* Diagram Police *

Fundamentals Control Structures
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RM: The feedback function equation at the bottom of Figure 1.4a should be CV = k R rather than CV = k S. The feedback function is correctly described in the text

AM: It is not correct.

RM: It is correct with respect to the purpose of the book, which is to show why the study of living control systems should be aimed at determining the variables they control rather than at observing how stimuli (independent variables) relate to their responses (dependent variables).

RM: the illusion is taking the value of the coefficient relating the observed values of R and S to be a characteristic of the person when, in fact, it is a characteristic of the feedback function relating R to CV

AM: …that is the illusion, so it doesn’t make sense to me to put the wrong (illusory) organism function in the part of the diagram representing the organism in the control loop.

RM: It makes sense to me because that is the function that behavioral scientists think they are seeing in the observed relationship between S and R (independent and dependent variables)

AM: The correct organism function would be more clear in its place because the high gain of the organism function explains why the F would be equal to -S, and why the inversion of the feedback function happens.

RM: But it doesn’t explain why the illusion happens – why it appears that S is the cause of R via the organism. This illusion, which is the basis of scientific psychology (and neurophysiology and behavioral biology, etc), results from failure to see that the behavior of organisms is organized around the control of perceptual variables – CVs. The aim of the book is to encourage those who currently or are planning to study the behavior of living control systems to orient their research toward the discovery of the variables organisms control (and, of course, how they control them).

Best

Rick

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RM: It is correct with respect to the purpose of the book.

Nice! Back to bull***ing again, eh. I pointed out the mistakes, you don’t care about having them corrected, so that is that I suppose.

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Do comparators need to be explicit rather than implicitly with a + and - input in a loop

e.g.

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I think both are fine. Btw. love that second paper.

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Adam, I very much like your take on the diagramming of control systems. As you surmised, in the LCS III diagram, there should indeed be a circle (adder) where the disturbance and feedback quantities combine. I had trouble getting the circle to stay on the top layer of the diagram (making it visible) and thought I had solved the problem (it was showing when I ran the demo within the Delphi IDE). I was surprised and disappointed when it resurfaced in the distributed program, and still don’t understand why.

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Here is a recent one:

Marken, Kennaway and Tauseef (2022), Figure 1

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The diagram has the usual problem - functions and variables look the same in their graphical representation, and they should be different.

Variables are quantities that change. Functions are like machines that take one or more variable as input and put another as output.

        ------>[ F ]----->
           a           b

Two variables, a and b, and the function F. The function F takes a as input and gives b as output. The lines with arrows are variables; the box is the function.

Ok, the variables and functions are named in Figure 1. so that helps, but look at the input and output variables - they appear between several lines, and the lines change from full to dashed. How do you translate this image into a formula?

The variable qe is named the “Environmental variable”, but both input and output variables are also in the environment. Better to stick to “disturbance”.

The organism bubble is too big and crossing over arrows unceccesarily.

Here is my take, the equations are the same as in the paper.

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Now the translation between the diagram and the formulas should be easier

qo = ko * qi
qi = + ke * qe - kf * qo

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Yes, your diagram is much better than ours. I viewed our paper as kind of a continuation of Powers (1978) paper, with the edition of “real life” examples of the illusion from the behavioral science research literature. The control system diagram Bill used in that paper was:

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This diagram is actually closer to yours inasmuch as he labelled the lines, though his lines were functions while your are variables.

But there are still problems with this diagram as there are with any diagram, even yours. For example, in all of these diagrams the input variable (or quantity), q.i, is shown to be outside the boundary of the system. This is true if q.i is taken to represent the physical variables that impinge on the senses. But q.i is usually taken to be the environmental correlate of the controlled variable, p, which is a function of the sensory effects of these physical variables. So q.i, as controlled quantity, actually exists only as a perception in the system doing the controlling (the one diagrammed) and (if an observer is present) in the observer of that control system – an observer who is aware of the existence of controlled variables.

So I think it’s great to have diagram police around but, just like real police, I believe that they should always keep in mind the reason they are there to enforce the laws. In the case of real police the laws are enforced to maintain the principle of having a civilized society; in the case of the diagram police, the laws are enforced to maintain the principle of communicating how the system actually works. In both cases, a good policeman knows when enforcing the “letter of the law” would actually violate the principle that the law is meant to maintain.

Best, Rick

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Thanks Rick & Adam, a helpful exchange for me….

