Ashby's Law of Requisite Variety

[From Rick Marken (2012.12.24.0950)]

Bill Powers (2012.12.23.1915 MST)--

My bark is apparently a lot worse than my bite.

> BP: However, there is a lawful chain of causation between disturbance
> and output, which we build into each model we run.

RM: I thought the chain of causation went from o+d to o and that this
chain is part of of a loop. Yes' there is a path from d to o but it is
completely confounded with the path from o to o. Saying there is a
chain of causation from d to o could suggest to those trying to avoid
doing research based on the Test for Controlled Variables that we can
study the characteristics of this chain using conventional IV-DV
methods.

BP: That conclusion would demonstrate a misunderstanding. Each function in
the loop has an input and an output, and is a straight-through cause-effect
function. When you solve the system of equations that describes all the
functions and their interconnections, however, you get the behavior of the
closed-loop system. In fact you can show that each system variable in the
loop, such as the output quantity, can be described as a function of the two
independent variables, d and r (where d may be the sum of many
disturbances). With r held constant, variations in o are a function of
variations in d alone unless system noise is important, which I don't think
is often the case.

RM: Yes, but is o really a causal function of d? My impression was
that the relationship between o and d is a side effect of the system
acting to to keep error at zero. Indeed, I thought that was one way of
looking at the "behavioral illusion"; the illusion being that the
relationship between d and o appears to reflect the causal path from
stimulus (disturbance) to response (output) when, in fact, no such
causal path exists. Do I have that wrong?

BP: The main difference between an S-R system and the closed-loop system is that
in the latter kind of system, the overall function connecting d and o has a
form determined mostly by the feedback function and to a lesser degree (how
much less depending on loop gain) by functions acting in the forward
direction, the perceptual input function, comparator, and output function.

RM: I see this as the second aspect of the "behavioral illusion", the
first being what I mention above; that the d - o relationship appears
to reflect a causal path through the organism (the organism function)
from d to o that doesn't actually exist. The second aspect being the
one you mention here: The form of the apparent causal relationship
between o and d is determined mostly by the feedback function. So the
complete "behavioral illusion" is that there is a causal path from d
to o and that the form of this path is determined by characteristics
of the organism. PCT shows that the reality is that there is no causal
path from d to o and that the form of this apparent causal path is
determined mainly by the feedback function connecting output to input,
not by characteristics of the organism. Do I have that wrong too?

RM: I'm barking up the same trees I've been barking up since 1980,
when the implications of PCT for my field (experimental psychology)
hit me squarely between the eyes. If Martin and Bruce would agree that
it is impossible to study the causal path from disturbance (S) to
output (R) in a control loop using the conventional methods of
experimental psychology then I'll stop barking.

BP: It is time to update your conception of the implications of PCT, if it is
that ancient (unchanged for 32 years?).

RM: I actually have (hopefully) been continuously improving my
understanding of those implications over the last 32 years. But I
always appreciate "feedback" on it.

BP: Your conclusions are of course, mostly correct,

RM: Well, thank heaven that those 32 years haven't been completely wasted.

BP: but you tend to express them in terms of idealized
approximations that result from letting loop gain go to infinity. When you
say "no information" you should be saying "almost no information" and so on.
And you probably shouldn't be mentioning information (Information) at all,
since those who do understand information theory are saying that you are
misrepresenting it.

RM: I said "no information" in the context of the varying feedback
function demo where I managed to get good control with virtually zero
correlation between d and o. I said "no information" under the
assumption that the correlatoin between d and o was proportional to
the information in o about d. I suppose I should have said "almost no
information" but if the correlation is something like .012 do I really
have to be that careful? And how can I not mention information when
that's what the whole discussion is about. If the observed correlatoin
between d and o is not an indication of the information about d in o
then all the information experts have to do is say so.

BP: It is perfectly possible to study the path from disturbance (S) to output
(R) using conventional methods of system analysis -- in fact that is exactly
what we do.

