Understanding the Behavior of Living Systems

[From Bruce Abbott (2014.03.02. 1505 EST)]

Rick Marken (2014.03.01.1415)]

[Martin Taylor 2014.03.01.16.41]

[From Rick Marken (2014.03.01.1230)]

RM: …The fact that you can’t understand the true input-output characteristics of a component of a closed-loop system by measuring the input-output characteristics of that component while it is part of a control loop – the subject of the arcane debate between Martin and I – means that the way behavioral scientists have been going about trying to understand the behavior of living systems is misguided.

MT: So you have retreated from trying to explain why you believe that “you can’t understand the true input-output characteristics of a component of a closed-loop system by measuring the input-output characteristics of that component while it is part of a control loop”.

RM: No, not at all. Actually, I’ve already explained (and provided a working demonstration) of why I believe this. I just wanted to explain to the audience (if we have one) why this debate is important (at least from my point of view) in a somewhat less technical way. I think it’s important because if I’m right, scientific psychology has to start all over again using research methods based on an understanding of the fact that the organisms under study are closed-loop systems. If you’re right, then scientific psychology has been using the right research methods all along; all that’s needed is a change in theory.

MT: Now you simply assert this falsehood as “a fact”, and that ends the discussion.

RM: No, I’m not asserting that at all. We haven’t resolved this debate and I doubt that we ever will. All I want to do is describe what I think are the stakes here. I’f you’re right then I’ve wasted my entire career trying to show that the input-output approach to studying the behavior of living systems is wrong. If I’m right then you’ve wasted your entire career studying behavior using input-output methodology. So the stakes are pretty high for us. But obviously the stakes are also pretty high for anyone interested in understanding the behavior of living control systems.

RM: As I said, I’ll get to a detailed rebuttal of your last post but I probably won’t be able to get to it for a while (like until tomorrow. This thread I just started on " Understanding the Behavior of Living Systems" is really just for the benefit of on-lookers who might be interested in why we’re debating what might seem like such an arcane question, the question of whether you can or cannot “understand the true input-output characteristics of a component of a closed-loop system by measuring the input-output characteristics of that component while it is part of a control loop”.

Rick, I’m puzzled by your position on this (I think Martin’s analysis is correct) and am hoping to gain some insight into your thinking through your answers to the following questions. (To keep the situation simple, both questions assume a constant reference signal.)

(1) In an effective negative feedback control system there is essentially no correlation between input and output. How, then, does the output “know” what values it needs to produce in order to keep the input (nearly) constant?

(2) In an ideal negative feedback control system there would be no variation in the CV and no error even though a variable disturbance to the CV is being applied. Would such an ideal control system actually work?

Bruce

[David Goldstein (2014, 03.01.17:16)]

Re.: [From Bruce Abbott (2014.03.02. 1505 EST)]

Bruce, I know that you addressed your question to Rick, but I wanted to share the following thoughts with you.

If the input quantity into a person is the result of the disturbance effect and the feedback effect, how could correlations between a measure of the input quantity and a measure of the output quantity inform a person about only the disturbance effect?

A second thought: If there is no error in the CV, and we are working with an ideal negative feedback control system, why would a person every change the output quantity which is resulting in the
zero error condition. Presumably, the error was not always zero in the beginning and a person had to find the control system to accomplish this. Powers talks about control systems developing in the order-- input component, then the comparator component and then the output component.

David

[From Bruce Abbott (2014.03.02. 1505 EST)]

Rick Marken (2014.03.01.1415)]

[Martin Taylor 2014.03.01.16.41]

[From Rick Marken (2014.03.01.1230)]

RM: …The fact that you can’t understand the true input-output characteristics of a component of a closed-loop system by measuring the input-output characteristics of that component while it is part of a control loop – the subject of the arcane
debate between Martin and I – means that the way behavioral scientists have been going about trying to understand the behavior of living systems is misguided.

MT: So you have retreated from trying to explain why you believe that “you can’t understand the true input-output characteristics of a component of a closed-loop system by measuring the input-output characteristics of that component while it is part of a control loop”.

RM: No, not at all. Actually, I’ve already explained (and provided a working demonstration) of why I believe this. I just wanted to explain to the audience (if we have one) why
this debate is important (at least from my point of view) in a somewhat less technical way. I think it’s important because if I’m right, scientific psychology has to start all over again using research methods based on an understanding of the fact that the organisms under study are closed-loop systems. If you’re right, then scientific psychology has been using the right research methods all along; all that’s needed is a change in theory.

MT: Now you simply assert this falsehood as “a fact”, and that ends the discussion.

RM: No, I’m not asserting that at all. We haven’t resolved this debate and I doubt
that we ever will. All I want to do is describe what I think are the stakes here. I’f you’re right then I’ve wasted my entire career trying to show that the input-output approach to studying the behavior of living systems is wrong. If I’m right then you’ve wasted your entire career studying behavior using input-output methodology. So the stakes are pretty high for us. But obviously the stakes are also pretty high for anyone interested in understanding the behavior of living control systems.

RM: As I said, I’ll get to a detailed rebuttal of your last post but I probably won’t be able to get to it for a while (like until tomorrow. This thread I just started on " Understanding the Behavior of Living Systems" is really just for the benefit of on-lookers who might be interested in why we’re debating
what might seem like such an arcane question, the question of whether you can or cannot “understand the true input-output characteristics of a component of a closed-loop system by measuring the input-output characteristics of that component while it is part of a control loop”.

Rick, I’m puzzled by your position on this (I think Martin’s analysis is correct) and am hoping to gain some insight into your thinking through your answers to the following questions. (To keep the situation simple, both questions assume a constant reference signal.)

(1)
In an effective negative feedback control system there is essentially no correlation between input and output. How, then, does the output “knowâ€? what values it needs to produce in order to keep the input (nearly) constant?

(2)

In an ideal negative feedback control system there would be no variation in the CV and no error even though a variable disturbance to the CV is being applied. Would such an ideal control system actually work?

Bruce

···

On Sunday, March 2, 2014 3:19 PM, Bruce Abbott bbabbott@FRONTIER.COM wrote:

[From Rick Marken (2014.03.02.1700)]

Bruce Abbott (2014.03.02. 1505 EST)--

RM: This thread I just started on " Understanding the Behavior of Living Systems" is really just for the benefit of on-lookers who might be interested in why we're debating what might seem like such an arcane question, the question of whether you can or cannot "understand the true input-output characteristics of a component of a closed-loop system by measuring the input-output characteristics of that component while it is part of a control loop".

BA: Rick, I’m puzzled by your position on this (I think Martin’s analysis is correct) and am hoping to gain some insight into your thinking through your answers to the following questions.

RM: If the position you are puzzled about is my claim that "you can't understand the true input-output characteristics of a component of a closed-loop system by measuring the input-output characteristics of that component while it is part of a control loop" then I'll try to unpuzzle you (and answer Martin's earlier post) after I answer your questions. But as a preview I will say that my position on that claim has "evolved" so stick with me.

BA: (1) In an effective negative feedback control system there is essentially no correlation between input and output. How, then, does the output “know” what values it needs to produce in order to keep the input (nearly) constant?

RM: The output doesn't have to "know" what values it needs to produce in order to keep the input at the reference (that's a Modern Control Theory notion of how control works -- see CH. 1 of LCS III). The output of a control system is simply driven by error which is, at the same time, being cancelled by the output itself. Because the error signal is in a negative feedback loop it is causing itself, via the output, to go to zero. And this, of course is also forcing the controlled variable into a match with the constant (or varying) reference signal. The only thing the output has to "know" is to do what the error signal tells it to do.

BA: (2) In an ideal negative feedback control system there would be no variation in the CV and no error even though a variable disturbance to the CV is being applied. Would such an ideal control system actually work?

