Disturbing disturbances

[From Fred Nickols (980222.1645 EST)]

After watching the exchanges dealing with disturbing disturbances
(Marc Abrams, Jeff Vancouver, and Rick Marken), I am really confused
and I think it once again traces to the use of language. I'll lay out
my confusion and then all are welcome to straighten me out.

I thought, in PCT terms, that a "disturbance" was a change in the
state of a controlled perception caused by some factor external to the
controlling system (e.g., the change in position of a car in response
to wind blowing against it). That this might "disturb" the driver in
the sense that word is used synonymously with annoy and perturb, is
beside the point (although "perturbances" seems almost as good a
choice as "disturbances").

Back to the good old keep-the-auto-in-the-lane example. It is the
changes in the automobile's position as a result of wind forces that
constitutes the "disturbance" in PCT terms, not the wind forces
themselves. The driver might curse the winds and even fail in his
or her attempt to control the position of the automobile (in which
case he or she might really be disturbed, even distraught), but as
I understand it, it is the change in the controlled perception owing
to external factors that constitutes a "disturbance" in PCT.

Thus, that Jeff, or Marc, or me, or anyone else might be "annoyed"
or "disturbed" by Rick's comments in no way constitutes a "disturbance"
in PCT. Do I have that correct or am I "not getting it" on this
count?

Regards,

Fred Nickols
The Distance Consulting Company
nickols@worldnet.att.net
http://home.att.net/~nickols/distance.htm

[From Bruce Gregory (980222.1822 EST)]

Fred Nickols (980222.1645 EST)

Thus, that Jeff, or Marc, or me, or anyone else might be "annoyed"
or "disturbed" by Rick's comments in no way constitutes a "disturbance"
in PCT. Do I have that correct or am I "not getting it" on this
count?

If Jeff, Marc, or you are controlling a perception that no critical remarks
are made on GSGnet, then Rick's comments constitute a disturbance to that
perception.

Bruce

[From Rick Marken (980222.1710)]

Fred Nickols (980222.1645 EST)]

I thought, in PCT terms, that a "disturbance" was a change in the
state of a controlled perception caused by some factor external
to the controlling system

No. A disturbance is a _variable_ that influences a controlled
variable A change in the state of the controlled variable is
_not_ a disturbance; it is simply a variation in the value of
the controlled variable. Such variation is a function of _both_
disturbance variables _and_ the output of the system (also a
variable). For example, in a tracking task, the value of the
controlled variable (cursor position, c) is a function of both
the disturbance (d) and the output variable (mouse position, o);
c = d + o.

Suppose, for example, that c is 10 at time t and then it's 12 at
time t+1. So the controlled variable has _changed_ (from 10 to 12).
This change is _not_ necessarily a result of the disturbance;
it could have happened because o increased by 2 while d remained
constant. Or it could have happened because o increased by 4
while d increase by only 2. Of course, it could have also been
the result of d changing by 2 while o was constant. The point is
that, in a real control situation, a change in the state of the
controlled variable is a result of _both_ o and d; it is never
a result of d alone. So a change in the controlled variable is
not a measure of the disturbance, d.

It is the changes in the automobile's position as a result of
wind forces that constitutes the "disturbance" in PCT terms,
not the wind forces themselves.

I hope you see now that this is not correct. The wind is a
disturbance variable that influences car position (the
controlled variable) but any change in car position we see is
_not_ the disturbance. Conversely, a lack of change in car
position is not a lack of disturbance. Can you see why?

Thus, that Jeff, or Marc, or me, or anyone else might be
"annoyed" or "disturbed" by Rick's comments in no way
constitutes a "disturbance" in PCT. Do I have that correct
or am I "not getting it" on this count?

Not quite. My comments are a disturbance simply because they
have an influence on the perception Jeff is controlling ("merits
of conventional psychology"). Jeff cannot control my comments
just as the driver cannot control the velocity of the wind;
variations in these variables (what I say; velocity of the
wind) are _independent_ of what the controller (Jeff or the driver)
do. But Jeff can control how much of an effect my comments have
on his perception of the "merits of conventional psychology" just
as the driver can control how much of an effect the wind has on
the position of the car.

Jeff will feel "disturbed" by my comments to the extend that
he is unable to counter (to his satisfaction) the effects of
those comments on the variable he is controlling ("merits of
conventional psychology"). This meaning of the word "disturbed"
is somewhat different than the meaning of "disturbed" when we
talk about a "disturbance" in PCT. The "disturbance" Jeff (and
others) feel in conversations with me is the unpleasant emotional
side effect of the chronic error that results from failure to
maintain control of a perception that is being influenced by an
insuperable disturbance (me;-)).

When the effects of disturbance variables on controlled
perceptions are being effectively countered we don't even
notice them -- even though they are there and we are acting
to counter them. Ordinarily, the wind is not even noticed
when we drive; we just turn the wheel, as necessary, to prevent
it from having an effect on the direction of the car; there is
a disturbance (PCT meaning) but we don't feel disturbed
(everyday meaning). The same is true of me; I am a disturbance
to some of the variables being controlled by, say, Bruce Abbott.
But he is so good at protecting those variables from the effects
of my disturbances (PCT meaning) that he doesn't find me
particulary disturbing (everyday meaning). At least I think
that's the way Bruce A. feels. Maybe not;-)

Best

Rick

···

--
Richard S. Marken Phone or Fax: 310 474-0313
Life Learning Associates e-mail: rmarken@earthlink.net
http://home.earthlink.net/~rmarken/

[From Bruce Gregory (980222.2114 EST)]

Rick Marken (980222.1710)]

When the effects of disturbance variables on controlled
perceptions are being effectively countered we don't even
notice them -- even though they are there and we are acting
to counter them. Ordinarily, the wind is not even noticed
when we drive; we just turn the wheel, as necessary, to prevent
it from having an effect on the direction of the car; there is
a disturbance (PCT meaning) but we don't feel disturbed
(everyday meaning).