RM: I think I have to disagree here. I don't believe you can study
this path without knowledge of the variable that is under control: the
controlled variable. Conventional methods are based on a causal model
that does not include the concept of a controlled variable. The only
aspect of conventional methods that we use is manipulation of an IV
(S) and measurement of a DV (R) under controlled conditions. This
methodology can be used to study the path from S to R in a control
system only if you know that both S and R influence the state of a
particular controlled variable.

BP: What this analysis does is to show the dominance of the feedback
function in determining the apparent properties of that path, a fact that
cannot be seen if one uses a model that has no feedback in it. That is the
real beef: using the wrong model.

RM: Yes, and that is how I now frame my objections to conventional
methodology. That methodology is based on the wrong model -- an
open-loop causal model that includes no reference to a controlled
variable.

BP: This is a very important point, because it
shows that S-R theory is not a consequence of stupidity or ancestor worship
or some other character defect, but simply a matter of not having discovered
the right model. When behaviorism was forming, nobody knew what the right
model was because control theory hadn't been invented yet.

RM: I have never believed and have tried never to imply that anyone is
"stupid" for continuing to do research based on the open-loop causal
model. But I am very aware of the fact that people often take
criticism of their work as implying that they are stupid. In my latest
paper on this topic I actually included a statement trying to reassure
readers that my criticisms of their methodology was not a criticism of
them personally.

BP: This gives us a way to try to enlighten conventional scientists without
their having to lose face. They can't be blamed for their teachers not
knowing about control systems, nor could their teachers be blamed when
nobody at all understood them. A disaster shared by everyone is not nearly
as hard to take as a disaster suffered by you alone, especially if it was
specifically your fault. We can tell behaviorists that failure to include
the facts of control in early analyses of behavior was not specifically
anyone's fault. The originators of behaviorism were doing the best they
could with what they did know. It just happened to be insufficient for
getting the right answers to their questions about organisms.

RM: Completely agree.

BP: We have to be very careful not to make Western scientists lose face.

RM: I'm not as concerned about this as you seem to be. I believe these
people are grown-ups and should be able to deal with criticism as
such. But I'm certainly willing to be "careful" not to have people
lose face. How do you suggest I do that and at the same time be true
to my understanding of PCT?

Best

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

[From Bill Powers (2012.12.24.1215 MST)]

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

that the relationship between o and d is a side effect of the system

acting to to keep error at zero. Indeed, I thought that was one way
of

looking at the “behavioral illusion”; the illusion being that
the

relationship between d and o appears to reflect the causal path from

stimulus (disturbance) to response (output) when, in fact, no such

causal path exists. Do I have that wrong?

