# Getting the PCT story straight

**URL:** <http://discourse.iapct.org/t/getting-the-pct-story-straight/4738>\
**Category:** CSG1994\
**Created:** [October 22, 1994, 1:24am UTC](http://discourse.iapct.org/t/getting-the-pct-story-straight/4738 "1994-10-22T01:24:29Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![William\_T\_Powers2](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/w/c67d28/32.png) [@William\_T\_Powers2](http://discourse.iapct.org/u/William_T_Powers2)\
**Post date:** [October 22, 1994, 1:24am UTC](http://discourse.iapct.org/t/getting-the-pct-story-straight/4738/1 "1994-10-22T01:24:29Z")

</div>

[From Bill Powers (941021.1635 MDT)]

Tom Bourbon and Rick Marken (various) --

Let's try not to totally confuse those who are trying to understand PCT.  
Perceptions DO cause actions. That is not the point on which PCT  
disagrees with standard psychological models. Even in an S-R model you  
can have a reference signal which sets the effective zero of the input  
stimulus; therefore even saying that action is caused by the difference  
between the level of input stimulus and the reference signal does not  
distinguish PCT from S-R psychology. There is always some level of input  
at which the output will be zero; all models contain at least an  
implicit reference signal which is not neccesarily zero. I think we have  
to go very carefully here to make sure that we don't make statements  
that won't hold up even in PCT, and that can confuse the willing  
learner.

