Behavioral illusion, based on Powers (1978)

The behavioral illusion has been a point of some disagreement in the past, both on CSG net and in published papers. For example, Rick defines the behavioral illusion as: “the illusion that behavior is a cause-effect process” (recent csg net post)

Here I’d like to argue for a more strict definition, as defined in Bill’s spadeworks paper from 1978.

Thus, in the relationship between bug movement and head turning, we are not seeing the function f that describes the bird; instead, we are seeing the function g that describes the physics of the feedback effects. This property of N systems is well known to control engineers and to those who work with analog computers. It is time behavioral scientists became aware of it, whatever the consequences.

Here is an example from analog computing:

# Diagram of a system calculating square roots
#
#                  |\
#            i     | \              o   
#           ──────>│+ >──────────┭───── 
#              ┌──>|-/           │
#              │   |/            │
#              └─────────(x^2)───┘    
#

To compare with Bill’s diagram, the f function is a high gain amplification in the comparator-amplifier, while the feedback function g is the x^2. The resulting input-output function will be the inverse of the feedback function, o will vary as the square root of i, even though there is no root function in the whole system.

download

This time plot shows that o calculated by the setup in the diagram closely tracks the value of sqrt(i) calculated numerically, (they are overlapping).

So, according to Bill’s definition from 1978, the behavioral illusion would happen only if someone would say “this amplifier contains a root function”.

Perhaps it is more common that the feedback function is just a multiplier with 1, not changing the output value, as we usually model it in a tracking task. In this case the inverse of the feedback function would be just division by 1. If the organism function is a high-gain amplifier, this means that the input and output would be the same (or same value, opposite sign, depending on the setup).

The behavioral illusion here would happen only if someone would say “the organism function is output = input”. or “organism function is o = f(i), where f = 1 * x”.

Simulation of the analog computer square root setup:
https://colab.research.google.com/drive/1uC15-Sol_dzwMgQGAU-esABFWNYDdg4h

Hi Adam

AM: The behavioral illusion has been a point of some disagreement in the past, both on CSG net and in published papers. For example, Rick defines the behavioral illusion as: “the illusion that behavior is a cause-effect process” (recent csg net post)

AM: Here I’d like to argue for a more strict definition, as defined in Bill’s [spadeworks paper from 1978]

BP: Thus, in the relationship between bug movement and head turning, we are not seeing the function f that describes the bird; instead, we are seeing the function g that describes the physics of the feedback effects.

AM: Here is an example from analog computing:…

AM: This time plot shows that o calculated by the setup in the diagram closely tracks the value of sqrt(i) calculated numerically, (they are overlapping).

AM: So, according to Bill’s definition from 1978, the behavioral illusion would happen only if someone would say “this amplifier contains a root function”.

AM: Perhaps it is more common that the feedback function is just a multiplier with 1… The behavioral illusion here would happen only if someone would say “the organism function is output = input”. or “organism function is o = f(i), where f = 1 * x”.

RM: Right, the behavioral illusion happens if someone says that the organism function is o = f(i), regardless of what the function appears to be. The relationship o = f(i) implies that behavior (o) is caused by input (i). So saying that the behavioral illusion involves seeing behavior as a cause-effect process is perfectly consistent with Bill’s definition of the behavioral illusion. “We are not seeing the function f that describes the bird” (that function is not a causal function) "instead, we are seeing the function g that describes the physics of the feedback effects., which is a causal function.

RM: By the way, this is not the only way we see a behavioral illusion. It also happens when we see o as a function of mental variables (m): o = f(m). This is the mistake you are making with the power law.

RM: The point of Bill discussion in the 1978 paper is that the behavioral illusion has led psychologists to ignore the most important feature of behavior: controlled variables. All versions of the behavioral illusion (which are described in my “Blind Men and the Elephant” paper in MORE MIND READINGS) result from failure to see that behavior is organized around the control of perceptual aspects of the environment – controlled variables.

RM: So saying that the behavioral illusion involves seeing behavior as a cause-effect process is perfectly consistent with Bill’s definition of the behavioral illusion.

Some people might make the mistake of saying the stimuli cause responses, this is certainly better expressed with dynamics of control loops, rather than causal statements. However. all elements of the control loop are “causal” in the behavior of the loop. The loop would not work the same if the amplifier gain was low or if the organism function gain was low. If you would change any element in the loop, the behavior would change, therefore all elements are causal. Changes in some will have bigger effects than changes in others, but those are questions of magnitude, not causality.

Check this out:

[From Bill Powers (2012.12.24.1215 MST)]

RM: Yes, but is o really a causal function of d? 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.

RM: The point of Bill discussion in the 1978 paper is that the behavioral illusion has led psychologists to ignore the most important feature of behavior: controlled variables.

Psychologists have certainly mostly ignored controlled variables, but that is not the point.The point of the behavioral illusion discussion in that paper is that the apparent organism function, which you get as o = f(i), does not describe the organism. Instead, as we both agree, describes some feedback path function.

The input-output function is really there, you can perfectly observe it in the analog computer for example. The output will vary as the root of input. The mistake is simply in ascribing it to the amplifier or to the organism.

This is important.

RM : The relationship o = f(i) implies that behavior (o) is caused by input (i).

Why would this be? I think that functional relationships are completely independent of any causal claims. A similar claim is “correlation does not imply causation”.

Hi Adam

RM: The point of Bill discussion in the 1978 paper is that the behavioral illusion has led psychologists to ignore the most important feature of behavior: controlled variables.

AM: Psychologists have certainly mostly ignored controlled variables,

RM: “Totally ignored” would be a better way to put it.

AM: but that is not the point.The point of the behavioral illusion discussion in that paper is that the apparent organism function, which you get as o = f(i), does not describe the organism. Instead, as we both agree, describes some feedback path function.

RM: Yes, as long as you understand that the i in that equation is the equivalent of the disturbance, d, to the controlled variable, qi, in Bill’s analysis. Conventional psychologists think of the disturbance as the stimulus input to the organism and assume it is correlated with the sensory input, i, that is the cause of output, o. The behavioral illusion is that the function relating d to o (independent to dependent variable in research) is a characteristic of the organism when, in fact, it is the inverse of the feedback connection from output, o, to the controlled variable, qi, to which d is a disturbance.

AM: The input-output function is really there, you can perfectly observe it in the analog computer for example. The output will vary as the root of input. The mistake is simply in ascribing it to the amplifier or to the organism.

RM: Yes, but the input-output function you are talking about is not the one that is illusory. The input-output function that is illusory is the one between disturbance and output. The problem with your analysis is that the labelings in your square root calculator are quite misleading with respect to how PCT maps control theory to living systems. Here’s is your diagram:

image

RM: The i in this diagram actually corresponds to the d in Bill’s 1978 analysis. The equivalent of the controlled variable is the difference between i, and o^2: qi = o^2 - i. Your variable o is actually the perceptual, error and output variables all rolled into one. The function x^2 is the feedback function that transforms o into an effect on the controlled variable.

RM: So in PCT terms, what you have shown is that the relationship between disturbance, i, and output, o, is a square root function, o = d^1/2, which is the inverse of the feedback function relating o to qi, which is the squared function, qi = o^2. That is (in terms of PCT notation) you show that o = d^1/2 when qi = o^2 - i. This happens because the implicit reference for the controlled variable – for o^2 - i – is 0 and in order to get that variable to be = 0, the output, o, must be the square root of the effect of o on the controlled variable.

