[From: Bruce Nevin (Thu 930923 09:20:54 EDT)]
Cliff Joslyn (930922) --
I was following the
information theory deabte quite closely, and I understand there's been
a resolution. Could someone (perhaps a NEUTRAL party?) summarize?
Martin has promised a detailed treatment, now in the works. He will be
back in October.
A misunderstanding was cleared up at Durango. (Nothing like interacting
where you can witness disturbances and resistance to disturbances!) Here
is some relevant prior mail:
ยทยทยท
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Date: Fri, 6 Aug 1993 07:53:47 -0600
From: "William T. Powers" <POWERS_W%FLC@vaxf.colorado.edu>
Subject: Info about disturbance
[From Bill Powers (930806.0745)]
Allan Randall (930805.1525) --
At the meeting, Martin Taylor and I cleared up the impasse about
"information in the disturbance." There's nothing like a face-to-
face discussion to cut through the crap.
As I understand it, you and Martin have been using "disturbance"
to mean the actual fluctuation in the perceptual signal due to a
change in the CEV that is induced by some external cause. Because
the CEV is explicitly represented in perception, such a
fluctuation does, of course, have an immediate and unique effect
on the perceptual signal. Knowing the organization of all the
components of the closed loop, one could deduce the amount of
that fluctuation due to the system's own output, and thus the
portion of it (unaccounted for by the system's output) that must
have resulted from some external influence. The control system
itself would not perform this calculation, but an informed
observer of the system could do so.
What Rick Marken and I have been referring to as "the
disturbance" is the external CAUSE of the fluctuation. Clearly,
the fluctuation in the CEV contains no information about what
caused it. Identically the same fluctuation in perceived light
intensity, for example, could be caused by a weak light source
close to the receptor or a powerful one far away. It could be
caused by a multiplicity of light sources, each contributing some
changing part of the total sensed flux. There is and can be no
information in the perceptual signal about the causes of
fluctuations in the CEV.
Does this take care of the problem for everyone?
Best,
Bill P.
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Date: Fri, 6 Aug 1993 18:29:02 EDT
From: randall@dretor.dciem.dnd.ca
Subject: Re: Info about disturbance
[Allan Randall (930806.1520)]
Bill Powers (930806.0745)
Hey, this posting actually clears quite a bit up! However, it raises
new concerns and also I want to be sure I've understood you. So:
As I understand it, you and Martin have been using "disturbance"
to mean the actual fluctuation in the perceptual signal due to a
change in the CEV that is induced by some external cause.
...
What Rick Marken and I have been referring to as "the
disturbance" is the external CAUSE of the fluctuation.
Just to make sure I understand, is the following a proper paraphrase?:
Disturbance(1) (Taylor & Randall): that part of the CEV fluctuation
that is not caused by the control system itself, and thus is due to an
external cause.
Disturbance(2) (Powers & Marken): the external cause of that part of
the CEV fluctuation that is not caused by the control system itself.
Assuming this is an accurate rewording, then I am happy with your
depiction of my use of the word "disturbance." If it is not accurate, then
you can ignore the rest of this posting.
It sounds like you agree that the percept contains information about
disturbance(1), but not about disturbance(2)? Is this right?
However, I do not think I see why anything changes when we switch to
definition (2). Perhaps the reason we have been talking past each other is
that you are making a distinction that I do not really see. Is there any
*meaningful* way in which disturbance(1) and disturbance(2) are different?
Isn't "that part of the fluctuation caused externally" simply a way of
describing "the external cause of the fluctuation"? How can something be
said to have information about (1) and not about (2)? Unless you can
provide some reasons to make this distinction, I have to say my arguments
about information in disturbance apply to both definitions.
If there *is* a meaningful distinction here, I'm not sure how definition
(2) fits into the arguments Rick Marken has been making. Rick and I have
been talking about reconstruction of the disturbance in a computer
simulation. What are the values Rick was looking for me to reconstruct if
he was using (2) as opposed to (1)? To Rick: do you concur with Bill's
analysis? Or do you feel that nonlinearities erase information about (1)
as well as (2)? If not, in what sense do the nonlinearities have anything
at all to do with erasing information about (2)?
