Uncertainty, Information and control part I: U, I, and M

[MartinT]

[Martin Taylor 2013.02.27.23.25]

From Adam Matic 2013.02.28.0000cet]

      (Martin

Taylor 2013.02.27.11.13)

      So, you're saying that information analysis might prove

useful for exploring development of complex, stable input
functions, reorganization in the input part and such
mysteries?

I really don't know where in complex control structures information

analysis might prove to be useful. The only place I originally was
thinking of using it was to find the best possible control that
could be achieved in a single simple noiseless control loop. All
control loops have some transport lag, which means that the the
effect of the output on the CEV at time t0 is based on the history
of the disturbance values only up to time t0-lag. Any change of the
disturbance value after that cannot be compensated. The sequential
statistical properties of the disturbance determine the uncertainty
of how much the disturbance is likely to have changed over the lag
time, and hence the upper bound on the possible quality of control.

Channel capacity limits also come into play, as, for example in the

integrator (if that is the form of the output function) which has a
channel capacity of, if I remember the number correctly, G*1.43…
bits/sec. That capacity translates into a time-slowed effect of
abrupt disturbance changes, which is a kind of distributed lag.

That's really all I was originally intending to use information

analysis for. The recent discussion about noisy channels opens up
quite another area where it might be useful, but I hadn’t wanted to
deal with that initially. Maybe the answer is as simple as that the
effect of noisy channels is a reduction in their channel capacity,
which would make the analysis the same as for the inherently
capacity-limited integrator output function.

And now you are suggesting yet other possible areas of application.

It would be nice if information analysis turned out to be useful in
such areas, but it’s pure speculation, at least in my mind, as to
whether that ever will be the case. (On the other hand, Rupert
mentioned Tononi a few days ago. Although I do not agree with
Tononi’s information-theoretic way of partitioning or modularizing
complex networks in the general case, it might well be applicable in
this particular case. Who knows?)

      MT: One of

the neat things about the information-theoretic approach is
that it is just as applicable when the variables in question
are discrete as it is when they are continuous. In your
example, “better precision” has to mean that there is less
uncertainty about the actual state of the project – is Joe
likely to finish his module in time to meet Ben’s timeline for
fitting it into the overall design of the bridge? Asking Joe
might make you less uncertain of his answer, increasing your
precision of perception of the project state (though not
necessarily your accuracy of perception, Joe being an eternal
optimist

AM:

      Nice. Asking Joe, then, might not be the best strategy for

improving control. An analogy to spatial averaging would be to
ask a lot of people what they think about where the project
is, or add some other “objective” sources of information.
Temporal averaging would be to just look at week reports
instead of daily reports.

      There are trade-offs to both. In spatial averaging, you

need a complex input function. In temporal averaging you loose
the ability to react quickly.

"The Wisdom of Crowds"?

Martin

[chadtgreen]

[Chad Green 2013.02.28.10:22 EST]

AM: So, you're saying that information analysis might prove useful for
exploring development of complex, stable input functions,
reorganization in the input part and such mysteries?

MT: I really don't know where in complex control structures information
analysis might prove to be useful. The only place I originally was
thinking of using it was to find the best possible control that could be
achieved in a single simple noiseless control loop.

CG: Martin, what about self-information? Where does this fit in your tutorial message?

Best,
Chad

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

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

[MartinT]

[Martin Taylor 2013.02.28.10.30]

···

On 2013/02/28 10:22 AM, Chad Green wrote:

[Chad Green 2013.02.28.10:22 EST]

CG: Martin, what about self-information? Where does this fit in your tutorial message?

What do you mean by self-information? Internal structural redundancy, or something else? If you mean structural redundancy, it doesn't apply to the kinds of thing I was discussing, but it might be interesting in connection with the structure of the complex of control units, such as is described by HPCT. If you mean something else, I must ask you to explain.

