Disturbing Disturbances

[From Fred Nickols (980224.1955 EST)]

Rick Marken (980223.1000) --

responding to Bruce Abbott (980223.0955 EST)--

Bruce:

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

Rick:

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

<snip>

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.

This is all proving very helpful to me so let me introduce a somewhat
different example to broaden my grasp of the concept. And let's go back
to my Navy days, on board a destroyer.

I've got a gun mount aft on the fantail, loaded with servomotors,
amplifiers, receiver-regulators, motor-generators, and all kinds of
mechanical and hydraulic means of moving the gun mount around.

Further forward, roughly amidships and down one deck, is a plotting room
with a computer that calculates and issues gun orders. The ordered position
from the computer is a signal to the gun mount. The ordered position
represents a reference condition. The gun mount has a comparator, a
receiver-regulator. If the actual position and the ordered position are
different, an error signal results and the motors move the gun mount to
align the two, that is, bring the ordered and actual positions into
correspondence -- and, try to keep them in correspondence (because the
ordered or reference position is usually changing).

The actual position of the gun mount is never, except fleetingly if at all,
in perfect correspondence with the ordered position. The gun mount "hunts"
or "oscillates" about the point of correspondence (error being necessary to
the functioning of a servomechanism, or so the engineers told me, and also
because of "lag" -- that is the rate of change in the changing ordered or
reference position; in other words, it takes the gun mount a little time to
catch up to the ordered position, by which time it has changed again.
Moreover, if it does catch up and stay in correspondence with an ordered or
reference condition that has a stable rate of change, if that rate of change
changes, the gun mount once again "lags" (or "leads" the ordered position if
the signal reverses direction/polarity). As I've mentioned before, torque
and stability are factors in how well the gun mount will "track" the ordered
position, but let's set that aside as momentarily irrelevant.

What I've described so far seems to me to be a "closed-loop" control system
that is perfectly consistent with PCT (the closed-loop control system is the
gun mount, not the entire fire control system -- as Mary pointed out a while
back, the overall fire control system is not a closed loop). So far, so
good...I hope.

Now, let's introduce a disturbance. The gun mount is out on the starboard
quarter (right rear for you landlubbers, moving slowly forward (to the
left). The ship now rolls to starboard, meaning that the gun mount moving
left must now also move up to counteract the effects of gravity. Let us
treat those effects as a disturbance, an external factor that affects the
correspondence between the gun mount's reference (ordered) position and its
perceived (actual) position.

If I understand what Rick was telling me earlier, this disturbance will have
no effect on the correspondence between the actual and the ordered position
of the gun mount (just as the wind will have no effect on my perception of
the alignment of the automobile I'm driving with my preferred position of
centered in the lane). Further, as I understand PCT, this is because the
control loop is a closed-loop and everything is "live" and happening
simultaneously.

To borrow Rick's words from the beginning of this post, "variations in
disturbance variables [gravity, in the case of the gun mount example] are
not reflected in variations of the controlled variable [the position of the
gun mount] you will be able to stop fighting so hard against PCT and start
acting as its true champion."

Do I have it right?

Regards,

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

[From Rick Marken (980225.1540)]

Fred Nickols (980224.1955 EST)

To borrow Rick's words from the beginning of this post, "variations
in disturbance variables [gravity, in the case of the gun mount
example] are not reflected in variations of the controlled variable
[the position of the gun mount] you will be able to stop fighting
so hard against PCT and start acting as its true champion."

Do I have it right?

Except for the non-sequiter about "fighting so hard against PCT"
I'd say that's exactly right.

Bruce Abbott (980225.1520 EST) --

I think it's fascinating that Bruce A.has hit on exactly the
same strategy Martin used several years ago to try to bring
lineal causality back to closed loop control. Like Martin, Bruce
uses the idea that information about d (which Bruce likes to call
"signal variations caused by d") is used as the basis for
generating the outputs that compensate for d. Like Martin, he
says that I believe in magic if I don't accept this explanation.
And like Martin, he tries to give the impression that I am the only
one (certainly not Bill Powers or anyone else who _really_
understands control systems like Bruce A. does) who disagrees
with his lineal causal analysis of control system operation (never
mind posts like [Bill Powers (980225.1320 MST].