BP: Yes. There is clearly a causal path from d to qi (the disturbance
function), another from qi to e (perceptual function and comparator with
an input from r), another from e to o (output function), and finally
another from o to qi (environmental feedback function). All but the last
work in the “forward” direction.
Nothing mysterious happens when the loop is closed. The forward functions
do not disappear. They are still there and are always working. The
feedback effect on qi almost cancels the disturbance’s effect, but
not quite. The loop gain is not literally infinite, and generally the
loop gain falls off above some frequency so high-frequency components of
the disturbance are less well counteracted. Within the frequency band of
good control, the amount of uncanceled effect of d on qi is small, but –
and this part is easy to overlook – it is amplified in the rest of the
forward part and modified in dynamics until it is just large enough and
of the right dynamic form to account exactly for the output of the system
and the amount of feedback effect that is produced by that
output.
However, when we solve the simultaneous equations we find that the
overall effect of this arrangement is that the output is very nearly the
inverse feedback function of the disturbance, at least over the frequency
range in which integral lags do not reduce the loop gain too far. And the
characteristics of the forward part of the loop can vary over quite a
large range without significantly changing the overall relationship
between disturbance and output. This, incidentally, is the most critical
difference between the PCT model and all the others that have been
offered (though the old engineering psychologists knew about
it).
If you subsitute for this more exact analysis the approximations
resulting when the loop gain goes to infinity, the entire form of the
output is then exactly determined by the feedback function of d ( or
rather, D(d)). The forward part of the loop, between qi and o, has no
effect at all on the overall response form. Of course that sounds very
mysterious, as if closing the loop somehow made the physical components
inside the organism unnecessary.
At the ages of 18-19, while taking the U.S. Navy course in electronics on
Navy Pier in Chicago, I learned about these properties of feedback
systems in audio amplifiers, where the electrical audio input corresponds
to the disturbance, the forward part of the control system (audio
amplifier) consists of vacuum-tube circuits and an output transformer,
and the feedback function is simply a few resistors that steal some of
the electrical signal that activates a loudspeaker and feeds it back to
the vacuum tube circuits where it subtracts from the electrical
“disturbance” at the input. We learned that this system works
by using extra high gain in the forward part, and then “throwing it
away” by using the negative feedback which greatly reduces the total
net gain. The result is a vast improvement of uniformity of frequency
response over the response a circuit without feedback could produce, and
even more important, an apparent disappearance of the nonlinearities in
the vacuum tubes and the transformer. In fact the overall effect is to
make the response depend completely on the simple linear network of
resistors in the feedback connection. Magic!
Then, having shown us what happens when we let the amplification in the
loop become very large, the instructor threw us a curve ball in a pop
quiz. After asking us to solve the system equations as we had just been
taught, the question was, “Why, then, can’t we just pull out the
vacuum tubes and clip the leads to the output transformer, and just leave
the feedback connection in place?”
Of course he had to take us by the hand and help us answer that question,
which is why I have remembered the answer for about 67 years. That’s what
I’m doing with you now, paying my education forward.
You can’t just leave out the sensors, the perceptual input function, the
comparator, and the output function and still have the neuromuscular
control system work. A few paragraphs ago I explained why: because the
tiny bit of uncanceled disturbance is amplified enough in the forward
part of the loop to generate exactly the output we see, and produce
exactly the amount of feedback the output provides to the input quantity,
“throwing away” almost all of that loop gain. If course
if we threw away all of that loop gain the control system wouldn’t
work at all. But that’s not what is done. We couldn’t just remove the
nerve cells and muscles and still expect the living controller to control
anything. Of course you knew that, just as we on Navy Pier knew that we
couldn’t just economize by not using vacuum tubes and transformers. But
we finally learned why we couldn’t, and I assume you have, too, as
well as a few onlookers.

Now all of you are saying, “Oh, of course, naturally, that’s
obvious.” But that is now. It wasn’t obvious before, was
it?

Best,

Bill P.

From Dag Forssell (2012.12.24.1245 PST)

This is a test and appreciation for Bill’s recent posts.

Christmas Eve. Celebration Swedish style.

At daugter Karin’s home. She and I have been working on a remodel for better than 3 1/2 months. Lots of hard work, but meaningful, fun and great togetherness.

A few months ago, I was unable to post to CSGnet. Never figured out why.

So testing once more.

Best to all, Dag

···

At 12:19 PM 12/24/2012, you wrote:

[From Bill Powers (2012.12.24.1215 MST)]

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

that the relationship between o and d is a side effect of the system

acting to to keep error at zero. Indeed, I thought that was one way of

looking at the “behavioral illusion”; the illusion being that the

relationship between d and o appears to reflect the causal path from

stimulus (disturbance) to response (output) when, in fact, no such

causal path exists. Do I have that wrong?