RM: The actual organism or input-output function in PCT is:

qo = f(qi -r).

The input variable is qi, which in simplest terms is qo + d. In terms of the notation used in your demo, the organism function is o = (o^2 - i ) - 0.

RM: So there certainly is an input-output function in a control system but you have no chance of knowing what it is unless you know what variable is being controlled; that is, you have to know the input variable to the system – controlled variable, qi.

RM: So the whole enchilada of understanding the behavior of living organisms hinges on knowing what variables organisms control. It’s all about controlled variables!

Best

Rick

RM: The behavioral illusion is that the function relating d to o (independent to dependent variable in research) is a characteristic of the organism when, in fact, it is the inverse of the feedback connection from output, o, to the controlled variable, qi, to which d is a disturbance.

Yes. Glad we agree, then.

(though, the feedback function relates qo to to qf in a living control system)

RM: Yes, but the input-output function you are talking about is not the one that is illusory. The problem with your analysis is that the labelings in your square root calculator are quite misleading with respect to how PCT maps control theory to living systems.

That demo is not meant to represent a living control system, and the labels don’t match, but the setup is analogous to any feedback system.

The input i in the demo would be equivalent to the reference signal, entering the comparator / amplifier with a positive sign. The other input to the comparator would be equivalent to the perceptual signal, entering with the negative sign. The simulated comparator first finds the error, then multiplies with gain, then adds the error to a leaky integrator, so the output o of the comparator is something like the behavioral output, but not quite.

For clarity, we can expand it to full pct diagram, replacing system function f from Bill’s diagram with the organism.

The qd-qo function will depend very little on the upper forward path, and mostly on the lower feedback path, given that the reference is zero, and that the forward gain is large. In the forward path, you have both the input function and the output function. In the feedback path, there is just the feedback function. In Bill’s paper, the reference is labeled qi*, being the reference level, and not reference signal, and set to 0.

I have the impression that the behavioral illusion, as defined here, is not very common. I have found very few examples in the literature. Maybe I’m not looking to the right places.

RM: So the whole enchilada of understanding the behavior of living organisms hinges on knowing what variables organisms control. It’s all about controlled variables!

Yeah, you’re preaching to the choir.

AM: Psychologists have certainly mostly ignored controlled variables,

RM: “Totally ignored” would be a better way to put it.

I’ve found a few examples where controlled variables are hypothesized, discussed and even tested for stability when disturbed, with reference to classical control theory. For example, the Center of Mass in maintaining balance literature, then various ‘muscle length’ , ‘muscle force’, ‘second derivative of force’, as measured by the muscle spindles and golgi tendon organs, etc. That is why I say mostly.

Hi Adam

RM: The behavioral illusion is that the function relating d to o (independent to dependent variable in research) is a characteristic of the organism when, in fact, it is the inverse of the feedback connection from output, o, to the controlled variable, qi, to which d is a disturbance.

AM: Yes. Glad we agree, then.

AM: (though, the feedback function relates qo to to qf in a living control system)

RM: Then we don’t agree. The feedback function relates qo to qi, output to controlled variable. The qf variable that you inserted in the PCT diagram below conceals this very important fact from both your readers and yourself. I will explain below why it’s important to understand that the feedback function relates qo to qi and not qo to qf.

RM: Yes, but the input-output function you are talking about is not the one that is illusory. The problem with your analysis is that the labelings in your square root calculator are quite misleading with respect to how PCT maps control theory to living systems.

AM: That demo is not meant to represent a living control system, and the labels don’t match, but the setup is analogous to any feedback system.

RM: But it is quite misleading. One of the main things that distinguishes PCT from other applications of control theory to behavior – and control theory was being used as a model of behavior well before Powers came along (as noted in the 1978 paper in the discussion of the “Input blunder”) – is how it maps control theory to behavior. While it’s true that the map is not the territory, a distorted map can eliminate any chance of your finding the treasure hidden in that territory.

AM: The input i in the demo would be equivalent to the reference signal, entering the comparator / amplifier with a positive sign. The other input to the comparator would be equivalent to the perceptual signal, entering with the negative sign. The simulated comparator first finds the error, then multiplies with gain, then adds the error to a leaky integrator, so the output o of the comparator is something like the behavioral output, but not quite.

RM: This way of mapping it rather effectively hides the behavioral illusion. In order to uncover the behavioral illusion from your simulation you have to see the variable i as an independent variable having an effect on a controlled variable. So the comparator in the simulation has to be seen as a perceptual function. And you have to know that qo^2, not qo, is the variable that enters the perceptual function along with i. Only after you get that rather significant amount of remapping done can you can see that the the square root relationship between i (disturbance) and qo (system output) is the behavioral illusion.

AM: For clarity, we can expand it to full pct diagram, replacing system function f from Bill’s diagram with the organism.

RM: Yes, that’s a much clearer way of describing things. Except for that added qf variable. That little addition screws it up big time.

AM: The qd-qo function will depend very little on the upper forward path,

RM: In fact, the qd-qo or S-R relationship depends not at all on the forward function. The relationship between qd and qo depends only on the nature of the connection between qo and qi. The qf in your diagram is what Powers calls g(qo) where g() is the feedback function connecting qo to qi. The derivation of the “behavioral illusion” equation:

qo = g-1 [qi* - h(qd] (1) (unnumbered equation in Powers, 1978)

is based on the assumption that

qi = g(qo) + h(qd) (2) (also equation 2 in Powers , 1978)

RM: There is no variable qf in Bill’s analysis. So why is it important to know that the behavioral illusion turns on the fact that control system output, qo, affects the controlled variable, qi, and not your variable, qf, which is equivalent to the output of the feedback function, g(qo), in Bill’s PCT analysis? Well, of course one reason is mathematical; you can’t derive equation (1) above from the forward and feedback equations of PCT without equation (2) above. If you substitute qf for g(qo) you no longer see the inverse of the feedback function relationship between qo and qd; you have hidden the feedback function in qf.

RM: But another reason that it’s important to know that the behavioral illusion turns on the fact that system output, qo, affects the controlled variable, qi, is that the nature of the observed relationship between disturbance and output in a control system depends on the nature of the controlled variable itself. This is demonstrated in my “What is size” demo:

https://www.mindreadings.com/ControlDemo/Size.html

RM: In this demo, the observed relationship between disturbance, qd, and output, qo, depends on the variable being controlled. If the variable controlled is the perimeter of the rectangle then the relationship between qo and qd is qo = - qd; if the variable controlled is the area of the rectangle then the relationship between qo and qd is qo = qd^1/2. In both cases the feedback function relating qo to qi is the same: g() = 1.

RM: The different observed relationships between stimulus, qd,and response, qo, result from the difference in controlled variables. When perimeter is controlled the controlled variable is qi = qd + qo; when area is controlled the controlled variable is qi = qd * qo. In order to keep qi constant when perimeter is controlled qo must equal -qd and in order to keep qi constant when area is controlled qo must equal qd^1/2. Ergo the different relationships between qd and qo when different aspects of the environment – different controlled variables – are controlled.

RM: So the observed relationship between independent variable,qd, and dependent variable, qo – the supposed “organism” function – changes dramatically with nothing more than a change in the mind of the system doing the controlling about what aspect of the environment to control, perimeter or area.

