe), but they assume they are looking at (7) qo = F (qe). They have misidentified an N system, thinking it is a Z system.

If they measure this in an experiment:
qo = 0.2 * qe

They will think that F(x) = 0.2 * x. That is the behavioral illusion, because F might really be F(x)= integral (1000x) or whatever, and the 0.2 was determined by their experimental setup where they had some G function G(x) = 5 * x.

RM: I meant that when the topic of discussion is the behavioral illusion as described in Powers (1978) – an illusion that results from failure to take into account the fact that qd and qo have opposing effects on a controlled variable , Qi, whatever that variable may be – it seems like the discussion should always focus on the fact that the illusion occurs because the existence of controlled variables is being ignored or missed.

I think that ignoring the existence of controlled variables is a consequence of having a wrong model of organism behavior. There is no such thing as a controlled variable if the model of behavior is a lineal causation, stimulus-response, R = O(S), which is equivalent to (7) qo = F(qe).

The behavioral illusion happens because of adopting (7) as the model of organism behavior and trying to find the organism function O by relating stimuli to responses. Sure, they are also ignoring controlled variables and dynamics of feedback systems and so on, but I think the core of the illusion is the R = O(S) model. An error in system identification.

RM: I never thought the power law was an example of the behavioral illusion described in Powers (1978).

No?

M&S (2018): In the present paper we answer these claims and show that the power law of movement is, indeed, an example of a behavioral illusion.
[…] we showed that this assumption is likely to be based on what Powers (1978) called a behavioral illusion

The title of the paper - “Power law as behavioral illusion” - really sounds like you think (or thought at the moment of writing) that the power law is an example of the behavioral illusion, as defined in 1978 paper. Now it sounds like you’ve changed your mind.

As for the side effects of control not revealing something about the organism, we might disagree there too, as side-effects often do reveal “something” about the organism (reaction time reveals something about the level of control, maybe), but that is a whole different discussion not related to the behavioral illusion.

RM: So let’s just leave it at our agreeing that the power law is not an example of the behavioral illusion described in Powers (1978).

Great, fine with me.

AM: To me, it seems like “the organism function” is always F, defined in equation (1) qo = F(qi). Bill is very consistent about it in the paper. The equation qo = f(h(qd)) is not the organism function, and he doesn’t refer to it as the organism function.

RM: The function qo = f[h(qd)] is the organism function from the point of view of scientific psychologists who view organisms as Z-systems. This equation is equivalent to the organism function in equation (1) because qi = h(qd) and experimental psychologists assume that h() is a multiplier of 1. And Bill certainly does refer to the f function in the equation for a Z-system – qo = f[h(qd)] – as “the organism function” when he says " …the organism function f in the Z-system equation is replaced by the inverse of the feedback function g-1 in the N-system equation".

AM: Specifically in the sentence where you highlighted “organism function”, he is referring to these two equations:

N-system equation: (5) qo = G^-1 ( qe )
Z-system equation: (7) qo = F ( qe )

AM: In the N-system equation, qo is determined by the feedback function’s inverse of qe. In the Z-system equation, the qo is determined by the F function of qe. That is why he says “the organism function F in the z-system equation is replaced by the feedback function g^-1 in the N system equation”.

RM: That’s mathematically correct because you have defined qe = h(qd). This hides the fact that it is qd – not qe – that is manipulated in a psychology experiment. Thus, you have effectively “buried the lede” of Bill’s paper, which is as follows: The foundation of experimental psychology is that DV = f(IV) or, in Bill’s terms, qo = f(qd), where f() represents functional characteristics of the organism under study.This foundational assumption is wrong if organisms are N-Systems.

RM: So while conventional psychologists are actually looking at the relationship qo = f[h(qd)] they assume they are looking directly at the system function qo = f(qi).

AM: If they are looking at an N system, they are looking at qo = G^-1 ( H (qd) ], or simplified (5) qo = G^-1(qe), but they assume they are looking at (7) qo = F (qe). They have misidentified an N system, thinking it is a Z system.

RM: Conventional psychologists can’t be looking at qo = G^-1(qe) or qo = F(qe) because they can’t see qe! The whole point of the 1978 paper is that experimental psychologists have been studying relationships between qd’s and qo’s (IV’s and DV’s) thinking that those relationships, when they are found, tell them something about the nature of the organism’s under study; about the organism function, f. But, in fact, they are looking at the inverse of the feedback function that relates qo to qi.

RM: By writing your equations in terms of qe, you have managed to conceal (from your readers as well as from yourself) the main point of Powers’ 1978 paper, which is: 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. In order to understand the behavior of a living control system you have to determine what variables it is controlling. This is the truly revolutionary point of PCT.

AM: If they measure this in an experiment:
qo = 0.2 * qe

RM: They can’t (and don’t) measure that in an experiment because they can’t measure qe. If they could, they would be measuring qi and they would, thus, already be doing PCT based experiments. But what conventional experimental psychologists can (and do) measure in an experiment is qd, the disturbance (IV) and qo, system output (DV).

AM: The behavioral illusion happens because of adopting (7) as the model of organism behavior and trying to find the organism function O by relating stimuli to responses. Sure, they are also ignoring controlled variables and dynamics of feedback systems and so on, but I think the core of the illusion is the R = O(S) model. An error in system identification.

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 – an N- System – controlling perceptual aspects of its own environment. Once you know that you have made this error you can stop studying the system as though it were a cause - effect system – a Z- System - and start studying it knowing that is is an N - System. And that means you can start doing research aimed at identifying the variables the system controls rather than the variables that “control” (or cause the behavior of) the system. Because there are no such variables.