RM: I don't think so. You can get close to perfection but only god is perfect and even he doesn't exist;-)
RM: Now to my claim that "you can't understand the true input-output characteristics of a component of a closed-loop system by measuring the input-output characteristics of that component while it is part of a control loop". It turns out I was wrong!! I discovered this when I realized that the "component" of a closed - loop system that Martin had diagrammed was just the perceptual function. I was thinking of "component" as either the "system" or "environment" component of the control loop. My little "black box" analysis was based on that assumption.
RM: But I finally understood from one of Martin's last posts that the component he was describing in his diagram was the perceptual function, not the "system function".The input to this perceptual function component was S, the sensory input at a receptor, and the output was p, the perceptual signal. I tested this out in my spreadsheet simulation and, sure enough, the measured functional relationship between S and p (input and output) corresponds to the true functional relationship whether this relationship is measured in an open or closed loop. So it looks like one can study the "open loop" characteristics of a component of a control loop -- the perceptual function component-- while it is part of the loop.
RM: My only consolation was that I couldn't think of many studies where the input-output of a perceptual function was studied in this way. The simulation shows that you can only get a true measure of the input-output characteristics of the perceptual function by measuring the sensory input (S), such as the actual stimulation at the retina in the case of visual perception, and measuring the neural output associated with that sensory input. I think Hubel and Weisel did something like this. But I'm not sure whether they measured the stimulation at the sensory surface or just assumed that their projected patterns corresponded to the patterns at the surface.The projected pattern corresponds to a disturbance, d, (independent variable), that causes, along with system output, the sensory stimulation, S, that is the input to the perceptual function. And my simulation shows that the relationship between d and p in a closed loop system does not correspond to the function relating S to p in the perceptual function. But I'll assume that Hubel and Weisel did measure S directly. I've always liked their work and I still think it's a good approach to learning about the perceptual function components of a control loop -- the most important component because, after all, behavior is the control of perception.
RM: After finding that the true open-loop input-output characteristics of the perceptual function could be determined in a closed loop I decided to keep going and find out just how wrong I was. And it turns out that that was the limit of my wrongness, luckily. My simulation showed that true open-loop input-output characteristics of every other component of a control loop cannot be determined by measuring the input-output characteristics of that component while it is in the loop. You can't do it for the comparator function (input = p, output = e); the output function (input = e, output = o) or the feedback function (input = o, output = S). Just the perceptual function. I have no idea why this is true -- if there is some deep reason for this -- but it seems to be the case.
RM: One interesting conclusion from this work is relevant to the discussion of the equilibrium point and Powers/Kennaway muscle models, which are both models of the output function component of a control loop. That is, the muscle is the functional component of the relationship o = f(e); the output function is the way the muscle turns a neural error signal (e, the input) into an output variable (o, force and/or length). What my simulation shows is that, unlike the perceptual function, you can't measure the true open-loop input-output characteristics of muscle by measuring the relationship between e and o while the muscle is still part of the loop. So when Powers talks about the "open loop" response of a muscle to stimulation (in the 1999 paper) he means the response when the muscle is in an in vitro rather than an in vivo preparation.
RM: A final thought. While it is important to know that the input-output characteristics of perceptual functions can be studied in physiological studies like those done by Hubel and Weisel, I think these studies would have to be conducted in the context of an understanding of what kinds of perceptual variables organisms control. After all, in order to determine the characteristics of the perceptual function relating S to p one has to know what S is -- or might be. Of course, S will be different for different behaviors. But I think hypotheses about what S is when testing the input-output characteristics of a perceptual function would have to come from behavioral research, such as the research on object interception.
RM: Also, the fact that you can determine the input-output characteristics of the perceptual function in vivo (by measuring S and p, which requires some serious physiological equipment) doesn't mean it can be done using conventional behavioral methods, like those used in psychophysical experiments. In such experiments you still have participants who are controlling perceptual variables -- like the perception of the relationship between their response and the stimulus -- so the observed relationship between stimulus (which is a disturbance) and response reflect characteristics of the feedback connection between response and controlled variable, not those of the perceptual function or even the system function.
Best regards
Rick

···

--
Richard S. Marken PhD
<http://www.mindreadings.com>www.mindreadings.com

The only thing that will redeem mankind is cooperation.
-- Bertrand Russell

[From Bruce Abbott (2014.03.02.2135 EST)]

[David Goldstein (2014, 03.01.17:16)]

Re.: [From Bruce Abbott (2014.03.02. 1505 EST)]

DG: Bruce, I know that you addressed your question to Rick, but I wanted to share the following thoughts with you.

DG: If the input quantity into a person is the result of the disturbance effect and the feedback effect, how could correlations between a measure of the input quantity and a measure of the output quantity inform a person about only the disturbance effect?

BA: It doesn’t.

DG: A second thought: If there is no error in the CV, and we are working with an ideal negative feedback control system, why would a person every change the output quantity which is resulting in the zero error condition. Presumably, the error was not always zero in the beginning and a person had to find the control system to accomplish this. Powers talks about control systems developing in the order-- input component, then the comparator component and then the output component.

BA: Remember, we’re having to contend with a time-varying disturbance. To compensate perfectly for the effect of that disturbance on the CV, the system must generate an output that has an equal and opposite effect to that of the disturbance, with zero lag. But the error signal of the perfect negative feedback control system never departs from zero, so how can the output (which equals the error times the output gain) ever be anything other than zero? And if the output is always zero, it can’t be varying in the way required to perfectly compensate (or indeed compensate at all) for the varying effect of the disturbance on the controlled variable.  It follows that such a “perfectâ€? negative feedback, error driven control system is in the same category as a perpetual motion machine – there isn’t any such thing.

Bruce

[From Bruce Abbott (2014.03.02.2215 EST)]

Rick Marken (2014.03.02.1700)–

Bruce Abbott (2014.03.02. 1505 EST)

RM: This thread I just started on " Understanding the Behavior of Living Systems" is really just for the benefit of on-lookers who might be interested in why we’re debating what might seem like such an arcane question, the question of whether you can or cannot “understand the true input-output characteristics of a component of a closed-loop system by measuring the input-output characteristics of that component while it is part of a control loop”.

BA: Rick, I’m puzzled by your position on this (I think Martin’s analysis is correct) and am hoping to gain some insight into your thinking through your answers to the following questions.

RM: If the position you are puzzled about is my claim that “you can’t understand the true input-output characteristics of a component of a closed-loop system by measuring the input-output characteristics of that component while it is part of a control loop” then I’ll try to unpuzzle you (and answer Martin’s earlier post) after I answer your questions. But as a preview I will say that my position on that claim has “evolved” so stick with me.

BA: (1) In an effective negative feedback control system there is essentially no correlation between input and output. How, then, does the output “know” what values it needs to produce in order to keep the input (nearly) constant?

RM: The output doesn’t have to “know” what values it needs to produce in order to keep the input at the reference (that’s a Modern Control Theory notion of how control works – see CH. 1 of LCS III). The output of a control system is simply driven by error which is, at the same time, being cancelled by the output itself. Because the error signal is in a negative feedback loop it is causing itself, via the output, to go to zero. And this, of course is also forcing the controlled variable into a match with the constant (or varying) reference signal. The only thing the output has to “know” is to do what the error signal tells it to do.

BA: O.K.

BA: (2) In an ideal negative feedback control system there would be no variation in the CV and no error even though a variable disturbance to the CV is being applied. Would such an ideal control system actually work?

RM: I don’t think so. You can get close to perfection but only god is perfect and even he doesn’t exist;-)

O.K. But God does exist – he looks exactly like Morgan Freeman.

RM: Now to my claim that “you can’t understand the true input-output characteristics of a component of a closed-loop system by measuring the input-output characteristics of that component while it is part of a control loop”. It turns out I was wrong!! I discovered this when I realized that the “component” of a closed - loop system that Martin had diagrammed was just the perceptual function. I was thinking of “component” as either the “system” or “environment” component of the control loop. My little “black box” analysis was based on that assumption.

RM: But I finally understood from one of Martin’s last posts that the component he was describing in his diagram was the perceptual function, not the “system function”.The input to this perceptual function component was S, the sensory input at a receptor, and the output was p, the perceptual signal. I tested this out in my spreadsheet simulation and, sure enough, the measured functional relationship between S and p (input and output) corresponds to the true functional relationship whether this relationship is measured in an open or closed loop. So it looks like one can study the “open loop” characteristics of a component of a control loop – the perceptual function component-- while it is part of the loop.

RM: My only consolation was that I couldn’t think of many studies where the input-output of a perceptual function was studied in this way. The simulation shows that you can only get a true measure of the input-output characteristics of the perceptual function by measuring the sensory input (S), such as the actual stimulation at the retina in the case of visual perception, and measuring the neural output associated with that sensory input. I think Hubel and Weisel did something like this. But I’m not sure whether they measured the stimulation at the sensory surface or just assumed that their projected patterns corresponded to the patterns at the surface.The projected pattern corresponds to a disturbance, d, (independent variable), that causes, along with system output, the sensory stimulation, S, that is the input to the perceptual function. And my simulation shows that the relationship between d and p in a closed loop system does not correspond to the function relating S to p in the perceptual function. But I’ll assume that Hubel and Weisel did measure S directly. I’ve always liked their work and I still think it’s a good approach to learning about the perceptual function components of a control loop – the most important component because, after all, behavior is the control of perception.

RM: After finding that the true open-loop input-output characteristics of the perceptual function could be determined in a closed loop I decided to keep going and find out just how wrong I was. And it turns out that that was the limit of my wrongness, luckily. My simulation showed that true open-loop input-output characteristics of every other component of a control loop cannot be determined by measuring the input-output characteristics of that component while it is in the loop. You can’t do it for the comparator function (input = p, output = e); the output function (input = e, output = o) or the feedback function (input = o, output = S). Just the perceptual function. I have no idea why this is true – if there is some deep reason for this – but it seems to be the case.

BA: Hmmm. I’ll have to think about that. It doesn’t seem likely. What exactly DO you get when measuring, say, the error versus output of the output function, in the steady state?

RM: One interesting conclusion from this work is relevant to the discussion of the equilibrium point and Powers/Kennaway muscle models, which are both models of the output function component of a control loop. That is, the muscle is the functional component of the relationship o = f(e); the output function is the way the muscle turns a neural error signal (e, the input) into an output variable (o, force and/or length). What my simulation shows is that, unlike the perceptual function, you can’t measure the true open-loop input-output characteristics of muscle by measuring the relationship between e and o while the muscle is still part of the loop. So when Powers talks about the “open loop” response of a muscle to stimulation (in the 1999 paper) he means the response when the muscle is in an in vitro rather than an in vivo preparation.

RM: A final thought. While it is important to know that the input-output characteristics of perceptual functions can be studied in physiological studies like those done by Hubel and Weisel, I think these studies would have to be conducted in the context of an understanding of what kinds of perceptual variables organisms control. After all, in order to determine the characteristics of the perceptual function relating S to p one has to know what S is – or might be. Of course, S will be different for different behaviors. But I think hypotheses about what S is when testing the input-output characteristics of a perceptual function would have to come from behavioral research, such as the research on object interception.