RM: The fact that the observed relationship between qd and qo depends completely on the nature of the relationship between system output, qo, and the controlled variable, qi, doesn’t mean that there is no causal connection between qd and qo. Thinking that it did mean that is the mistake I made that Bill chided me for in the interaction between Bill and me that you posted. I had said:

RM: Yes, but is o really a causal function of d?

RM: And Bill explained that there certainly is:

BP: Yes .

RM: The fact that as late as 2012 I thought that the behavioral illusion meant that there was no causal connection between disturbance and system output shows that it is not that easy to understand PCT. In 2012 I had been working on PCT for over 30 years and I still didn’t fully understand some of the subtleties. All that the behavioral illusion shows is that the observed relationship between qd and qo – the relationship observed in virtually all psychological experiments – tells you nothing about the actual causal relationship between qd and qo.

RM: As Bill notes in his reply to me, the actual causal path from qd to qo goes from qd to qi to e to qo. Note that qi is in that path. So in order to understand the “forward” causal path through a control system from qd to qo you have to know qi – the controlled variable. So while I got it wrong about there not being a “forward” causal path from qd to qo in a control loop, I have always gotten right what is the most important lesson from the behavioral illusion, which is: in order to understand the behavior of a living control system you have to know what variables it is controlling – its controlled variables, qi.

AM: I have the impression that the behavioral illusion, as defined here, is not very common. I have found very few examples in the literature. Maybe I’m not looking to the right places.

RM: I think if you read on in the “behavioral illusion” section of the 1978 paper you will see that this illusion can be found in virtually every psychological experiment where it is reported that an independent variable was found to have an effect on a dependent variable. Here’s how Bill puts it:

image
image

RM: So the whole enchilada of understanding the behavior of living organisms hinges on knowing what variables organisms control. It’s all about controlled variables!

AM: Yeah, you’re preaching to the choir.

RM: Perhaps. But it looks to me like I am in the wrong church. I have not seen any evidence of research aimed at testing for controlled variables coming out of your lab. And your analysis of the behavioral illusion suggests that you don’t quite understand where controlled variables fit into the behavioral illusion.

AM: Psychologists have certainly mostly ignored controlled variables,

RM: “Totally ignored” would be a better way to put it.

AM: I’ve found a few examples where controlled variables are hypothesized, discussed and even tested for stability when disturbed, with reference to classical control theory. For example, the Center of Mass in maintaining balance literature, then various ‘muscle length’ , ‘muscle force’, ‘second derivative of force’, as measured by the muscle spindles and golgi tendon organs, etc. That is why I say mostly.

RM: I have found such examples as well. So how about “virtually totally ignored”.

Best regards

Rick

Let’s argue with models and simulations then. Above is a picture of Bill’s LCSIII model, here is an online version: http://pct-labs.com/demos/live-block/index.html

RM: Then we don’t agree. The feedback function relates qo to qi, output to controlled variable

Nope, qi is a function of both the qd and qf, in fact it is their sum in Bill’s diagrams.

The variable qf is short for “Feedback quantity”, just like qi is input quantity and qo output quantity. It is right there in every model where the feedback function is explicitly mentioned.

RM: In fact, the qd-qo or S-R relationship depends not at all on the forward function. The relationship between qd and qo depends only on the nature of the connection between qo and qi.

No, this is demonstrably wrong. The forward path is always affecting the S-R relationship. The forward function has to have large gain in order for the input-output relationship to reflect the inverse of the feedback function. The forward function is always affecting the behavior of the loop. Try it yourself in Bill’s demo, or look at this plot:

Here, the disturbance is the blue line, and the output quantity the brown line. The gain is low, and the input-output, or qd-qo function is nowhere near 1, or rather -1, as it would be in the high gain case.

And of course that the input function affects the qd-qo relationship, as you show in the control of size demo. The input function is in the forward path, and any changes in the forward path affect the relationship between qd and qo. In this case, for control of area, the input function is a multiplication, and that can have a very large effect on the qd-qo function.

I was playing with this a bit, you can make it look pretty linear if you choose disturbance values to be higher:
https://colab.research.google.com/drive/130qRskjScKWSw9kJc0hnspdFgGLw8AK8#scrollTo=12UemofIFu29

In your demo of size control, you have shown how the FORWARD PATH, that contains the controlled variable and the input function can affect SR relationship very severely, while two paragraphs before you say that the forward path doesn’t affect the SR relationship at all.

A bit of history: the gain of early amplifiers was very variable with age, temperature, etc. This means that the I-O function was variable, and this was not great for communications networks. What HS Black did with the negative feedback amplifier by adding feedback was to make the the I-O function (mostly) independent of the variations in the amplifier gain, and (mostly) dependent on the function in the feedback path. More here: https://en.wikipedia.org/wiki/Negative-feedback_amplifier

RM: There is no variable qf in Bill’s analysis. So why is it important to know that the behavioral illusion turns on the fact that control system output, qo, affects the controlled variable, qi, and not your variable, qf, which is equivalent to the output of the feedback function, g(qo), in Bill’s PCT analysis? Well, of course one reason is mathematical; you can’t derive equation (1) above from the forward and feedback equations of PCT without equation (2) above. If you substitute qf for g(qo) you no longer see the inverse of the feedback function relationship between qo and qd; you have hidden the feedback function in qf.

It is hidden? Nonsense. The feedback function is qf = g(qo), it is right there on every diagram and in Bill’s demos, sometimes there is g(qo), sometimes qf, you use what you need.

RM: I think if you read on in the “behavioral illusion” section of the 1978 paper you will see that this illusion can be found in virtually every psychological experiment where it is reported that an independent variable was found to have an effect on a dependent variable.

No, to prove that someone was under the “behavioral illusion” you would need to first find a controlled variable, then make a model of the system, with all the functions, then show that IV-DV relationship is the inverse of the feedback function. .

BP. (971209.0232 MST)
P.S.The behavioral illusion is an illusion only if you interpret the disturbance as a stimulus that acts via the organism to produce a response, and assume that it reveals the organism function. It’s the same as with any illusion; the plumber’s illusion or the Ames Window illusion is an illusion only if you are fooled into taking appearances as a true picture of nature.

Hi Adam

AM: Let’s argue with models and simulations then.

RM: Actually, why don’t we not argue at all. You seem to have your understanding of the behavioral illusion that is quite impervious to my models and demonstrations and I have mine that is equally impervious to your models and demonstrations.

RM: To me, the implication of the behavioral illusion – and the reason Powers brings it up in the 1978 Psych Review paper – is that it shows why conventional behavioral scientists have ignored the existence of controlled variables. It’s because they can do experiments and see what they want to see – apparent cause-effect relationships between independent variables (IVs) and dependent variables (DVs).The behavioral illusion shows that these observed IV-DV relationships tell us nothing about the actual causal relationships between IV and DV when the organisms under study are closed-loop, negative feedback control systems (what Powers calls N-Systems).

RM: In order to understand the behavior of N-Systems you have to know what variables they are controlling – controlled variables. The last sections of the 1978 paper – particularly Experiments 5 and 6 – demonstrate how to do research aimed at determining the variables an organism is controlling. It is done using a methodology called the test for the controlled variable. Powers’ 1978 Psych Review paper is thus trying to show how behavioral scientists should be going about their business if the organisms they study are, indeed, N-Systems (and there is considerable evidence that they are). Researchers should be studying the behavior of organisms using some version of the test for the controlled variable.