... Identically the same fluctuation in perceived light
intensity, for example, could be caused by a weak light source
close to the receptor or a powerful one far away.
If they both really do give identical fluctuations, then there is no point
in making any distinction at all between them. Certainly calling this extra
aspect (which doesn't even affect the CEV) part of the "disturbance" seems
a tad bizaare, considering that it's actually the part that doesn't disturb
the CEV at all! Why call it "disturbance," then? Why include it as part
of the external cause of the fluctuation if it has no effect on the
fluctuation whatsoever? What is it even doing in our control system
diagrams, for that matter? Why do you even care enough about it to label it?
I won't say any more until I find out if I've paraphrased you correctly or
not (I haven't talked to Martin yet to get his version of things).
Anyway, it sounds like the Durango meeting was productive with respect to
the information issue. I hope it was equally useful in other areas.
-----------------------------------------
Allan Randall, randall@dciem.dciem.dnd.ca
NTT Systems, Inc.
Toronto, ON
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Date: Fri, 6 Aug 1993 21:02:43 -0600
From: "William T. Powers" <POWERS_W%FLC@vaxf.colorado.edu>
Subject: Counter-rolling; Information in d(1) about d(2)
[From Bill Powers (930806.1945)]
Rick Marken (930805.1900) --
It seems to me that the French derivation of "counter-roll"
doesn't quite capture the meaning we now use. Which set of
figures is the reference set? When I get the bank statement, I
have two representations of the state of my account: the bank's
and mine. While I'll admit that the bank probably makes fewer
errors, bank errors are not unknown. The reference condition I'm
after isn't patterned after either account: it's for the two to
agree.
----------------------------------------------------------------
Allan Randall (930806.1520) --
Just to make sure I understand, is the following a proper
paraphrase?:
Disturbance(1) (Taylor & Randall): that part of the CEV
fluctuation that is not caused by the control system itself,
and thus is due to an external cause.
Disturbance(2) (Powers & Marken): the external cause of that
part of the CEV fluctuation that is not caused by the control
system itself.
Yes, that's the difference.
It sounds like you agree that the percept contains information
about disturbance(1), but not about disturbance(2)? Is this
right?
Disturbance (1) would seem to be the difference between the state
of the perceptual signal in the absence of an external disturbing
influence and the state with that influence present. If the
reference signal is set to 10, with an integrating output
function the perceptual signal will also be at 10 with a constant
disturbing influence (zero or nonzero). Departures of the
perceptual signal from a value of 10 then indicate the presence
of some transient disturbing influence, and in the first instant
after a disturbance commences directly indicate the amount of
fluctutation due to the external influence. From then on the
contribution from external sources can be found only by solving
the system equations. Is that what you're after?
Disturbance (2) is not deducible by this means because so many
different external events could produce the same transient
fluctuation in the CEV and the perceptual signal.
However, I do not think I see why anything changes when we
switch to definition (2). Perhaps the reason we have been
talking past each other is that you are making a distinction
that I do not really see. Is there any *meaningful* way in
which disturbance(1) and disturbance(2) are different?
Yes. Behavior seen from outside the behaving system appears to
consist of responses to stimuli, where stimuli are customarily
defined not as changes in a CEV, but as changes in environmental
variables remote from the organism. These remote variables may
contribute to the state of a CEV, but they do not determine it.
In our tracking experiments, we define the disturbing variable
not as a change in the cursor position or cursor-target distance,
but as the magnitude of an independent variable that is added to
the existing cursor position, contributing to the cursor position
but not determining it (the control handle position also
contributes to it). The actual state of the CEV is not
predetermined; it arises from the operation of the system and the
influences from disturbances. It is a dependent variable.
Further, disturbance (2) is different from disturbance (1) in
that it may be multiple. In the example of steering a car, there
may be simultaneous disturbances (2) consisting of soft tires,
misaligned wheels, tilts in the roadbed, crosswinds, and so on.
The controlling system can't distinguish among these disturbing
quantities, and need not. It's necessary to make this point in
distinguishing PCT from SR psychology. The controlling system can
control by paying attention ONLY to the state of the CEV. It
needs to know only that the CEV -- that is, the perceptual signal
-- changed; it does not need to know what caused the change.