In other words, disturbances (PCT) only become disturbances (everyday) when
errors are not reduced by our actions. In fact, the disturbances (everyday)
are more closely linked to the persistence of error than to the magnitude of
the disturbances (PCT).

Bruce

[From Rick Marken (980222.0810)]

Bruce Gregory (980222.2114 EST) --

In other words, disturbances (PCT) only become disturbances
(everyday) when errors are not reduced by our actions. In fact,
the disturbances (everyday) are more closely linked to the
persistence of error than to the magnitude of the disturbances
(PCT).

Perfect! Your statement (a PCT disturbance) does not distrub
(everyday) me. In fact, it makes me rather happy (everyday and
PCT).

Best

Rick

···

--

Richard S. Marken Phone or Fax: 310 474-0313
Life Learning Associates e-mail: rmarken@earthlink.net
http://home.earthlink.net/~rmarken/

[From Bill Powers (980222.0447 MST)]

Bruce Gregory (980222.2114 EST)--

Rick Marken (980222.1710)]

When the effects of disturbance variables on controlled
perceptions are being effectively countered we don't even
notice them -- even though they are there and we are acting
to counter them. Ordinarily, the wind is not even noticed
when we drive; we just turn the wheel, as necessary, to prevent
it from having an effect on the direction of the car; there is
a disturbance (PCT meaning) but we don't feel disturbed
(everyday meaning).

In other words, disturbances (PCT) only become disturbances (everyday) when
errors are not reduced by our actions. In fact, the disturbances (everyday)
are more closely linked to the persistence of error than to the magnitude of
the disturbances (PCT).

This was a very important interchange. The reason that disturbances are
shown in the model as separate variables is that disturbances do not
necessarily disturb. This point can be extraordinarily hard to get across.
Many people want to think of a disturbance as a change in the controlled
variable itself, as if the experimenter were manipulating this variable
directly, as an independent variable. But the effect of the disturbing
variable on the controlled variable depends entirely on how good the
control is. The tighter the control, the harder it is for external
influences to change the controlled variable, because the control system's
action becomes more nearly equal and opposite to the disturbance,
preventing most of its potential effect.

If the experimenter directly manipulates the controlled variable itself,
the loop is broken because the action can no longer prevent the changes in
the controlled variable (assuming that the experimenter is stronger than
the test organism, or has physically removed the feedback path). Now we
are no longer seeing the same system. The controlled variable now changes
far more, relative to the reference setting, than it ever would with the
loop closed. Nonlinearities that normally have only negligible effects now
become predominant. The action of the system becomes extreme.

This is why, during the Test, disturbances must be used that only _tend_ to
alter the controlled variable, without preventing the system's own output
from being fully effective in counteracting the disturbing effects.

In terms of the rubber band experiment, the experimenter must generate
disturbances by pulling on one end of the rubber bands, not by seizing the
knot and moving it. Try that and see what happens. Gary Cziko actually used
a piece of string on the experiments's end, tied to the knot, to show this
point.

Best,

Bill P.

[From Bruce Abbott (980223.0955 EST)]

Rick Marken (980222.1710) --

Fred Nickols (980222.1645 EST)

I thought, in PCT terms, that a "disturbance" was a change in the
state of a controlled perception caused by some factor external
to the controlling system

No. A disturbance is a _variable_ that influences a controlled
variable A change in the state of the controlled variable is
_not_ a disturbance; it is simply a variation in the value of
the controlled variable. Such variation is a function of _both_
disturbance variables _and_ the output of the system (also a
variable). For example, in a tracking task, the value of the
controlled variable (cursor position, c) is a function of both
the disturbance (d) and the output variable (mouse position, o);
c = d + o.

There are two points at which Fred's and Rick's definitions of disturbance
differ. First, Fred defines the disturbance as the changes in the
controlled variable produced by an outside variable (the effect), whereas
Rick defines the disturbance as variable having this effect (the cause).
Second, Fred restricts the disturbance to changes produced by a variable
external to the control system (a true independent variable), whereas Rick
is silent as to whether the disturbance must be external to the control
system (although I assume that he would agree that it must be). Below is
part of the diagram of immediate effects for the system in question

                                [c]<---------[o]
                                 ^
                                 >
                                 >
                                [d]

To complete this portion of the diagram, we would need two functions, one
relating o to c [ f(o), the environmental feedback function ] and one
relating d to c [ g(d), the disturbance function ]. It would appear that
Rick's disagreement with Fred comes down to whether the disturbance should
be defined as d or as g(d). In this regard, I have seen some inconsistency
of usage on CSGnet. Usually g(d) has been omitted from the diagram and
implicitly treated as a multiplier of 1.0 (probably to simplify exposition);
in that case it doesn't matter whether you call d or g(d) the disturbance as
they have the same values.

Defining the disturbance as an external variable makes it clear which
variable you are talking about, but it there is one case where it might be
desirable to use the term another way. Sometimes control systems are too
sensitive and underdamped, and for these reasons go into oscillation. In
that case the output itself can be viewed as creating its own "disturbance"
to the control system, by changing too strongly, too quickly, thus driving
the controlled variable to overshoot the reference. In other words, the
control actions themselves become the problem. But perhaps in that case we
should carefully avoid using the word "disturbance" to describe this
self-induced instability.