Martin

[rsmarken]

[From Rick Marken (2013.02.28.2030)]

Martin Taylor (2013.02.27.15.31)–

      RM: I have seen no evidence that information theory

contributes anything other than obfuscation to our
understanding of control, particularly the controlling done by
living systems. I think that, like the GLM, it’s just the
wrong tool for understanding control.

MT: Then don't try to use it, or to learn enough about it to be able to

discuss why you might be right or wrong.

      RM: Well, it would be more interesting if you showed how information theory can contribute to our understanding of control. But you seem to believe you already have so I guess the phrase "evidence that information theory

contributes to our
understanding of control" means different things to each of us.

        RM: But I don't see what calculating the uncertainly gets

you.

MT: I know you don’t. And won’t.

RM: Well, I certainly won’t if you don’t tell me what it gets you. But I guess I’m supposed to see what it gets you after reading your treatise on information theory. So I guess I am hopeless.

        There is a huge contrast between information theory and

control theory glasses.

        MT: How would we test for whether the absolute difference in

level or the angle between the ellipses is the controlled
variable?

        RM: One way is the way I did it: using modeling. If the

model with absolute distance doesn’t should reduced control
with separation (which, of course, it wouldn’t) then try a
different controlled variable.

MT: I don't understand this. It isn't English and none of my attempts at

correcting it into English make any sense.

RM: I built one model that controls the distance between vertical positions of cursor and target (the controlled perception p1 = c-t, where c is vertical cursor position and t is vertical target position) and another model that controls the angle between c and t [the controlled perception p2 = arctan((t-t’)/(c-t’)), where t’ is the position of the target in the cursor column; so t-t’ is the base of a triangle with length equal to the separation distance – your independent variable – and c-t’ is the length of the adjacent side so the ratio is the tangent of the triangle – (t-t’)/(c-t’)].

So there are two models controlling two different perceptions, p1 and p2. The behavior of the model controlling p2 seems to behave very much like the subject when t-t’, which is determined by the separation between target and cursor, is varied. So that’s evidence that what is controlled is p2 rather than p1. This is a version of the test for the controlled variable because you are seeing which definition of the controlled variable results in better predictions of the actual behavior.

MT: My problem with distinguishing the two suggested possibilities for

the controlled variable (vertical location difference and angle of
imaginary connecting line between the ellipses) is that I can’t
think of a way of doing The Test that would distinguish them.
Everything you do to disturb the vertical separation also disturbs
the angle to the same proportionate extent. That’s why I asked if
you could think of such a test.

RM: And I described such a test above. Your little experiment is actually a lovely way to test whether the variable controlled in a compensatory tracking is p1 or p2. There are other possibilities that may give even better results. But your experiment provides one nice way to test which of these two perceptions is actually under control.

MT: You are good at thinking of critical experiments for purposes such

as this. I hoped you would think of one now, because I couldn’t.

RM: I would like to see the data from this experiment – the actual time traces – and try to fit some models to it before going on to other experiments. The experiment you have programmed is just fine for a first shot at testing to see what variable is controlled in this task, I think. If you could put some of the data for different separations into an excel file I could see how well the different models (controlling different perceptions) fit the data. This could be fun.

Best

Rick

···

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

[MartinT]

[Martin Taylor 2013.02.28.23.51]

[From Rick Marken (2013.02.28.2030)]

        Martin Taylor

(2013.02.27.15.31)–

          RM: I have seen no evidence that

information theory contributes anything other than
obfuscation to our understanding of control, particularly
the controlling done by living systems. I think that, like
the GLM, it’s just the wrong tool for understanding
control.

        MT: Then don't try to use it, or to learn enough about it to

be able to discuss why you might be right or wrong.

      RM: Well, it would be more interesting if you showed how

information theory can contribute to our understanding of
control.

I said I would produce part 2 of the tutorial to do that, but, s I

also said, it will take time. I thought I could do it all in a
couple of days, but rewrites of Part 1 took a couple of months, and
rewrite 5 (or was it 6) wasn’t finished when it was inadvertently
sent off. However, if you understand M(X:Y) and M(X:XHistory) that
will be a good start toward understanding Part 2 when it is done.

