Bruce,
I have puzzled over this message of yours now for 3 days, and I still can
make no sense out of it. It seems largely incoherent.
Rather than saying this publicly, I ask you for some clarification. (After
finishing commenting your message, I realize that I really don't know
enough about what you were saying to know what to ask for clarification
about. That's really bad. But bear with me, read my comments, and see if
you can make sense of what I don't understand).
[From Bruce Nevin (980304.1530)]
(Martin Taylor 980228 17:50)--
Martin, this post to me comes in for some scrutiny here. It started as my
own private exercise. It seemed apt to Bruce Abbot's comment (below). The
intention is constructive; I hope you make it so.Bruce Abbott (980304.1150 EST)--
Bill Powers (980304.0415 MST) --
The idea of the compensating response is also behind the use of information
theory in explaining control (and Ashby dealt with this, too, long before
Martin started talking about it on this List). If the basic system you're
talking about simply transmits the sensed state of a disturbing variable to
a critical variable, then the capacity to control can be expressed in terms
of the channel capacity to carry information. This is where "requisite
variety" and all the other cybernetic -- stuff -- comes in.Ah, so this is where you got the idea that Martin was talking about the
control system "using" (extracting?) information "about the disturbance" as
the means by which control is established.No, Martin has brought this up himself. The idea that information gets into
the control system from the environment and that the control system somehow
uses that information "without extracting it" seems to be a sticking place.
Consider Martin's post to me (980228 17:50) as an example. Let's step
through it a bit at a time.
Let's start at the back end of your message.
Information theory is about measuring the capacity of channels of
communication, the number of degrees of freedom available in a channel for
making distinctions; and it is about measuring redundancy in an ensemble of
distinctions. Continuous circular-causative negative feedback control does
not involve the transmission of distinctions, though it can have the effect
of making distinctions. One can use tools of information theory to evaluate
elements of control systems and their capacities, degrees of freedom
available and so on, but no notion of information is involved in the
function of control systems.
If you were on CSGnet, as I believe you were, when this first came up, you
should know that information theory is _used_ for measuring the capacity of
channels of information, but that is not what it is _about_. It is about the
correlations among variables, just as linear correlation is. It is about
what can be learned about one variable from measurements on one or more
others. Any time there are two or more variables for which measures are
available, information theory is potentially an appropriate tool.
Now back to the beginning
(Martin Taylor 980228 17:50)
It was because originally I unwittingly took the control system's
view while Bill P and Rick were taking the analyst's view that we
got into the recently reawakened hassle about the word
"disturbance" and "information about the disturbance".[...]
why would anyone [...]
use the word "disturbance" not to refer to an effect seen
by the control system, but to refer to unknowable and irrelevant
distant sources of influence? But that turned out to be what Bill
and Rick were doing, as I eventually discovered.This clearly says that a disturbance is "an effect seen by the control
system". I don't think this is what Martin intends to say. He immediately
afterward says that a disturbance is an effect that only the outside
observer can see:from the control system's view it is not possible to construct
from the perceptual signal the waveform of the disturbing
influence, for the simple reason that the control system has
nowhere to represent such a construction,and nowhere to store
it if it could construct it.This says the disturbance cannot be "an effect seen by the control system".
Perhaps the contradiction is an unintended side effect of conflict?
I'm afraid I see no contradiction. The control system consists of static
processes and values of variables. If the processes cause one variable to
affect others, though the variable itself is not isolated within the system,
how is that a contradiciton or conflict?
But an analyst who knows the loop functions and the reference
signal can indeed recover the waveform of the disturbance signal
to within the precision of control, if allowed access to the
perceptual signal.This says that an external observer privy to internal values (themselves
not available as such to the internal point of view) can derive a certain
variable, let's call it x. The internal values needed to derive x are
measured properties of the control system (the loop functions) and its
inputs (perceptual input and reference input).
Aha. This is where the "x" came from in your other message. I thought you
were referring to the x I had used in writing the equations of the loop.