BP: Yes. There is clearly a causal path from d to qi (the disturbance function), another from qi to e (perceptual function and comparator with an input from r), another from e to o (output function), and finally another from o to qi (environmental feedback function). All but the last work in the “forward” direction.
Nothing mysterious happens when the loop is closed. The forward functions do not disappear. They are still there and are always working. The feedback effect on qi almost cancels the disturbance’s effect, but not quite. The loop gain is not literally infinite, and generally the loop gain falls off above some frequency so high-frequency components of the disturbance are less well counteracted. Within the frequency band of good control, the amount of uncanceled effect of d on qi is small, but – and this part is easy to overlook – it is amplified in the rest of the forward part and modified in dynamics until it is just large enough and of the right dynamic form to account exactly for the output of the system and the amount of feedback effect that is produced by that output.
However, when we solve the simultaneous equations we find that the overall effect of this arrangement is that the output is very nearly the inverse feedback function of the disturbance, at least over the frequency range in which integral lags do not reduce the loop gain too far. And the characteristics of the forward part of the loop can vary over quite a large range without significantly changing the overall relationship between disturbance and output. This, incidentally, is the most critical difference between the PCT model and all the others that have been offered (though the old engineering psychologists knew about it).
If you subsitute for this more exact analysis the approximations resulting when the loop gain goes to infinity, the entire form of the output is then exactly determined by the feedback function of d ( or rather, D(d)). The forward part of the loop, between qi and o, has no effect at all on the overall response form. Of course that sounds very mysterious, as if closing the loop somehow made the physical components inside the organism unnecessary.
At the ages of 18-19, while taking the U.S. Navy course in electronics on Navy Pier in Chicago, I learned about these properties of feedback systems in audio amplifiers, where the electrical audio input corresponds to the disturbance, the forward part of the control system (audio amplifier) consists of vacuum-tube circuits and an output transformer, and the feedback function is simply a few resistors that steal some of the electrical signal that activates a loudspeaker and feeds it back to the vacuum tube circuits where it subtracts from the electrical “disturbance” at the input. We learned that this system works by using extra high gain in the forward part, and then “throwing it away” by using the negative feedback which greatly reduces the total net gain. The result is a vast improvement of uniformity of frequency response over the response a circuit without feedback could produce, and even more important, an apparent disappearance of the nonlinearities in the vacuum tubes and the transformer. In fact the overall effect is to make the response depend completely on the simple linear network of resistors in the feedback connection. Magic!
Then, having shown us what happens when we let the amplification in the loop become very large, the instructor threw us a curve ball in a pop quiz. After asking us to solve the system equations as we had just been taught, the question was, “Why, then, can’t we just pull out the vacuum tubes and clip the leads to the output transformer, and just leave the feedback connection in place?”
Of course he had to take us by the hand and help us answer that question, which is why I have remembered the answer for about 67 years. That’s what I’m doing with you now, paying my education forward.
You can’t just leave out the sensors, the perceptual input function, the comparator, and the output function and still have the neuromuscular control system work. A few paragraphs ago I explained why: because the tiny bit of uncanceled disturbance is amplified enough in the forward part of the loop to generate exactly the output we see, and produce exactly the amount of feedback the output provides to the input quantity, “throwing away” almost all of that loop gain. If course if we threw away all of that loop gain the control system wouldn’t work at all. But that’s not what is done. We couldn’t just remove the nerve cells and muscles and still expect the living controller to control anything. Of course you knew that, just as we on Navy Pier knew that we couldn’t just economize by not using vacuum tubes and transformers. But we finally learned why we couldn’t, and I assume you have, too, as well as a few onlookers.

Now all of you are saying, “Oh, of course, naturally, that’s obvious.” But that is now. It wasn’t obvious before, was it?

Best,

Bill P.

From Dag Forssell (2012.12.24.1245 PST)

This is a test and appreciation for Bill’s recent posts.

Christmas Eve. Celebration Swedish style.

At daugter Karin’s home. She and I have been working on a remodel for
better than 3 1/2 months. Lots of hard work, but meaningful, fun and
great togetherness.

A few months ago, I was unable to post to CSGnet. Never figured out
why.

So testing once more.

Best to all, Dag

···

At 12:19 PM 12/24/2012, you wrote:

[From Bill Powers
(2012.12.24.1215 MST)]

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

that the relationship between o and d is a side effect of the system

acting to to keep error at zero. Indeed, I thought that was one way
of

looking at the “behavioral illusion”; the illusion being that
the

relationship between d and o appears to reflect the causal path from

stimulus (disturbance) to response (output) when, in fact, no such

causal path exists. Do I have that wrong?