    RM. There is a huge contrast between

information theory and control theory glasses.

I repeat that this is an impossible statement, since in the context

of control systems, both glasses are worn together.

                MT: How would we test for

whether the absolute difference in level or the
angle between the ellipses is the controlled
variable?

                RM: One way is the way I did it: using modeling. If

the model with absolute distance doesn’t should
reduced control with separation (which, of course,
it wouldn’t) then try a different controlled
variable.

        MT: I don't understand this. It isn't English and none of my

attempts at correcting it into English make any sense.

      RM: I built one model that controls the distance between

vertical positions of cursor and target (the controlled
perception p1 = c-t, where c is vertical cursor position and t
is vertical target position) and another model that controls
the angle between c and t [the controlled perception p2 =
arctan((t-t’)/(c-t’)), where t’ is the position of the target
in the cursor column; so t-t’ is the base of a triangle with
length equal to the separation distance – your independent
variable – and c-t’ is the length of the adjacent side so the
ratio is the tangent of the triangle – (t-t’)/(c-t’)].

      So there are two models controlling two different perceptions,

p1 and p2. The behavior of the model controlling p2 seems to
behave very much like the subject when t-t’, which is
determined by the separation between target and cursor, is
varied. So that’s evidence that what is controlled is p2
rather than p1. This is a version of the test for the
controlled variable because you are seeing which definition of
the controlled variable results in better predictions of the
actual behavior.

I don't see that you have tested anything related to human

performance by doing this. Do you know what it is about the two
models that makes them behave differently? My problem in
understanding is that whatever variation you make in angle is ipso
facto a proportionate variation in the difference in level (and
vice-versa), so an appropriately parameterized model should behave
the same whichever is chosen as the controlled variable. Maybe I’m
missing something about the difference between the two models. In
any case, making a couple of models does not perform “The Test for
the Controlled Variable”, which you have always claimed (and I
believe) is the best way to tell what correlates closely with the
true controlled variable.

      RM:  Your little experiment is actually a lovely way to test

whether the variable controlled in a compensatory tracking is
p1 or p2.

It is a pursuit tracking study, but that doesn't really matter. Each

run ends with a 10-second very slow compensatory segment to estimate
the resolution.

      RM: I would like to see the data from this experiment -- the

actual time traces – and try to fit some models to it before
going on to other experiments. The experiment you have
programmed is just fine for a first shot at testing to see
what variable is controlled in this task, I think. If you
could put some of the data for different separations into an
excel file I could see how well the different models
(controlling different perceptions) fit the data. This could
be fun.

I attach about 100 .csv files that feed directly into excel if you

tell it that the separator is “comma”. They are laid out with six
data columns, of which only three are populated, because I haven’t
yet programmed a model and an optimizing routine, the results of
which are supposed to go into the remaining columns.

Here's how the experiment was run and the meaning of the entries.

The files have names like Sp2Sep180_3.csv or Sp3Sep450Bg9_2.csv. Sp
means speed choice out of 5 possibilities. The speeds are kind of
arbitrary and the actual speed identified with the possibility was
changed from day to day as I continued programming. That means the
Sp1 probably means the same for different files done on the same
day, particularly if they are close in time. Files in the “Old Data”
folder are likely to be less consistent than files in the “data”
folder. Sep means lateral pixel separation between the centres of
the target and cursor ellipses, both of which were 20 pixels wide
and 10 pixels high. Bg refers to the number of interfering randomly
oriented short lines on the screen. To get the actual number,
multiply by 100 for files created before about 6pm today (Feb 28)
and by 20 for later files – I found that if there are more than
about 200, the frame rate goes down. The lines were an attempt at
trying to disturb the orientation perception without disturbing the
vertical offset perception, but I don’t think it works.