Why is x called "the waveform of the disturbance signal"? Is it similar to
the variables or `signals' that can be measured in a modelled control
system (input, reference, error)?
Yes. Precisely analogous.
In another place it is called "the
waveform of the disturbance influence". What this says is that the
unpredictably many and diverse disturbances in the environment are summed
into a single waveform as though it were a single phenomenon in the
environment.
And so it is.
I have to agree with Bill (980301.1123 MST)
Martin, the CCEV is a figment of your imagination.
It is a figment of whoever is perceiving something. To my mind, it is totally
ridiculous to assert that some perceived observables are in some way more
real than others.
There is no single
environmental variable that corresponds to the perceptual signal. There are
only the component input variables. I've never liked this idea of a CEV,
because it seems to sneak naive realism back into the theory even though it
is basically denied by the theory. It's like saying, "Sure, I know that the
taste of lemonade isn't really there in the mixture of acids, salts, and
oils -- but let's pretend it's really there anyway." That's all it is, a
pretense.
Why is "acid" "salt" and "oil" acceptable as a variable, but "the taste of
lemon" not? It is Bill that is putting naive realism into the theory. All
we know is that we perceive "the taste of lemon" to a certain degree. The
"lemon taste" perception knows nothing of acid, salt, and oil. And neither
do most of the people who enjoy that taste.
The perceptual signal is not "complex." It is a simple scalar. There is no
CEV and no CCEV, except in the eye of the external analyst.
The perceptual signal is scalar precisely because it is possible for the
various components (if such there be, they not being perceived) to be
combined through one function. Remember, the CCEV has the function in the
external environment that the comparator has in the other half of the
control loop. It is where two influences, one internal to the loop and
one external, are combined.
Maybe this is encouraged by the presence of a variable d in experiments and
demos. In an artificially constrained lab situation like a tracking
experiment you can identify one significant disturbance that is introduced
by a computer program and ignore all the others, such as variable drag on
the mouse, variable traction of the mouse ball, variable hand pressure,
variable muscle fatigue, dirt, and so on. (A game joystick reduces these
but does not eliminate them entirely.) In any other situation, the only
practicable way to identify the sum of disturbances is to meter the
countervailing output of the control system and subtract it from the state
of the controlled variable; d is whatever is left. But note well, d is only
useful to demonstrate the nature of control to an external observer, or to
measure how well a controlled variable (CV) is being controlled. As far as
the control system is concerned, d does not exist as such.
That I don't understand. You simply cannot describe a control system properly
without dealing with its two inputs and its two outputs. If you omit one,
the control system is something different.
The variable x is derived from factors internal to the control system.
Actually, it _may be_ derived from factors internal to the control system.
That is a fact that has stuck like a bone in the throat of Rick and Bill
for six years, and they won't admit it. Where it comes from is, as Bill
keeps saying, Fd1(d1) + Fd2(d2) + ... In other words, from a lot of sources
through a lot of channels. When we deal with the interactions among control
systems, we have to deal with those sources and channels. Not when we deal
with a single control system by itself.
The
only justification for including "disturbance" in its name is that it is
correlated with the sum of externally measured disturbances of the
perceptual input.
Huh? Isn't that just what it is. A thing is usually not talked about as
"correlating" with itself.
But the notion that "information about the disturbance"
is somehow getting inside the control system is exactly what is being
contended. This tendentious phrase begs the question.
Look. The fundamental, initial contention was that the purpose of control
was to reduce or eliminate the "information about the disturbance" within
the organism--to act as an active shield so that the organism can sustain
its organization in the face of a thermodynamically hostile world.
Now maybe I've missed a process of debate by which Martin backed
defensively into inventing this term in order to make clear that he was not
talking about the sources of disturbance.
Three (at least) assumptions here. (1) "process of debate." There was none.