BP: Yes. There is clearly a causal path from d to qi (the disturbance
function), another from qi to e (perceptual function and comparator with
an input from r), another from e to o (output function), and finally
another from o to qi (environmental feedback function). All but the last
work in the “forward” direction.
Nothing mysterious happens when the loop is closed. The forward functions
do not disappear. They are still there and are always working. The
feedback effect on qi almost cancels the disturbance’s effect, but
not quite. The loop gain is not literally infinite, and generally the
loop gain falls off above some frequency so high-frequency components of
the disturbance are less well counteracted. Within the frequency band of
good control, the amount of uncanceled effect of d on qi is small, but –
and this part is easy to overlook – it is amplified in the rest of the
forward part and modified in dynamics until it is just large enough and
of the right dynamic form to account exactly for the output of the system
and the amount of feedback effect that is produced by that output.
However, when we solve the simultaneous equations we find that the
overall effect of this arrangement is that the output is very nearly the
inverse feedback function of the disturbance, at least over the frequency
range in which integral lags do not reduce the loop gain too far. And the
characteristics of the forward part of the loop can vary over quite a
large range without significantly changing the overall relationship
between disturbance and output. This, incidentally, is the most critical
difference between the PCT model and all the others that have been
offered (though the old engineering psychologists knew about
it).
If you subsitute for this more exact analysis the approximations
resulting when the loop gain goes to infinity, the entire form of the
output is then exactly determined by the feedback function of d ( or
rather, D(d)). The forward part of the loop, between qi and o, has no
effect at all on the overall response form. Of course that sounds very
mysterious, as if closing the loop somehow made the physical components
inside the organism unnecessary.
At the ages of 18-19, while taking the U.S. Navy course in electronics on
Navy Pier in Chicago, I learned about these properties of feedback
systems in audio amplifiers, where the electrical audio input corresponds
to the disturbance, the forward part of the control system (audio
amplifier) consists of vacuum-tube circuits and an output transformer,
and the feedback function is simply a few resistors that steal some of
the electrical signal that activates a loudspeaker and feeds it back to
the vacuum tube circuits where it subtracts from the electrical
“disturbance” at the input. We learned that this system works
by using extra high gain in the forward part, and then “throwing it
away” by using the negative feedback which greatly reduces the total
net gain. The result is a vast improvement of uniformity of frequency
response over the response a circuit without feedback could produce, and
even more important, an apparent disappearance of the nonlinearities in
the vacuum tubes and the transformer. In fact the overall effect is to
make the response depend completely on the simple linear network of
resistors in the feedback connection. Magic!
Then, having shown us what happens when we let the amplification in the
loop become very large, the instructor threw us a curve ball in a pop
quiz. After asking us to solve the system equations as we had just been
taught, the question was, “Why, then, can’t we just pull out the
vacuum tubes and clip the leads to the output transformer, and just leave
the feedback connection in place?”
Of course he had to take us by the hand and help us answer that question,
which is why I have remembered the answer for about 67 years. That’s what
I’m doing with you now, paying my education forward.
You can’t just leave out the sensors, the perceptual input function, the
comparator, and the output function and still have the neuromuscular
control system work. A few paragraphs ago I explained why: because the
tiny bit of uncanceled disturbance is amplified enough in the forward
part of the loop to generate exactly the output we see, and produce
exactly the amount of feedback the output provides to the input quantity,
“throwing away” almost all of that loop gain. If course
if we threw away all of that loop gain the control system wouldn’t
work at all. But that’s not what is done. We couldn’t just remove the
nerve cells and muscles and still expect the living controller to control
anything. Of course you knew that, just as we on Navy Pier knew that we
couldn’t just economize by not using vacuum tubes and transformers. But
we finally learned why we couldn’t, and I assume you have, too, as
well as a few onlookers.

Now all of you are saying, “Oh, of course, naturally, that’s
obvious.” But that is now. It wasn’t obvious before, was
it?

Best,

Bill P.

[From Rick Marken (2012.12.24.1415)]

Bill Powers (2012.12.24.1215 MST)--

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

BP: Yes...

Nothing mysterious happens when the loop is closed. The forward functions do
not disappear. They are still there and are always working...

However, when we solve the simultaneous equations we find that the overall
effect of this arrangement is that the output is very nearly the inverse feedback
function of the disturbance...

RM: Yes, I see. Of course there is a forward causal path from d to o
via q.i. I guess, then, a better way to state the behavioral illusion
is that the observed relationship between d and o doesn't correspond
to the actual forward causal connection between these variables. Is
that better?