> **···**
>
> ---------------------------  
> What really causes actions is the error signal. That's firm, no matter  
> what the gain of the control system: the error signal is the immediate  
> determinant of actions.
> 
> Where does the error signal come from? From the difference between the  
> perceptual signal and the reference signal.
> 
> If the reference signal is constant, then the only thing that can cause  
> a change in action is a change in the perceptual signal. So changes in  
> the perceptual signal cause actions when the reference signal is  
> constant. No way out of it: they do.
> 
> However, as usual, we have a problem with speaking qualitatively about a  
> quantitative question. \_How much\_ change in the perceptual signal is  
> required to cause any substantial change in the output, the action? That  
> depends entirely on the gain of the output function. With a low-gain  
> output function, a large change in the error signal is required to  
> produce a given change in action, in comparison with the amount needed  
> when the output gain is high. Thus a large change in the perceptual  
> signal is needed to produce an action (still with constant reference  
> signal) when the output gain is low.
> 
> So far the reasoning is perfectly straightforward, because we're talking  
> about only part of the control loop. We could be talking about an S-R  
> system just as well as a control system. The difference begins to show  
> up only when we close the loop.
> 
> When we complete the loop, recognizing that the state of the perceptual  
> signal depends in part on the output, the reasoning is less simple, and  
> it leads to the real difference between PCT and S-R theories.
> 
> How do we produce changes in the perceptual signal? Not by changing it  
> directly and arbitrarily; that would break the loop. We do it by  
> adjusting another variable, a disturbing variable, which contributes to  
> the state of the perceptual signal. This is the first important  
> difference between PCT and S-R theory: in PCT we recognize that the  
> input to a control system can't be treated as an independent variable;  
> to do so is to make it independent of the output, destroying the closed-  
> loop organization and changing the character of the behavior entirely.
> 
> As soon as the perceptual signal starts to change, the error signal  
> changes. The output will begin to change, but in doing so it cancels  
> part of the effect of the disturbing variable, so the perceptual signal  
> will change less than it would if the disturbance alone were affecting  
> it. As the effect of the disturbing variable begins to appear, the  
> output changes in the opposite direction, cancelling part of the effect  
> of the disturbing variable. We can arbitrarily change the disturbing  
> variable because it is not part of the loop; we cannot, however,
> 
> arbitrarily determine the effect on the perceptual signal that way. The  
> system's own output simultaneously affects the same perceptual signal.
> 
> If the gain of the system is low, then the output changes will be  
> relatively small, and only a small part of the effect of the disturbance  
> will be counteracted. The change in the perceptual signal that is left  
> over passes through the comparator, becomes an opposite change in the  
> error signal, and drives the action. This process comes quickly to a  
> balance, with the output just large enough to keep the effect of the  
> disturbance on the perceptual signal from getting any larger.
> 
> Now if the gain of the system is increased, the balance point will be  
> reached for a smaller change in the perceptual signal. Because of the  
> increased amplification, a smaller change in the perceptual signal will  
> now be enough to produce an output sufficient to keep that change from  
> becoming larger. As the output gain of the system keeps increasing, a  
> smaller and smaller change in the perceptual signal is sufficient to  
> bring the output into a balance with the disturbance. In the limit, with  
> infinite gain, the perceptual signal changes only infinitesimally and  
> the ouput approaches a perfect balance with the disturbance, cancelling  
> essentially all of its effect on the perceptual signal.
> 
> But that is only in the limit. By speaking as if the control system is  
> perfect, with infinite gain, one can give the impression that the  
> perceptual signal has nothing to do with the output, because it "does  
> not change" when disturbed. However, in any real system with finite  
> output gain, the perceptual signal \_does\_ change, even if only by a  
> small amount, and with a constant reference signal it is that change in  
> the perceptual signal that accounts \_entirely\_ for the change in the  
> output.
> 
> It is high gain in the output function that accounts for the fact that  
> the perceptual signal changes by only a small amount. But that same high  
> gain assures that even if the amount of change in the perceptual signal  
> is microscopic, it is sufficient to cause a macroscopic change in the  
> output. At all levels of gain, the changes in output are caused by  
> changes in the perceptual signal -- once again, with the reference  
> signal constant.
> 
> We can now see the second main difference between PCT and other models.  
> The difference is in \_which variable is identified as the external  
> counterpart of the perceptual signal\_. Under S-R theory, the "stimulus"  
> for a system that is really a control system will be identified as the  
> disturbing variable -- that is, the disturbing variable will be seen as  
> the cause of the system's output actions, and it will be assumed that  
> this variable is what the system is sensing. In fact, the operational  
> definition of stimulus assures that this misidentification will be made.  
> The stimulus is the physical variable for which changes correlate the  
> most highly with changes in the output action.
> 
> In behaviorism, that is taken as a sufficient demonstration that the  
> physical variable in question is a stimulus for the observed response.  
> If we do not speculate about sensory processes, as a pure Skinnerian  
> psychologist would not do, then this definition of stimulus is perfectly  
> consistent with observations. We would simply translate directly from  
> the behaviorist's "stimulus" into the PCT "disturbing variable."
> 
> Which brings us to the third major difference. A disturbance does not  
> directly affect the input to the control system; it influences, but does  
> not determine, the state of an input quantity, the quantity actually  
> sensed by the control system. The loop is closed by output effects on  
