Information theory in control (was: Information Theory Misleads About Control)

[Martin Taylor 2012.12.08.13.58]

[From Rick Marken (2012.12.08.1045)]

I'm moving this to a new subject head which I think better reflects
the subject of the debate.

No, it misleads about the subject of the debate, if one can actually have a useful debate about whether 2+2=4.

Martin Taylor (2012.12.07.16.15])--

RM: I'm afraid that you have fallen completely for the behavioral illusion.
MT: Them's fightin' words, buddy!

MT: Are you trying to say that the equations we usually use to describe the operation of a control system are wrong? It certainly sounds like it. Or are you saying that there is no signal path from sensory input through the perceptual function, the comparator, the output function and the environmental feedback path?

RM: No, I'm saying that the idea that variations in the output of a
control system are based on information about the disturbance to the
input to the system is an S-R concept. And the idea that S causes R in
a control system is the behavioral illusion.

That's not the behavioural illusion as I have understood it.

The behavioural illusion is that the pattern of output movements that counter a particular disturbance reflect properties of the internal circuitry of the brain, whereas they actually reflect properties of the environmental feedback path.

The behavioural illusion has nothing to do with the FACT that all the path elements in a closed loop are individually S-R, or with the FACT that the value of the output at any moment after, say, a unit step change in the value of a disturbance can be computed precisely, given the properties of the paths and functions in the control loop. That's S-R, it's PCT, and it is not a behavioural illusion.

  S (disturbances to a
controlled variable) are not the cause of R (outputs that also affect
the controlled variable. This "behavioral illusion" -- the appearance
that disturbances are the cause of outputs when they are not -- are
derived from the solution of the simultaneous equations for a negative
feedback control system.

That doesn't make sense. The control equations have two independent variables, the reference input and the disturbance input. If the reference input stays constant, the ONLY influence on the dependent variables such as the input quantity, the perceptual variable, or the output quantity, is the disturbance. Variation in S (the disturbance) is the cause of variation in R (R could be any one of the other variables). That what is derived from the solution of the simultaneous equations for a negative feedback system. It is the opposite of what you say is derived from them.

Bruce Abbott (2012.12.07.1830 EST)--
RM: You are assuming that the only way for information about the disturbance to appear at the output is for this information to have gone through the organism.
BA: How else could it get there? Magic?

RM: Actually, there is no "it" (information) to get there.

???

  Is "information" an object that can be slung around like a ball? Shannon definition: Information is a change in uncertainty (or entropy, to use the word he came to use because Von Neumann pointed out the identity between the entropy equations and the uncertainty equations).

  The
information about the disturbance in output is in the mind of the
observer who sees a correlation between disturbance and output.

Correct. But how do you reconcile this with your previous sentence that says it isn't there at all? If the observer can see it, isn't it as much there as anything else in the (supposed to exist) real world that gives rise to a perceptual signal?

  So
when I say that there is information about the disturbance in the
output of a control system I just mean that we do see a correlation
between disturbance and output when a system is controlling a
controlled variable. But that doesn't mean that there is really
something called "information" that is telling the system how to vary
its output in a way that compensates for the disturbance.

What do you mean by "telling". That sounds as though you want a new perceptual signal somewhere in the system, and there isn't one. It sounds as though "information" should be an actor of some kind. It sounds as though you think of information as an object, rather than a relationship. All of that is rather weird.

  And we know
from the equations of PCT that there is no such information becaust
the observed relationship between disturbance and output depends not
on characteristics of the organism but on characteristics of the
feedback connection between system outputs and controlled variable.

We know that, yes, but how does the comment relate to what you said earlier. that there is no informational relationship between output and the controlled variable. On the one hand you say there isn't, and on the other you say words that mean that there is.

You make no sense.

RM: One way to show, sans mathematics, that information about the
disturbance could not possibly be the cause of outputs that keep a
variable under control is by changing the feedback connection from
output to controlled variable during a tracking task. For example, if
cv = k*o+d then if you vary the value of k you are varying the gain of
the feedback connection from output to controlled input (cv).

OK.

  When
you do this you will find that the subject is perfectly capable of
keeping cv at a reference value (assuming you don't vary k too
quickly)

OK

  but that there is no longer any information about the
disturbance in the output;

What a strange non-sequitur. How do you get from your premise to your consequence? There seems to be no logical route from one to the other.

  that is, there is no longer any correlation
between o and d. That's because information about d was never
necessary. All that was needed was a perception of the state of cv
which could be continuously compared to a reference resulting in
variations in o that prevent the cv from moving very far from the
reference.

"that is, there is no longer any correlation between o and d." There is a correlation but it is continuously varying. That's different from no correlation. And you are perfectly aware, I presume, that there can be zero correlation even when there is the mutual information is substantial. You must also be aware that if x = f(y,z) the fact that z varies does not mean that there is no mutual information between x and y. In spite of the fact that you must know these things, that's what you do seem to be saying.

"That's because information about d was never necessary." That is a personal statement for which you have never provided evidence other than your own repeated statements. "What I say three times is true", but Lewis Carrol's world is luckily not the one we live in.