RM: Also, the fact that you can determine the input-output characteristics of the perceptual function in vivo (by measuring S and p, which requires some serious physiological equipment) doesn’t mean it can be done using conventional behavioral methods, like those used in psychophysical experiments. In such experiments you still have participants who are controlling perceptual variables – like the perception of the relationship between their response and the stimulus – so the observed relationship between stimulus (which is a disturbance) and response reflect characteristics of the feedback connection between response and controlled variable, not those of the perceptual function or even the system function.

BA: That doesn’t seem to agree with the results of psychophysical experiments on, for example, sensory adaptation to darkness. The change in threshold for detecting a light reflects the light-sensitivity characteristics of the rods and cones as they adapt to darkness, not the characteristics of the feedback connection imposed by the experimenter.

I’m not saying that the “behavioral illusion” is a myth; it clearly does occur. But one must be careful not to make blanket pronouncements suggesting that research “using conventional behavioral methods” always succumbs to the behavioral illusion. Whether a given example does or does not must be judged based on a careful analysis of the particular methods used.

Bruce

[David Goldstein (2014.03.01.22:17)]

Re.: [From Bruce Abbott (2014.03.02.2135 EST)]

Thanks for your answer to my questions. I have some follow-up questions.

You answered to the first question: “It doesn’t”. Then how does
studying input/out relationships help us identify what a person is controlling? In standard psychological methods, I was always frustrated by the fact that the independent variable interacted with a bunch of other variables, namely, “interaction effects.” This placed a limit on the way one could generalize about an independent variable. What I liked about PCT was that once you have found a perceptual variable that a person was controlling, one could generalize more about what the person would do if something which disturbed the controlled variable happened.

You answered the second question by saying that no such control system could exist. What places a limit on the size of the error signal? Gain–the higher the gain, the smaller the error signal tolerated. Practice–the more one practices a skill, like hitting a forehand in tennis, the more automatic it becomes. It is handled without awareness needed? Level of perception–higher levels take longer to form. It might take longer to detect when the perception is not being controlled and harder to correct errors. Supreme court decisions may be an example of this.

David

···

On Sunday, March 2, 2014 9:36 PM, Bruce Abbott bbabbott@FRONTIER.COM wrote:

[From Bruce Abbott (2014.03.02.2135 EST)]

[David Goldstein (2014, 03.01.17:16)]

Re.: [From Bruce Abbott (2014.03.02. 1505 EST)]

DG: Bruce, I know that you addressed your question to
Rick, but I wanted to share the following thoughts with you.

DG: If the input quantity into a person is the result of the disturbance effect and the feedback effect, how could correlations between a measure of the input quantity and a measure of the output quantity inform a person about only the disturbance effect?

BA: It doesn’t.

DG:
A second thought: If there is no error in the CV, and we are working with an ideal negative feedback control system, why would a person every change the output quantity which is resulting in the zero error condition. Presumably, the error was not always zero in the beginning and a person had to find the control system to accomplish this. Powers talks about control systems developing in the order-- input component, then the comparator component and then the output component.

BA: Remember, we’re having to contend with a time-varying disturbance. To compensate perfectly for the effect of that disturbance on the CV, the system must generate an output that has an equal and opposite effect to that of the disturbance, with zero
lag. But the error signal of the perfect negative feedback control system never departs from zero, so how can the output (which equals the error times the output gain) ever be anything other than zero? And if the output is always zero, it can’t be varying in the way required to perfectly compensate (or indeed compensate at all) for the varying effect of the disturbance on the controlled variable. It follows that such a “perfectâ€? negative feedback, error driven control system is in the same category as a perpetual motion machine – there isnâ’t any such thing.

Bruce

[Martin Taylor 2014.03.02.23.09]

That's just one of the components. Each connector and each function,

including those in the environmental feedback path, is a component.
That is fair comment. I quite agree with that particular aspect,
though it’s not the whole story. But that wasn’t ever in question.
What was in question was your assertion, oft repeated over the
years, that “You cannot measure the open loop behavior of components
of a control loop when those components are still part of an active
control loop.”
That contention is at the heart of your incorrect dismissal of
classical psychophysics. So it matters.
How did you come to this conclusion?
I very much doubt it. If it were true, it would hit at the
foundations of physics. You are saying that, for example, if the
output function is an integrator when the output doesn’t influence
the input, it ceases to be an integrator when the feedback loop is
complete. Magic!
I know you know that the output of an integrator is uncorrelated
with its input (as is the output of a differentiator), so you
wouldn’t have made the mistake of considering correlation as any
part of a test of whether the function can be determined from
comparing input and output waveforms. And for the comparator, you
wouldn’t have made the mistake of varying the reference value, I
hope.
Martin

···

On 2014/03/2 8:02 PM, Richard Marken
wrote:

[From Rick Marken (2014.03.02.1700)]

          RM: Now to my claim that "you can't understand the true

input-output characteristics of a component of a
closed-loop system by measuring the input-output
characteristics of that component while it is part of a
control loop". It turns out I was wrong!! I discovered
this when I realized that the “component” of a closed -
loop system that Martin had diagrammed was just the
perceptual function. I was thinking of “component” as
either the “system” or “environment” component of the
control loop. My little “black box” analysis was based on
that assumption.

          RM: But I finally understood from one of Martin's last

posts that the component he was describing in his diagram
was the perceptual function, not the “system function”.

          The input to this perceptual function component was S,

the sensory input at a receptor, and the output was p, the
perceptual signal. I tested this out in my spreadsheet
simulation and, sure enough, the measured functional
relationship between S and p (input and output)
corresponds to the true functional relationship whether
this relationship is measured in an open or closed loop.
So it looks like one can study the “open loop”
characteristics of a component of a control loop – the
perceptual function component-- while it is part of the
loop.

          RM: My only consolation was that I couldn't think of

many studies where the input-output of a perceptual
function was studied in this way. The simulation shows
that you can only get a true measure of the input-output
characteristics of the perceptual function by measuring
the sensory input (S), such as the actual stimulation at
the retina in the case of visual perception, and measuring
the neural output associated with that sensory input.

          RM: After finding that the true open-loop input-output

characteristics of the perceptual function could be
determined in a closed loop I decided to keep going and
find out just how wrong I was. And it turns out that that
was the limit of my wrongness, luckily. My simulation
showed that true open-loop input-output characteristics of
every other component of a control loop cannot be
determined by measuring the input-output characteristics
of that component while it is in the loop. You can’t do it
for the comparator function (input = p, output = e); the
output function (input = e, output = o) or the feedback
function (input = o, output = S). Just the perceptual
function.

          I have no idea why this is true -- if there is some

deep reason for this – but it seems to be the case.

[Martin Taylor 2014.03.02.23.38]

The fundamental limit is set by the transport lag and the speed and

range of variation of the disturbance. If the disturbance has moved
on since its value one transport lag time previously, its current
value will not be correctly opposed by the output. Of course, if its
variation is predictable, then the fact that it changed over the
time of the transport lag matters less, and the error minimum is
determined not by the actual change but by the magnitude of the
failure of prediction. No physical control system can overcome this
limit, which is a mathematical bound. What you mention (Gain and
Practice) can reduce the error as compared to the error of a
low-gain novice system, but they can’t reduce it beyond that bound.
Yes, within bounds. Too high gain will set the loop into
oscillation, because there always is some transport lag. This means
that there are some ranges of frequencies for which the loop gain
becomes positive. If the overall gain increases enough to make the
positive gain at one of those frequencies greater than unity, the
system goes into a sustained oscillation.
Yes. I think in part this is an aspect of the prediction mentioned
above, though in relation to the effect of the output rather than to
the disturbance, which is handled in Bill’s simulation by the
artificial cerebellum, and perhaps in life by the real cerebellum.
The Artificial cerebellum, and perhaps the real one, allows the
output to compensate for the dynamic characteristics of the muscular
and tool structure. It takes time (practice) to develop in the
artificial case, and presumably in real life. It may be also that
practice reduces the transport lag, thereby allowing higher gain to
be useful.
Martin

···

I’m responding in part becasue I think I have something to offer,
and in part to ask David why each successive message has a larger
typeface than its predecessor.

[David Goldstein (2014.03.01.22:17)]

Re.: [From
Bruce Abbott (2014.03.02.2135 EST)]

        Thanks for your answer to my

questions. I have some follow-up questions.

… . What places a limit on the size of the error signal?

      Gain--the

higher the gain, the smaller the error signal tolerated.

      Practice--the more one practices a skill, like hitting a

forehand in tennis, the more automatic it becomes.

[From Bruce Abbott (2014.03.02. 1505 EST)]

···

Rick Marken (2014.03.01.1415)]

[Martin Taylor 2014.03.01.16.41]

[From Rick Marken (2014.03.01.1230)]

RM: …The fact that you can’t understand the true input-output characteristics of a component of a closed-loop system by measuring the input-output characteristics of that component while it is part of a control loop – the subject of the arcane debate between Martin and I – means that the way behavioral scientists have been going about trying to understand the behavior of living systems is misguided.

MT: So you have retreated from trying to explain why you believe that “you can’t understand the true input-output characteristics of a component of a closed-loop system by measuring the input-output characteristics of that component while it is part of a control loop”.