> this quantity. Depending on the gain, this input quantity is stabilized  
> more or less close to a value set by the internal reference signal. As  
> the disturbing variable changes in magnitude, the output of the control  
> system changes in approximately an equal and opposite way, \_preventing\_  
> the disturbing variable, or the stimulus, from having any large effect  
> on the input quantity, the actual physical variable that affects the  
> sensory apparatus.
> 
> This input quantity is undetectable by the experimental methods normally  
> used in psychology. Even if the input quantity is directly observed, as  
> it often can be, its variations will be very small because of the  
> control process, while the variations in both the disturbing variable  
> and the system's output action will be far larger. The higher the gain  
> of the control system, the smaller will be the variations in the input  
> quantity in comparison with the disturbance and the output action.
> 
> Here is where another factor comes into play: system noise. Inside the  
> control system in various places are noise sources which create  
> spontaneous fluctuations in signals in the loop. These fluctuations are  
> small, and act as small disturbances of the loop which create small  
> fluctations in the action even when the disturbing variable is constant.
> 
> In a reasonably high-gain control system, the changes in the input  
> quantity that are allowed when the disturbing variable changes are  
> comparable in size to the spontaneous fluctuations due to system noise.  
> In fact, the control system can often maintain changes in the \_short-  
> term average\_ value of the input quantity at a level smaller than the  
> changes due to system noise. As a result, even if the real input  
> quantity is identified, when it is tested as a possible stimulus by  
> correlating it with the changes in action, the correlation will prove to  
> be very low -- in tracking experiments it is typically less than 0.1. In  
> the same situation, changes in the disturbing variable will correlate  
> with changes in the action at a level typically of 0.9 and upward  
> (negative). The result will be that the actual input quantity, even if  
> it is noticed, will be rejected as a candidate stimulus and the  
> disturbing quantity will be chosen instead.
> 
> In this situation, it appears that changes in the input quantity (and  
> thus the perceptual signal or perception) have no relationship to the  
> actions worth speaking about. However, if we could measure the system  
> noise and add that noise to the systematic changes in the input  
> quantity, we would find that changes in the perceptual signal still  
> account exactly for the output actions. Perceptions \_do\_ cause actions  
> -- but the wrong external variable is very easily identified as the  
> correlate of the (assumed) perception.
> 
> Then there is the final and most obvious difference between PCT and  
> other models: the reference signal which we had been assuming constant  
> throughout this development. The reference signal is the output of a  
> higher level of control system, and in general can change in ways not  
> related to the input quantity and the disturbance associated with the  
> lower level system. When we look only at the input of one control  
> system, we tend to give undue significance to the variations in the  
> input quantity because we have nothing against which to compare them.  
> But when the reference signal changes to a new value somewhere else  
> within its range, we suddenly see the mean value of the input quantity  
> changing by 10, 20 or 50 times the size of the fluctuations we had been  
> looking at. What had seemed significant fluctuations are now shrunk to  
> their proper scale; they are only a few percent of the range of values  
> at which the input quantity might be maintained with different settings  
> of the reference signal.
> 
> The values over which the input quantity might change with changes in  
> reference signal are comparable to the total range of values that the  
> system can sense. Output changes required to bring the input quantity to  
> various levels set by the reference signal may be anything up to the  
> maximum output of which the system is capable. In short, we can see  
> output changes occurring spontaneously which are comparable in size to  
> those that are needed to oppose the largest disturbances that the system  
> can handle. They are equivalent to the largest "responses" to the  
> largest "stimuli." These spontaneous changes reflect the changing  
> higher-order purposes of the system as a whole. This is a very great  
> difference from traditional models of behavior, in which the only  
> actions that were recognized were those due to external causes.  
> -------------------------------------  
> Lastly, a word on statistics, about which we have given conventional  
> psychologists a hard time. I think we can maintain a firm stand against  
> trying to explain individual behavior in terms of statistical  
> relationships, however good, obtainable only from measures of  
> populations. But we should not give the impression that there are no  
> useful and legitimate applications of statistical methods, in or out of  
> PCT. All scientific investigations begin with trying to find a regular  
> relationship among variables. Such relationships are not always obvious  
> from the start; we may get very low correlations even in applying the  
> test for the controlled variable (and correlations are a useful tool for  
> applying the Test). The main difference between the way we would use  
> such correlations and the way they are traditionally used is that we  
> would not settle for a low correlation, however significant. The point  
> of PCT is to get into that realm of correlations where we can expect one  
> wrong prediction in 2,000,000 instead of one in 20. As I have been  
> pointing out lately, achieving this improvement of 100,000:1 is simply a  
> matter of refining hypotheses and methods enough to reduce standard  
> errors of prediction to 40% or less of the values normally considered  
> acceptable (nobody has yet told me I am wrong about this).
> 
> Our arguments with conventional uses of statistics are very simple.  
> First, we say that mass measures cannot be used to determine individual  
> characteristics. Second, we say that experiments should end only when  
> the predictivity of a correlation (or its associated regression  
> equation) is high enough to achieve 2,000,000 to 1 chances against a  
> wrong prediction -- or, preferably, better.  
> ------------------------------------------------------------------------  
> Best to all,
> 
> Bill P.