In the spreadsheet, there are numbers at the top. In the earlier

files (perhaps all of those in “Old Data” and maybe more) those
numbers represent variances. Later they represent RMS values. It
should be easy to tell which is which.

The actual runs consisted of 5 seconds of run-in that is not

recorded, 4096 samples (to make it easy to do FFT anaysis) of
pursuit tracking at the speed given in the file name – but you can
analyze the target column to find actual velocities and spectrum,
which I have not done – and 600 samples of compensatory tracking,
always at the same disturbance speed. (Having just checked my code,
I note that the measure of RMS error called “static”, which refers
to this section, is wrong. It misses the first 100 samples of
pursuit tracking and includes 100 trailing zeros, so you will have
to recompute that number if you want to use it).

I guess that's it. have fun, and ask me if you run into problems.

I’m still learning the “Processing” language, and using this
experiment as the medium in which to learn it.

Martin

Old Data1.zip (763 KB)

data1.zip (244 KB)

[amatic]

[From Adam Matic, 2013.03.01.17.20cet]

(Martin Taylor 2013.02.27.23.25)

I really don't know where in complex control structures information

analysis might prove to be useful. The only place I originally was
thinking of using it was to find the best possible control that
could be achieved in a single simple noiseless control loop. All
control loops have some transport lag, which means that the the
effect of the output on the CEV at time t0 is based on the history
of the disturbance values only up to time t0-lag. Any change of the
disturbance value after that cannot be compensated. The sequential
statistical properties of the disturbance determine the uncertainty
of how much the disturbance is likely to have changed over the lag
time, and hence the upper bound on the possible quality of control.

AM:

I remember reading something along those lines in your posts, but I didn’t quite understand it at the time. It still seems like there should be a simpler way of stating the same, especially the last sentence.

By the way, limits of control are dependent on d, only given that r is stable, right? If r somehow varies with changes in d, perhaps some variance in p could be reduced.

Adam

[rsmarken]

[From Rick Marken (2013.03.01.0815)]

Martin Taylor (2013.02.28.23.51)–

      RM: I built one model that controls the distance between

vertical positions of cursor and target (the controlled
perception p1 = c-t, where c is vertical cursor position and t
is vertical target position) and another model that controls
the angle between c and t [the controlled perception p2 =
arctan((t-t’)/(c-t’)), where t’ is the position of the target
in the cursor column; so t-t’ is the base of a triangle with
length equal to the separation distance – your independent
variable – and c-t’ is the length of the adjacent side so the
ratio is the tangent of the triangle – (t-t’)/(c-t’)].

MT: I don't see that you have tested anything related to human

performance by doing this. Do you know what it is about the two
models that makes them behave differently? My problem in
understanding is that whatever variation you make in angle is ipso
facto a proportionate variation in the difference in level (and
vice-versa), so an appropriately parameterized model should behave
the same whichever is chosen as the controlled variable. Maybe I’m
missing something about the difference between the two models. In
any case, making a couple of models does not perform “The Test for
the Controlled Variable”, which you have always claimed (and I
believe) is the best way to tell what correlates closely with the
true controlled variable.

RM: OK, I can see that our differences run far deeper than a disagreement about information theory. So thanks for the data but I won’t have time to do anything with it for a while. And I think it would be better if you did whatever you were going to do with it first and present it so I (we) can see what you have in mind. You went to all the trouble to program up this little study so you must be interested in using it to test you theory of behavior. So I’d like to see your tests before I set aside the time to do mine.