I guess there's really no where to go besides "information
about d" or "signal variations caused by d" to preserve the
causal foundations of conventional psychology once you get to
a certain point in your understanding of control theory. Once
you get to this point, you either accept the fact that lineal
causality doesn't apply to the behavior of purposive systems
(ie. you become a PCTer) or you make up ways for it to keep
applying to these systems (even in the face of overwhelming
evidence to the contrary, like the low correlations between
d and cv between cv and o and the very high correlation
between d and o).

I think the only problem with this lineal causality fantasy is
that it will keep those who embrace it from doing the kind of
research we need in the study of purposive behavior: research
aimed at determining _controlled perceptual variables. But maybe
not. We shall see.

Best

Rick

···

--
Richard S. Marken Phone or Fax: 310 474-0313

[Martin Taylor 980227 03:45]

Rick Marken (980225.1540)

Oh, how quickly we forget! Or at least how quickly Rick forgets:-)

Rick Marken (980224 13.30)

+Martin Taylor (980224 14:45) to Bill Powers --

···

+
+>> 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 the record, I don't think this statement is incorrect.
+I think it is precisely correct.

Rick Marken (980225 15.40)

Like Martin, Bruce
uses the idea that information about d (which Bruce likes to call
"signal variations caused by d") is used as the basis for
generating the outputs that compensate for d. Like Martin, he
says that I believe in magic if I don't accept this explanation.
And like Martin, he tries to give the impression that I am the only
one (certainly not Bill Powers or anyone else who _really_
understands control systems like Bruce A. does) who disagrees
with his lineal causal analysis of control system operation (never
mind posts like [Bill Powers (980225.1320 MST].

On Tuesday Rick accepts that p is a function of d, given that the
loop functions and the reference level don't change, and on Wednesday
he returns to his old position that it isn't. Talk about controlling
a perception against even the strongest disturbances:-)

And I would be mildly interested in how Rick thinks the post he cites
by Bill Powers is relevant to the issue.

Martin

[From Bill Powers (980227.0814 MST)]

Martin Taylor 980227 03:45--

On Tuesday Rick accepts that p is a function of d, given that the
loop functions and the reference level don't change, and on Wednesday
he returns to his old position that it isn't. Talk about controlling
a perception against even the strongest disturbances:-)

Neither Rick nor I accepts that p is a function of d. P is a function of d
and o, where o is a function of r and p, so we have

p = f(d,r,p)

in which, in general, we cannot assume p to be separable.

You have a strange way of defining "is a function of." The way I learned
the meaning of "function," if y is a function of x, then given x I can
compute y. If y is a function of x1, x2, and x3, then it is not a function
of x1 alone, x2 alone, or x3 alone: I must know all three x's to compute
the value of y. In fact, if I know only x1, the value of y is indeterminate.

The _ceteris paribus_ convention is inapplicable, because there is no _a
priori_ or most-likely value we can assume for reference signals in
general, nor is there any general basis for choosing one solution when the
input function is multiple-valued (as it most often is).

Best,

Bill P.

[From Bill Powers (980227.0814 MST)]

Martin Taylor 980227 03:45--

On Tuesday Rick accepts that p is a function of d, given that the
loop functions and the reference level don't change, and on Wednesday
he returns to his old position that it isn't. Talk about controlling
a perception against even the strongest disturbances:-)

Neither Rick nor I accepts that p is a function of d. P is a function of d
and o, where o is a function of r and p, so we have

p = f(d,r,p)

in which, in general, we cannot assume p to be separable.

You have a strange way of defining "is a function of." The way I learned
the meaning of "function," if y is a function of x, then given x I can
compute y. If y is a function of x1, x2, and x3, then it is not a function
of x1 alone, x2 alone, or x3 alone: I must know all three x's to compute
the value of y. In fact, if I know only x1, the value of y is indeterminate.