Regards,

Bruce

i.kurtzer (980223.1700)
[From Bruce Gregory (980222.2114 EST)]

Rick Marken (980222.1710)]

>>When the effects of disturbance variables on controlled
>>perceptions are being effectively countered we don't even
>>notice them -- even though they are there and we are acting
>>to counter them. Ordinarily, the wind is not even noticed
>>when we drive; we just turn the wheel, as necessary, to prevent
>>it from having an effect on the direction of the car; there is
>>a disturbance (PCT meaning) but we don't feel disturbed
>>(everyday meaning).

>In other words, disturbances (PCT) only become disturbances (everyday) when
>errors are not reduced by our actions. In fact, the disturbances (everyday)
>are more closely linked to the persistence of error than to the magnitude of
>the disturbances (PCT).

  There is no study I know, feel free to send references, in which some one
tracked the magnitude of disturbances (PCT) and any subjective report.

i.

i.kurtzer (980223.1530)

oops, i am wrong. I have found one reference.
R.Pavlovski "The Physiological Stress of Thwarted Intentions" in Conation and
Control. I will reread it. On the side there are some that would say that we
"already know" how to make these mappings [perception=afferent (for a
system/phsyio. example) or error=yuch (for a system/subjective example)] .
That is simply not true. There is no reason to a priori consider the
"experience" of yuckiness the "flip side" of a signal in the PCT model,
whatever that signal might be technically called.
And as far as the mapping that have previously beeen made...we all should know
ala the behavioal illusion that IF THE BEHVIOR IS A CONTROL PROCESS then these
experiments should be redone with the Test in mind.

i.

[From Bruce Abbott (980223.2005 EST)]

Rick Marken (980223.1000) --

Bruce Abbott (980223.0955 EST)

It would appear that Rick's disagreement with Fred comes down to
whether the disturbance should be defined as d or as g(d).

No. It's whether the disturbance should be defined as d (variations
in environmental variables) or c (variations in controlled variables).

O.K., maybe I misunderstood Fred Nichols' position. We'll have to wait and
see what Fred has to say.

I think you would do well to carefully re-read this thread
(particularly Rick Marken (980222.1710),Bruce Gregory(980222.2114 EST)
and Bill Powers (980222.0447 MST)) because (as Bill noted) this is
a _very_ important topic. The most important thing to understand
is that, in a well-functioning ("tight") control system, disturbance
variations (variations in d or g(d)) hardly show up _at all_ as
variations in the controlled variable.

I assume that you write this for the general audience and not me in
particular, as I do understand this. But let me test _your_ understanding.
Assume that you had an ideal control system of the type we usually diagram
-- one that continuously and perfectly countered all disturbances to the
controlled variable (except for the constant residual error needed to
maintain output against a constant disturbance). The correlation between d
and the cv is 0.0. Yet the correlation between d and o is 1.0. How is o
able to vary perfectly with d if d is uncorrelated with e, through which the
influence of d must pass?

This is what destroys the foundations of conventional psychology.
It does it by rejecting the causal model of behavior (the model
on which all behavioral research to date has been based). I think
that once you are able to understand and/or accept this point
[that variations in disturbance variables are _not_ reflected
in variations of the controlled variable] you will be able to
stop fighting so hard against PCT and start acting as its true
champion.

Your "once you are able . . ." assertion begs the question of whether I do
understand and accept the point you make. (I do, so the rest of the
sentence is moot.) A control system controls its input by varying its
output so as to oppose the effects of any disturbances that would otherwise
push the input away from its current reference level. The output acts on
the input via an environmental feedback function. Because the output varies
so as to oppose the effects of disturbances on the input, the input varies
relatively little (how much depends on control system parameters). The
disturbance pushes, and the control system pushes back. You get a nice
negative correlation between push and counter-push, and little correlation
between push and input. That about it?

You also beg the question as to whether or not I have fought against PCT. I
haven't fought at all against PCT. Where I've fought at all, it has been
against assertions said to be based on PCT which I find do not follow from
PCT at all. (One of them is the assertion that the behavioral illusion
destroys the foundations of "conventional" psychology, but I don't want to
open THAT can of worms again.)

Regards,

Bruce

[From Rick Marken (980223.2000)]

Me:

I think you would do well to carefully re-read this thread
(particularly Rick Marken (980222.1710),Bruce Gregory
(980222.2114 EST) and Bill Powers (980222.0447 MST))
because (as Bill noted) this is a _very_ important topic.

Bruce Abbott (980223.2005 EST) --

I assume that you write this for the general audience and not
me in particular, as I do understand this.

If you understood this you would not be fighting Bill and me
tooth and nail over the merits of conventional research and you
would already have publicly repudiated everything in your
research methods textbook. Trust me, Bruce, you don't understand
this _at all_.

How is o able to vary perfectly with d if d is uncorrelated
with e, through which the influence of d must pass?

The correlation between o and d is a _side effect_ of the process
of control. o is able to vary perfectly with d even when d is
completely uncorrelated with e becuase o is _not based on
d_!! o is based on the difference between r and p; d has nothing
to do with it. The result of continuously varying o as a
function of r-p _in a closed loop_ is that o ~ -d (where ~ means
"approximately equal to"). With high enough gain, the approximation
is nearly an equality so that the observed correlation between
o and d is nearly -1.0.

The influence of d does not "pass" to the control system via
e. The control system (as we have proved in a _long_ discussion
of this topic about 5 years ago with Martin) has _no way of
knowing_ what d is (assuming that there is only one disturbance
variable acting on the controlled variable). Remember, e = r-p
and p = o + d. All the control system "sees" is variations in p.
The system itself has no way of knowing which component of this
variation is due to d and which is due to o.