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Adam,

I agree about the diagrams, but the formulas seem a little strange:

qo = ko * qi
qi = + ke * qe - kf * qo

“q”:s are variables and “k”:s should be functions, but now they are put in an equal way to the formulas as if they both we just variables. Of course a function is in a way a variable, but shouldn’t we rather stress their difference, that function is rather like a “machice” as you said. Then I would write the formulas as something like this:

qo = ko(qi)
qi = + ke(qe) – kf(qo)

Or then the mechanism of the function “machines” should be written out as something like this:

qo = x * qi + y

What you think?

As for Rick’s worry:

“…q.i, is shown to be outside the boundary of the system. This is true if q.i is taken to represent the physical variables that impinge on the senses. But q.i is usually taken to be the environmental correlate of the controlled variable, p, which is a function of the sensory effects of these physical variables. So q.i, as controlled quantity, actually exists only as a perception in the system doing the controlling (the one diagrammed) and (if an observer is present) in the observer of that control system – an observer who is aware of the existence of controlled variables.”

I think it is inconsistent nonsense. If qi is the result of the environment function then it is definitely outside the system. If p is a result of input function then it is inside the system. qi and p are not the same thing even though the latter depends on the previous in the way which is defined in the form of the input function. In these diagrams the input functions seems to be embedded inside the organism function, but still qi remains outside and as argument of the system.

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Yeah, that is a good point, the k’s are not functions, they are inputs or parameters to multiplication functions. The organism function, if we name it O, could be written as O(x) = ko * x. Written like that, it means it is a multiplication of any variable x with a constant ko. The same goes for the feedback function, F(x) = kf * x, and the disturbance function D(x) = ke * x
So, for a clear explanation, we could start a bit more abstract than the paper:

qo = O(qi)
qi = D(qe) - F(qo)

Then we can insert the explicit functions we defined:
qo = ko * qi
qi = ke *qe - kf * qo

etc.

Control system diagrams are ambiguous sometimes with single letters in boxes. ---->[ F ]—> could mean function F, or it could mean multiplication with constant F. Usually description needs to be added in the legend or the text.

Also math idioms can be confusing. If we say “qo is a function of qi” this does not mean that qi is a function. “y is a function of x” means that y is a variable that depends on another variable x

For the rest, I agree. The diagram is marked from the perspective of the researcher, and the system/environment line is a limit between environmental variables and neural variables.

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I don’t think it’s inconsistent nonsense but it may be a point that is irrelevant depending on what one what’s to know about human behavior

Actually, qi, the controlled variable, is a result of a perceptual, not an environmental, function. The perceptual function that defines qi is in the person controlling qi (as p) and, if there is an observer around, it is in the observer as well. So the environmental basis of q.i is outside the systems (both controller and observer) but q.i itself exists only as a perceptual function of that environmental basis. So qi exists only in systems that can compute those perceptual functions.

But this fact is irrelevant to one, such as an educator, trainer or manager, whose interest is in determining how well a person can control a variable that they should be able to control. In this case, the educator/trainer/manager sees qi as a variable in the environment outside the system doing the controlling and wants to see how well a person can control that variable.

For example, if the educator/trainer/manager wants to see how well a person can keep a cursor (c) aligned with a target (t), the distance between cursor and target position (t - c) is taken to be a controlled variable (q.i) that is out in the environment. And the results of the tracking task give the educator/trainer/manager a measure of how well q.i is being controlled.

But it is possible that that the person is not controlling t - c but, rather, some other function of t and c that is very closely related, such as arcsine [(t-c)/s] (this possibility was tested in a paper reprinted as Chapter 4 in my book Doing Research on Purpose). That is, the person could be controlling a different perceptual function of the variables t and c than the one assumed by the educator/trainer/manager. This would be of no concern to the educator/trainer/manager who only cares if the person can control t - c, which is what they are supposed to control. It would only be of concern to a PCT researcher who wants to know what perception(s) a person is controlling when they are doing some behavior.

This is related to what Powers’ called the “man -machine blunder” (Powers, 1978). It’s the error of incorrectly mapping a control system model to human behavior. In this case, the mistake is mapping a variable, q.i, that is actually a perceptual variable in the controller and observer, as an environmental variable outside of both. As Powers notes, this “blunder” is not a problem at all if one has a practical interest in knowing how well a person can control a variable that they should be able to control; it is only a problem if one’s interest is in understanding human nature. As Powers put it:

“If one’s primary purpose is to keep pilots from flying airplanes into the ground or to make sure that a gunner hits a target with the shell, that is, if one’s purposes concern objectivized side effects of control behavior, the man-machine blunder amounts to nothing worse than a few mislabelings having no practical consequences. If one’s interest is in the properties of persons, however, the man-machine blunder pulls a red herring across the path of progress”. (Powers, 1978).