Isn't "that part of the fluctuation caused externally" simply a
way of describing "the external cause of the fluctuation"?
No. Think of steering the car. If the car veers to the left, the
CEV is experienced as changing and the system exerts a steering
effort to the right. But that veering to the left does not
indicate whether the road tilted to the left, a crosswind from
the right appeared, or the left front tire went flat. Or all
three.
How can something be said to have information about (1) and not
about (2)?
Y = a+b+c. Y is observed to change. Does this give any
information about the behavior of a, b, or c? Is there not an
infinite number of behaviors of a, b, and c that would produce
exactly the same change in Y?
If there *is* a meaningful distinction here, I'm not sure how
definition (2) fits into the arguments Rick Marken has been
making. Rick and I have been talking about reconstruction of
the disturbance in a computer simulation. What are the values
Rick was looking for me to reconstruct if he was using (2) as
opposed to (1)?
Rick was looking for you to reconstruct a, b, and c from
variations in Y (or, equivalently, variations in a perceptual
signal representing Y). This is clearly impossible using only
information in Y or the representing signal. Perhaps all of this
would have been clearer if Rick had said that there is no
information IN THE CEV about the disturbance -- that is, there is
no information in Y from which you could deduce the states of a,
b, and c -- disturbance (2). Or even more clearly, now that you
have supplied the language: there is no information in
disturbance (1) from which you can deduce disturbance (2).
If they both (two different light sources) really do give
identical fluctuations, then there is no point in making any
distinction at all between them. Certainly calling this extra
aspect (which doesn't even affect the CEV) part of the
"disturbance" seems a tad bizaare, considering that it's
actually the part that doesn't disturb the CEV at all!
From the standpoint of the control system, there is no point. But
to an external observer, the "equipotentiality" of two different
stimuli may be puzzling indeed. Why do opening a window and
letting the fire in the fireplace go out both cause the response
of putting on a sweater? Why does opening the window today cause
that response when opening it yesterday caused the person to
build a fire in the fireplace instead? Psychology has been trying
to search the environment for clues about such similar and
different effects of stimuli, without knowing about controlled
variables.
I have already made the point that a CEV can be caused to
fluctuate in many different ways. The fluctations are perceived.
Their causes, which may be continually changing, are not.
-------------------------------------------------------------
Best to all,
Bill P.
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Date: Tue, 17 Aug 1993 17:24:46 EDT
From: mmt@ben.dciem.dnd.ca
Subject: Re: Info about disturbance
[Martin Taylor 930817 17:10]
(Bill Powers 930806.0745, Allan Randall 930806.1520, Bill P 930806.1945)
I'm back at work, after a delightful meeting (with all my e-mail friends
in the flesh) and a wonderful view of parts of the USA I've never before
seen. So now it's back to electronic communication. As Dag Forsell noted,
it's easier when you can point to pictures while you talk.
I agree wholly with Bill in the cited exchange with Allan on the "information
in the disturbance". In all of our previous discussions, Allan and I
started from the premise that there is nothing in the perceptual
signal except for the state of the CEV (possibly a noisy representation
of that state, which is the basis for the computational argument). That
is what I cleared up, as Bill says, in face-to-face conversation. I had
thought that this point had been made quite clear in several postings, but
apparently it hadn't.
Allan, in his posting noted above, was not clear on the importance of the
distinction between "disturbance (1)" and "disturbance (2)", (1) being the
fluctuation that would occur in the CEV if it were not opposed by the output
of the ECS, and (2) being the external cause of that fluctuation. I agree
wholly with Bill that the distinction is very important, because whatever
perceives the disturbance (2), it is not the ECS that counters disturbance (1).
It may be an analyst; it may be another PIF that observed somewhat more
than the CEV of interest; but it is not the ECS that is the object of our
analysis.
Bill suggested in our conversation that we should use the term "fluctuation"
in the CEV to express what we wanted to say when we used "disturbance."
That may be better, but I can imagine quite a few ways in which that wording
could also lead to misunderstandings. But we can try it. I'd like, some
day, to get on with the development of the information analysis. Not now,
pressures back at work being what I knew they would be.
Martin
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Bruce
bn@bbn.com (still)