The idea that the influence of d is passed through the control
system (presumably so that the system can generate an o ~ -d)
is just what one would expect from someone who is controlling
for a cause-effect view of behavior: ergo, it is just what one
would expect to hear from _you_:wink:

You also beg the question as to whether or not I have fought
against PCT. I haven't fought at all against PCT. Where I've
fought at all, it has been against assertions said to be based
on PCT which I find do not follow from PCT at all. (One of
them is the assertion that the behavioral illusion destroys the
foundations of "conventional" psychology, but I don't want to
open THAT can of worms again.)

One man's can of worms is another man's jar of caviar. If you
are ever able to give up your committment to the cause-effect
view of behavior (embodied in your belief that disturbance
causes output via the perceptual signal) you're are in for a
real treat; I'll even buy the champagne;-)

Best

Rick

···

--

Richard S. Marken Phone or Fax: 310 474-0313
Life Learning Associates e-mail: rmarken@earthlink.net
http://home.earthlink.net/~rmarken/

[From Bill Powers (980224.0158MST)]

Bruce Abbott (980223.2005 EST)--
(writing to Rick)

I assume that you write this for the general audience and not me in
particular, as I do understand this. But let me test _your_ understanding.
Assume that you had an ideal control system of the type we usually diagram
-- one that continuously and perfectly countered all disturbances to the
controlled variable (except for the constant residual error needed to
maintain output against a constant disturbance). The correlation between d
and the cv is 0.0. Yet the correlation between d and o is 1.0. How is o
able to vary perfectly with d if d is uncorrelated with e, through which the
influence of d must pass?

There are two issues here, of which the less important is Rick's
idealization of the control equations. The more important one is that we do
find, experimentally, that the correlation between d and o is close to -1,
while the correlation between d and cv, or between cv and o, is usually 0.2
or less (disregarding sign). Just run the demos in Demo 1, many of which
actually compute these numbers from a short run that the user does.

If you think of d affecting cv, cv affecting e, and e affecting o, it is
impossible for the correlation between d and o to be greater than any of
the intervening correlations. Yet that is what we see, reproducibly and
even with a randomly-selected participant. The fact that we see this
"impossible" relationship among correlations is what proves that the lineal
model can't be correct. It is not correct because the causation is not
lineal; feedback is involved.

If you model a control system with an integrating output, you can find high
correlations between d and cv, and between cv and o. This is because in the
computer model there is no noise. If you add a small amount of noise
anywhere in the loop (for example, in the error signal), you will find that
the intermediate correlations drop sharply, while the overall correlation
between d and o remains high (and negative). The system is now keeping the
error signal small, but the noise is comparable to the error signal, so
this destroys the intermediate correlations. This is what is happening with
the real experiments; the noise in the human control system is about the
same as the minimum error that the person can maintain.

This changes your question from rhetorical to a literal request for
information:

How is o able to vary perfectly with d if d is uncorrelated with e,

through >which the influence of d must pass?

Stated more realistically, the question is, "How can the correlation of d
with the cv and e be lower than the correlation between d and o, when the
influence of d on o must pass through the cv and e?" Since this is what we
actually observe, the question presumably has an answer that doesn't rely
on magic. And it does. The answer is control theory.

Where I've fought at all, it has been
against assertions said to be based on PCT which I find do not follow from
PCT at all. (One of them is the assertion that the behavioral illusion
destroys the foundations of "conventional" psychology, but I don't want to
open THAT can of worms again.).

The behavioral illusion reveals a relationship among correlations that is
impossible under the conventional input-output interpretations of behavior.
Not only does it show this correlational paradox, but it shows that the
apparent relationship between a stimulus and a response, conventionally
defined, may have nothing to do with the actual relationship mediated by
the organism. I don't think you have really understood either of these
points. Your lack of understanding of the correlational paradox is shown by
your rhetorical question above, and your lack of understanding of the
second point is shown by your claim of an exemption for stimuli you have
used, not realizing that a mere response to a stimulus does not prove that
the stimulus is actually what is being sensed. If you had understood the
second point, your objection would have taken a different form: you would
have shown that all disturbances tending to alter the stimulus would be
counteracted by corresponding changes in the system's action. The
indications are that you still believe there are some stimuli that cause
behavior directly, through an open-loop sensory-motor link.

Just to be as explicit as possible: PCT is based on the idea that _ALL_
behavior is produced as a means of controlling some perceptual variable.
This means that there are NO stimuli that produce behavior in an open-loop
way -- and that includes "responses" to puffs of air on the eyeball and
pinpricks and loud bangs behind the head. In all cases where such
"responses" appear to happen, there is really some controlled variable that
is affected one way by the apparent stimulus, and the opposite way by the
supposed "response." The apparent stimulus is only a physical disturbance
of some controlled variable, and the apparent response is an attempt by a
control system to resist the effects of the disturbance. If the disturbance
is applied slowly enough for control to succeed, it will be clear that the
so-called response actually prevents the disturbance from having any
significant effect on the organism.

The behavioral illusion creates a _highly convincing_ illusion of direct
cause and effect. For example, if you apply a shock to a rat, doesn't it
seem that what the rat does is truly caused by the shock? But a PCT
analysis would say that the shock merely disturbs a controlled variable
(more likely, a whole lot of them) and that whatever part of the reaction
is not caused by the shock itself acting directly on muscles is an attempt
by one or more control systems to restore their controlled variables to
their preferred conditions. The shock itself is obviously not a controlled
variable; there are no specialized sensors for electricity. The shock acts
on sensory nerve-endings that normally detect such things as temperature,
pressure, vibration, pain, position, and so on; the control systems
involved exist to maintain these variables, not electric currents per se,
at particular reference levels. The reaction is not a reaction to
electricity; it is an attempt to restore the disturbed variables to their
reference states.