RM: Powers knew that this new approach to doing behavioral science was quite revolutionary, which is why he gave the paper the subtitle “Some Spadework at the Foundations of Scientific Psychology”. So I see the paper as being a 'manifesto" arguing for a new way of doing psychological research. And at the heart of that manifesto is the behavioral illusion, which shows why the revolution – why the move from looking for causes to testing to determine the purposes of behavior – is necessary.

RM: Your take on the behavioral illusion seems a bit different than mine. You seem to think that once you know what the behavioral illusion is you can go ahead and use conventional IV-DV techniques to study the “forward” causal processes that produce the organism’s behavior. This is very different than my understanding of the behavioral illusion. But you also say that your goal is to discover the variable(s) organisms are controlling – controlled variables – which is certainly also my understanding of the implications of the behavioral illusion. So I guess we only differ in whether there is anything to be learned from IV-DV relationships; I think there is not and I think that you think that there is.

RM: But the best way to “resolve” this apparent conflict is by looking at your research. If I can see that you are doing the kind of research that is an appropriate test of the PCT model of behavior then the conflict will be resolved and I’ll have material for the second edition of my research methods book (that is coming out in the beginning of 2021!). If not, then the conflict will also be resolved because I can just ignore your research (or critique it) just as I do other research that purports to be a test of (or based on) PCT, and isn’t.

RM: I’ll try to quickly answer some of your points below. But I think any further discussion of the behavioral illusion should be oriented toward a description of some of the research that you have done (or would do) based on your understanding of the implications of that illusion. Again, the implication for me is that the only appropriate way to study living control systems is using some version of the test for the controlled variable. I think I could get a better understanding of what the implications are for you if you would describe some of your relevant research.

RM: Here are my comments on your post:

RM: Then we don’t agree. The feedback function relates qo to qi, output to controlled variable

AM: Nope, qi is a function of both the qd and qf, in fact it is their sum in Bill’s diagrams.

RM: What I said is correct: the feedback function relates qo to qi via the feedback function g().

RM: In fact, the qd-qo or S-R relationship depends not at all on the forward function. The relationship between qd and qo depends only on the nature of the connection between qo and qi.

AM: No, this is demonstrably wrong. The forward path is always affecting the S-R relationship.

RM: I should have said "the OBSERVED relationship between qd and qo depends not at all on the forward function. Of course, the ACTUAL relationship between qo and qd depends on the forward path through the organism.

AM: In your demo of size control, you have shown how the FORWARD PATH, that contains the controlled variable and the input function can affect SR relationship very severely, while two paragraphs before you say that the forward path doesn’t affect the SR relationship at all.

RM: In the size control demo you are actually comparing two different forward paths – one where qi = perimeter and the other where qi = area. I only presented it to show that it’s the feedback connection from qo to qi that determines the behavioral illusion.

RM: …If you substitute qf for g(qo) you no longer see the inverse of the feedback function relationship between qo and qd; you have hidden the feedback function in qf.

AM: It is hidden? Nonsense. The feedback function is qf = g(qo), it is right there on every diagram and in Bill’s demos, sometimes there is g(qo), sometimes qf, you use what you need.

RM: I mean it is hidden in the mathematics. I think it’s important to write qi = f[h(d) + g(o)] rather than qi = f[h(d) + qf] in order to see that the OBSERVED relationship between qo and h(qd) is qo = g-1(h(gd)) – that is, to see that qo is related to h(d) as the inverse of the feedback function.

RM: I think if you read on in the “behavioral illusion” section of the 1978 paper you will see that this illusion can be found in virtually every psychological experiment where it is reported that an independent variable was found to have an effect on a dependent variable.

AD: No, to prove that someone was under the “behavioral illusion” you would need to first find a controlled variable, then make a model of the system, with all the functions, then show that IV-DV relationship is the inverse of the feedback function. .

RM: No one’s trying to prove that anyone is “under the behavioral illusion”. The point of the 1978 PSych Review paper is this: IF organisms are N-systems then OBSERVED IV-DV relationships tell you nothing about the ACTUAL causal path from IV to DV. if researchers are dealing with N-Systems and they take these OBSERVED IV-DV relationships to be telling them something about the causal path from IV to DV then they are making a MISTAKE based on an ILLUSION – the behavioral illusion. Another way of putting it is like this: If organisms are N-Systems then taking OBSERVED IV-DV relationships as revealing something about the ACTUAL causal path from IV to DV is the same as taking the OBSERVED bending of a stick placed in water as revealing the ACTUAL shape of the stick.

Best regards

Rick

RM: All that the behavioral illusion shows is that the observed relationship between qd and qo – the relationship observed in virtually all psychological experiments – tells you nothing about the actual causal relationship between qd and qo
It’s because they can do experiments and see what they want to see – apparent cause-effect relationships between independent variables (IVs) and dependent variables (DVs).The behavioral illusion shows that these observed IV-DV relationships tell us nothing about the actual causal relationships between IV and DV when the organisms under study are closed-loop, negative feedback control systems (what Powers calls N-Systems).

RM: should have said "the OBSERVED relationship between qd and qo depends not at all on the forward function. Of course, the ACTUAL relationship between qo and qd depends on the forward path through the organism.

One thing you need to understand is:

OBSERVED functional relationship = ACTUAL functional relationship

You’ve confused the ‘correlation does not imply causation’ with the behavioral illusion.

Here, in Bill’s experiment on the behavioral illusion, the functional OBSERVED relationship between qd and qo is also the ACTUAL relationship. He is not talking about causality. In the same way, if you take an analog computer that does square roots, the OBSERVED AND ACTUAL relationship between I and O is o = sqrt(i), they are one and the same thing.

An observed relationship does not imply causation. If someone does a correlational study, then says that IV causes DV, he is making a mistake of implying causation from correlation. This has absolutely nothing to do with Bill’s original definition of the behavioral illusion, it is a common mistake people do.

The behavioral illusion happens when someone says that the observed functional relationship reflects organism properties (the forward path), while in fact it reflects environment properties (the feedback path). You can see that up in Figure 7, reporting the result of Bill’s experiment on the behavioral illusion: subject’s behavior follows the inverse of the feedback function of the stimulus.

Causation is always there. Every element in the feedback loop is causal in the sense that changes in the element will be reflected in the behavior of the loop.

The approach Bill takes with PCT is to simply not use causal claims, and instead use functional relationships that describe mechanisms.

Take a look here, Bill’s paper on causes vs mechanisms: http://www.pctweb.org/Cause.pdf
Describing behavior in terms of causes and effects is very unparsimonious, in that every new
cause has to be separately linked to its effects. The functional approach can do better than that.

You’ve been using your strange mix of causal and functional talk, and Bill has corrected you as late as 2012, but you’ve been repeating the same strange language and confused understanding of the behavioral illusion in 2018, and also now in 2020. I mean, sure, keep your definition, use what ever you want, but if you’re referring to Bill’s 1978 definition, get it right. It is not just the error of “stimuli cause responses”.

RM: No one’s trying to prove that anyone is “under the behavioral illusion”.

Sure they are - you’ve argued in your papers that the power law of movement, between curvature and speed, is an example of the behavioral illusion.

What you meant was “speed is not caused by curvature”. I agree. It is not caused by curvature. Everyone else also agrees. Functional relationships do not imply causation.