RM: I never thought the power law was an example of the behavioral illusion described in Powers (1978).

AM: No?

M&S (2018): In the present paper we answer these claims and show that the power law of movement is, indeed, an example of a behavioral illusion.
[…] we showed that this assumption is likely to be based on what Powers (1978) called a behavioral illusion

RM: In English (and, according to linguist John McWhorter, in all European languages) articles are very important. So notice that I referred to “a behavioral illusion” (using the indefinite article “a”) rather than “the behavioral illusion” (using the definite article “the”). Once you understand that organisms are N- rather than Z- Systems you can see that experimental psychologists have been subject to several illusions, all of which result from failure to notice controlled variables. Another obvious illusion – one that Powers has discussed (though not in the 1978 paper) – Is the reinforcement illusion; the illusion that consequences select actions when, in fact, actions control consequences.

AM: The title of the paper - “Power law as behavioral illusion” - really sounds like you think (or thought at the moment of writing) that the power law is an example of the behavioral illusion, as defined in 1978 paper. Now it sounds like you’ve changed your mind.

RM: That time I left out the article. In English that implies the indefinite article. 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. In both of our papers on the power law I tried to make clear what we meant by “behavioral illusion”. Here’s a quote from the second paper: " …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". The power law (like the S-R illusion) is a behavioral illusion in this sense.

AM: As for the side effects of control not revealing something about the organism, we might disagree there too, as side-effects often do reveal “something” about the organism (reaction time reveals something about the level of control, maybe), but that is a whole different discussion not related to the behavioral illusion.

RM: Reaction time is not a side effect of control; it is as aspect of control system operation.

RM: So let’s just leave it at our agreeing that the power law is not an example of the behavioral illusion described in Powers (1978).

AM Great, fine with me.

RM: But I do admit that I am interested in knowing what you think the power law tells us about how an N-System produces curved movements. Well, maybe not that interested;-)

Best

Rick

RM: The function qo = f[h(qd)] is the organism function from the point of view of scientific psychologists who view organisms as Z-systems.

Well,that is the solution of a Z system, in terms of the 1978 paper, it is NOT the organism function. From the point of view of scientific psychologists, it is something like R = O (S), they don’t usually speak about disturbances or quantities, etc.

RM: This equation is equivalent to the organism function in equation (1) because qi = h(qd) and experimental psychologists assume that h() is a multiplier of 1.

Good. For no feedback effects in a Z-system, qi = h(qd) is correct.

RM And Bill certainly does refer to the f function in the equation for a Z-system – qo = f[h(qd)] – as “the organism function” when he says " …the organism function f in the Z-system equation is replaced by the inverse of the feedback function g-1 in the N-system equation".

Yes, he refers to F as the organism function.

He does not refer to qo = f[h(qd)] as the organism function, as you claimed two posts ago. There is no other organism function in the 1978 paper. Glad we have that settled. You were not doing damage control, you really misunderstood the text.

RM: That’s mathematically correct because you have defined qe = h(qd). This hides the fact that it is qd – not qe – that is manipulated in a psychology experiment. Thus, you have effectively “buried the lede” of Bill’s paper, which is as follows: The foundation of experimental psychology is that DV = f(IV) or, in Bill’s terms, qo = f(qd), where f() represents functional characteristics of the organism under study.This foundational assumption is wrong if organisms are N-Systems.

In Bill’s terms, it is qo = F(H(qd)), so bold is not quite correct. If you put H(x) = x, then it is correct.

Also, for H(x) = x, you get a nice: qe = qd, so you can replace qe with qd in the equations of Z-systems.

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

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).

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).

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)).

There, now with H. The only difference between these two equations is that the F is replaced by G^-1. 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: inverse of the feedback function that relates qo to qi.

Nope. The feedback function relates qo to effects on qi. The organism function F relates qo and qi.

Organism function: qo = F(qi)
Feedback function: qf = G(qo)
Disturbance function: qe = H(qd)
Environment function: qi = G(qo) + H(qd), or equivalently: qi = qf + qe

RM the main point of Powers’ 1978 paper, which is: 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. In order to understand the behavior of a living control system you have to determine what variables it is controlling. This is the truly revolutionary point of PCT.

That is good, the bold part. I agree that is one of the main points of the paper. There are many other minor points, one of which is the behavioral illusion (topic of the current discussion), and others are various blunders and mistakes.

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.

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.

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: 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

“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.”

Yes, I agree. An error in system identification is an error in system identification. They did not notice there is feedback in behavior, or they did not think it is important. Their error is possibly going to result with the behavioral illusion, if they claim they found the organism function in the S-R relationship, and then we can reveal the error by pointing out “hey, that is a behavioral illusion, your S-R relationship will change when you change the environment feedback function G”.

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. In both of our papers on the power law I tried to make clear what we meant by “behavioral illusion”. Here’s a quote from the second paper: " …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". The power law (like the S-R illusion) is a behavioral illusion in this sense.

Hm. So, you quote the 1978 paper for people to look up the definition of the behavioral illusion, which is taking the observed S-R relationship as the organism function F when the S-R relationship reveals the inverse of the environmental feedback function G.

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: Reaction time is not a side effect of control; it is as aspect of control system operation.

Sure it is. The main effect of control is keeping the controlled variable stable or at reference level. All other effects are side-effects. And many times, they do reveal something about the organism or the “mechanisms that produce behavior”.

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.

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