RM: No, not at all. Actually, I’ve already explained (and provided a working demonstration) of why I believe this. I just wanted to explain to the audience (if we have one) why this debate is important (at least from my point of view) in a somewhat less technical way. I think it’s important because if I’m right, scientific psychology has to start all over again using research methods based on an understanding of the fact that the organisms under study are closed-loop systems. If you’re right, then scientific psychology has been using the right research methods all along; all that’s needed is a change in theory.

MT: Now you simply assert this falsehood as “a fact”, and that ends the discussion.

RM: No, I’m not asserting that at all. We haven’t resolved this debate and I doubt that we ever will. All I want to do is describe what I think are the stakes here. I’f you’re right then I’ve wasted my entire career trying to show that the input-output approach to studying the behavior of living systems is wrong. If I’m right then you’ve wasted your entire career studying behavior using input-output methodology. So the stakes are pretty high for us. But obviously the stakes are also pretty high for anyone interested in understanding the behavior of living control systems.

RM: As I said, I’ll get to a detailed rebuttal of your last post but I probably won’t be able to get to it for a while (like until tomorrow. This thread I just started on " Understanding the Behavior of Living Systems" is really just for the benefit of on-lookers who might be interested in why we’re debating what might seem like such an arcane question, the question of whether you can or cannot “understand the true input-output characteristics of a component of a closed-loop system by measuring the input-output characteristics of that component while it is part of a control loop”.

Rick, I’m puzzled by your position on this (I think Martin’s analysis is correct) and am hoping to gain some insight into your thinking through your answers to the following questions. (To keep the situation simple, both questions assume a constant reference signal.)

(1) In an effective negative feedback control system there is essentially no correlation between input and output. How, then, does the output “know� what values it needs to produce in order to keep the input (nearly) constant?

(2) In an ideal negative feedback control system there would be no variation in the CV and no error even though a variable disturbance to the CV is being applied. Would such an ideal control system actually work?

Bruce

[Martin Taylor 2014.03.03.10.13]

My understanding -- or possibly misunderstanding -- of Rick's

position is that the input-output relationship of a functional
element changes when it is part of a complete feedback loop. In
other words, the relation between input waveform and output waveform
changes. I have not been able to reconcile this with his view that
you can model a control system using a simulation in which the
different components’ open-loop behaviours are each described by a
program, and that program remains unchanged when the component is
connected into a simulated control loop. If the input-output
relations of the living control system must change when the loop is
closed, how can such a simulation properly describe its behaviour?
Alternatively, how can the simulated component subroutine change its
behaviour when it is incorporated in a larger program that defines a
control loop?
Most recently [From Rick Marken (2014.03.02.1700)], Rick has
accepted that the perceptual function does not change between
open-loop and closed loop settings, but he says that the comparator
function and output function do change, even in his simulation in
which the sub-program that defines them does not change. I don’t think it has anything to do with reorganization. It has to
do with a basic misunderstanding of how control systems work, a
basic misunderstanding that I had not recognized until the last day
or two, but that I believe has been at the heart of many of our
weird long-thread disagreements over the last two decades. All
along, I have just assumed an understanding that was not there –
that functions behave the same way whether they are or are not
incorporated in a feedback loop. Now I look back on some of those
arguments, that was precisely the unrecognized sticking point, the
reason why the disagreements were never resolved but were allowed to
lapse.
By the way, have you looked at my analysis of the Behavioral
Illusion? It depends on the same idea that a function will not
change its input-output relations just because it is incorporated
into a feedback loop.
Martin

···

On 2014/03/3 3:55 AM, Warren Mansell
wrote:

Hi everyone,

    Following on from Bruce's point, I think we all agree that

there are parameters of a control system that need to be ‘tuned’
by reorganisation to control optimally? Some of these parameters
are part of the output function, yes? We can therefore build a
closed loop PCT model of the real control system and adjust the
output function through reorganisation until it produces a
closer match with the behaviour of the real system. This could
work if reorganisation only changed the output function whereas
it is likely to change parameters through out the neural
components of the closed loop. Nevertheless, like Bruce, this
though experiment indicates that ‘knowing’ the output function
better is possible, surely Rick?

Warren

David Goldstein (2014.03.03.11:37)

Martin, please define transport
lag in terms of the live block diagram we are reviewing.

David

···

I’m responding in part becasue I think I have something to offer,
and in part to ask David why each successive message has a larger
typeface than its predecessor.

[David Goldstein (2014.03.01.22:17)]

Re.: [From
Bruce Abbott (2014.03.02.2135 EST)]

        Thanks for your answer to my

questions. I have some follow-up questions.

… . What places a limit on the size of the error signal?

      Gain--the

higher the gain, the smaller the error signal tolerated.

      Practice--the more one practices a skill, like hitting a

forehand in tennis, the more automatic it becomes.

[Martin Taylor 2014.03.03.13.25]

I suppose you mean Fig 2-3, but it doesn't matter. The concept is

quite general, so I’ll treat it as such.
Take any two points in any circuit (network of connected function,
for example a control loop). Inject an impulse or a step at one
point, and measure how long it takes for the first effect of that
injection to be detectable at the second point. That is the
transport lag between the two points in that direction. It would
probably be different in the other direction.
Transport lag should not be confused with the delay inherent in
having an integrator in the loop. Consider an integrator by itself,
not in a loop, and apply a unit step at its input. What the
integrator does is to make that first detectable effect be
infinitesimally small. The integrator output starts at zero and
continues to increase at a steady rate so long as its input doesn’t
change, so in practice, if you want to know whether there is any
transport lag associated with the integrator, you have to
extrapolate backward after the output has become measurable to
determine when that first infinitesimal effect appeared at the
output.
Loop transport lag is measured the same way, except that the two
points are now one. In the case of a control loop such as Fig 2-3,
suppose that the reference value changes stepwise at time t0. At
time t1, the first effect of that step begins to appear again at the
reference input. t1-t0 is the loop transport lag. The same loop
transport lag would be measured if the step were to occur at the
disturbance input rather than at the reference input. In real physical systems, there is always some transport lag, if
only because of the finite speed of light. In most, the transport
lag is much greater than that, and in the case of everyday (as
opposed to experimental laboratory) control, most of the loop
transport lag is in the environmental feedback path.
Both loop transport lag and the slow growth of the output of an
integrator contribute to the limit on how rapidly changes in a
disturbance can be countered in control. The transport lag is
irrelevant if the disturbance and reference remain static, and the
limit to control is then set by the ratio of gain rate to leak rate
of the integrator.
Does this address the question you asked?
Martin

···

David Goldstein (2014.03.03.11:37)

Martin, please define transport

    lag in terms of the live block diagram we are reviewing.

David

    Sent from my iPhone
    On Mar 2, 2014, at 11:55 PM, Martin Taylor <mmt-csg@MMTAYLOR.NET        >

wrote:

[Martin Taylor 2014.03.02.23.38]

      The fundamental limit is set by the transport lag and the

speed and range of variation of the disturbance. If the
disturbance has moved on since its value one transport lag
time previously, its current value will not be correctly
opposed by the output. Of course, if its variation is
predictable, then the fact that it changed over the time of
the transport lag matters less, and the error minimum is
determined not by the actual change but by the magnitude of
the failure of prediction. No physical control system can
overcome this limit, which is a mathematical bound. What you
mention (Gain and Practice) can reduce the error as compared
to the error of a low-gain novice system, but they can’t
reduce it beyond that bound.
Yes, within bounds. Too high gain will set the loop into
oscillation, because there always is some transport lag. This
means that there are some ranges of frequencies for which the
loop gain becomes positive. If the overall gain increases
enough to make the positive gain at one of those frequencies
greater than unity, the system goes into a sustained
oscillation.
Yes. I think in part this is an aspect of the prediction
mentioned above, though in relation to the effect of the
output rather than to the disturbance, which is handled in
Bill’s simulation by the artificial cerebellum, and perhaps in
life by the real cerebellum. The Artificial cerebellum, and
perhaps the real one, allows the output to compensate for the
dynamic characteristics of the muscular and tool structure. It
takes time (practice) to develop in the artificial case, and
presumably in real life. It may be also that practice reduces
the transport lag, thereby allowing higher gain to be useful.
Martin

        I'm responding in part becasue I think I have something to

offer, and in part to ask David why each successive message
has a larger typeface than its predecessor.

[David Goldstein (2014.03.01.22:17)]

Re.: [From Bruce Abbott (2014.03.02.2135
EST)]

              Thanks for your

answer to my questions. I have some follow-up
questions.

… . What places a limit on the size of
the error signal?

            Gain--the higher the gain, the smaller

the error signal tolerated.

Practice–the more one practices a
skill, like hitting a forehand in tennis, the more
automatic it becomes.

David Goldstein (2014.03.04.13:00)

Martin, Thanks, that helps.

The figure is 3-1 on page 43.

We have input delay, and time constant parameters in the

Expanded model. How do these relate to transport lag?

David

···

David Goldstein (2014.03.03.11:37)

Martin, please define transport

    lag in terms of the live block diagram we are reviewing.