It was necessary, six years ago, to say that we were not talking about the
sources of disturbance. To say it once should have been enough. The so-called
"debate" consists of repeated assertions by Bill and Rick that we ought to
have been talking about the sources of disturbance, and that being the case,
our arguments were unfounded because if we were talking about the sources of
disturbance, the control system could not know anything about them--which
was why in the first place we had no concept that anyone could conceive of
talking about the sources of disturbance in this context.
(2) "backed." When two people use the same word to mean different things
and a confusion results, it is a good idea to decide on using different
words for the two things. That is what Bill and I did, for all that he
now denies it.
(3) "defensively." I'm not clear what assumption the use of this word implies,
but whatever it is, the assumption is unwarranted.
(4) "invented." I did not invent the term "information" or "disturbance."
I did fail to appreciate at first that to Bill the word "disturbance" implied
a source of disturbance rather than an effect of disturbance. But the
phrase "information about X" has been around for a long time, and was given
a precise definition by Claude Shannon over 50 years ago.
That is your claim in response to
Bill (citations at the top of the present post):Martin Taylor has confused this issue by introducing a new definition of
the disturbance, which he calls the "disturbance signal". This "signal" is
not actually a separate physical entity. It is merely the part of the state
of the cv that is not accounted for by the effect of the system's own
output. If the output is momentarily zero, then the disturbance signal is
simply the state of the cv itself.I think that Martin has _always_ been talking about the independent
influence of the disturbance on the cv, whereas you have been taking him to
be talking about the disturbance source. He has attempted to remedy this
situation by introducing terms to distinguish these two variables. If one
knew the function relating the disturbance source to its influence on the
cv, and the environment function giving the influence of the output on the
cv, one would be able to reconstruct the waveform of the disturbance source
within the limits of the system's ability to control.The point is that there is no there there. An external analyst can derive d
by subtracting o from the state of the CV, and can derive x from internal
characteristics of the loop,
An external analyst can also derive d by looking at the sources of disturbance
and the transfer functions that relate them to the CCEV. The point at issue
was always whether anything about the time variation (waveform) of d could
be determined from knowledge of things that the disturbance sources do not
influence, plus a knowledge of p. Bill and Rick made strong statements that
this was not possible. It is only now that the contrary has been shown
quite explicitly that these questions about the reality of d and of the
CCEV are being brought up. Bill says he always had doubts about the CCEV,
but he was happy enough in his writing about it, until very recently.
but d and x do not exist without the external
observer making measurements and performing calculations on those
measurements. By contrast, i, r, e, o, and the input and output functions
around internal portion of the loop exist whether or not the external
analyst measures them (assuming control occurs and that our model of
control is correct) and the only "calculation" involved in their derivation
is the analog computing done by the loop functions, including the comparator.
How does "o," in particular, have any more claim to existence than "d"?
Both are influences on the CCEV, both are in the same domain. If "d" does
not affect the taste of lemon, because the taste of lemon is "really"
(really, how naive can you get?) only acid, salt, and oils, then how can
"o" affect the taste of lemon. They are of the same kind, and equally
measurable.
Resuming Martin's post:
This seems to me to be incontrovertible proof that information
about the disturbance waveform is "in" (to use Rick's word)
the perceptual signal.This is a rather startling conclusion. It jumps from "the disturbance
waveform" to "information about the disturbance waveform".
A technical moment. If A can be determined precisely from B, then the
mutual information metween A and B is the uncertainty of A. That is what
Rick's word "in" means. All the information about A is "in" B. Likewise,
some of the information about B is "in" A. How much is "some?" Precisely
the uncertainty of A. There is no startling conclusion, but a plain
statement of mathematical fact. If A cannot be precisely recovered from
a knowledge of B, but its uncertainty is reduced by knowing B, then the
mutual information between them is the amount of uncertainty reduction.
It says that
information about d is incontrovertably proven to be "in" the perceptual
input, because the externally-measured sum of disturbances d corresponds
directly to the internally-derived value x. The reason, which is not
stated, seems to be "otherwise where could the information about d have
come from?"