I suppose that if I said "I was at the lake today" and you knew my wife
had been there with me, you would say "No you weren't; you were
not there alone." Did I say that p was a function of d alone? No. I said
that p was a function of d, r and the loop properties, and even explicitly
presented the function for a linear system, as follows:

p = d/(1+G) + Gr/(1+G)

That's what I wrote. Then I said that if r was constant, p was pure function
of d. Rick even acknowledged explicitly that he believed me to be correct,
so I think it is a bit, shall we say, "odd" that you can assert of Rick's
behalf that he doesn't believe it.

The _ceteris paribus_ convention is inapplicable, because there is no _a
priori_ or most-likely value we can assume for reference signals in
general, ..

What that has to do with anything? The stated condition was that the
reference value was (temporarily) constant, not that it had some specific
value. You are really working hard not to accept the notion that p
is a function of d (i.e. F(d), me not being Rick) and r, aren't you?
Why?

nor is there any general basis for choosing one solution when the
input function is multiple-valued (as it most often is).

Are you saying (today) that p can take many values for a given condition
of the Controlled CEV (i.e. a particular set of sensory values, along with
their histories if the PIF is a time-function such as an integrator or
differentiator)? That's what a muliple-valued function is. If
p = P(x1, x2, x3...), the function P is multiple valued if a single set
of values of x1, x2, ... can lead to several values of p.

One simple function that has this property is a square root. If p = sqrt(x),
then p has two possible values. Are you asserting that it most often is
true that perceptual functions are like that?

Let's repeat, in unison:

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.

Bill Powers (980224.1755 MST)
What's this "disturbance signal?" You must mean Fd(d), not d.

Yes, as we agreed to use the words, that's it. But I realize I'm not Rick,
because if I were, then I could use "disturbance" and "d" here, without
disturbing any of your controlled perceptions.

Martin

[From Rick Marken (980227.1920)]

Martin Taylor (980227) --

I said that p was a function of d, r and the loop properties,
and even explicitly presented the function for a linear system,
as follows:

p = d/(1+G) + Gr/(1+G)

That's what I wrote. Then I said that if r was constant, p was pure
function of d. Rick even acknowledged explicitly that he believed
me to be correct,

Again for the record, I never knowing acknowledged that the
above formula is correct. In fact, I think it must be wrong.
Could you please show the derivation, Martin.

Best

Rick

···

--

Richard S. Marken Phone or Fax: 310 474-0313

[From Bill Powers (980228.0308 MST)]

Bill Powers (980227.0814 MST)--

I suppose that if I said "I was at the lake today" and you knew my wife
had been there with me, you would say "No you weren't; you were
not there alone."

I don't understand how this illustration applies. If your wife is in
different places each time you make this statement, the value of the
statement would not be affected. But that's not true if your wife's
location can affect the value of the statement.

Did I say that p was a function of d alone? No. I said
that p was a function of d, r and the loop properties, and even explicitly
presented the function for a linear system, as follows:

p = d/(1+G) + Gr/(1+G)

That's what I wrote. Then I said that if r was constant, p was pure function
of d.

Yes, but r is not in general constant. You're trying to treat a partial
derivative as if it is no different from a full derivative. A partial
derivative can be obtained only under artificially constrained conditions,
and it is valid ONLY under those conditions.

The _ceteris paribus_ convention is inapplicable, because there is no _a
priori_ or most-likely value we can assume for reference signals in
general, ..

What that has to do with anything? The stated condition was that the
reference value was (temporarily) constant, not that it had some specific
value.

But the particular level at which the reference value is constant makes a
difference in the value of p for any given value of d. Just saying it's
constant is not enough.

Anyway, as Rick points out, your formula is not correct for the present
discussion. It should be written as

p = Fd(d)/(1+G) + Gr/(1+G)

Since the control system does not sense the form of Fd, there is no way for
it to know what d is. If we assume that Fd is a multiplier of 1, as we
often do when making some other kind of point, you would be right. But Fd
is not, in general, 1.

You are really working hard not to accept the notion that p
is a function of d (i.e. F(d), me not being Rick) and r, aren't you?
Why?