---

<div class="post-metadata">

**Author:** ![Tom\_BOURBON3](http://discourse.iapct.org/letter_avatar_proxy/v4/letter/t/85e7bf/32.png) [@Tom\_BOURBON3](http://discourse.iapct.org/u/Tom_BOURBON3)\
**Post date:** [October 24, 1994, 3:27pm UTC](http://discourse.iapct.org/t/getting-the-pct-story-straight/4738/2 "1994-10-24T15:27:48Z")

</div>

Tom Bourbon [941024.0913]

> [From Bill Powers (941021.1635 MDT)]
> 
> Tom Bourbon and Rick Marken (various) --
> 
> Let's try not to totally confuse those who are trying to understand PCT.  
> Perceptions DO cause actions. That is not the point on which PCT  
> disagrees with standard psychological models. Even in an S-R model you  
> can have a reference signal which sets the effective zero of the input  
> stimulus; therefore even saying that action is caused by the difference  
> between the level of input stimulus and the reference signal does not  
> distinguish PCT from S-R psychology.

Of course, but show me the S-R theorists who acknowledge the reference  
signal implicit in every S-R model. Saying that, "action is caused by the  
difference between the level of input stimulus and the reference signal"  
does inded distinguish PCT science from S-R science. I am not willing to say  
because \_we\_ know S-R paths contain implicit reference signals, that S-R  
theorists know the same thing. They don't.

> There is always some level of input  
> at which the output will be zero; all models contain at least an  
> implicit reference signal which is not neccesarily zero. I think we have  
> to go very carefully here to make sure that we don't make statements  
> that won't hold up even in PCT, and that can confuse the willing  
> learner.

I don't think I made statements that won't hold up in PCT. Perhaps I was  
unaware of them. As for whether someone was confused by some of my  
statements, I didn't know it in advance. If anyone is confused by anything  
I have said, please tell me. I will try to clean up my presentation. No  
offense was intended.

> ---------------------------  
> What really causes actions is the error signal. That's firm, no matter  
> what the gain of the control system: the error signal is the immediate  
> determinant of actions.

Bill, I thought that was what I said. I thought that was what I \_always\_  
said. Where did I get off of the straight and narrow?

> Where does the error signal come from? From the difference between the  
> perceptual signal and the reference signal.

Yes. Where else could it come from?

> If the reference signal is constant, then the only thing that can cause  
> a change in action is a change in the perceptual signal. So changes in  
> the perceptual signal cause actions when the reference signal is  
> constant. No way out of it: they do.

Yes, but only because:

> What really causes actions is the error signal.

Perhaps I your earlier statement might be restated:

> That's firm, no matter  
> what the gain of the control system, \_and no matter whether the reference  
> signal is constant or variable\_: the error signal is the immediate  
> determinant of actions.