"All that was needed was a perception of the state of cv which could be continuously compared to a reference resulting in variations in o that prevent the cv from moving very far from the reference." Exactly so. Why, then are you so persistent in your assertions about there being no information from the disturbance waveform in the output signal?

RM: By making believe that outputs are driven by information about the
disturbance you are not only ignoring a fundamental insight of PCT
(that the apparent causal link between disturbance and output is an
illusion)

Again you deny the validity of the control equations. You shouldn't really do that if you want to be taken seriously.

but you are also ignoring the central feature of control
that is the reason why the illusory causal connection between
disturbance and output exists (when the feedback function is
constant): the controlled variable.

???

RM: I care about you guys getting this right -- understanding that
information about the disturbance is not what "guides" the output in
control

True, it doesn't do any "Guiding". It is just one way of analysing the mechanism of control. Has anyone on CSGnet ever suggested that "information about the disturbance is ... what "guides" the output in control" ? What determines the output are the signal values and the functions.

  -- only because I think not getting this right takes your eye
off what I think is the main "ball" in PCT: controlled variables.

Actually, controlled variables are the essential element in the whole informational analysis. They must be, because it is all about control. You can't do the informational or any other analysis if you "take your eye off" that ball.

This
is the revolutionary and powerful new concept that is provided by PCT
(compared not only to conventional psychology but to other
applications of control theory to behavior as well).

No complaints here. Except that William James might dispute the "revolutionary" word, if he were alive to do so.

When you
understand that behavior is organized around the control of perceptual
variables -- controlled variables -- and you see how this explains the
variations in "outputs" that we see as behavior, then it reorients (or
_should_ reorient) the goal of research in behavioral science

Yes.

  from the
search for the information that guides output to a search for the
perceptual variables that organisms control.

No.

Once again, you try to put a straightjacket not only on how control systems are allowed to be analyzed, but also on the research into the ramifications of perceptual control theory.

I have never understood why your personal wish only to seek the variables a particular person is controlling at a particular time should disallow other people from researching other consequences of the fact of perceptual control.

Martin

[From Rick Marken (2012.12.08.1830)]

Martin Taylor (2012.12.08.13.58)_-

RM: One way to show, sans mathematics, that information about the
disturbance could not possibly be the cause of outputs that keep a
variable under control is by changing the feedback connection from
output to controlled variable during a tracking task. For example, if
cv = k*o+d then if you vary the value of k you are varying the gain of
the feedback connection from output to controlled input (cv). When
you do this you will find that the subject is perfectly capable of
keeping cv at a reference value (assuming you don't vary k too
quickly) but that there is no longer any information about the
disturbance in the output; that is, there is no longer any correlation
between o and d. That's because information about d was never
necessary. All that was needed was a perception of the state of cv
which could be continuously compared to a reference resulting in
variations in o that prevent the cv from moving very far from the
reference.

MT: "that is, there is no longer any correlation between o and d." There is a
correlation but it is continuously varying. That's different from no
correlation. And you are perfectly aware, I presume, that there can be zero
correlation even when there is the mutual information is substantial. You
must also be aware that if x = f(y,z) the fact that z varies does not mean
that there is no mutual information between x and y. In spite of the fact
that you must know these things, that's what you do seem to be saying.

RM: So apparently if I develop a demonstration where I show that a
person can control nearly perfectly even though the correlation
between output and disturbance is close to 0.0 this would not weaken
your belief in the relevance of information theory. Nevertheless, I'll
develop it anyway, just for the fun of watching the verbal
calisthenics you (and Bruce) will go through to defend an information
theory view of control.

MT: "That's because information about d was never necessary." That is a personal
statement for which you have never provided evidence other than your own
repeated statements.

RM: I've now have published two papers that present data directly
relevant to this claim:

Marken, R. S. (1980) The Cause of Control Movements in a Tracking
Task. Perceptual and Motor Skills, 51, 755-758.

and more recently

Marken, R. S. and Horth, B. (2011) When Causality Does Not Imply Correlation:
More Spadework at the Foundations of Scientific Psychology,
Psychological Reports, 108, 1-12

You should read that 2011 paper; it (like much of my work) was
inspired by you. Thanks!

MT: Has anyone on CSGnet ever suggested that "information
about the disturbance is ... what "guides" the output in control" ? What
determines the output are the signal values and the functions.

RM: So of what use is the information?

MT: Actually, controlled variables are the essential element in the whole
informational analysis. They must be, because it is all about control. You
can't do the informational or any other analysis if you "take your eye off"
that ball.

RM: Well, that's a relief. So how does the informational analysis
explain the results of the area/perimeter control experiment that I
described, where the relationship between output and the same
disturbance differs depending on what perception is being controlled?
How does information theory explain the change in the information
about that disturbance so that in one case it informs the subject that
o should be proportional to -d and in the other that o should be
proportional to 1/d.

RM: When you
understand that behavior is organized around the control of perceptual
variables -- controlled variables -- and you see how this explains the
variations in "outputs" that we see as behavior, then it reorients (or
_should_ reorient) the goal of research in behavioral science

MT: Yes.