If you want to demonstrate the behavioral illusion, as BIll said, and I’ve repeated, you would need to build the model that reproduces the behavior. That means first finding the controlled variable, putting in all the functional relationships in a model, then modifying the feedback function to demonstrate how this change is reflected in the qd - qo relationship. It should show the inverse. That is the heart of the behavioral illusion.

The heart of PCT research is of course finding controlled variables. You have hypothesized about controlled variables in fast movement, but you have done no TCV, no models that reproduce observed behavior, nothing but strange statistics. So, I suppose I will also be observing your future research and books to see if you will correct your understanding of what PCT research should be, and if I see you did not, just ignore it.

Some of your older research was pretty good, I hope you return to that level.

RM: The point of the 1978 PSych Review paper is this: IF organisms are N-systems then OBSERVED IV-DV relationships tell you nothing about the ACTUAL causal path from IV to DV. if researchers are dealing with N-Systems and they take these OBSERVED IV-DV relationships to be telling them something about the causal path from IV to DV then they are making a MISTAKE based on an ILLUSION – the behavioral illusion.

AM:
Here is another way to explain why your explanation above is incorrect.

If you apply a disturbance qd to an organism, a control system (N system) and you observe a strong correlation to qo, say qd = -qo with r = 0.99, THIS TELLS YOU A LOT about the forward path, the “actual causal forward path”, including the input function, reference and the output function. For one, you probably did a very good guess of the controlled variable. Two, because of the high correlation, the system probably has a high gain. Also, it tells you that the feedback function is just multiplication by 1.

The illusion would be there only if someone says that the forward path, the organism function, is multiplication by 1, that the organism is sensing the qd and responding with qo. Actually, it is sensing qi and varying qo to maintain it at the reference level.

On the other hand, if you observe a low correlation, this also tells you something about the organism. Either you did not make a good guess at the controlled variable (more probably), or the control system is very low gain (less probably).

Hi Adam

RM: OK, so we argue.

RM: should have said "the OBSERVED relationship between qd and qo depends not at all on the forward function. Of course, the ACTUAL relationship between qo and qd depends on the forward path through the organism.

AM: One thing you need to understand is:

AM: OBSERVED functional relationship = ACTUAL functional relationship

AM: You’ve confused the ‘correlation does not imply causation’ with the behavioral illusion.

AM: Here, in Bill’s experiment on the behavioral illusion, the functional OBSERVED relationship between qd and qo is also the ACTUAL relationship. He is not talking about causality. In the same way, if you take an analog computer that does square roots, the OBSERVED AND ACTUAL relationship between I and O is o = sqrt(i), they are one and the same thing.

RM: What the behavioral illusion shows is that the observed functional relationship between qd and qo is not a reflection of the actual “organism function”, which is the “forward” functional relationship between qi and qo. This is important for scientific psychology because the typical psychological experiment is aimed at discovering the “organism function”, qo = f(qi), by determining whether there is a functional relationship between qd and qo.

RM: The assumption that observed functional relationship between qd and qo corresponds to the actual functional relationship between qi and qo is the “foundation of scientific psychology” at which Powers is doing his “spadework” in the 1978 paper. And the “spade” that is doing this work is the behavioral illusion, which shows that observed functional relationships between qd and qo do not correspond to the actual functional relationship between qi and qo.

RM: However, the fact that the observed functional relationship between qd and qo does not correspond to the actual functional relationship between qi and qo means that the observed functional relationship between qd and qo also does not correspond to the actual functional relationship between qd and qo. This follows from the fact that the actual functional relationship between qi and qo is part of the actual functional relationship between qd and qo. I can show this most easily with a linear analysis.

RM: Assume that the actual functional relationships between qd and qi and qi and qo are:

qi = ki (qd)
qo = ko (qi)

RM: Then the actual functional relationship between qd and qo is

qo = koki (qd)

RM: For an N-System the observed functional relationship between qd and qo is

qo = 1/kf (qd)

where kf is the feedback function relating qo to qi.

RM: So the observed functional relationship between qd and qo will be the same as the actual functional relationship between qd and qo only when koki = 1/kf,. And it seems highly unlikely that koki would ever = 1/kf, especially when these functions are to quite non-linear, as they are the tracking experiment, the results of which are shown in Figure 7 above. It’s very unlikely that this highly non-linear observed functional relationship between qo and qd is anything like the actual functional relationship between the disturbance (qd) and the subject’s handle movements (qo).

RM: So I humbly suggest that maybe one thing you need to understand is that OBSERVED functional relationships are not always = to ACTUAL functional relationships.

RM: And there is no need to mention “causality” in this analysis. I mention causality here (and in my once pretty darn good papers) because scientific psychologists assume that the functional relationships between qd and qo found in their experiments are causal.

AM: The behavioral illusion happens when someone says that the observed functional relationship [between qo and qd - RM] reflects organism properties (the forward path [actual functional relationship between qi and qo – RM]), while in fact it reflects environment properties (the feedback path).

RM: Exactly, as I spell out above. But that illusion also happens when would-be PCTers say that the observed functional relationship between qo and qd is equal to the actual functional relationship between qo and qd.

Best

Rick

RM: And so it goes.

RM: No one’s trying to prove that anyone is “under the behavioral illusion”.

AM: Sure they are - you’ve argued in your papers that the power law of movement, between curvature and speed, is an example of the behavioral illusion.

RM: I guess you could say it that way. That was certainly Powers’ goal in the 1978 paper.

AM: If you want to demonstrate the behavioral illusion, as BIll said, and I’ve repeated, you would need to build the model that reproduces the behavior. That means first finding the controlled variable, putting in all the functional relationships in a model, then modifying the feedback function to demonstrate how this change is reflected in the qd - qo relationship. It should show the inverse. That is the heart of the behavioral illusion.

RM: Actually, I did use models to demonstrate that the power law is a version of the behavioral illusion. It was in the reply to your reply to our paper. But it didn’t have much of an impact. So maybe I’ll try writing another paper about it showing some of the modeling that I didn’t publish.

AM: The heart of PCT research is of course finding controlled variables.

RM: I think it’s better to say that the heart of PCT research is refining the definition of controlled variables and then using the model to explain their existence. PCT research should start with a hypothesis about what the controlled variable is around which a particular behavior is organized. Saying that the heart of PCT research is finding controlled variables makes it sound like controlled variables are hiding somewhere. In fact, if you know how to look at behavior through control theory glasses, controlled variables are all over the place. But these controlled variables will be defined very loosely at first: “cursor on target”, “balance”, “movement”, etc. The main goal of PCT research is to refine your initial definition of there variables. In the coin game, for example, E tests to determine the variable S is controlling becuase E knows – because E has instructed S to do it – that S is controlling something about the arrangement of coins. The test for the controlled variable is really a way of refining one’s definition of the controlled variable once you have a pretty good idea about what is being controlled.

AM: You have hypothesized about controlled variables in fast movement, but you have done no TCV, no models that reproduce observed behavior, nothing but strange statistics. So, I suppose I will also be observing your future research and books to see if you will correct your understanding of what PCT research should be, and if I see you did not, just ignore it.

RM: I don’t see it that way but I’m flattered that you will be observing my future research with such critical care.

AM: Some of your older research was pretty good, I hope you return to that level.

RM: I’ll take that as a compliment and return the compliment by noting that some of your older work on PCT was pretty good, too. You are lucky because you probably have a lot more time available to you to return to your good work than I have to return to mine. But I’ll do my best.