Huh? I don't understand this comment.
The criciticsm of that statement is
sometimes couched in language like "the control system
doesn't know its own functions." True, it doesn't. It
embodies them--to touch on another current thread.No substantive point is made here. There has been some inchoate discussion
of how the form of input functions and output functions, as evolved through
reorganization, constitutes one form of "knowledge" meaning skill or
know-how. That bears no relation to the value x abstracted from loop
functions and input values.
Nor this one.
Neither does it demonstrate that the control system extracts the
disturbance waveform separately in generating the output signal.
It doesn't. There is only one output signal, and again (looking
from the viewpoint of the control system) where would the control
system represent the extracted disturbance waveform if it did
extract it from the perception of the changing CEV, the changes
in which are caused by a combination of the output and the
disturbance signals? There is no place in a canonical Elementary
Control System for storing extra stuff like that.This reaffirms that nothing about the disturbance is accessible to the
control system.
Accessible to? No. Used by? Well, the influence of the disturbance affects
the perceptual signal, and is countered by the output. I would say that
even without knowing the internal circuitry, that would strongly suggest
"used by." When one knows the internal circuitry, the point becomes manifest.
From the analyst's viewpoint, one can demonstrate the information
about the disturbance waveform to be available from the perceptual
signal.The derived value x, and "information about it," is available to the
external analyst from i, r, and loop functions. (I take Martin's word for
this, I haven't followed the derivation.) It is not available to the
control system. The tendentious phrase "disburbance waveform" is so much
arm waving.
All I can say to this is "Oh, Pooh." You use words, but I guess I can say
that to use words is just so much finger waggling at a keybourd, and make
as much sense as this.
Here is where Martin makes the claim about the control system "using"
information "about the disturbance" (see quote from Bruce Abbott
(980304.1150 EST) at the beginning):The control system uses this information, but it doesn't
extract it.There is no evidence that the control system uses x or "information about
x" or "information about d" and we have just agreed that there is no way
for the control system to access x or "information about" x.
You really are on a roll here, with uninterpretable and evaluative
comments, aren't you? I really don't understand what is going on in your
mind.
This is an
assertion without evidence. The arms are really flying now. Why?One might indeed begin to believe in magic if it were
_not_ possible to extract the disturbance waveform from the waveform
of the perceptual signal, since the perceptual signal is the _only_
access the control system has to anything about the external world.Aha. Here's the rub. Martin cannot see how x, a value that he sees to be
"embodied" in the control system, can correspond to d, similarly "embodied"
in the environment,
Neither your x nor d is embodied in the control system. Both are measurable
quantities. I don't know where you got that notion from, or why you
attribute it to me.
unless information about d is communicated into the
control system through the communication channel afforded by the perceptual
input signal. He believes the alternative has to be to say that the
information (the correspondence of x to d) gets there by magic. And here's
the penalty for failure to make this explanatory principle stick:But luckily, the system proves to be physical and non-paradoxical,
after all.If information about d in the environment is not transmitted to become
embodied as x inside the control system, then the control system must be
paradoxical or it must have some non-physical attributes. I asked Martin to
state clearly and explicitly how negative feedback control is paradoxical,
absent "information about the disturbance influence/signal waveform." I
don't believe he can.
Well, I did that, once you made clear what the question was.
Martin's explanation for the correspondence of x to d is that it gets there
because information about the disturbance is communicated by linear
causation from the environment into the organism.
I thought from the first half of your message that x _was_ d. Now I don't
know what you mean by x. What is this "x" in the control system, and how
does it correspond to "d"?
The control system does
not extract this information, but it uses it. (Now *that* seems to me to
qualify as paradox.) Without this information from the environment, control
would not be possible. It follows from this explanation (like it or not)
that information from the environment causes behavior.
Why? An equal, if not greater "cause" (a term I dislike because of its
connotations) is the waveform of the reference signal.