It seems to me that the observed relationship between d and o also
depends on the nature of q.i. I base this on my experience with the
area/perimeter control experiment where you find a linear relationship
between o and d when perimeter is controlled and a non-linear
relationship between o and d when area is controlled.

Which brings to the more crucial aspect of this discussion (at least
for me) and that in focusing on the causal connection between d - o
psychological researchers have ignored the fact that this relationship
exists only when there is a controlled variable involved. You said
earlier:

BP: It is perfectly possible to study the path from disturbance (S) to output
(R) using conventional methods of system analysis -- in fact that is exactly
what we do.

To which I replied:

RM: I think I have to disagree here. I don't believe you can study
this path without knowledge of the variable that is under control: the
controlled variable. Conventional methods are based on a causal model
that does not include the concept of a controlled variable. The only
aspect of conventional methods that we use is manipulation of an IV
(S) and measurement of a DV (R) under controlled conditions. This
methodology can be used to study the path from S to R in a control
system only if you know that both S and R influence the state of a
particular controlled variable.

I wonder if you disagree with my disagreement here and, if so, why. If
you do convincingly do disagree I will happily disavow all my work in
PCT over the last 32 years and go into another field, like politics;-)

Merry Xmas

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

[From Bill Powers (2012.12.25.0600 MST)]

Rick Marken (2012.12.24.1415) –

BP:> Nothing mysterious
happens when the loop is closed. The forward functions do

not disappear. They are still there and are always working…

However, when we solve the simultaneous equations we find that the
overall

effect of this arrangement is that the output is very nearly the
inverse feedback

function of the disturbance…

RM: Yes, I see. Of course there is a forward causal path from d to o

via q.i. I guess, then, a better way to state the behavioral
illusion

is that the observed relationship between d and o doesn’t correspond

to the actual forward causal connection between these variables. Is

that better?

BP: Yes. This is a somewhat subtle point and maybe that’s why I seem to
have such trouble communicating it.

RM: It seems to me that the
observed relationship between d and o also

depends on the nature of q.i. I base this on my experience with the

area/perimeter control experiment where you find a linear
relationship

between o and d when perimeter is controlled and a non-linear

relationship between o and d when area is controlled.

BP: As I remember your experiment, the subject was to keep one figure
equal in “size” to another one, so the size of the other one
was remembered and used as a reference and the size of the first one was
varied by the person. The question was, what function of the input
variables was being controlled? In other words, what does
“size” mean?

The disturbance is the side of the figure being varied by the computer
(side 1) and the effect of the output is the length of a adjacent side
(side 2). If area is being controlled, then side1 * side2 = constant, the
constant (which is used as a reference signal) being obtained from the
other figure. If perimeter is being controlled, the constant is 2*(side1

  • side2).

Our choice is then between

side1 * side2 = constant or o*d = r

and

side1 + side2 = constant or 2*(o+d) = r

This clearly makes one relationship between o and d nonlinear and the
other one nearly linear, when control is good enough to keep errors small
enough to ignore. The form of the input function is what makes the
difference.

RM: Which brings to the more
crucial aspect of this discussion (at least

for me) and that in focusing on the causal connection between d - o

psychological researchers have ignored the fact that this
relationship

exists only when there is a controlled variable involved. You said

earlier:

BP: It is perfectly possible to study the path from disturbance
(S) to output

(R) using conventional methods of system analysis – in fact that is
exactly

what we do.

To which I replied:

RM: I think I have to disagree here. I don’t believe you can
study

this path without knowledge of the variable that is under control:
the

controlled variable.

BP: What I was referring to is the conventional method of control
system analysis, about which many psychologists apparently know nothing.
I didn’t invent it; I learned it in the Navy, then again in physics
courses, then again reading textbooks on control theory. If you look at
the control system equations that we use, and the physical system they
describe, you will find nothing that disagrees with conventional ways of
setting up system equations and solving them.

RM: Conventional methods are
based on a causal model

that does not include the concept of a controlled variable.

BP:You’re thinking of methods only as they exist in psychology. I learned
these things in physics and engineering courses where they are
commonplace.