Best

Rick

RM: What the behavioral illusion shows is that the observed functional relationship between qd and qo is not a reflection of the actual “organism function”, which is the “forward” functional relationship between qi and qo.

Great, agreed with all this and your next few paragraphs. The qd - qo function is not the same as qi - qo function.

Here is where we might disagree, depending on what you mean by “actual”…

RM: However, the fact that the observed functional relationship between qd and qo does not correspond to the actual functional relationship between qi and qo means that the observed functional relationship between qd and qo also does not correspond to the actual functional relationship between qd and qo.

The feedback function is Bill’s experiment is g(x) = Ax + Bx^2, (above figure 6). The prediction, if the subject is an IDEAL control system, and if the function g is invertible across all the range of qd, is that qo = g^-1 ( qd ).

Because the subject is not an ideal control system, and there is some strangeness in the function g near zero, we get a relationship near the inverse of the g function as the qd-qo relationship.

For A = 10, B=5, relatively high gain, I get this:
image
https://colab.research.google.com/drive/1uC15-Sol_dzwMgQGAU-esABFWNYDdg4h#scrollTo=IP4_EcOnJSc2

So, if you are saying that the “actual” function is the one predicted by algebra (theory), and the observed one is measured in an experiment, then I agree, they can be different. I guess that is what you mean, because of the analysis you wrote.

I would just call them theoretical and observed, or predicted and observed, but ok. The prediction can get closer by either using more realistic functions in the prediction, or by using a better control control system. They are approximately equal, but not exactly.

I don’t think your analysis is quite right. For one, you write ki as a function in the first equation, and then treat it as a multiplier later. I’ll deffer to Bill to this one (2010.05.21.1010 MDT)

BP:
(1) qi = Kf * qo + d
(2) qo = Ko * e
(3) e = r - p
(4) p = Ki * qi

       Ko*(r - Ki*d)
 qo = ---------------
       1 + Ko*Ki*Kf


Now let's investigate the behavioral illusion.

Let Ki = 1, Kf = 1, and Ko = 1. We find that

qo = -0.5*d

According to the behavioral illusion, the output should be the inverse
feedback function of the disturbance. The feedback function is a
multiplier of 1, making the inverse also 1. The behavioral illusion
predicts that the output with r = 0 should be

qo = -d.

What's wrong? The output is negative but it's only half as large as it
should be. Half of the effect of the disturbance will be uncorrected.

The answer lies in the loop gain. Let's just change Kf to 1000. Now we
get

       1*(r - d)
 qo = ------------------ 
        1 + 1009

With r = 0, we now have

qo = -0.00099*d

The inverse of the feedback function with sign (Kf = 1000) is -0.001. the
actual factor connecting qo and d is -0.00099, within 1% of the value**
predicted by the behavior illusion.

RM: The main goal of PCT research is to refine your initial definition of there variables.

Ok, sure.

Hi Adam

AM: Here is where we might disagree, depending on what you mean by “actual”…

RM: However, the fact that the observed functional relationship between qd and qo does not correspond to the actual functional relationship between qi and qo means that the observed functional relationship between qd and qo also does not correspond to the actual functional relationship between qd and qo.

AM: Because the subject is not an ideal control system, and there is some strangeness in the function g near zero, we get a relationship near the inverse of the g function as the qd-qo relationship. …

AM: So, if you are saying that the “actual” function is the one predicted by algebra (theory), and the observed one is measured in an experiment, then I agree, they can be different. I guess that is what you mean, because of the analysis you wrote.

RM: No, that’s not what I mean. I mean the actual forward functional relationship between qd and qo that is the "open loop"relationship between qd and qo that “goes through” the organism. The actual functional relationship is the one psychologists think they are looking at when they find a relationship between IV-DV (qd-qo) in an experiment.

AM: I don’t think your analysis is quite right. For one, you write ki as a function in the first equation, and then treat it as a multiplier later. I’ll deffer to Bill to this one (2010.05.21.1010 MDT)

BP:
(1) qi = Kf * qo + d
(2) qo = Ko * e
(3) e = r - p
(4) p = Ki * qi

RM: These are the closed loop equations that give you the behavioral illusion. The fact that they are the closed loop equations \ can be seen in equation (1) where qi is a function of both d and the feedback effect of qo (Kf*qo).

RM: My analysis is basically the same but I leave out the feedback effect. So:
(5) qi = Kd* d
(6) qo = Ko * e
(7) e = r - p
(8) p = Ki * qi

The only difference between my equations and the ones for a closed loop system is between equation (1) and (5). My equation (5) leaves out the feedback effect of qo on qi in equation (1). Setting Kd =1 and r = 0 in equations (5) - (8) and solving for qo we get the “forward” equation from qd to qo for a Z- Systems (zero feedback system):

(9) qo = - KoKi *d

RM: Compare that to Bill’s equation with feedback (and the same settings of Kd and r)

(10) qo = - 1/(1 + Kf) *d

RM: Notice how the functions that characterize the organism in equation (9) – Ki and Ko – fall out of equation (10). Equation (10) describes the observed relationship between qo and d when there is negative feedback (when the system is an N-System). When there is negative feedback the observed relationship between qo and qd depends only on the feedback function Kf.

RM: But the actual forward functional relationship between qd and qo – the one described by equation (9) – is still in effect! Equation (10) just says that you can’t “see” that forward functional relationship between qo and d when there is negative feedback from the system’s output, qo, to its input, qi.

RM: The comparison between equations (9) and (10) reveals the behavioral illusion. The functional relationship between qo and qd that actually exists is given by equation (9); the functional relationship between qo and qd that will be observed when dealing with an N-System is given by equation (10). The illusion is that what is observed (equation (10)) is the actual functional relationship (equation (9)) between qd and qo (between IV and DV in psychological experiments).

RM: This comparison, using linear coefficients instead of functional notation, is precisely equivalent to the comparison of equations that Bill made in the 1978 paper:

image

RM: The bottom equation is equivalent to equation (9) above; the function f [ ] in that equation corresponds to KoKi in equation (9). The upper equation is equivalent to equation (10) above; the function g [ ] in that equation corresponds to Kf in equation (10). It was the comparison between those two equations – equivalent to comparing equations (9) and (10) that led Bill to say: “This comparison reveals a behavioral illusion of such significance that one hesitates to believe it could exist”. Of course, the illusion is that, when you are dealing with an N-System, the observed relationship between qo and qd, which appears to be the actual organism function relating input to output, is actually just the inverse of the feedback function relating qo to qi. That is, it looks like you are seeing the function described in the lower equation (and in our equation (9)) when, in fact, you are seeing the function described in the upper equation (and in our equation (10)).

RM: So when you are dealing with an N-system you can’t learn about its “system function” – the function f [ ] in the lower equation – using the conventional methods of scientific psychology. This is the large scoop out of its foundations that Powers’ spadework took out of scientific psychology. Is there, then, any wonder why scientific psychologists haven’t been rushing to adopt PCT, let alone understand it.

RM: The main goal of PCT research is to refine your initial definition of there variables.

AM: Ok, sure.

RM: I hope you will now take this seriously and stop trying to find controlled variables when the possible candidates are right in front of you. A lesson in this comes from the movie “Double Indemnity” – possibly the finest Film Noir ever made. Fred MacMurray plays Walter Neff, an insurance salesman whose mentor is expert insurance fraud detective Barton Keyes, played by Edward G. Robinson. Keyes feels very fatherly towards Neff. But Neff is lured by “bad dame” Barbara Stanwyck into murdering her husband and making it look like an accident that will pay “double indemnity” on the insurance policy Neff sold her.