Because the question is what the control system can know, not what the
omniscient observer can know. Saying p is a function of d is NOT the same
as saying p is (the same) function of Fd(d). And saying it is a function of
Fd(d) would be correctly only if the output were not having an effect on p
at the same time: actually,

p = Fi(Fd(d) + Fe(o)).

It is possible for p to be changing while d is constant, because o can be
changing while d is constant.

P is a function -- Fi -- of the input quantity qi, otherwise known as the
CEV. There is no way to tell, from observing p alone, whether the output or
the disturbance is changing, or whether both are changing, or whether the
forms of Fd and Fo are changing. Thus p is not a unique indicator of either
d or o. The only way to make any deductions about d is from outside the
control system, where the form of Fd can be observed as well as d itself.
That information is not available to the control system; it is available
ONLY to the omniscient external observer.

nor is there any general basis for choosing one solution when the
input function is multiple-valued (as it most often is).

Are you saying (today) that p can take many values for a given condition
of the Controlled CEV (i.e. a particular set of sensory values, along with
their histories if the PIF is a time-function such as an integrator or
differentiator)? That's what a muliple-valued function is.

No, it's not. If p = x^2, then CEV = x^2. p is the same for x = 10 and
x = -10. The CEV is not x, but x^2. The control system controls only p. It
doesn't care whether the value of p is obtained from one possible set of
inputs or a different set that yields the same value. The CEV is defined
not by some particular state of the environmental variables, but by the
state of the perceptual signal.

If
p = P(x1, x2, x3...), the function P is multiple valued if a single set
of values of x1, x2, ... can lead to several values of p.

One simple function that has this property is a square root. If p = sqrt(x),
then p has two possible values.

No, p can only be positive. This is a bad example because x can't be
negative. That's why I chose x^2 above.

Another simple function that has the property of multiple values is

p = x1 + x2.

We can have the SAME value of p for an infinity of pairs x1,x2. I think
you've got the problem reversed in your head. It's not that the same
environment can produce two values of the controlled perception; it's that
the same value of the controlled perception can represent a multiplicity of
states of the environment. The controlled perception is the given; the
state of the environment needed to produce that given perception is what is
multiple-valued. Many different states of the environment can produce the
same perception; this is why a _single_ perception can't be used to deduce
the state of anything in the environment.

Are you asserting that it most often is
true that perceptual functions are like that?

Yes, but not in the reversed sense you're talking about. In general, most
perceptions are functions of multiple input variables, and so the state of
a given perception can't be used to deduce the actual state of the input
variables.

Best,

Bill P.

[Martin Taylor 980228 17:35]

Rick Marken (980227.1920)]

Martin Taylor (980227) --

I said that p was a function of d, r and the loop properties,
and even explicitly presented the function for a linear system,
as follows:

p = d/(1+G) + Gr/(1+G)

That's what I wrote. Then I said that if r was constant, p was pure
function of d. Rick even acknowledged explicitly that he believed
me to be correct,

Again for the record, I never knowing acknowledged that the
above formula is correct. In fact, I think it must be wrong.
Could you please show the derivation, Martin.

OK, though perhaps you are already satisfied, since Bill P (980228.0308 MST)
wrote:

+It should be written as p = Fd(d)/(1+G) + Gr/(1+G)

where Fd(d) is what you and I have been calling "d"--the influence of the
disturbing variable on the CCEV, which we long ago agreed to call the
disturbance signal.

Anyway, here's the derivation. The assumptions are (1) that all functions
around the loop (and, if you want, also the coupling of the disturbing
variable to the CCEV) except the output function are unit transforms
(their output equals their input), (2) that the output function is linear,
and can be represented by "G", which is either a simple multiplier or,
if the output function is a time function such as a (possibly leaky)
integrator, G is the Laplace transform of the output function, (3) the
influence on the CCEV is the sum of the influence of the output and the
influence of the disturbance variable. For this I'll use the notation
you prefer, which so disturbs Bill when I use it--but since this message
is directed to RM, and not Bill P, I'll use the RM notation "p=o+d".