David

    Sent from my iPhone
    On Mar 2, 2014, at 11:55 PM, Martin Taylor <mmt-csg@MMTAYLOR.NET        >

wrote:

[Martin Taylor 2014.03.02.23.38]

      The fundamental limit is set by the transport lag and the

speed and range of variation of the disturbance. If the
disturbance has moved on since its value one transport lag
time previously, its current value will not be correctly
opposed by the output. Of course, if its variation is
predictable, then the fact that it changed over the time of
the transport lag matters less, and the error minimum is
determined not by the actual change but by the magnitude of
the failure of prediction. No physical control system can
overcome this limit, which is a mathematical bound. What you
mention (Gain and Practice) can reduce the error as compared
to the error of a low-gain novice system, but they can’t
reduce it beyond that bound.
Yes, within bounds. Too high gain will set the loop into
oscillation, because there always is some transport lag. This
means that there are some ranges of frequencies for which the
loop gain becomes positive. If the overall gain increases
enough to make the positive gain at one of those frequencies
greater than unity, the system goes into a sustained
oscillation.
Yes. I think in part this is an aspect of the prediction
mentioned above, though in relation to the effect of the
output rather than to the disturbance, which is handled in
Bill’s simulation by the artificial cerebellum, and perhaps in
life by the real cerebellum. The Artificial cerebellum, and
perhaps the real one, allows the output to compensate for the
dynamic characteristics of the muscular and tool structure. It
takes time (practice) to develop in the artificial case, and
presumably in real life. It may be also that practice reduces
the transport lag, thereby allowing higher gain to be useful.
Martin

        I'm responding in part becasue I think I have something to

offer, and in part to ask David why each successive message
has a larger typeface than its predecessor.

[David Goldstein (2014.03.01.22:17)]

Re.: [From Bruce Abbott (2014.03.02.2135
EST)]

              Thanks for your

answer to my questions. I have some follow-up
questions.

… . What places a limit on the size of
the error signal?

            Gain--the higher the gain, the smaller

the error signal tolerated.

Practice–the more one practices a
skill, like hitting a forehand in tennis, the more
automatic it becomes.

[Martin Taylor 2014.03.04.14.36]

The input delay is an explicit component of the transport lag. I'd

have to look at the programming to be sure, but I suspect that in
addition there is one frame (1/60 sec or 16.6 msec?) delay as well,
though that might be already incorporated into the input delay in
the little box. No other delays are made explicit in the figure, so
the sum of those two is the total transport lag, although there
could easily be additional transport lag components in the various
loop functions. In my own program of which I presented an early version a while
back, I put the transport lag into the environmental feedback path
between the mouse movement and the effect of that movement on cursor
or target (depending on whether the task is pursuit or
compensatory), although again you have to add one frame to get the
actual delay. In the environmental feedback path is just about the
only place you can put a delay experimentally, though you do have a
choice as to whether the delay is inserted before the disturbance
input or after it (which is equivalent to an input delay). In my
program the delay is always before the disturbance input, because to
me the interesting issue is the transport lag between perception and
disturbance.
The time-constant parameters do affect the dynamics of the loop, but
they are not relevant to the transport lag. There are several ways to look at what the time-constant parameters
do. Here are two. In Fig 3-1 there are two time-constants, though
one is labelled “Output Gain Factor”. That time constant is how fast
the output integrator integrates, and therefore how fast the loop
responds to a change in the disturbance. The other is how fast it
leaks, or so I assume. Bill and Rick have called the leak a “slowing
factor”. Together they determine the static gain, but considered
individually they serve to define a filter that tails off at
6db/octave at the higher frequencies and is flat at low frequencies.
That filter is what prevents the loop from oscillating at high
frequencies, which it would do anyway if the gain is high enough or
the transport lag long enough.
Martin

···

On 2014/03/4 1:02 PM, D Goldstein
wrote:

David Goldstein (2014.03.04.13:00)

Martin, Thanks, that helps.

The figure is 3-1 on page 43.

We have input delay, and time constant parameters in the

Expanded model. How do these relate to transport lag?

David

[From Rick Marken (2014.03.04.1250)]

So many things have been going on in this discussion that I can’t possibly answer all of them in detail so I will just address what I see as the two main points of contention here, which are actually related. These are:

  1. My claim that you can’t measure the open-loop input-output characteristics of the components of a control loop while these components are part of an active control loop and

  2. The nature of the “behavioral illusion”.

I’ll address these topics in terms of the diagram (and notation) below:

image2.png

Regarding point 1:

There are three main input-output components of a control loop represented in the diagram by the boxes containing the linear coefficients k.i, k.o and k.f. These input-output components can be written as equations with the inputs on the right and outputs on the left:

p = k.i*q.i

q.o = k.o*e

q.i = k.f*q.o

The first equation is the input-output relationship between sensory input, q.i, and perceptual signal output, p. The second is the input-output relationship between error signal input, e, and system output (such as muscle force), q.o. The thid is the input-output relationship between system output and sensory input.

These are the open loop input -output components of the control loop in the sense that the (linear) functions, k.i, k.o and k.f, represent characteristics of these functions whether they are carried out inside or outside of the loop. For example, if the output function, k.o, is 100, then q.o will be 100 times the value of e, whether this function is carried out inside a control loop or outside it (open loop).

My claim was that you can’t measure the true open-loop input-output characteristics of the components of a control loop while these components are part of an active control loop. So, for example, I was claiming that if you measured the relationship between q.o and e in an active control loop, and the actual open loop input - output relationship between these variables was q.o = 100e, that you would not find that q.o was 100e.

This claim is, of course, completely wrong. I should have known this just from the equations above. But I figured it out when I finally got my spreadsheet simulation working properly. So the question is “why would I make such a boneheaded claim”? Which takes us to point 2, the behavioral illusion.

Regarding point 2.

The “behavioral illusion” refers to the fact that the observed relationship between disturbance and output (between d and q.o) in a control system will be proportional to the inverse of the feedback connection (k.e) between output and controlled variable (between q.o and q.i). In linear equation form, using the notation from the diagram above, the behavioral illusion is:

q.o = -1/k.e*d

The “illusion” exists when the observed relationship between d and q.o is taken to reflect input-output characteristics of the system itself. That is, the illusion exists when the observed relationship between d and q.o is assumed to reflect characteristics of the processes in the system relating input, q.i, to output, q.o as in:

q.o = k.o*(r-k.i*q.i)

which is the actual input-output relationship for the system. It is this illusion that led me to make my ridiculous claim that about not being able to determine the input-output characteristics of components of a loop when those components are part of a loop.

The behavioral illusion shows that you can’t determine the input - output characteristics of the “system” components of a control loop – that is, the characteristics of the relationship between q.i and q.o, which are the input and output of the control system – in an active control loop. My mistake was to overgeneralized this fact about the “system” component of a control loop to the input-output components of the loop. This mistake was probably motivated by my strong desire to move psychologists – who are trying to understand the behavior of living control systems – away from approaching this understanding from an input-output perspective.

But the fact is that the problem with the input-output approach to understanding control, as illustrated by the behavioral illusion, exists at the behavioral level – the level at which behavior is the control of perception – not at the level of the components of the system that produce this behavior. So while conventional psychological experiments, which look at input-output relationships at the behavioral level, can produce results that are misleading (per the behavioral illusion) or miss the point of behavior (controlled variables), studies of the input-output components of the behaving system – mainly the perceptual and output components, k.i and k.o – will provide results that are a correct (non-illusory) reflection of the characteristics of theses components. These would have to be physiological rather than behavioral studies since the output of the perceptual function component and the input to the motor output component of the control loop are neural signals.

One last point about the implications of the behavioral illusion for conventional psychological experiments. In such experiments the independent variable (IV) corresponds to d and the dependent variable (DV) corresponds to q.o. So according to the behavioral illusion relationship between IV and DV observed in such experiments reflects characteristics of the feedback connection, k.e, between the DV and the variable controlled by the subjects in the experiment. That is

DV = -1/k.e*IV

rather than

DV = k.s*IV

where k.s is the actual input-output characteristics of the system under study. This illusion does not depend on the system controlling perfectly. Indeed, the illusion occurs even if the system controls quite poorly. We can see this by looking at the complete for of the derivation of the behavioral illusion equation, as given by Eq. 12 p. 277 in B:CP (first edition):

q.o = (k.or)/(1+k.ok.e)-(k.ok.dd)/(1+kek.o)

setting the reference, r, to 0 and k.d to 1 for simplicity we get:

q.o = - k.o/(1+ke*k.o) * d

The derivation assumes that k.i = 1.0. How well a system controls depends on loop gain, which is the product k.ik.ok.e. Assuming k.i and k.e are constant the main determinate of how well a system controls is k.o, the output gain, which appears in both the numerator ad denominator on the right side of the equation above. So when control is good (k.o is large, like 10000) the observed relationship between q.o and d is nearly exactly q.o = -1/k.ed. But when k.o is small – say just 10 – the observed relationship between q.o and d will be q.o = .9(-1/k.e)*d. When k.o is zero (there is no control at all) then there will be no relationship at all between q.o and d. This is because the relationship between q.o and d exists only when the system is acting, by varying q.o, to protect q.i from d. When q.o is 0 the system is not controlling; there is no controlled variable.

If you are able to run java on you machine you can see the behavioral illusion in action at:

http://www.mindreadings.com/ControlDemosJava/Illusion.html

In that demo, you (the subject) appear to be more or less responsive to stimulation (disturbances to the shape or orientation of a figure) due simply to a change in the gain of the feedback connection (k.e) to the controlled variable. When the feedback gain is high you appear less responsive than when it is small. This change in apparent responsiveness is completely illusory; you are just as responsive in both feedback gain conditions (k.o is the same in both conditions); all that has change is k.e.