Best, Rick

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Rick,

It’s nice that you try to understand different interests, but I would still appreciate consistence much more.

What do you mean by: “The perceptual function that defines qi is in the person controlling qi (as p) and, if there is an observer around, it is in the observer as well”?

What is the relationship between qi and p? Are they the same variable or different variables? If they are different, are they functionally depended and what is the function between them?

How does the perceptual function define qi?

How can a qi defined inside the controller be also inside the observer?

Do you really think that qi should be the name of the controlled variable inside the organism? Then the name p which is usually used if organism’s internal variables are drawn visible is redundant and may be forgotten? But how should then be named the (possible complex) variable which is, as you say, the environmental basis for the perception and which is changed as a result of changes in disturbance variable (qe in the original diagrams of this thread) and output variable (qo)? Will it be CEV?

I must return to the question of the situations of a PCT researcher and an educator/trainer/manager sometimes later when I have more time for it. At the moment I can only say that it has not much relevance for the naming of different variables in the diagrams and formulas.

T. Eetu

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Let’s look at it in terms of a simple tracking task, like the one here. When you do the tracking task, both you (the controller) and someone looking over your shoulder (the observer) can see this display:

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And both of you can perceive the variable you are controlling, which is the horizontal distance between the position of the upper, stationary line (the target, t) and the lower, moving line (the cursor, c). So both you and the observer are perceiving the same controlled variable, qi, which is t - c.

I think the best way to think of the relationship between qi and p is that qi is the controlled variable from the point of view of an observer – it is data – while p is the controlled variable from the point of view of the person doing the tracking – it is theory.

In the tracking task, qi is the observer’s perception of the varying horizontal distance between t and c; p is what the PCT model assumes is the controller’s perception of the the varying horizontal distance between t and c. So in both cases, what is perceived is t - c. So qi = t - c and p = t - c.

Another way to look at it is qi is an observed (perceived) phenomenon – a controlled variable – and p is a component of a model that explains that phenomenon – a controlled perceptual variable;

In the best case, the perceptual function defines qi (and p) mathematically. In the tracking task, the perceptual function is typically assumed to be a computation of the distance between target and cursor, p = t - c. So the function that defines the controlled variable, qi, (and the controlled perceptual variable, p) is just a subtraction.

As long as both controller and observer can sense the basis of the perception (in the tracking task that’s the positions of t and c) and do the equivalent computations to implement the perceptual function (in the tracking task, simply a subtraction) then qi can be defined inside both the controlled and observer. Again, that’s what is going on when a person watching the tracking task perceives the variable that is being perceived (and controlled) by the controller, the variable t - c.

No, I think qi should be reserved as the name of the controlled variable as seen by the observer; the existence of qi is the phenomenon to be explained. It is explained by PCT as resulting from control of a perceptual analog of qi, called p, that is inside the system that is doing the controlling; qi is data, p is theory.

No, I think we can keep it!

I think CEV is an unnecessary and confusing concept. It was never part of PCT, at least as PCT was developed by Powers. I don’t know what it could possibly refer to other than what “controlled variable” refers to.

I hope I cleared up the relationship between qi and p.

Best, Rick

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Rick,

it seems that you are quite firmly stuck to epistemological idealism: real environment is not needed or at least we should not talk about it.

When I perceive those two lines on the screen, I can’t help thinking and believing that there is a real computer display (manufactured in real factory etc.) with real pixels and at some moment some of those pixels are really emitting real light while others are dark or emit light with different wave length (or whatever light really is). When I perceive those lines, the environmental basis of my perception is the current arrangement of those lighted and not lighted pixels. (Btw. I think that my perceptual function defines the distance between those lines rather as an approximated amount of pixels between them than as a subtraction of the distances of those both for some zero point. However it is a handy way to express that distance variable as t-c.)

I think that we perceive variables (“things”) in the environment. We don’t perceive others’ or our own perceptions. (Even though in principle we could perceive someone’s perceptual signal by some neurological instrument, but that is a different case. And in our imagination we can in a way perceive our earlier perceptions, and the hierarchically higher perceptual functions in a way perceive the perceptions of the lower ones – but these are also different cases from what we talking about.)