RM: from the
search for the information that guides output to a search for the
perceptual variables that organisms control.

MT: No.

MT: Once again, you try to put a straightjacket not only on how control systems
are allowed to be analyzed, but also on the research into the ramifications
of perceptual control theory.

RM: But if information doesn't guide output in a control system then
why study how it does that?

MT: I have never understood why your personal wish only to seek the variables a
particular person is controlling at a particular time should disallow other
people from researching other consequences of the fact of perceptual
control.

RM: The only thing I'm trying to discourage is research aimed at
understanding an illusion. But if studying illusions is what plucks
your magic twanger then go for it. You've got a LOT of company.

Best

Rick

···

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

from Fred Nickols (2012.12,08.2042 AZ)

I'm sitting here with my wife watching and listening to a Rod Stewart Xmas special on PBS, sipping a little Drambuie and enjoying some quiet time. I figure I understand maybe a third of this thread but I also think I'm learning something so thanks to all you real thinkers on this list. Thanks to you all most of all for your tolerance and forbearance of one another. In the end that is what makes this list hum and what makes it of inestimable value. Happy Holidays y'all and I hope the new year is as rich in thought and ideas as this one has been. We are blessed to have such good company.

Fred Nickols

···

Sent from my iPad

On Dec 8, 2012, at 19:36, Richard Marken <rsmarken@GMAIL.COM> wrote:

[From Rick Marken (2012.12.08.1830)]

Martin Taylor (2012.12.08.13.58)_-

RM: One way to show, sans mathematics, that information about the
disturbance could not possibly be the cause of outputs that keep a
variable under control is by changing the feedback connection from
output to controlled variable during a tracking task. For example, if
cv = k*o+d then if you vary the value of k you are varying the gain of
the feedback connection from output to controlled input (cv). When
you do this you will find that the subject is perfectly capable of
keeping cv at a reference value (assuming you don't vary k too
quickly) but that there is no longer any information about the
disturbance in the output; that is, there is no longer any correlation
between o and d. That's because information about d was never
necessary. All that was needed was a perception of the state of cv
which could be continuously compared to a reference resulting in
variations in o that prevent the cv from moving very far from the
reference.

MT: "that is, there is no longer any correlation between o and d." There is a
correlation but it is continuously varying. That's different from no
correlation. And you are perfectly aware, I presume, that there can be zero
correlation even when there is the mutual information is substantial. You
must also be aware that if x = f(y,z) the fact that z varies does not mean
that there is no mutual information between x and y. In spite of the fact
that you must know these things, that's what you do seem to be saying.

RM: So apparently if I develop a demonstration where I show that a
person can control nearly perfectly even though the correlation
between output and disturbance is close to 0.0 this would not weaken
your belief in the relevance of information theory. Nevertheless, I'll
develop it anyway, just for the fun of watching the verbal
calisthenics you (and Bruce) will go through to defend an information
theory view of control.

MT: "That's because information about d was never necessary." That is a personal
statement for which you have never provided evidence other than your own
repeated statements.

RM: I've now have published two papers that present data directly
relevant to this claim:

Marken, R. S. (1980) The Cause of Control Movements in a Tracking
Task. Perceptual and Motor Skills, 51, 755-758.

and more recently

Marken, R. S. and Horth, B. (2011) When Causality Does Not Imply Correlation:
More Spadework at the Foundations of Scientific Psychology,
Psychological Reports, 108, 1-12

You should read that 2011 paper; it (like much of my work) was
inspired by you. Thanks!

MT: Has anyone on CSGnet ever suggested that "information
about the disturbance is ... what "guides" the output in control" ? What
determines the output are the signal values and the functions.

RM: So of what use is the information?

MT: Actually, controlled variables are the essential element in the whole
informational analysis. They must be, because it is all about control. You
can't do the informational or any other analysis if you "take your eye off"
that ball.

RM: Well, that's a relief. So how does the informational analysis
explain the results of the area/perimeter control experiment that I
described, where the relationship between output and the same
disturbance differs depending on what perception is being controlled?
How does information theory explain the change in the information
about that disturbance so that in one case it informs the subject that
o should be proportional to -d and in the other that o should be
proportional to 1/d.

RM: When you
understand that behavior is organized around the control of perceptual
variables -- controlled variables -- and you see how this explains the
variations in "outputs" that we see as behavior, then it reorients (or
_should_ reorient) the goal of research in behavioral science

MT: Yes.

RM: from the
search for the information that guides output to a search for the
perceptual variables that organisms control.

MT: No.

MT: Once again, you try to put a straightjacket not only on how control systems
are allowed to be analyzed, but also on the research into the ramifications
of perceptual control theory.

RM: But if information doesn't guide output in a control system then
why study how it does that?

MT: I have never understood why your personal wish only to seek the variables a
particular person is controlling at a particular time should disallow other
people from researching other consequences of the fact of perceptual
control.

RM: The only thing I'm trying to discourage is research aimed at
understanding an illusion. But if studying illusions is what plucks
your magic twanger then go for it. You've got a LOT of company.

Best

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