So you can measure the true input-output characteristics of the components of a control system (such as a living organism) but not the true input-output characteristics of the system itself. To study the the components of a living control system you would have to do some input -output measurements involving physiological measures; to study the overall system you have to take into account the fact that the system is controlling perceptual variables so you have to find out what perceptual variables it is controlling in order to understand the input-output characteristics of the system.

OK, one last, last point regarding the behavioral illusion. I think the importance of the behavioral illusion is that is suggests that the study of living control systems should proceed in a new direction, based on an understanding of the fact that the systems under study are controlling perceptual inputs. The behavioral illusion just shows that the input-output approach to understanding the nature of such systems produces results that can be misleading. A new approach is needed – an approach aimed at determining what variables the system controls and how it controls them.

But I think using the behavioral illusion to make this point has backfired, to some extent, because it can sound like we are saying that psychological researchers are either stupid or have been saps. So rather than continuing to argue that the behavioral illusion implies that psychologists should do research in a new way I think the best way to proceed is to just do the research in a new way and see if anyone follows. I’ve tried to do a little of this in my research on object interception as well as in a couple other areas. But I haven’t done nearly enough, mainly because I have neither the facilities nor the talent.

So what I would like to propose is that, rather than arguing about whether we or can’t study living control systems using conventional input-output methodology, we talk about ideas for doing research using methodology based on PCT. Let’s just start doing some PCT based research and see what happens. So if there are any scientific types out there who are interested in trying out a PCT approach to understanding living systems let’s discuss your ideas.

Best regards

Rick

···


Richard S. Marken PhD
www.mindreadings.com
The only thing that will redeem mankind is cooperation.
– Bertrand Russel

[Martin Taylor 2014.03.04.23.06]

Well, I'm glad we got that sorted out.

Did you read my analysis of the behavioral illusion [Martin Taylor
2014.03.01.12.09]? In case you did not, I quote here the summary at the end. The
reasoning behind the statements in the summary are the body of the
message – two different approaches that give the same answers. I
insert the figure that is labelled with the variables mentioned in
the summary. The “Behavioural Illusion” is the illusion that by
comparing d and o you are measuring something about the
i->p->e->o part of the loop, when actually you are
measuring the inverse of E( ).
Martin

loopFunctionsSwitchedOutput.jpg

···

[From Rick Marken (2014.03.04.1250)]

      So many things have been going on in this discussion that I

can’t possibly answer all of them in detail so I will just
address what I see as the two main points of contention here,
which are actually related. These are:

      1. My claim that you can't measure the open-loop

input-output characteristics of the components of a control
loop while these components are part of an active control loop
and

  1. The nature of the “behavioral illusion”.


My claim was that you can’t measure the true open-loop
input-output characteristics of the components of a control
loop while these components are part of an active control
loop. So, for example, I was claiming that if you measured
the relationship between q.o and e in an active control
loop, and the actual open loop input - output relationship
between these variables was q.o = 100e, that you would not
find that q.o was 100
e.

        This claim is, of course, completely wrong. I should have

known this just from the equations above. But I figured it
out when I finally got my spreadsheet simulation working
properly. So the question is “why would I make such a
boneheaded claim”? Which takes us to point 2, the behavioral
illusion.

Regarding point 2.

  [MT] The bottom line of all this is that there is no

black-and-white, all-or-nothing, distinction between open and
closed loops in respect of the Behavioral Illusion. If control is
good, the Behavioral Illusion overwhelms any practical possibility
of measuring the organism properties. If control is intermediate
or poor, the organism properties can be determined from measures
of i and o, but not from measures of d and o, and the Behavioral
Illusion becomes inaccurate because d ceases to be a good
surrogate for v. I like to think the Illusion fades away like the
Cheshire Cat, until when there is no control although the loop is
closed, it vanishes. Only if the loop is physically broken can the
organism properties be estimated from comparing the disturbance d
with the behaviour o.

[From Rick Marken (2014.03.05.1600)]

Martin Taylor (2014.03.04.23.06)–

MT: Did you read my analysis of the behavioral illusion [Martin Taylor 2014.03.01.12.09]?
RM: Yes I did but I’m afraid I didn’t quite follow it.

MT: In case you did not, I quote here the summary at the end…

[MT] The bottom line of all this is that there is no black-and-white, all-or-nothing, distinction between open and closed loops in respect of the Behavioral Illusion. If control is good, the Behavioral Illusion overwhelms any practical possibility of measuring the organism properties. If control is intermediate or poor, the organism properties can be determined from measures of i and o, but not from measures of d and o, and the Behavioral Illusion becomes inaccurate because d ceases to be a good surrogate for v.
RM: These conclusions suggest to me that there may be something wrong with your analysis (but maybe not; read on). The behavioral illusion, per the linear analysis in B:CP, is

q.o = - k.o/(1+ke*k.o) * d

There is really no “degree” of this illusion, at least not in terms of the degree to which it reflects characteristics of the feedback rather than the organism function (which, assuming a constant input function, k.i, is k.o).

RM: The relationship between d and q.o in a closed loop system reflects only the inverse of the feedback function, 1/k.e; the organism function is not seen no matter how good (or poor) control is. The goodness of control affects only the degree to which the observed relationship between q.o and d reflects the actual inverse of the feedback function. If control is good (high gain, say k.o = 10000) then the observed relationship between q.o and d will be nearly equal to q.o = 1/k.ed. If control is poor (low gain, k.o = 10) then the observed relationship between q.o and d will be something like q.o = (.91/k.e)d. But no matter how poor the control, the relationship between q.o and d will never be proportional to the system function.
RM: I think your analysis agrees with this because you say that when control is poor the organism properties still cannot be determined from measures of d and q.o. But you do say they they can be determined from measures of i and q.o. This sounds wrong but given my track record on claims about what can and can’t be measured in a control loop I think I’ll just give you the benefit of the doubt until I can check it out for myself using simulation.
RM: Your last point – that the behavioral Illusion becomes inaccurate as control becomes poorer – is also consistent with the B:CP analysis if by “inaccurate” you mean that, as control becomes poorer, the observed relationship between d and q.o becomes a less accurate reflection of 1/k.e.
RM: I think this is a good point at which to address an issue that was raised by both you and Bruce. The issue can be stated as a question: If the behavioral illusion is such a real problem for conventional experimental psychology then why do the results of psychological experiments, particularly those in the area of sensory and perceptual measurement, make so much sense? You, Martin, brought up this issue when you alluded to my suspicions about the results of psychophysical experiments; Bruce brought it up when he pointed to the consistency of behavioral measures of dark adaptation curves with the physiological results. These were extremely good points and I’ve been thinking about them since you guys brought them up. And I think I have finally come to understand the issue in a way that I think with be acceptable to both you and Bruce.
RM: The main realization I had is that the behavioral illusion will exist only in experiments where the dependent variable (DV) is used to compensate for the effect of the independent variable (IV) on a controlled variable (CV). That’s because the IV in such experiments is equivalent to d and the DV is equivalent to q.o so the behavioral illusion exists when both the IV and DV have an effect on a CV so that
DV = 1/k.e
IV
RM: That’s the ideal situation (for the illusion) and it’s probably close to being the case in many if not most conventional psychology experiments. I suppose I could go through a journal, like Psychological Science, and see which experiments seem to meet this criterion and which don’t. But I think most psychophysical experiments – including the dark adaptation study-- do not meet this criterion. This is because what we would see as the DV in these experiments – simply because it was plotted against an IV-- is really a physical correlate of a CV. For example, in the dark adaptation studies what is plotted is the light level that corresponds to the subject saying “yes, I see it” on 75% of the trials as a function of the various times that the subject has been in the dark. The time in the dark is the IV; the light level would be called a DV but it’s clearly a measure of the physical correlate of a CV: the light level that is just detectable.
RM: I think there are many conventional experiments where what is called the DV is really a measure of a CV. This is probably most often true in studies of sensation and perception but it may be true of studies in other areas as well. It’s true in one of the recent experiments I did with Warren Mansell and his student Zahra Khatib on motor control:
Marken, R. S., Khatib, Z. and Mansell, W. (2013) Motor Control as the Control of Perception*, Perceptual and Motor Skills*, 117, 236-247

In this study the IV was the rate of presentation of the stimulus; the DV was a measure of how well an aspect of the stimulus was controlled. So the DV in this case was explicitly a measure of a CV.

RM: So you and Bruce have made me realize that I should caveat my “indictments” of conventional psychological research by noting that the behavioral illusion will only be seen in research where the DV is an output that can affect a variable – a CV – that is also affected by the IV. I would imagine that the vast majority of conventional psychology experiments are of this sort. But still, there are, indeed, many studies where the results could be a useful basis for PCT research.

RM: But I, personally, would still prefer to set out on a research path that involves doing research based explicitly on an understanding that organisms are perceptual control systems; research that doesn’t look back (to how research is currently done, based on an input-output view of organisms) but, rather, looks forward, (to how research will be done when the perceptual control view of organisms is taken for granted). I want to show how PCT based research is done so future students of human nature will have something they can imitate and improve upon So, again, if anyone is listening in, I would love to hear some suggestions for research studies – or, even better, research programs – that are aimed at understanding behavior in terms of perceptual control theory.

Best

Rick

loopFunctionsSwitchedOutput.jpg

···


Richard S. Marken PhD
www.mindreadings.com

The only thing that will redeem mankind is cooperation.