So the use of shocks as a stimulus, as in some experiments you have done,
is a clear invitation to be fooled by the behavioral illusion. When you
said that in YOUR experiments this illusion was irrelevant, I wondered
whether you were thinking of the shocks. In fact, your statement made me
wonder if you even understood how the behavioral illusion works. Unless you
have proven, by using the Test, that a specific stimulus is in fact being
controlled by variations in an organism's actions, NO stimulus can be
automatically exempt from the suspicion that the behavioral illusion is
involved. Any stimulus that can be freely varied without direct opposition
by the organism is by definition a disturbing variable, not a controlled
variable or controlled perception.

Best,

Bill P.

[Martin Taylor 980224 08:55]

[From Rick Marken (980223.2000)

I know this is foolhardy, but as a good S-R system, I must respond
to this obvious stimulus:-)

... The control system (as we have proved in a _long_ discussion
of this topic about 5 years ago with Martin) has _no way of
knowing_ what d is (assuming that there is only one disturbance
variable acting on the controlled variable).

I think the wording you want is "as we have _dis_proved". What was
proved, and demonstrated, was that it is possible to reconstruct the
disturbance waveform from the perceptual signal as precisely as the
ECU controls, using additional knowledge _about the control system
and the environmental feedback function_ which is not influenced by the
disturbance.

What was neither proved nor claimed (and what Rick chooses to use as
a proof that the control system has no way of knowing what d is) was
that the control system "knows" its own properties.

What was not claimed was that the control system ever generates a
reconstruction of the disturbance waveform, except at the CEV, where
the disturbance is counteracted.

The term "knowing" is very strange, as applied to a control system.
The control system has properties that can be known to an outside
observer, and it has signal values that can be measured by an outside
observer. What was proved was that an outside observer who knows the
control system properties and then measures the variations in the
perceptual signal can then determine the waveform of the disturbance.

What is also strange is the wording "(assuming that there is only one
disturbance variable acting on the controlled variable)" given that
the CEV is influenced by some effects of all disturbing variables,
and it is that total influence that is usually labelled "d".

···

-------------------------

The mis-statements about the old discussion ought to stop, but I'm quite
sure they won't, from past experience. I had initially decided not to
re-enter this discussion, since it has proved not amenable to simple
logic. But a bald falsity is not good to leave unchallenged, when it
is near the heart of any analysis of the action of control systems.

The problem is, I think, that Rick does not distinguish two pairs of
concepts: "control" versus "perfect control" and "simultaneous variation"
versus "physically necssary transport delay." This failure to discriminate
makes it impossible for him to accept that the input-output relationships
of the different functions that form the control loop do go from sensory
to perceptual, from perceptual and reference to error, from error to
output, and from output and disturbance to sensory. Physically, that's
the way signals flow. Analytically, you have to analyze the control
loop in reverse, but if you want to examine the properties of its
components, you look at how the output of each one depends on its input.

The recent discussion with Tracy Harms about whether the output function
was a true function was about whether you could retrieve the input of
the output function (the error signal), given the output of the function.
You can't. An infinite variety of error waveforms can give the same
present value of the output signal. The same is true of the sensory
input given the perceptual signal (compounded by there being multiple
sensory inputs to the Perceptual Input Function, all of which vary over
time). You can determine the perceptual signal value give the time
history of the sensory imputs, but not the reverse.

If you know the properties of all the functions in the loop, and
if control is good, then you can determine the waveform of the disturbance
signal given the waveform of the perceptual signal (not the current
disturbance signal value given the current perceptual signal value).

And that was both proved and demonstrated.

Martin

[From Rick Marken (980224.0745)]

Martin Taylor (980224 08:55) --

Everything you say in your post is completely and utterly
irrelevant to the point Bill and I are making in response
to Bruce's question about how the correlation between
d and o can be higher than that between d and cv or between
d and e. The point, that Bill Powers (980224.0158MST) makes
far more clearly than I did [Rick Marken (980223.2000)], is this:

The fact that we see this "impossible" relationship among
correlations [between d, o and cv] is what proves that the
lineal model can't be correct. It is not correct because the
causation is not lineal; feedback is involved.

I suggest that you, Bruce A. and Jeff V. run the demos in Demo 1
and/or the first two demos at my site _over and over again_, and
read Bill's statement above _after each run_. Maybe after doing
this four or five trillion times it will finally dawn on you all
that what Bill has shown in these simple little demos of control
is that the lineal causal (input-output) model of behavior -- the
model that is the basis of scientific psychology and of the
research methods that support it -- IS WRONG!!! Apparently
this simple little point is too strong for some people. My
advice to those people is "deal with it! That's the way
things are".

Note that Bill and I gave the same answer to Bruce's question
about how the correlation between d and o can be higher than
that between d and cv or between d and e. The answer,
of course, is "control theory", which explains what the lineal
causal model cannot explain -- the behavior of variables
that are linked in a negative feedback loop.

Best

Rick

···

--
Richard S. Marken Phone or Fax: 310 474-0313
Life Learning Associates e-mail: rmarken@earthlink.net
http://home.earthlink.net/~rmarken

[from Jeff Vancouver 980224.1140 EST]

[Martin Taylor 980224 08:55] to [From Rick Marken (980223.2000)

The problem is, I think, that Rick does not distinguish two pairs of
concepts: "control" versus "perfect control" and "simultaneous variation"
versus "physically necssary transport delay." This failure to discriminate
makes it impossible for him to accept that the input-output relationships
of the different functions that form the control loop do go from sensory
to perceptual, from perceptual and reference to error, from error to
output, and from output and disturbance to sensory. Physically, that's
the way signals flow. Analytically, you have to analyze the control
loop in reverse, but if you want to examine the properties of its
components, you look at how the output of each one depends on its input.