RM: I wonder if you disagree
with my disagreement here and, if so, why. If

you do convincingly do disagree I will happily disavow all my work
in

PCT over the last 32 years and go into another field, like
politics;-)

BP: Relax, your disaqreement is valid if you use “conventional”
to refer only to psychology rather than to science and engineering in
general. I speak only as a sort of general-purpose scientist, not as a
psychologist.

Anyway, I think you get what I am talking about, so we’ve about finished
with this, right?

Best,

Bill P.

[From Rick Marken (2012.12.25.1300)]

Bill Powers (2012.12.25.0600 MST)--

RM: Just got back from Les Miserables and can still barely see through
my tears. I loved it. Perfect Xmas present.

RM: Yes, I see. Of course there is a forward causal path from d to o
via q.i. I guess, then, a better way to state the behavioral illusion
is that the observed relationship between d and o doesn't correspond
to the actual forward causal connection between these variables. Is
that better?

BP: Yes. This is a somewhat subtle point and maybe that's why I seem to have
such trouble communicating it.

RM: Your communication has been just fine. It was my fault for not
correctly understanding what the behavioral illusion implies.

RM: It seems to me that the observed relationship between d and o also
depends on the nature of q.i.

BP: The form of the input function is what makes the difference.

RM: Yes, And I believe this is because the form of the input function
(which defines q.i) determines the form of the feedback function,
right?

RM: I wonder if you disagree with my disagreement here and, if so, why. If
you do convincingly do disagree I will happily disavow all my work in
PCT over the last 32 years and go into another field, like politics;-)

BP: Relax, your disaqreement is valid if you use "conventional" to refer
only to psychology rather than to science and engineering in general. I
speak only as a sort of general-purpose scientist, not as a psychologist.

RM: Yes, I am relaxed now. Thanks;-) And in particular I am much more
relaxed about Martin and Bruce's efforts to apply information theory
to understand control. I see now that it is possible to conceive of
information about the disturbance being carried by the "forward"
function that connects d to q.i to o. I can also see how learning
about this information path could tell us something about the nature
of this forward function. But I'm reluctant to jump on the
information bandwagon myself mainly because I think it's more
important (for me, anyway) to focus on the search for controlled
variables -- determining what kinds of perceptions organisms control
and how they control them -- than on learning the nature of the
forward path. One reason I have for rating the search for controlled
variables as more important than understanding the forward function
(other than the controlled variable, q.i, component of it) in a
control loop was mentioned by Bill in his earlier post ( Bill Powers
(2012.12.24.1215 MST) where he says:

BP: And the characteristics of the forward part of the loop can vary over quite
a large range without significantly changing the overall relationship
between disturbance and output.

RM: What this suggests to me is that there can be considerable
variation in the form of the forward function from d to o (changes in
gain, types of non-linearity, etc) and yet there will be good control
of q.i. What seems most important to me, in terms of achieving the
goal of understanding behavior, is understanding what is controlled --
what is q.i -- since that is rarely obvious, and not so much what are
the characteristics of the forward function that make this control
possible; many different forward functions will do.

So good luck to Bruce and Martin on applying information theory to
control. I would like to see some examples of what they find but I
think I will just continue working on the testing for controlled
variables thing.

And Merry Xmas to all.

Best

Rick

···

--
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

[From Bill Powers (2012.12.25.1425 MST)]

Rick Marken (2012.12.25.1300) --

> RM: It seems to me that the observed relationship between d and o also
> depends on the nature of q.i.

BP: The form of the input function is what makes the difference.

RM: Yes, And I believe this is because the form of the input function
(which defines q.i) determines the form of the feedback function,
right?

BP: To some extent, yes. If the output function is an integrator, the feedback function should not also be an integrator; that would result in oscillations, not control. But stability is a rather complex subject and I don't claim to be an expert about it. Fortunately, we don't have to design stable systems with rather wierd functions in them -- we're studying systems that are demonstrably stable in most cases, so while ignoring advanced stability considerations we can still find some useful things to say and do. And we have to be thoughtful and considerate -- it would not be kind of us to leave unemployed all those smart people who can do the really hard math. So you see, ignorance can be a virtue.