Best

Rick

···

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

[MartinT]

[Martin Taylor 2013.03.01.13.10]

Probably. Maybe you can think of easier wording. Something along the

lines of “If it takes some time for the effect of a control action
to arrive at the CEV, the disturbance value may have changed. If the
disturbance is changing only slowly, control could still be good,
but if it is likely to change much during that lag time, control
will not be very successful.”?
Looking only at a single control system, there’s no way r could
covary with d. But if r were to be derived from the output of
another control system that observed d directly, it could. I’m not
sure what such a connection would do for control, though.
Martin

···

[From Adam Matic, 2013.03.01.17.20cet]

(Martin Taylor 2013.02.27.23.25)

        I really don't know

where in complex control structures information analysis
might prove to be useful. The only place I originally was
thinking of using it was to find the best possible control
that could be achieved in a single simple noiseless control
loop. All control loops have some transport lag, which means
that the the effect of the output on the CEV at time t0 is
based on the history of the disturbance values only up to
time t0-lag. Any change of the disturbance value after that
cannot be compensated. The sequential statistical properties
of the disturbance determine the uncertainty of how much the
disturbance is likely to have changed over the lag time, and
hence the upper bound on the possible quality of control.

AM:

      I remember reading something along those lines in your

posts, but I didn’t quite understand it at the time. It still
seems like there should be a simpler way of stating the same,
especially the last sentence.

      By the way, limits of control are dependent on d, only

given that r is stable, right? If r somehow varies with
changes in d, perhaps some variance in p could be reduced.

[MartinT]

[Martin Taylor 2013.03.01.15.14]

[From Rick Marken (2013.03.01.0815)]

        Martin Taylor

(2013.02.28.23.51)–

          RM: I built one model that controls the distance between

vertical positions of cursor and target (the controlled
perception p1 = c-t, where c is vertical cursor position
and t is vertical target position) and another model that
controls the angle between c and t [the controlled
perception p2 = arctan((t-t’)/(c-t’)), where t’ is the
position of the target in the cursor column; so t-t’ is
the base of a triangle with length equal to the separation
distance – your independent variable – and c-t’ is the
length of the adjacent side so the ratio is the tangent of
the triangle – (t-t’)/(c-t’)].

        MT: I don't see that you have tested anything related to

human performance by doing this. Do you know what it is
about the two models that makes them behave differently? My
problem in understanding is that whatever variation you make
in angle is ipso facto a proportionate variation in the
difference in level (and vice-versa), so an appropriately
parameterized model should behave the same whichever is
chosen as the controlled variable. Maybe I’m missing
something about the difference between the two models. In
any case, making a couple of models does not perform “The
Test for the Controlled Variable”, which you have always
claimed (and I believe) is the best way to tell what
correlates closely with the true controlled variable.

      RM: OK, I can see that our differences run far deeper than a

disagreement about information theory.

I keep hoping our differences will dissipate, but it seems that

whenever I agree with you you find something else to disagree about.
Now it seems to be about the nature of the “Test for the Controlled
Variable”.

I think that The Test has to involve a human subject. You don't. I

think that if “The Test” is to distinguish between two hypothesised
controlled variable, the experimenter arranges a disturbance that
influences the two candidates differently. You don’t. I believe that
you used to think “The Test” involved human subjects and a
disturbance that influenced candidate controlled variables
differently. I believe that because you produced a nice Demo that
demonstrated it.

Why have you changed your opinion?

      So thanks for the data

but I won’t have time to do anything with it for a while.

You were very eager for it yesterday. What changed?

      And I think it would be

better if you did whatever you were going to do with it first
and present it so I (we) can see what you have in mind.

I wasn't planning to do anything serious with the experiment. My

plan is to continue to elaborate it as a way of learning to program
in “Processing”. As part of that, I do hope to be able to create a
“control system” class or class hierarchy and to be able to optimize
both the fit to human and the ability of the control system to
track. Then I hope to be able to create different tracking tasks,
that can be chosen from a menu in much the way that the parameters
are now chosen in the ellipse pursuit tracking task. And so on, for
as long as continuing to do it enhances my ability to code in
Processing. If, along the way, some results interesting for PCT
emerge, so much the better.