RM: Keyes is investigating the accident and keeping Neff posted on how he’s doing. Keyes can’t figure it out even though Neff has done it all right under his nose. Eventually, things all come apart between Neff and the bad dame. He kills her after she mortally wounds him. He returns to the office to write his confession and collapses from the wound. Keyes finds him collapsed in the hall and cradles him in his arms. Neff looks up at Keyes and says: “Know why you couldn’t figure this one, Keyes? I’ll tell ya. 'Cause the guy you were looking for was too close. Right across the desk from ya”. and Keyes replies “Closer than that, Walter”. Great line!

RM: Don’t be like Keyes. Those controlled variables are right in front of you. Maybe closer than that.

Best

Rick

RM: But the actual forward functional relationship between qd and qo – the one described by equation (9) – is still in effect ! Equation (10) just says that you can’t “see” that forward functional relationship between qo and d when there is negative feedback from the system’s output, qo, to its input, qi.

No, this is not correct. The forward path is still in effect, but the functional relationships are changed because of feedback.

Your function 9 is only valid in an open loop, and does not “actually” exist in a closed loop, and it is certainly not in effect. causal path =/= functional relationship.

RM: Equation (10) describes the observed relationship between qo and d when there is negative feedback (when the system is an N-System).

When there is negative feedback the observed relationship between qo and qd depends only on the feedback function Kf.

Yes, the first sentence is correct. Correction for the second sentence: not only. It depends strongly on the Kf factor if the total loop gain is high. Look at Bill’s explanation of what happens with low loop gain. You can get the same effect varying Ko.

RM: The comparison between equations (9) and (10) reveals the behavioral illusion.The functional relationship between qo and qd that actually exists is given by equation (9); the functional relationship between qo and qd that will be observed when dealing with an N-System is given by equation (10). The illusion is that what is observed (equation (10)) is the actual functional relationship (equation (9)) between qd and qo (between IV and DV in psychological experiments).

The equation 9 does not “actually exist” in a closed loop, it only exists in the open loop. (Causal paths exist in both versions, but that does not say much if anything about functional relationships).

Therefore, what is observed as the qd-qo relationship IS the actual closed loop relationship between qd and qo. That even sounds a bit tautological.

You should just drop the whole “actual qd-qo” and “observed qd-qo” distinction. It is nowhere in the the original definition.

RM: This comparison, using linear coefficients instead of functional notation, is precisely equivalent to the comparison of equations that Bill made in the 1978 paper:

image

Sure, your equations 10 and 9 are equivalent to the first and second there. Here is how I read it: If you assume that the system is open loop (9), you will think that qd-qo relationship reflects organism properties, the function F, the O in S-O-R.
If the system is ACTUALLY a negative feedback, high gain system, then the qd-qo relationship does NOT describe the organism function, but very nearly the inverse of G (equation 10)

RM:
Of course, the illusion is that, when you are dealing with an N-System, the observed relationship between qo and qd, which appears to be the actual organism function relating input to output, is actually just the inverse of the feedback function.

That is a pretty good explanation! You can drop the first actual with no loss in meaning.

*The observed relationship between qd and qo appears to be the organism function, but is actually the inverse of the feedback function."

Maybe you’d prefer it this way:
The actually observed relationship between qd and qo actually appears to be the actual organism function, but is actually the inverse of the actual feedback function.

In the behavioral illusion, there is no difference between “observed qd-qo” and “actual qd-qo”. The distinction is between “illusion that qd-qo describes the organism function F”, using equation 9; and the “actual function described by qd-qo” being G^1, as in equation 10.

RM: So when you are dealing with an N-system you can’t learn about its “system function” – the function f [ ] in the lower equation – using the conventional methods of scientific psychology. This is the large scoop out of its foundations that Powers’ spadework took out of scientific psychology. Is there, then, any wonder why scientific psychologists haven’t been rushing to adopt PCT, let alone understand it.

Correction - you cannot learn about the system function if you are using the conventional MODELS of scientific psychology, the SR, SOR, S-PSI-R, or whatever. Most of the methods are also gone, but in PCT, we are still very much applying stimuli and measuring responses. A well formed qd is a stimulus disturbing a controlled variable, and the response is the qo. The difference is that we assume we are dealing with a closed loops system, and we know where to look for the organism function, and how to modify the feedback function, and how to verify our guess of the controlled variable.

When we know this, then measuring our qd - qo relationships tells us a LOT about the forward and feedback path and the controlled variables. We can also make a model and fit it to observed behavior (this is not exclusively a PCT method).

RM: stop trying to find controlled variables when the possible candidates are right in front of you

To me, finding controlled variables means going for the best possible candidates, with the lowest qo -qi correlations, with models replicating all relevant behavioral features of human behavior. Publishing any model that just appears to be correct on first glance, without strict experimental evidence is just wasting everyone’s time.

I agree that the job is to refine our guesses for control variables, and proceed until they are very, very good guesses.

Hi Adam

RM: But the actual forward functional relationship between qd and qo – the one described by equation (9) – is still in effect ! Equation (10) just says that you can’t “see” that forward functional relationship between qo and d when there is negative feedback from the system’s output, qo, to its input, qi.

AM: No, this is not correct. The forward path is still in effect, but the functional relationships are changed because of feedback.

RM: I don’t see anything in the 1978 paper that suggests that this is the case. And I have a demo that rather clearly shows that it is not the case. It’s called, cleverly enough, the “Behavioral Illusion” demo: https://www.mindreadings.com/ControlDemo/Illusion.html

RM: The demo is just a tracking task. In the middle of the task the feedback function connecting mouse position (qo) to the position of a spider (qi) changes from a multiplier of .5 (weak feedback) to a multiplier of 1.5 (strong feedback). The expected result is that the slope of the qo-qd (or S-R) function will be the inverse of the feedback function. So the slope of a plot of qo against qd (R against S) should be steep (2) when the feedback is weak (.5) and shallow (.67) when the feedback is strong (1.5). And this is what is always found, as shown in the graph below.

image

RM: According to you, the change in the qd-qo relationship with a change in the feedback function reflects an actual change in the forward path through the organism from qd to qo. In this demo it would mean that the subject doing the tracking actually changed in terms of their sensitivity to changes in the disturbance when the feedback function changed. I suppose this is a possibility. But there is pretty compelling evidence that this is not the case. One piece of evidence is that subjects experience no subjective change in themselves when the feedback function changes. More compelling is the fact that these results can be precisely replicated by a model in which the functional relationship between qd and qo remains exactly the same when the feedback function changes from weak to strong. And, finally, there is nothing in the 1978 POwers paper that suggests that there is a change in the forward path function, f [ ], when there is a change in the feedback function, g[ ].

AM: Your function 9 is only valid in an open loop, and does not “actually” exist in a closed loop, and it is certainly not in effect. causal path =/= functional relationship.

RM: Again, I don’t know what could possibly be your basis for saying this. I think there is no evidence at all that this is the case. Indeed, the only relevant evidence I know of is consistent with the idea that this is not the case.

RM: Equation (10) describes the observed relationship between qo and d when there is negative feedback (when the system is an N-System).
When there is negative feedback the observed relationship between qo and qd depends only on the feedback function Kf.