Later,

Tom

> **···**
>
> > However, as usual, we have a problem with speaking qualitatively about a  
> > quantitative question. \_How much\_ change in the perceptual signal is  
> > required to cause any substantial change in the output, the action? That  
> > depends entirely on the gain of the output function. With a low-gain  
> > output function, a large change in the error signal is required to  
> > produce a given change in action, in comparison with the amount needed  
> > when the output gain is high. Thus a large change in the perceptual  
> > signal is needed to produce an action (still with constant reference  
> > signal) when the output gain is low.
> > 
> > So far the reasoning is perfectly straightforward, because we're talking  
> > about only part of the control loop. We could be talking about an S-R  
> > system just as well as a control system. The difference begins to show  
> > up only when we close the loop.
> > 
> > When we complete the loop, recognizing that the state of the perceptual  
> > signal depends in part on the output, the reasoning is less simple, and  
> > it leads to the real difference between PCT and S-R theories.
> > 
> > How do we produce changes in the perceptual signal? Not by changing it  
> > directly and arbitrarily; that would break the loop. We do it by  
> > adjusting another variable, a disturbing variable, which contributes to  
> > the state of the perceptual signal. This is the first important  
> > difference between PCT and S-R theory: in PCT we recognize that the  
> > input to a control system can't be treated as an independent variable;  
> > to do so is to make it independent of the output, destroying the closed-  
> > loop organization and changing the character of the behavior entirely.
> > 
> > As soon as the perceptual signal starts to change, the error signal  
> > changes. The output will begin to change, but in doing so it cancels  
> > part of the effect of the disturbing variable, so the perceptual signal  
> > will change less than it would if the disturbance alone were affecting  
> > it. As the effect of the disturbing variable begins to appear, the  
> > output changes in the opposite direction, cancelling part of the effect  
> > of the disturbing variable. We can arbitrarily change the disturbing  
> > variable because it is not part of the loop; we cannot, however,
> > 
> > arbitrarily determine the effect on the perceptual signal that way. The  
> > system's own output simultaneously affects the same perceptual signal.
> > 
> > If the gain of the system is low, then the output changes will be  
> > relatively small, and only a small part of the effect of the disturbance  
> > will be counteracted. The change in the perceptual signal that is left  
> > over passes through the comparator, becomes an opposite change in the  
> > error signal, and drives the action. This process comes quickly to a  
> > balance, with the output just large enough to keep the effect of the  
> > disturbance on the perceptual signal from getting any larger.
> > 
> > Now if the gain of the system is increased, the balance point will be  
> > reached for a smaller change in the perceptual signal. Because of the  
> > increased amplification, a smaller change in the perceptual signal will  
> > now be enough to produce an output sufficient to keep that change from  
> > becoming larger. As the output gain of the system keeps increasing, a  
> > smaller and smaller change in the perceptual signal is sufficient to  
> > bring the output into a balance with the disturbance. In the limit, with  
> > infinite gain, the perceptual signal changes only infinitesimally and  
> > the ouput approaches a perfect balance with the disturbance, cancelling  
> > essentially all of its effect on the perceptual signal.
> > 
> > But that is only in the limit. By speaking as if the control system is  
> > perfect, with infinite gain, one can give the impression that the  
> > perceptual signal has nothing to do with the output, because it "does  
> > not change" when disturbed. However, in any real system with finite  
> > output gain, the perceptual signal \_does\_ change, even if only by a  
> > small amount, and with a constant reference signal it is that change in  
> > the perceptual signal that accounts \_entirely\_ for the change in the  
> > output.
> > 
> > It is high gain in the output function that accounts for the fact that  
> > the perceptual signal changes by only a small amount. But that same high  
> > gain assures that even if the amount of change in the perceptual signal  
> > is microscopic, it is sufficient to cause a macroscopic change in the  
> > output. At all levels of gain, the changes in output are caused by  
> > changes in the perceptual signal -- once again, with the reference  
> > signal constant.
> > 
> > We can now see the second main difference between PCT and other models.  
> > The difference is in \_which variable is identified as the external  
> > counterpart of the perceptual signal\_. Under S-R theory, the "stimulus"  
> > for a system that is really a control system will be identified as the  
> > disturbing variable -- that is, the disturbing variable will be seen as  
> > the cause of the system's output actions, and it will be assumed that  
> > this variable is what the system is sensing. In fact, the operational  
> > definition of stimulus assures that this misidentification will be made.  
> > The stimulus is the physical variable for which changes correlate the  
> > most highly with changes in the output action.
> > 
> > In behaviorism, that is taken as a sufficient demonstration that the  
> > physical variable in question is a stimulus for the observed response.  
> > If we do not speculate about sensory processes, as a pure Skinnerian  
> > psychologist would not do, then this definition of stimulus is perfectly  
> > consistent with observations. We would simply translate directly from  
> > the behaviorist's "stimulus" into the PCT "disturbing variable."
> > 
> > Which brings us to the third major difference. A disturbance does not  
> > directly affect the input to the control system; it influences, but does  
> > not determine, the state of an input quantity, the quantity actually  
> > sensed by the control system. The loop is closed by output effects on  
> > this quantity. Depending on the gain, this input quantity is stabilized  
> > more or less close to a value set by the internal reference signal. As  
> > the disturbing variable changes in magnitude, the output of the control  
> > system changes in approximately an equal and opposite way, \_preventing\_  