                                               -- Bertrand Russemeasurethe physicza

Thank you Rick, that is a really helpful summary.

Warren

···

Sent from my iPhone

On 6 Mar 2014, at 00:04, Richard Marken rsmarken@GMAIL.COM wrote:

[From Rick Marken (2014.03.05.1600)]

Martin Taylor (2014.03.04.23.06)–

MT: Did you read my analysis of the behavioral illusion [Martin Taylor 2014.03.01.12.09]?
RM: Yes I did but I’m afraid I didn’t quite follow it.

MT: In case you did not, I quote here the summary at the end…

[MT] The bottom line of all this is that there is no black-and-white, all-or-nothing, distinction between open and closed loops in respect of the Behavioral Illusion. If control is good, the Behavioral Illusion overwhelms any practical possibility of measuring the organism properties. If control is intermediate or poor, the organism properties can be determined from measures of i and o, but not from measures of d and o, and the Behavioral Illusion becomes inaccurate because d ceases to be a good surrogate for v.
RM: These conclusions suggest to me that there may be something wrong with your analysis (but maybe not; read on). The behavioral illusion, per the linear analysis in B:CP, is

q.o = - k.o/(1+ke*k.o) * d

There is really no “degree” of this illusion, at least not in terms of the degree to which it reflects characteristics of the feedback rather than the organism function (which, assuming a constant input function, k.i, is k.o).

RM: The relationship between d and q.o in a closed loop system reflects only the inverse of the feedback function, 1/k.e; the organism function is not seen no matter how good (or poor) control is. The goodness of control affects only the degree to which the observed relationship between q.o and d reflects the actual inverse of the feedback function. If control is good (high gain, say k.o = 10000) then the observed relationship between q.o and d will be nearly equal to q.o = 1/k.ed. If control is poor (low gain, k.o = 10) then the observed relationship between q.o and d will be something like q.o = (.91/k.e)d. But no matter how poor the control, the relationship between q.o and d will never be proportional to the system function.
RM: I think your analysis agrees with this because you say that when control is poor the organism properties still cannot be determined from measures of d and q.o. But you do say they they can be determined from measures of i and q.o. This sounds wrong but given my track record on claims about what can and can’t be measured in a control loop I think I’ll just give you the benefit of the doubt until I can check it out for myself using simulation.
RM: Your last point – that the behavioral Illusion becomes inaccurate as control becomes poorer – is also consistent with the B:CP analysis if by “inaccurate” you mean that, as control becomes poorer, the observed relationship between d and q.o becomes a less accurate reflection of 1/k.e.
RM: I think this is a good point at which to address an issue that was raised by both you and Bruce. The issue can be stated as a question: If the behavioral illusion is such a real problem for conventional experimental psychology then why do the results of psychological experiments, particularly those in the area of sensory and perceptual measurement, make so much sense? You, Martin, brought up this issue when you alluded to my suspicions about the results of psychophysical experiments; Bruce brought it up when he pointed to the consistency of behavioral measures of dark adaptation curves with the physiological results. These were extremely good points and I’ve been thinking about them since you guys brought them up. And I think I have finally come to understand the issue in a way that I think with be acceptable to both you and Bruce.
RM: The main realization I had is that the behavioral illusion will exist only in experiments where the dependent variable (DV) is used to compensate for the effect of the independent variable (IV) on a controlled variable (CV). That’s because the IV in such experiments is equivalent to d and the DV is equivalent to q.o so the behavioral illusion exists when both the IV and DV have an effect on a CV so that
DV = 1/k.e
IV
RM: That’s the ideal situation (for the illusion) and it’s probably close to being the case in many if not most conventional psychology experiments. I suppose I could go through a journal, like Psychological Science, and see which experiments seem to meet this criterion and which don’t. But I think most psychophysical experiments – including the dark adaptation study-- do not meet this criterion. This is because what we would see as the DV in these experiments – simply because it was plotted against an IV-- is really a physical correlate of a CV. For example, in the dark adaptation studies what is plotted is the light level that corresponds to the subject saying “yes, I see it” on 75% of the trials as a function of the various times that the subject has been in the dark. The time in the dark is the IV; the light level would be called a DV but it’s clearly a measure of the physical correlate of a CV: the light level that is just detectab!
le.
RM: I think there are many conventional experiments where what is called the DV is really a measure of a CV. This is probably most often true in studies of sensation and perception but it may be true of studies in other areas as well. It’s true in one of the recent experiments I did with Warren Mansell and his student Zahra Khatib on motor control:
Marken, R. S., Khatib, Z. and Mansell, W. (2013) Motor Control as the Control of Perception*, Perceptual and Motor Skills*, 117, 236-247

In this study the IV was the rate of presentation of the stimulus; the DV was a measure of how well an aspect of the stimulus was controlled. So the DV in this case was explicitly a measure of a CV.

RM: So you and Bruce have made me realize that I should caveat my “indictments” of conventional psychological research by noting that the behavioral illusion will only be seen in research where the DV is an output that can affect a variable – a CV – that is also affected by the IV. I would imagine that the vast majority of conventional psychology experiments are of this sort. But still, there are, indeed, many studies where the results could be a useful basis for PCT research.

RM: But I, personally, would still prefer to set out on a research path that involves doing research based explicitly on an understanding that organisms are perceptual control systems; research that doesn’t look back (to how research is currently done, based on an input-output view of organisms) but, rather, looks forward, (to how research will be done when the perceptual control view of organisms is taken for granted). I want to show how PCT based research is done so future students of human nature will have something they can imitate and improve upon So, again, if anyone is listening in, I would love to hear some suggestions for research studies – or, even better, research programs – that are aimed at understanding behavior in terms of perceptual control theory.

Best

Rick


Richard S. Marken PhD
www.mindreadings.com

The only thing that will redeem mankind is cooperation.

                                               -- Bertrand Russemeasurethe physicza

<loopFunctionsSwitchedOutput.jpg>

[Martin Taylor 2014.03.06.14.11]

[From Rick Marken (2014.03.05.1600)]

    > Martin Taylor (2014.03.04.23.06)--

    >

    > MT: Did you read my analysis of the behavioral illusion

[Martin Taylor 2014.03.01.12.09]?

    RM: Yes I did but I'm afraid I didn't quite follow it.
Sorry about that. Could you point to the difficult place(s) and I'll

see what I can do about it.

    > MT: In case you did not, I quote here the summary at the

end…
>
> [MT] The bottom line of all this is that there is no
black-and-white, all-or-nothing, distinction between open and
closed loops in respect of the Behavioral Illusion. If control
is good, the Behavioral Illusion overwhelms any practical
possibility of measuring the organism properties. If control is
intermediate or poor, the organism properties can be determined
from measures of i and o, but not from measures of d and o, and
the Behavioral Illusion becomes inaccurate because d ceases to
be a good surrogate for v.

    RM: These conclusions suggest to me that there *may* be

something wrong with your analysis (but maybe not; read on). The
behavioral illusion, per the linear analysis in B:CP, is

    q.o = - k.o/(1+ke*k.o) * d



    There is really no "degree" of this illusion, at least not in

terms of the degree to which it reflects characteristics of the
feedback rather than the organism function (which, assuming a
constant input function, k.i, is k.o).

Maybe "degree" was not quite the right word. I intended to imply

that although the illusion is still ther so long as the loop is
closed, it gets lost in the noise as control gets worse and worse.
The vector-graphic representation should make this clear.

      RM: The relationship between d and q.o in a closed loop

system reflects only the inverse of the feedback function,
1/k.e; the organism function is not seen no matter how good
(or poor) control is.

No, that's not quite right. If you replace "reflects only" by

“incorporates” it would be correct. The reason is that the inverse
function is actually the relation between “v” and “o” in the
diagram, not between “d” and “o”. But if control is very good, “v”
is almost the same as “d”, so “d” can serve as a good estimator of
“v”. If control is poor, “v” doesn’t compensate for “d” very well,
so although E( )^-1 is still exactly the “v”->“o” relationship,
it is quite different from the “d”->“o” relationship.

![loopFunctionsSwitchedOutput.jpg|237x259](upload://jbv6MrpuYtKLDV4h7KnTzk0lMUL.jpeg)
      The goodness of control affects only the degree to which

the observed relationship between q.o and d reflects the
actual inverse of the feedback function.

Yes, that's what I said earlier, that you did not follow, and that I

explained just above.

      RM: I think this is a good point at which to address an issue

that was raised by both you and Bruce. The issue can be stated
as a question: If the behavioral illusion is such a real
problem for conventional experimental psychology then why do
the results of psychological experiments, particularly those
in the area of sensory and perceptual measurement, make so
much sense? You, Martin, brought up this issue when you
alluded to my suspicions about the results of psychophysical
experiments; Bruce brought it up when he pointed to the
consistency of behavioral measures of dark adaptation curves
with the physiological results. These were extremely good
points and I’ve been thinking about them since you guys
brought them up. And I think I have finally come to understand
the issue in a way that I think with be acceptable to both you
and Bruce.

      RM: The main realization I had is that the behavioral illusion

will exist only in experiments where the dependent variable
(DV) is used to compensate for the effect of the independent
variable (IV) on a controlled variable (CV).

That's true, but one has to remember that the whole IV->DV

connection is just a component of at least one active control loop.
That’s why I was concerned to complete the “arcane” discussion about
the ability to measure the input-output relationship of a component
in open- and closed-loop situations.