Martin, I think you nailed it. Very good.

Sincerely,

Jeff

[From Bill Powers (980224.1041 MST)]

Martin Taylor 980224 08:55--

(Rick:)>>... The control system (as we have proved in a _long_ discussion

of this topic about 5 years ago with Martin) has _no way of
knowing_ what d is (assuming that there is only one disturbance
variable acting on the controlled variable).

(Martin:)>I think the wording you want is "as we have _dis_proved". What was

proved, and demonstrated, was that it is possible to reconstruct the
disturbance waveform from the perceptual signal as precisely as the
ECU controls, using additional knowledge _about the control system
and the environmental feedback function_ which is not influenced by the
disturbance.

Martin, your capacity for changing the rules on the fly is phenomenal. What
we finally agree upon is that d, the disturbing variable or variables,
cannot be reconstructed by the control system on the basis of any
information in the system, by any means. Every time I have explained
exactly what this statement means, you have gone into a snit at the idea
that I could ever have thought you meant anything else. And then you go
right back to your OWN meaning of "disturbance," which is "net contribution
to the state of the controlled variable," which is something entirely
different and is not what is meant in PCT by "d". The net contribution is
Fd(d), which is not the same thing as d. For multiple disturbances (the
normal case), the net contribution is the sum of Fd1(d1) + Fd2(d2) + ...
Fdn(dn). The control system has no way to find out how many different
disturbances are acting at the same time through different environmental
connections.

This, of course, is your cue to say "But I never said anything to the
contrary about that; that you could think I might say anything different is
insulting."

Bill P.

[From Bruce Abbott (980224.1400 EST)]

Rick Marken (980223.2000) --

Bruce Abbott (980223.2005 EST)

I assume that you write this for the general audience and not
me in particular, as I do understand this.

If you understood this you would not be fighting Bill and me
tooth and nail over the merits of conventional research and you
would already have publicly repudiated everything in your
research methods textbook. Trust me, Bruce, you don't understand
this _at all_.

You are entitled to your _opinion_.

How is o able to vary perfectly with d if d is uncorrelated
with e, through which the influence of d must pass?

The correlation between o and d is a _side effect_ of the process
of control.

It is an essential feature of the process. If o and d were not strongly and
negatively correlated, control would be poor or absent. o opposes d so as
to keep i from changing much (if control is good).

o is able to vary perfectly with d even when d is
completely uncorrelated with e becuase o is _not based on
d_!!

Let us assume (to simplify the argument) that r is constant. At time t, d
changes, inducing a change in i. The change in i causes p to change (via
the input function), thus altering r-p similarly. Now r-p = e, so e
changes, inducing a change in o (via the output function). The change in o
induces a change in i (via the environmental feedback function), which
exactly opposes the change in i induced by d. In this ideal control system,
all these changes are assumed to occur simultaneously around the loop. But
this leads to a paradox: the influence of d on i is opposed in the same time
instant in which it occurs. Because it is completely canceled, there can
have been _no_ change in i, _no_ change in p, _no_ change in o to oppose the
influence of d on i! It can't work!

The solution to this paradox (Zeno's paradox, actually) is that the opposing
reaction of the system arrives at time t+dt, where dt is some infinitessimal
but positive value. The opposing influence of o arrives a tiny fraction of
time (as small as you like) after d has acted on i (which acts on p which
acts on e which acts on o, with time-delays around the loop as small as you
like but not zero).

So you see, Rick, with r fixed, o _is_ based on d.

o is based on the difference between r and p; d has nothing
to do with it.

Hmmm. Change in d ---> change in i -----> change in p ----> change in e
-----> change in o (all simultaneously) and you say that change in d has
_nothing to do_ with change in o? Poppycock.

The result of continuously varying o as a
function of r-p _in a closed loop_ is that o ~ -d (where ~ means
"approximately equal to"). With high enough gain, the approximation
is nearly an equality so that the observed correlation between
o and d is nearly -1.0.

You have forgotten that I had assumed an _ideal_ control system (infinite
gain). I did this for the same reason that physicists assume, say, an ideal
spring: such cases tend to be simpler to analyze. Be that as it may, I
accept your description of a less-than-ideal system. Where does the
variation in r-p come from which produces continuous variation in o? Magic?
You think that by closing the loop something magical happens to produce
variation in e without any variation in i due to the influence of d on i?
Wow. A miracle occurs!!

The influence of d does not "pass" to the control system via
e. The control system (as we have proved in a _long_ discussion
of this topic about 5 years ago with Martin) has _no way of
knowing_ what d is (assuming that there is only one disturbance
variable acting on the controlled variable). Remember, e = r-p
and p = o + d. All the control system "sees" is variations in p.
The system itself has no way of knowing which component of this
variation is due to d and which is due to o.

You have again forgotten that I posited an ideal control system. In the
ideal system there is NO VARIATION IN i DUE TO o going around the loop!!! o
completely cancels the influence of d on i in the first trip around the
loop. Thus, there is no residual uncanceled disturbance to recirculate
around the loop; the only changes p, e, and o ever see are due to d.

Also, I did not say that the influence of d passes "to the control system
via e," oh doctor of distortion. I said (essentially) that the influence of
d passes to o through e. To be complete, it passes to i to p to e to o, and
then back to i (inverted) where it cancels itself (all "simultaneously"
around the loop).