> > the disturbing variable, or the stimulus, from having any large effect  
> > on the input quantity, the actual physical variable that affects the  
> > sensory apparatus.
> > 
> > This input quantity is undetectable by the experimental methods normally  
> > used in psychology. Even if the input quantity is directly observed, as  
> > it often can be, its variations will be very small because of the  
> > control process, while the variations in both the disturbing variable  
> > and the system's output action will be far larger. The higher the gain  
> > of the control system, the smaller will be the variations in the input  
> > quantity in comparison with the disturbance and the output action.
> > 
> > Here is where another factor comes into play: system noise. Inside the  
> > control system in various places are noise sources which create  
> > spontaneous fluctuations in signals in the loop. These fluctuations are  
> > small, and act as small disturbances of the loop which create small  
> > fluctations in the action even when the disturbing variable is constant.
> > 
> > In a reasonably high-gain control system, the changes in the input  
> > quantity that are allowed when the disturbing variable changes are  
> > comparable in size to the spontaneous fluctuations due to system noise.  
> > In fact, the control system can often maintain changes in the \_short-  
> > term average\_ value of the input quantity at a level smaller than the  
> > changes due to system noise. As a result, even if the real input  
> > quantity is identified, when it is tested as a possible stimulus by  
> > correlating it with the changes in action, the correlation will prove to  
> > be very low -- in tracking experiments it is typically less than 0.1. In  
> > the same situation, changes in the disturbing variable will correlate  
> > with changes in the action at a level typically of 0.9 and upward  
> > (negative). The result will be that the actual input quantity, even if  
> > it is noticed, will be rejected as a candidate stimulus and the  
> > disturbing quantity will be chosen instead.
> > 
> > In this situation, it appears that changes in the input quantity (and  
> > thus the perceptual signal or perception) have no relationship to the  
> > actions worth speaking about. However, if we could measure the system  
> > noise and add that noise to the systematic changes in the input  
> > quantity, we would find that changes in the perceptual signal still  
> > account exactly for the output actions. Perceptions \_do\_ cause actions  
> > -- but the wrong external variable is very easily identified as the  
> > correlate of the (assumed) perception.
> > 
> > Then there is the final and most obvious difference between PCT and  
> > other models: the reference signal which we had been assuming constant  
> > throughout this development. The reference signal is the output of a  
> > higher level of control system, and in general can change in ways not  
> > related to the input quantity and the disturbance associated with the  
> > lower level system. When we look only at the input of one control  
> > system, we tend to give undue significance to the variations in the  
> > input quantity because we have nothing against which to compare them.  
> > But when the reference signal changes to a new value somewhere else  
> > within its range, we suddenly see the mean value of the input quantity  
> > changing by 10, 20 or 50 times the size of the fluctuations we had been  
> > looking at. What had seemed significant fluctuations are now shrunk to  
> > their proper scale; they are only a few percent of the range of values  
> > at which the input quantity might be maintained with different settings  
> > of the reference signal.
> > 
> > The values over which the input quantity might change with changes in  
> > reference signal are comparable to the total range of values that the  
> > system can sense. Output changes required to bring the input quantity to  
> > various levels set by the reference signal may be anything up to the  
> > maximum output of which the system is capable. In short, we can see  
> > output changes occurring spontaneously which are comparable in size to  
> > those that are needed to oppose the largest disturbances that the system  
> > can handle. They are equivalent to the largest "responses" to the  
> > largest "stimuli." These spontaneous changes reflect the changing  
> > higher-order purposes of the system as a whole. This is a very great  
> > difference from traditional models of behavior, in which the only  
> > actions that were recognized were those due to external causes.  
> > -------------------------------------  
> > Lastly, a word on statistics, about which we have given conventional  
> > psychologists a hard time. I think we can maintain a firm stand against  
> > trying to explain individual behavior in terms of statistical  
> > relationships, however good, obtainable only from measures of  
> > populations. But we should not give the impression that there are no  
> > useful and legitimate applications of statistical methods, in or out of  
> > PCT. All scientific investigations begin with trying to find a regular  
> > relationship among variables. Such relationships are not always obvious  
> > from the start; we may get very low correlations even in applying the  
> > test for the controlled variable (and correlations are a useful tool for  
> > applying the Test). The main difference between the way we would use  
> > such correlations and the way they are traditionally used is that we  
> > would not settle for a low correlation, however significant. The point  
> > of PCT is to get into that realm of correlations where we can expect one  
> > wrong prediction in 2,000,000 instead of one in 20. As I have been  
> > pointing out lately, achieving this improvement of 100,000:1 is simply a  
> > matter of refining hypotheses and methods enough to reduce standard  
> > errors of prediction to 40% or less of the values normally considered  
> > acceptable (nobody has yet told me I am wrong about this).
> > 
> > Our arguments with conventional uses of statistics are very simple.  
> > First, we say that mass measures cannot be used to determine individual  
> > characteristics. Second, we say that experiments should end only when  
> > the predictivity of a correlation (or its associated regression  
> > equation) is high enough to achieve 2,000,000 to 1 chances against a  
> > wrong prediction -- or, preferably, better.  
> > ------------------------------------------------------------------------  
> > Best to all,
> > 
> > Bill P.