> BP: And the characteristics of the forward part of the loop can vary over quite
> a large range without significantly changing the overall relationship
> between disturbance and output.

RM: What this suggests to me is that there can be considerable
variation in the form of the forward function from d to o (changes in
gain, types of non-linearity, etc) and yet there will be good control
of q.i.

BP: There's a way of understanding this that makes it clearer to me. When a control system is controlling well, it keeps the error small, meaning that the maximum difference between p and r is kept very small. With a gain of 30, the difference will be only about 3% of the value of the reference signal. As disturbances vary, however, the difference can vary, and depending on the details of the functions in the loop, it can vary quite a lot as a percentage of the maximum difference, because gain changes are partly a result of nonlinearities in various loop functions.

But small variations in error are amplified in the forward part of the loop, and get into the feedback path where they can have an opposing effect on the input quantity, which is what keeps those variations from having very much effect. You can see this in models if you make changes in the gain of the output function and see how much effect this has on the output of the control system. It's pretty small. You can show that cutting the gain of the output function in half, say from 100 to 50, causes only a 1 or 2 percent change in the actual output.

RM: What seems most important to me, in terms of achieving the
goal of understanding behavior, is understanding what is controlled --
what is q.i -- since that is rarely obvious, and not so much what are
the characteristics of the forward function that make this control
possible; many different forward functions will do.

BP: I agree completely. If you can't figure out what variable is being controlled, you won't end up understanding the behavior, or much of anything about the system.

So good luck to Bruce and Martin on applying information theory to
control. I would like to see some examples of what they find but I
think I will just continue working on the testing for controlled
variables thing.

And Merry Xmas to all.

BP: Yup. Well said. Peace on earth and good will amongst all of us. That's about the limit of my religious impulse, but it's enough to matter to me. Let's hope that Martin and supporters surprise us with some really important insights that show some of our major ideas are flawed. That's about the most exciting thing that can happen in science, isn't it? Cavorite is clearly an impossible substance, so the story of its invention and use in a trip to the moon is correspondingly fascinating. Some people actually hate the idea of real breakthroughs in science, because that means somebody has to have been wrong. Hard to imagine that sort of reaction. When an important scientific belief is overthrown, we should celebrate.

Best,

Bill P.

[Martin Taylor 2012.12.25.17.19]

[From Bill Powers (2012.12.25.1425 MST)]

Rick Marken (2012.12.25.1300) --

So good luck to Bruce and Martin on applying information theory to
control. I would like to see some examples of what they find but I
think I will just continue working on the testing for controlled
variables thing.

And Merry Xmas to all.

BP: Yup. Well said. Peace on earth and good will amongst all of us. That's about the limit of my religious impulse, but it's enough to matter to me. Let's hope that Martin and supporters surprise us with some really important insights that show some of our major ideas are flawed.

I'm expecting that you will be disappointed, at least by the results of any kind of informational analysis of control systems. If there seems to be a contradiction, then what I would first distrust is the analysis, not the "major idea".

But I think it's a good kind of disappointment, conducive to peace on Earth and goodwill amongst all of us.

Thanks for your recent tutorial postings, Bill, especially the one about the "transport metaphor". That one should be archived for easy future reference.

Happy Holidays.

Martin

[Chad Green 2012.12.27.1339 EST]

BP: Let's hope that Martin and supporters surprise us with some really important insights that show some of our major ideas are flawed.

MT: I'm expecting that you will be disappointed, at least by the results of any kind of informational analysis of control systems. If there seems to be a contradiction, then what I would first distrust is the analysis, not the "major idea".

CG: Agreed. In a Kantian sense, analytical judgment leads only to contradiction, which is why I prefer the synthetical approach.

BTW, my apologies for not replying to e-mails addressed to me earlier. I have learned that, in certain contexts, the best response to a challenge question is silence, especially if the person you are trying to change is yourself.

Happy holidays!

Best,
Chad

Chad Green, PMP
Program Analyst
Loudoun County Public Schools
21000 Education Court
Ashburn, VA 20148
Voice: 571-252-1486
Fax: 571-252-1633

"If you want sense, you'll have to make it yourself." - Norton Juster