AM: Yes, the first sentence is correct. Correction for the second sentence: not only. It depends strongly on the Kf factor if the total loop gain is high. Look at Bill’s explanation of what happens with low loop gain. You can get the same effect varying Ko.

RM: Again, I have no idea why you think this is true. In my simulations, varying ko determines how well the observed relationship between qd and qo reflects the feedback function connecting qo to qi; the greater ko (with the appropriate slowing to prevent instability) the more precisely the observed relationship between qd and qo reflects the feedback function. This is because the better the control, the more precisely g(qo) counters the effect of qd on qi. So the better the control the more precisely qo approximates g-1(qo).

RM: The comparison between equations (9) and (10) reveals the behavioral illusion.The functional relationship between qo and qd that actually exists is given by equation (9); the functional relationship between qo and qd that will be observed when dealing with an N-System is given by equation (10). The illusion is that what is observed (equation (10)) is the actual functional relationship (equation (9)) between qd and qo (between IV and DV in psychological experiments).

AM: The equation 9 does not “actually exist” in a closed loop, it only exists in the open loop.

RM: I’m sorry, I can’t just take your word for it. I have to see some evidence that this is the case before I can believe it.

AM: Therefore, what is observed as the qd-qo relationship IS the actual closed loop relationship between qd and qo. That even sounds a bit tautological.

RM: If this were true then there would be no such thing as the behavioral illusion. It contradicts the most important point made in the 1978 paper. Take a look at it again:

image

RM: What you are saying is that the observed functional relationship g-1 between qd and qo for a closed loop system (top equation) is now the actual system function, the equivalent of the function f [ ] for the same system if it were open loop. If this were the case then there would be no “illusion” involved when you look at the relationship between qd and qo for a closed-loop system. What you are seeing, according to you, is the organism function, which the closed-loop has changed from f [ ] to g-1 [ ].

RM: This is definitely NOT what the behavioral illusion is about. This is shown clearly by my model of the behavior in my “Behavioral Illusion” demo. The model shows that the change in the observed relationship between qd and qo with a change in the feedback function, g [ ], occurs with no change at all in the actual function, f [ ], relating qd to qo. The illusion is that the the observed functional relationship between qd and qo in an N-Systems reflects characteristics of the organism when they actually reflect characteristics of the environment in which the organism is behaving.

RM: Here’s how Bill put it:

BP: If one varies a distal stimulus qd and observes that a measure of behavior qo shows a strong regular dependence on qd, there is certainly a temptation to assume that the form of the dependence reveals something about the organism. Yet, the comparison we have just seen indicates that the form of the dependence may reflect only properties of the local environment.

AD: You should just drop the whole “actual qd-qo” and “observed qd-qo” distinction. It is nowhere in the the original definition.

RM: I suggest that you should adopt the whole “actual qd-qo” and “observed qd-qo” distinction because it is central to the definition of the behavioral illusion.

RM: Of course, the illusion is that, when you are dealing with an N-System, the observed relationship between qo and qd, which appears to be the actual organism function relating input to output, is actually just the inverse of the feedback function.

AM: That is a pretty good explanation! You can drop the first actual with no loss in meaning:
*The observed relationship between qd and qo appears to be the organism function, but is actually the inverse of the feedback function."

RM: Works for me. But I think including that first “actual” makes it even clearer.

AM: In the behavioral illusion, there is no difference between “observed qd-qo” and “actual qd-qo”.

RM: I think that’s about as wrong as you can get. I don’t know how you are able to read the 1978 paper and not understand that the observed relationship between qd and qo not the same as the actual relationship between qd and qo; the former is the inverse of the feedback function, g-1[ ], and the latter is the organism function, f[ ].

AM: The distinction is between “illusion that qd-qo describes the organism function F”, using equation 9; and the “actual function described by qd-qo” being G^1, as in equation 10.

RM: I agree that the behavioral illusion is that qd-qo reflects the organism function when it doesn’t ; it reflects the inverse of the feedback function relating qo to qi. But I think we are taking away different lessons from that. The lesson I get – and the one that Powers clearly hoped people would get from reading the 1978 paper – is this: If organisms are N-systems then studying their behavior by looking for relationships between variations in qd and qo (IV-DV relationships) will tell you nothing at best and be misleading at worst regarding how their behavior actually works.

RM: So when you are dealing with an N-system you can’t learn about its “system function” – the function f [ ] in the lower equation – using the conventional methods of scientific psychology. This is the large scoop out of its foundations that Powers’ spadework took out of scientific psychology. Is there, then, any wonder why scientific psychologists haven’t been rushing to adopt PCT, let alone understand it.

AM: Correction - you cannot learn about the system function if you are using the conventional MODELS of scientific psychology, the SR, SOR, S-PSI-R, or whatever. Most of the methods are also gone, but in PCT, we are still very much applying stimuli and measuring responses. A well formed qd is a stimulus disturbing a controlled variable, and the response is the qo. The difference is that we assume we are dealing with a closed loops system, and we know where to look for the organism function, and how to modify the feedback function, and how to verify our guess of the controlled variable.

RM: Central to all this is the controlled variable. You can’t apply disturbances and measure compensating responses unless you know what variable is being controlled. So while PCT research does involve manipulating stimuli (disturbances) and observing responses, all this is done as part of the process of determining the variables around which behavior is organized. And this is usually done by looking for a lack of relationship between stimuli (qd) and hypothesized controlled variables (qi) rather than between stimuli (qd) and responses (qo).

AM: When we know this, then measuring our qd - qo relationships tells us a LOT about the forward and feedback path and the controlled variables.

RM: Observed qd - qo relationships can tell you a lot about forward and backward feedback paths but only after you know what variables are under control. Simply measuring qd - qo relationships tells you nothing about controlled variables. Indeed, you don’t even know if what you call qd is a disturbance unless you know the controlled variable; a disturbances is a variable that affects a controlled variable.

AM: We can also make a model and fit it to observed behavior (this is not exclusively a PCT method).

RM: The only thing that is unique to PCT - based research is the emphasis on determining the variables that organisms control – controlled variables. Indeed, the main focus of PCT is on finding the perceptual variables around which various behaviors are organized.

RM: stop trying to find controlled variables when the possible candidates are right in front of you

AM: To me, finding controlled variables means going for the best possible candidates, with the lowest qo -qi correlations, with models replicating all relevant behavioral features of human behavior. Publishing any model that just appears to be correct on first glance, without strict experimental evidence is just wasting everyone’s time.

RM: That sounds exactly right. Though given the dearth of anything like PCT - based research that’s out there I think it would not be a waste of anyone’s time to publish something showing how you are progressing towards a model that includes variables that are obviously close to being the right controlled variables.

AM: I agree that the job is to refine our guesses for control variables, and proceed until they are very, very good guesses.

RM: I think “very good” is probably sufficient for now. But “very, very good” is not uncommon in this kind of research. Look at how well Powers did at fitting the shock avoidance data with his estimates of the controlled variable. The fit of the model to the data, measured in terms of r2 was very good (r2 >.97) when the controlled variable was assumed to be shock rate or shock probability. But shock probability proved to be the better description of the controlled variable when fit is measured in terms of rms deviation. But I’m sure it would not be a waste of people’s time if you came up with controlled variables that produced model fits with r2 values as low as .9 and rms error of less than 3%.

Best

Rick