I'll attempt another explanation. This should really be expressed by
integration of differential equations, but that is not my strength. (Yet.)There is another explanation for why x corresponds to d, namely, continuous
feedback control. The control loop is resisting d.
Exactly!!!!! Now, why, having come to this grand conclusion, do you find
my mathematical approach to be "arm-waving." I guess to say "it is just
control" is much more precise. No arm-waving there. But there is when we
discuss how control actually functions. Come, now. I'm sure you can
produce better rhetoric than that, with your linguistic background.
The control system does not use "information about d". It only uses the
difference between r and i. The difference between r and i happens to
correlate to the difference between the actual state of the CV and the
desired state, the state it would be in if it were being controlled
perfectly. This is why there appears to be information about d inside the
control system.
Well, you got that part right. (I assume that by "i" you mean what Bill
calls "qi", the value of of the CCEV).
However, the control system only knows i (not cv or d),
It doesn't "know" i. It has a signal value that varies with i, as an
external analyst knows.
and
the external observer can only infer the desired state of the CV, and hence
d, by observing the current state of o and the current state of the CV,
both of which are measurable in the environment.
The external observer has to know what the perceptual input function is,
in order to construct a measurement tool that can observe the CCEV. To
the external observer, nothing is "real" except the observer's own
perceptions, just as to the subject, the CCEV is real because it is being
perceived. If the external observer can measure qi, having a tool that
produces, say, 3*x1 + 5*x2^2 (x1, and x2 being variables he knows how to
perceive), then the external observer can alos measure the forces acting
on x1 and x2, and thereby determine Fe1(o1), Fe2(o2), Fd1(d1) and Fd2(d2),
from which he can determine Fe(o) and Fd(d). There's no justification for
an a priori assertion that one set of variables is measurable and another
isn't.
Inverse correspondence of o to d is a product of negative feedback control.
No variable called "information about d" is required.
I'd like to know where I said it was required for the operation of the
control system. I have said that it is required for understand the operation
of the control system. I said that to tease Rick in a message I posted in
1992, and I think that's why he reacts so strongly against the idea whenever
it comes up. But I was half serious.
To borrow an
expression from LaPlace, we do not have need of that hypothesis.Rick (980223.2000) said much the same in reply to you
(Bruce Abbott (980223.2005 EST)
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_!!
Actually, Rick is wrong about this. d is uncorrelated with e because of
the control (not, as Bill says, because of noise in the system). And
it is wrong to say d and e are completely uncorrelated. All the practical
measurements give positive correlations ranging around 0.1. I'm not
sure that my analysis is quite right, because it seems too simple, so
I'm holding it back until I can convince myself or find my mistake, but
if I am right, a control system with a pure integrator output function
has a correlation between e and d that is equal to the control ratio
(the ratio between the fluctuation amplitude in the perception with and
without control).
Which raises another point. If "d" (or I should say Fd(d)) is unmeasurable
and has no independent existence, how is it used--as Rick and Bill say it
is--to determine what the changes in p would be in the absence of control?
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).
It is this assertion that disturbs my controlled perception that the
discourse should be at least historically accurate. Whenever he says it,
I am tempted to give him the lie. Sometimes I fall to the temptation, and
we go into another round of nonsense, like this one. The fact that d
can be precisely determined from a knowledge of e (or of p) is irrelevant
to Rick, because the following argument is more convincing than the
mathematical demonstration that the argument fails, or than a simulation
demonstration that the mathematics works in practice.