Let's start there.

p = o+d

o = Ge

e = r-p

which, when put together, give

p = d + G(r-p) or p = d + Gr - Gp

Collecting terms in p, we get

p*(1+G) = d + Gr

Dividing both sides by (1+G),

p = d/(1+G) + Gr/(1+G)

which is the form you wanted derived. To keep Bill happy, I'll acknowledge
that if I were writing this for him, I would use Fd(d) where I used "d"
in the above. And I would say stuff like "the influence of the output
on the CCEV is Fe(o)" rather than the simple "o" I used above. But we worked
with the assumption of unit transforms, so we can ignore thse complications.

But I rather think you will understand the visual simplification one gets
when one uses single letter variables and treats the functions as unit
multipliers, since they don't matter to the analysis. That's why you do the
same when you write equivalent formulae, after all, isn't it?

Martin

[From Bill Powers (980301.0940 MST)]

Martin Taylor 980228 17:35]

+It should be written as p = Fd(d)/(1+G) + Gr/(1+G)

where Fd(d) is what you and I have been calling "d"--the influence of the
disturbing variable on the CCEV, which we long ago agreed to call the
disturbance signal.

Martin, I never agreed to call anything the "disturbance signal." I
grudgingly agreed that you probably meant something by it, but I would
never use it. It doesn't mean anything to me. It's especially meaningless
when you realize that "Fd(d)" is itself shorthand for the true general
case, in which multiple disturbances contribute to the state of qi via
multiple paths, each embodying its own disturbance function. Just think of
steering the car when it is simultaneously affected by tilts in the

As I recall, this whole line of argument sprang up after I had asserted
that a control system can control its input quantity without knowing
anything about what is causing disturbances. This was in opposition to the
Ashby model of control, in which the control system senses the cause of the
disturbance and generates a compensating output that affects the controlled
variable oppositely to the direct effect of the disturbance. You seemed
then to have a belief that control-system design requires knowing what
kinds of disturbances are going to appear, and that led into the
"information about disturbance in perceptual signal" argument.

You're dealing only in special cases here, which is hardly a basis for
drawing general conclusions. In general, Fd is NOT a unity transform. It
represents the physical connection between the disturbing variable
(example, the position of the experimenter's end of the rubber bands) and
the controlled quantity (example, the position of the knot). Fd, in
general, is not even a linear function, nor is there any requirement that
it be single-valued. There is no requirement that the control system even
know what Fd is.

You want to equate Fd(d) to d so you can defend your statement that there
is enough information in the perceptual signal from which to reconstruct
"d" -- meaning, of course, Fd(d), and NOT d. Even if you prove your case
with Fd set to be a unity transform, your argument becomes invalid for any
forms of Fd EXCEPT the unity transform, when you try to show that you can
reconstruct d.

To see how vacuous your point has become, all you have to do is write out
the environmental equations, not even considering the loop.

qi = Fd(d) + Fe(o)

We have here a controlled variable that is the sum of effects from two
sources: the disturbing variable and the output variable. Obviously, we can
solve for Fd(d):

Fd(d) = qi - Fe(o)

So the value of your "disturbing signal" is simply the difference between
the observed value of qi and the calculated effect of output on qi. Your
"signal" is simply the amount of qi that is unaccounted for by the effect
of the output.

Another and more general way to write this equation is

qi = Fd1(d1) + Fd2(d2) + ... Fdn(dn) + Fe(o)

This is the case where multiple disturbing variables act through multiple
paths. We can still solve this equation for the "disturbing signal":

Fd1(d1) + Fd2(d2) + ... Fdn(dn) = qi - Fe(o).

Now it becomes clear that we can't even backtrack to a unique disturbing
function. ALL that the control system can sense is qi, its own input
quantity. That is all it needs to know about. It does not need to know what
is disturbing qi, or through what path, in order to work. And that is the
point I was trying to make lo those many years ago.

Best,

Bill P.

[Martin Taylor 980305 16:30

259 unread messages to deal with, among which, this:

Bill Powers (980301.0940 MST)]

Martin Taylor 980228 17:35]

+It should be written as p = Fd(d)/(1+G) + Gr/(1+G)

where Fd(d) is what you and I have been calling "d"--the influence of the
disturbing variable on the CCEV, which we long ago agreed to call the
disturbance signal.