I think you need to go back to control school.

The idea that the influence of d is passed through the control
system (presumably so that the system can generate an o ~ -d)
is just what one would expect from someone who is controlling
for a cause-effect view of behavior: ergo, it is just what one
would expect to hear from _you_:wink:

Look at the diagram of the system, Rick. Do you not see little arrowheads
pointing in a certain direction (from d to i to p to e to o to i)? What do
you suppose those little arrowheads are there for? Decoration?

Regards,

Bruce

[Martin Taylor 980224 13:40]

Bill Powers (980224.0158MST) to Bruce Abbott (980223.2005 EST)--

... The correlation between d
and the cv is 0.0. Yet the correlation between d and o is 1.0. How is o
able to vary perfectly with d if d is uncorrelated with e, through which the
influence of d must pass?

There are two issues here... The more important one is that we do
find, experimentally, that the correlation between d and o is close to -1,
while the correlation between d and cv, or between cv and o, is usually 0.2
or less (disregarding sign).
...
If you think of d affecting cv, cv affecting e, and e affecting o, it is
impossible for the correlation between d and o to be greater than any of
the intervening correlations. Yet that is what we see, reproducibly and
even with a randomly-selected participant. The fact that we see this
"impossible" relationship among correlations is what proves that the lineal
model can't be correct. It is not correct because the causation is not
lineal; feedback is involved.

+Bill Powers (980220.1103 MST) to Tracy Harms about why there is no
  correlation between the error signal and the output signal, even though
  the output signal is a pure function of the error signal:

+The output does not "correlate" with the error signal; it is _driven by_
+the error signal, which is a physical signal like a voltage.

and earlier, also to Tracy Harms:

One form of output function that works very
well is

do/dt = k1*e - k2*o

This function can clearly yield different values of o with the same value
of e, and the same value of o for different values of e. It's a perfectly
regular and predictable function involving time.

Parenthetical note: the causation here _is_ lineal, and feedback is not
involved. Yet the correlation between input and output can be very close
to zero (it is exactly zero if there is no leak, at least if the input
is a sine wave, and I suspect for other inputs as well).

Back to Bill Powers (980224.0158MST):

If you model a control system with an integrating output,
... [and] If you add a small amount of noise
anywhere in the loop (for example, in the error signal), you will find that
the intermediate correlations drop sharply, while the overall correlation
between d and o remains high (and negative).
...
This changes your question from rhetorical to a literal request for
information:

How is o able to vary perfectly with d if d is uncorrelated with e,

through >which the influence of d must pass?
...
The behavioral illusion reveals a relationship among correlations that is
impossible under the conventional input-output interpretations of behavior.
Not only does it show this correlational paradox,...

I'm a little puzzled. To Tracy Harms, but not to you, it is a paradox that
the output signal can be a function of the error signal, but not correlated
with it. To you, but not to me, it is a paradox that the perceptual signal
can be a function of the disturbance signal (and of the reference signal)
but not correlated with it. My puzzlement is how you can find the one to
be a paradox, but not the other.

We actually write the functional relationship between p and d when we
analyze the control loop, don't we?

p = Gr/(1+G) + d/(1+G) if my memory doesn't fail me.

If r is constant, as it usually is most of the time in our experiments,
p = d/(1+G) + K

Since p, d, and G are actually functions of time (G normally being an
integrator or a leaky integrator), of course the current value of p does
not correlate with the current value of d; at least it wouldn't if control
were perfect. Nevertheless, so long as the reference signal and the loop
properties are constant, p is as pure a function of d as the output signal
is of the error signal.

It might be helpful to remember that the long-ago thread that keeps
resurfacing about "information about the disturbance in the perceptual
signal" was started when I mentioned that the evolutionary "purpose" of
control was to exclude disturbances from the outer world from penetrating
the organism, even though the only information available for control was
passed through the perceptual signal. This seemed to be a paradox that
caused a lot of confusion, and evoked claims that information about the
disturbance could not be "in" the perceptual signal since experiments show
that the better the control, the lower the correlation between disturbing
signal and perceptual signal. I have never been able to see whering the
paradox lies, any more than Bill can see where Tracy Harms sees paradox
in the lack of correlation between the input and output of an integrator.

But I have hope that this time it will be different. I am encouraged in
this hope by Bill Powers message (980221.0315 MST) to Tracy Harms:

*You've decided that "o = f(e) just isn't so," and you're looking for
*evidence to support this conclusion. Give up: it is so. An output function
*is a physical device. An error signal and an output signal are physical
*signals. The output signal is generated by the output function and the
*output function is caused to act by the error signal. This means that the
*output is a function of the error signal. No way around it.

···

*
*Ouch, reorganization hurts. Grin and bear it.

A control loop is a physical device. The perceptual signal, the reference
signal, the output signal and the disturbance signal are physical signals.
The two outputs (the output signal and the perceptual signal) are generated
by the control loop, and the control loop is caused to act by the reference
signal and the disturbance signal. This means that the output signal and
the perceptual signal are functions of the reference signal and the
disturbance signal. No way around it.

Martin

[Martin Taylor 980224 14:30]

[From Rick Marken (980224.0745)]

Martin Taylor (980224 08:55) --

Everything you say in your post is completely and utterly
irrelevant to the point Bill and I are making in response
to Bruce's question about how the correlation between
d and o can be higher than that between d and cv or between
d and e. The point, that Bill Powers (980224.0158MST) makes
far more clearly than I did [Rick Marken (980223.2000)], is this:

The fact that we see this "impossible" relationship among
correlations [between d, o and cv] is what proves that the
lineal model can't be correct. It is not correct because the
causation is not lineal; feedback is involved.