We disagree here, but I know that this whole question does not matter much or at all to the way how you do PCT research – at least not to the results of that research. But it affects the way how outsiders see the theory. If you say them that this research has nothing to do with real environment, they will probably be no more interested about it. And if you in addition use concepts inconsistently it will still worsen the situation.

Here is the way how I could try to understand your way of thinking and talking in a somewhat consistent way (as for qi):

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The question marks are there just to show the variables which have no name and about which in PCT should be talked about. What is not consistent is that there are two q variables in the environment (and as such they should be hidden) and one in the observer. And if, as you say, qi is “controlled variable” then what the controller controls is an other person’s perceptions, which sounds really mystical!

Here is how I would think:

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Here there is a common real environment which makes it possible that the both subjects can have very similar perceptions. This will happen if the qi(c) and qi(o) (the environmental effects against their sense organs) happen to be similar. This will be the case when the observer is looking over the shoulder of the controller as in your example. Then the perceptions (pc and po) will similar if the both perceptual functions are similar. And in a happy case you can reasonably say that the perceptions are same.

(Attachment image001.emz is missing)

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Although it might look like Eetu & Rick are disagreeing about the importance of the real environment in PCT, I don’t think they are. They both us the same closed loop that requires it. The problem is that even to try to describe reality at the concrete level that Eetu attempts, he’s still using perceptual functions. He has to. He’s human. The real environment is integral to perceptual control but we can’t describe it to each other without the use of perceptual functions. Its part of the fact of control that is unknowable in any direct way.

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Warren,

I believe too, that at bottom even the most radical constructivist and solipsist must somehow admit the meaning of reality, even though we get information about that reality only via perceptions. However, I am not worried about that question but the way how we talk (about our theory). Rick consistently denies the relevance of any concept (be it named as CEV or Qi etc.) which refers to the variables in real reality which may correspond to our perceptual variables (being the arguments of the perceptual function) and which only can explain why different perceivers sometimes get reliably same or similar perceptions. This denial then leads to funny inconsistencies like: Qe and Qo may be drawn in the environment but Qi in the observer. If there is no observer then there is no Qi (= no controlled variable) - but still Qe and Qo. Controller controls nothing in the environment but instead something in the observer. etc.

Actually, I am not trying “to describe reality at the concrete level” but instead at the abstract theoretical level. The pixels on the screen was just an instructional example. I was not talking primarily about perceived pixel but real pixels which were assumedly built there in the (real) factory and which assumedly emit (real) light in certain (real) conditions. Qe, Qo and Qi are all assumed (and in the diagrams drawn) as variables which are in the environment even though all perceived values of them are determined via perceptions.

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Hi Eetu. I think people are getting stuck on binary concepts of reality, and control. The degree of overlap in the perceptual functions between different agents is on a continuum, and the degree of control that an agent has over any variable, either perceived or ‘real’, is on a continuum too. In a highly practised task requiring control of a very concrete variable, the overlap is so high that these issues of perception and reality are somewhat academic. But in the real world where control can be drawn out over time and imperfect, they become more of an issue.

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Warren, I agree !

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To me, the problem is mixing experiences with perceptions.

A diagram of a control loop in a tracking task says that a researcher can measure the controlled variable, the distance between the cursor and the target, in millimeters or pixels. It also says that there is a perceptual signal in the brain of the participant that can be measured with appropriate equipment as a rate of firing of some population of neurons, in units of spikes per second, or something like that.

The diagram says nothing about the experience of the participant, because it is made from the perspective of the researcher. To the researcher, all the variables on the diagram are ‘out there’. The environment-organism limit does not mark the limit between participant’s experience and the outside world. It marks the limit between different types of quantites that the researcher can measure.

Then if we try to say where is this experience, it gets unwieldly. We feel the cursor and target are ‘out there’ as a quantitiy, but we believe it is created by our brain, so it is also “inside” as a perception, but do we mean perception as experience or perception as a neural signal? and maybe both are inside and outside because the reality we perceive depends on the outside reality. I don’t know, to me, it gets confusing very soon.

The point being, in a diagram, there is nothing about the experience of the participant, organism or model. All of the quantities and signals are theoretically measureable. If we identify correct controlled variables in some task, something fitting really well with participant’s behavior, then we can hope to find a neural signal correlated to our modelled perceptual signal.

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Great!