As I recall, this whole line of argument sprang up after I had asserted
that a control system can control its input quantity without knowing
anything about what is causing disturbances. This was in opposition to the
Ashby model of control, in which the control system senses the cause of the
disturbance and generates a compensating output that affects the controlled
variable oppositely to the direct effect of the disturbance. You seemed
then to have a belief that control-system design requires knowing what
kinds of disturbances are going to appear, and that led into the
"information about disturbance in perceptual signal" argument.

The last time you started making these assertions, I took the trouble to
dig into the archives and post the relevant messages from the thread in
question. You then stopped saying things like this. Will you stop again,
or should I see if I can dig up the archives again?

(Parenthetically, I don't remember Ashby saying what you claim, but you
have probably read him more recently than I have, so I'll grant that you
could well be right.)

Now it becomes clear that we can't even backtrack to a unique disturbing
function.

We know, knew, and never disputed that. We assumed it from the beginning
of that whole "tar-baby" thread. It was _never_ at issue, despite
the loooong messages devoted to trying to ensure that other CSG readers
might believe the contrary.

ALL that the control system can sense is qi, its own input
quantity. That is all it needs to know about. It does not need to know what
is disturbing qi, or through what path, in order to work. And that is the
point I was trying to make lo those many years ago.

A point you might have needed to make to other readers. Never to me. My
argument was directed entirely differently. I believe you know this.

Anyway, there's no point in playing back the history of old threads. Can
we take it from here on in that I am well aware that no ECU needs to,
or could conceivably detect "what is disturbing qi, or through what path."
Can you please assume, even if you don't believe, that I have no interest
in that question, and never have had, regardless of what you have written
about what I believe, believed, and tried to show?

My analysis of individual control loops has always been limited precisely
to those waveforms that are inputs to the loop, outputs from the loop, or
signals within the loop. No other signals _could possibly_ be part of the
analysis of the behaviour of the single control loop by itself.

That is the position from which I started in 1992, and that is the
position I hold to. If to say this is "trying to prove that I am right, by
hook or by crook," so be it. Prove that this position is wrong, and I'll
change it. So far, all your (I must say) strong criticisms have been
devoted to trying to prove that my position is correct, while asserting
that I hold and held some other position. I don't like that.

When there are multiple interacting control loops in the analysis, then
it is possible that the effects of one enter into the perceptual signal
of another. Then, the analysis of the interacting set _may_ involve
consideration of some of the paths whereby a source of disturbance affects
qi (the value of the CCEV).

(Reading ahead in the message backlog, I see Rick also asserting that I
am holding to, and defending, a posoition in which I don't believe (Rick
Marken (980301.1050)):

+We see people
+"reacting" to verbal and non-verbal stimuli all the time. It
+looks like these "disturbances" cause (or select) behavior.
+This is the view of behavior that Bruce A., Martin, and Jeff V.
+are defending in the "Disturbing disturbances" thread....
+... Bill and I are trying
+to show that this is not the case; that lineal cause-effect
+doesn't apply to the behavior of control systems: cause-effect
+and control of input are not equivalent.

I wonder why Rick thinks it necessary to repeat this falsehood so often--
at least I can assert with assurance that it is false in my case, and I
have seen little evidence of its truth in the case of the others being
splattered by the same tar brush. Anyway, as I say, I wonder why Rick
says this. Is it one of his tests for what perception Bruce, Jeff, and I
are controlling? If so, I can assure him that I am at least controlling
for "not being perceived by others as believing behaviour to be due to
lineal cause and effect."

I suppose it is possible that Rick believes that the fact p and o (the
output signals from the loop) are mathematically precise functions of r
and d (the input signals to the loop) threatens the position that control
is of the input. Perhaps he would not worry so much if he looked a
bit more closely at the formulae, which show output p to be dominated by
input r and output o to be dominated by input d. Control is indeed control
of perception to a reference value. None of which contradicts anything I
have written, and none of which say I believe more about cause and effect
than that if there is an effect that has a cause, the cause must come first.

Martin