I suggest that you, Bruce A. and Jeff V. run the demos in Demo 1
and/or the first two demos at my site _over and over again_, and
read Bill's statement above _after each run_. Maybe after doing
this four or five trillion times it will finally dawn on you all
that what Bill has shown in these simple little demos of control
is that the lineal causal (input-output) model of behavior -- the
model that is the basis of scientific psychology and of the
research methods that support it -- IS WRONG!!!

We know that. At least I know it, and everyuthing I read from Bruce
Abbott suggests that he knows it, too.

Note that Bill and I gave the same answer to Bruce's question
about how the correlation between d and o can be higher than
that between d and cv or between d and e.

The fact that the answers were the same doesn't mean they were correct.
Or that they weren't.

See my reply to Bill's message to Bruce Abbott, just sent.

The answer,
of course, is "control theory", which explains what the lineal
causal model cannot explain -- the behavior of variables
that are linked in a negative feedback loop.

OK. You like demos. Here's one. If you don't like it in symbolic form,
you can program it and try it out.

F1: x = integral y dt
F2: y = dz/dt

This is a purely lineal causal pair of functional relationships, which
one can diagram

x --> F1 --> y --> F2 --> z

What is the correlation between x and y? Between y and z? Between x and z?

Too hard? Try it with a sine wave input. The answers are 0.0, 0.0, 1.0.
Try it with any sinusoidal spectral component of a waveform.

Control is a _method_ of getting rid of the correlation between
disturbance signal and perceptual signal. It is not a demonstration that
the two are unrelated, even when they are uncorrelated.

Martin

[Martin Taylor 980224 14:45]

Bill Powers (980224.1041 MST)

Martin, your capacity for changing the rules on the fly is phenomenal.

Well, at least someone's memory is variable, I'll grant you that.

What
we finally agree upon is that d, the disturbing variable or variables,
cannot be reconstructed by the control system on the basis of any
information in the system, by any means.

Which is why I long have made sure to say "disturbance _signal_" or
"disturbance waveform" when this topic comes up. We long ago clarified
the usage of this terminology, and I try to be careful in using it. I do
not appreciate your attempt to deflect the point of the message by asserting
that (a) I use the terminology wrongly, or (b) I'm claiming what I am
not claiming. I do not, and never have, made any claim with respect to
disturbing _variables_. So there's no point in your writing a comment
on something on which, as you say, we do agree.

But I hope you can't find anwhere in my messages on this topic where
I have used "disturbing variable" or even "disturbance" in place of
"disturbance signal" or "disturbance waveform". I rather suspect you
have imagined it, for reasons that might be interesting to investigate.

If you can find such instances, I apologize, but suggest that you could
reasonably assume that when "disturbance signal" is used in most places,
it is also intended in other equivalent places where "disturbance" has
been inadvertently substituted.

Every time I have explained
exactly what this statement means, you have gone into a snit at the idea
that I could ever have thought you meant anything else. And then you go
right back to your OWN meaning of "disturbance,"...

I have tried diligently not to do exactly that, being very sensitive to
this precise issue.

... which is "net contribution
to the state of the controlled variable," which is something entirely
different and is not what is meant in PCT by "d". The net contribution is
Fd(d), which is not the same thing as d.

Which will come as a surprise to those who are so often confronted with
expressions that include "o+d" as the total influence on the CEV. Complain
not to me, but to Rick, whose symbology I followed in writing my
comment on his false statement.

As in:

+Rick Marken (980223.2000):

+ The result of continuously varying o as a
+function of r-p _in a closed loop_ is that o ~ -d (where ~ means
+"approximately equal to")

and

+The influence of d does not "pass" to the control system via
+e. The control system (as we have proved in a _long_ discussion
+of this topic about 5 years ago with Martin) has _no way of
+knowing_ what d is (assuming that there is only one disturbance
+variable acting on the controlled variable). Remember, e = r-p
+and p = o + d.

I think I have every right to use the terminology so introduced,
especially when replying to this particular message. Furthermore,
I think you also should refer to the _precise_ statement that I used
to replace Rick's weird notion that the control system can "know" something
about its environment. I repeat the statement to which you seem to object,

What was
proved, and demonstrated, was that it is possible to reconstruct the
disturbance waveform from the perceptual signal as precisely as the
ECU controls, using additional knowledge _about the control system
and the environmental feedback function_ which is not influenced by the
disturbance.

Do you say that this statement is incorrect? Rick does.

For multiple disturbances (the
normal case), the net contribution is the sum of Fd1(d1) + Fd2(d2) + ...
Fdn(dn). The control system has no way to find out how many different
disturbances are acting at the same time through different environmental
connections.

This, of course, is your cue to say "But I never said anything to the
contrary about that; that you could think I might say anything different is
insulting."

If you like. Your hypothetical quote is, of course, correct. But rather
than say it (because you already know it) I'm more inclined to ask why you
direct toward me rather than toward Rick your severe criticism of the
notion that "d" represents an influence on the controlled CEV.

Anyway, to recap. Rick's point is that in no way can the perceptual
signal be used to recover the influence of disturbing variables on the
controlled CEV. Your point (about which I never said anything to the
contrary--ever) is that more than one disturbing variable can influence
any CCEV, and nothing in the perceptual signal can tease them apart.

I agree with your point, though it is, of course, irrelevant to my
correction of Rick's statement. Rick's point has been demonstrated
to be false, and will remain so.

Martin

···

from my reply to Rick (italics in the original):