      That's because the IV in such experiments is equivalent to

d and the DV is equivalent to q.o so the behavioral illusion
exists when both the IV and DV have an effect on a CV so that

      DV = 1/k.e*IV



      RM: That's the ideal situation (for the illusion) and it's

probably close to being the case in many if not most
conventional psychology experiments. I suppose I could go
through a journal, like Psychological Science, and see which
experiments seem to meet this criterion and which don’t. But
I think most psychophysical experiments – including the dark
adaptation study-- do not meet this criterion. This is because
what we would see as the DV in these experiments – simply
because it was plotted against an IV-- is really a physical
correlate of a CV.

I don't think this is correct, except in the sense that the output

of any component of a control loop is a physical correlate of (or
more simply “is”) an input to another component of the loop.

      For example, in the dark adaptation studies what is

plotted is the light level that corresponds to the subject
saying “yes, I see it” on 75% of the trials as a function of
the various times that the subject has been in the dark. The
time in the dark is the IV; the light level would be called a
DV but it’s clearly a measure of the physical correlate of a
CV: the light level that is just detectable.

How do you control that CV at the time you say "I see it"? As the

subject in the experiment, the only thing that could allow you to
see or not see it is to close your eyes, and a cooperative subject
doesn’t do that. You can’t influence the brightness itself unless
the experimenter is controlling by tracking.

But the experimenter IS controlling a perception of the brightness

being just enough for the subject to see it. IIn the
experimenter’s control loop, the subject’s “I do/don’t see it” is
to the experimenter an input to his controlled variable. What the
experimenter measures is the inverse of his environmental feedback
function, the subject’s IV->DV connection.

You may argue that the experimenter need not be involved at all at

that level, and you would be right. The situation is that of Bekesy
audiometry, in which the subject acts as does a thermostat that
switch a furnace on and off depending on whether the temperature is
above or below the reference. In the experiment, the subject is
setting a perceptual value equal to a reference of “just visible”.
Here, the subject is doing the loop switching as his perceptual
function changes. The loop is entirely within the subject. It
becomes a tracking study in the normal way.

      RM: I think there are many conventional experiments where what

is called the DV is really a measure of a CV.

I suspect it has always to be true, but the CV in question is likely

to be in the experimenter unless the study is an explicit tracking
study.

      This is probably most often true in studies of sensation

and perception but it may be true of studies in other areas as
well. It’s true in one of the recent experiments I did with
Warren Mansell and his student Zahra Khatib on motor control:

      Marken, R. S., Khatib, Z. and  Mansell, W. (2013) Motor

Control as the Control of Perception* , Perceptual and Motor
Skills*, 117, 236-247

        In this study the IV was the rate of presentation of the

stimulus; the DV was a measure of how well an aspect of the
stimulus was controlled. So the DV in this case was
explicitly a measure of a CV.

        RM: So you and Bruce have made me realize that I should

caveat my “indictments” of conventional psychological
research by noting that the behavioral illusion will only be
seen in research where the DV is an output that can affect a
variable – a CV – that is also affected by the IV. I would
imagine that the vast majority of conventional psychology
experiments are of this sort. But still, there are, indeed,
many studies where the results could be a useful basis for
PCT research.

         RM: But I, personally, would still prefer to set out on a

research path that involves doing research based explicitly
on an understanding that organisms are perceptual control
systems; research that doesn’t look back (to how research is
currently done, based on an input-output view of organisms)
but, rather, looks forward, (to how research will be done
when the perceptual control view of organisms is taken for
granted). I want to show how PCT based research is done so
future students of human nature will have something they can
imitate and improve upon So, again, if anyone is listening
in, I would love to hear some suggestions for research
studies – or, even better, research programs – that are
aimed at understanding behavior in terms of perceptual
control theory.

Fair enough. What psychophysical studies do is provide parameters

that sometimes can be plugged into, or that can sometimes set limits
on variables in models of control.

In the wider world, I would like to see research programs on the

characteristic ways in which multiple control loops interact – in
other words, the sociology of control, both within a individual and
among individuals. Why, for example, do the peoples of the words
wind up with modular social structures that often result in conflict
not obviously related to resource limitation. Is this an inevitable
consequence of PCT? What was the point of the Spanish Inquisition,
for example? Are there coupling parameters that have regions such as
those in the phases of physical matter in which the behaviour is
characteristically different, and if so, when are those boundaries
sharp, and when are they diffuse?

Martin

[From Rick Marken (2014.03.08.1250)]

···

Martin Taylor (2014.03.06.14.11)–

    > MT: Did you read my analysis of the behavioral illusion

[Martin Taylor 2014.03.01.12.09]?

RM: Yes I did but I’m afraid I didn’t quite follow it.

MT: Sorry about that. Could you point to the difficult place(s) and I'll

see what I can do about it.

RM: OK. Here are the points I found difficult:

RM: 1. You said “Often ignored when the words “behavioral
illusion” are used in discussion is that Bill correctly limited the statement
to “an ideal N system” – a perfect controller”.

I didn’t understand Bill to be limiting the behavioral illusion to a perfect controller. The illusion happens with any controller. Bill used a perfect controller to illustrate the behavioral illusion to make the phenomenon clearer mathematically. The linear version of the behavioral illusion formula is:

q.o = - k.o/(1+k.e*k.o) * d

RM: A perfect controller is one with infinite output gain, k.o, in which case the behavioral illusion formula reduces to:

q.o = - 1/k.e * d

showing that the organism function doesn’t show up at all in the observed relationship between d and q.o. That’s the illusion; you think you are seeing q.o = k.o * d when in fact you are seeing q.o = -1/k.e*d. When control isn’t perfect the organism function still doesn’t show up in the relationship between q.o and d but in that case the observed relationship between q.o and d is not a perfect reflection of -1/k.e. The accuracy with which the observed relationship between q.o and d for an imperfect controller reflects -1/k.e will be reduced as k.o is reduced, in proportion to k.o/(1+k.o).

RM: 2. I understand your derivation of the behavioral illusion up to this point:

MT: using GP as a short form for G(P( )) and taking advantage of linearity to move
the minus sign outside the functions.
o + GPE(o) = -GPd

RM: But I don’t understand why your next step is

MT: Now we need another assumption, that the
function GP is invertible.
(GP)^-1(o) + E(o) = -d

RM: Why not just solve o +
GPE(o) = -GPd for o as a function of d, as in:

o(1+ GPE) = - GPd

             =  -GPd/(1+GPE)

             =  -GP/(1+GPE) d

and setting P to 1 we get:

             =G/(1+GE) d

which is equivalent to Bill’s formula q.o = - k.o/(1+k.e*k.o) * d since o = q.o, G = k.o and E = k.e.

RM: 3. I don’t understand the approach described in the whole section that starts: " Now let’s start a completely different approach
to the same question, which does not require assumptions of the linearity or
the invertibility of functions". But your bottom line conclusion that “there is no black-and-white, all-or-nothing,
distinction between open and closed loops in respect of the Behavioral
Illusion” seems wrong. The illusion always exists in a closed loop system; the observed relationship between d and q.o, regardless of how well the system controls, does not reflect anything about the organism function that transforms i into q.o.

RM: You may be right, however, that the organism function can be determined from measures of q.i and q.o. But I wonder why anyone would be interested in doing that. If we know we are dealing with a closed loop system then “understanding its behavior” means, first and foremost, figuring out what variable(s) is it controlling; that is, what is q.i? We’d have to know this before trying to figure out the organism function connecting q.i to q.o anyway, right? It seems to me that the importance of the behavioral illusion is not so much to show that the results of much of conventional psychological research is misleading but, rather, that this research has been focused on the wrong thing (input-output relationships) while ignoring what is most important about the behavior of living control systems: the perceptual variables around which this behavior is organized.

      RM: For example, in the dark adaptation studies what is

plotted is the light level that corresponds to the subject
saying “yes, I see it” on 75% of the trials as a function of
the various times that the subject has been in the dark. The
time in the dark is the IV; the light level would be called a
DV but it’s clearly a measure of the physical correlate of a
CV: the light level that is just detectable.

MT: How do you control that CV at the time you say “I see it”?

RM: I think you do it in the same way as you do it in the “Coin Game” demo; you are not directly controlling the state of the CV (as you would in the method of adjustment) but you are saying what levels of the perception constitute an “error” by saying “no” and which are not (by saying “yes”). So the light level plotted is the inferred reference state ("just detectable) of the perception of the light.

MT: But the experimenter IS controlling a perception of the brightness

being just enough for the subject to see it.

RM: Right. It’s clearer that the light level is a controlled variable if the experimenter lets the subject adjust the light level themselves so that it is “just detectable”.

RM: But again I don’t think we are seeing a behavioral illusion in this dark adaptation study because the DV (the just detectable light level) is not something the system does – an output – that can compensate for the effect of the IV (time in the dark) on some CV. But I think there is evidence of a lower level of control involved here; it’s the control that is involved in making the retina more sensitive to light as time in the dark increases. If the increased sensitivity in the dark were simply due to the rod vision then it would show up as soon as it got dark. The dark adaptation curve suggest that there is an active process at the retinal level (or one up from that level) that is controlling, by varying the sensitivity of the rods, for something like the more than 0 (or noise level) neural firing.

Best regards

Rick


Richard S. Marken PhD
www.mindreadings.com
The only thing that will redeem mankind is cooperation.

                                               -- Bertrand Russell