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.There are two pairs of values that correspond closely: internally, control
brings the value of the perceptual input i toward correspondence with the
reference input r; externally, control brings the value of the behavioral
output o toward opposition to the net effect of all disturbances, d, so as
to cancel them out. Depending on your point of view, you can say the
control system intends the internal correspondence or the external one,
they are two aspects of a single phenomenon, control. It is the loop of
circular causation that enables that derived value x
I'm still mystified as to what this "derived value X" might be.
to correspond to the
sum of disturbances d, and not the transmission of information from the
environment into the organism. The value x does not exist without someone
measuring attributes of the control system that it cannot measure for
itself, and making calculations with those measured values. There is no
thing, no function, that at any point can sense or access such information,
and there is no function that can make use of it. "The control system has
nowhere to represent such a construction,and nowhere to store it if it
could construct it." The external analyst who can has no effect on the
process of control.I suggested that the slip about a disturbance being "an effect seen by the
control system" was a symptom of conflict. I think the conflict arises in
the struggle to integrate two belief systems, one associated with Martin's
work with information theory in applied psychology, the other associated
with Martin's learning of PCT. This is a difficult process. It is not easy
to acknowledge that one's favorite tools have no application.
If there is conflict, it is hidden from me. Usually, I can detect the
symptoms of conflict in myself, even if I can't go up a level and resolve
the conflict.
Information theory is about measuring the capacity of channels of
communication, the number of degrees of freedom available in a channel for
making distinctions; and it is about measuring redundancy in an ensemble of
distinctions. Continuous circular-causative negative feedback control does
not involve the transmission of distinctions, though it can have the effect
of making distinctions. One can use tools of information theory to evaluate
elements of control systems and their capacities, degrees of freedom
available and so on, but no notion of information is involved in the
function of control systems.Information theory has been a favored source of metaphor
There's no "metaphor" about information theory, any more than there is
about Laplace transforms. It's just a mathematical way of describing the
relations among measurements.
because it
promises a link between physiology and psychology, so that experiments in
one field can be seen as shedding light on the other. Control theory
provides an actual basis, not a merely metaphorical one, for integrating
physiology and psychology (and more).
If information theory were a metaphor, there might be some basis of
comparison. But as I said (quite forcefully and more than once) in earlier
rounds of this discussion, if Laplace transform theory is a competitor
against control theory, then so is information theory. But neither is.
Both are ways of analysis, both can be applied to control systems. Laplace
transform theory applies only to linear control systems, information
theory to all. The issue isn't whether it applies, but whether the
application is useful.
I have had misgivings about posting earlier versions of this. I thought
perhaps it should only be my own private exercise in trying to understand
Martin more clearly. Martin is a proud man, and justifiably so for many
achievements I am sure. He does not like to be made to seem ridiculous any
more than the rest of us. I wish fervently that he would work his way
through this contradiction and stop making himself seem ridiculous.
Now I ask you, what is it that makes me seem ridiculous? Perhaps I am less
concerned about my "seeming" than you think, and more about the precision
of the argument and the advancement of the theory. I don't mind seeming
ridiculous if the ridiculous position is correct. But if it is not
correct, I'm more concerned about that than about the fact that holding
the position made me seem ridiculous. I need more than arm-waving dismissal
to convince me of the error of my ways.
His
actual and potential contributions are too important to be wasted in
thrashing.
But they will not be realized, if every attempt to contribute is met by
specious and ever-shifting reasons why I must be wrong. Look at Bill,
yesterday. I made an argument that in the simplest control system with
an integrator output function the S-R experimenter would find an imprecise
behavioural illusion. Bill says this is wrong on the grounds that it
wasn't proved for more complex and non-linear control systems (presumably
they give more precise behavioural illusions). Now, my analysis may well
be wrong. But Bill's way of showing it is truly ridiculous. Rather than
thinking through the problem, he finds that the analysis doesn't apply
somewhere where the situation is likely to be even worse! He _must_
show that I am wrong in any contribution I attempt, without spending time
to find a valid reason I am wrong.
My thinking recently has been that I should start to ignore Bill's comments,
and just get on with developing the theory in the directions that interest
me.
Anyway, I guess I haven't been too clear on what questions I want you to
answer. That's probably because I am not too clear on what you were trying
to say. Much of it makes no sense to me, and much of the rest is based on
a misunderstanding of "information."
Martin