By the way, Adam Matic put me onto Processing, which is free and

open source but based on Java. I am hoping to compare it with Live
Code, of which a free and open source version is slated to be
released this month. I believe it is built around a core coded in
C++, but is largely built in LiveCode. If you liked HyperCard, you
should love LiveCode. Both of these langauges are pretty much
platform-agnostic, though in processing there are some things you
can’t do in a web app, and some differences if the target is an iOS
or Android device. I expect that’s also true of LiveCode.

      You went to all the

trouble to program up this little study so you must be
interested in using it to test you theory of behavior.

No, I believe the standard PCT theory is quite adequate. All I might

possibly try is whether control loop properties that should be
independent of the disturbance waveform actually are. Unless I think
of something else to look at.

      So I'd like to see your

tests before I set aside the time to do mine.

You will wait a long time, I suspect. You wanted the data for your

own purposes, not mine. Use them as you will.

Martin

[amatic]

[Martin Taylor 2013.03.01.13.10]

Probably. Maybe you can think of easier wording. Something along the

lines of “If it takes some time for the effect of a control action
to arrive at the CEV, the disturbance value may have changed. If the
disturbance is changing only slowly, control could still be good,
but if it is likely to change much during that lag time, control
will not be very successful.”?

AM:

Yes, something like that.

Is there a mathematical formulation with frequencies?

As in: if frequency of d is smaller than 1/timelag, then control will not be good.

MT: Looking only at a single control system, there's no way r could

covary with d. But if r were to be derived from the output of
another control system that observed d directly, it could. I’m not
sure what such a connection would do for control, though.

AM:
Perhaps not observing d, but using memory to approximate it.

Adam

···

On Fri, Mar 1, 2013 at 7:17 PM, Martin Taylor mmt-csg@mmtaylor.net wrote:

[rsmarken]

[From Rick Marken (2013.03.02.1000)]

Martin Taylor (2013.03.01.15.14)–

      RM: OK, I can see that our differences run far deeper than a

disagreement about information theory.

MT: I keep hoping our differences will dissipate, but it seems that

whenever I agree with you you find something else to disagree about.
Now it seems to be about the nature of the “Test for the Controlled
Variable”.

I think that The Test has to involve a human subject. You don't.

RM: Not true. Your experiment does involve a human subject: you.

I

think that if “The Test” is to distinguish between two hypothesised
controlled variable, the experimenter arranges a disturbance that
influences the two candidates differently. You don’t.

RM: Again, not true. In your experiment, the two hypothesized controlled variables that I suggested are affected differently by the separation between cursor and target, the disturbance.

I believe that

you used to think “The Test” involved human subjects and a
disturbance that influenced candidate controlled variables
differently. I believe that because you produced a nice Demo that
demonstrated it.

Why have you changed your opinion?

RM: I haven’t. Here’s a diagram that might make it clearer.

I think this is a reasonable representation of one frame of you pursuit tracking task. The subject is to keep the Cursor ellipse aligned with the moving Target ellipse. I proposed two possible controlled variables in this task; vertical separation between Cursor and Target (v in the diagram) or the angular separation between cursor and target (alpha in the diagram). The separation between Cursor and Target (s in the diagram) is different. This variable (s) is a disturbance to alpha but not to v. So if the subject is controlling v then s should have no effect on control; if the subject is controlling alpha then s will have an effect on control (as shown by the model; control will become worse with increases in s).

So your experiment does perform a version of the TCV. It shows control becoming worse with increases in s, suggesting that you (the subject) are controlling alpha rather than v. Of course, this is just one test and more would be needed to show that the decrease in control is due to the fact that you are controlling alpha rather than for some other reason (such as an increase in noise while v is controlled, as you suggested). But that’s what PCT science is about; you keep looking (via experimentation) for the best model of the observed phenomenon.

Best

Rick

···

---

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

[rsmarken]

[From Rick Marken (2013.03.02.1002)]

I see the diagram didn’t get included in the post so I’m attaching it; hope this works.

Best

Rick

···

On Sat, Mar 2, 2013 at 9:57 AM, Richard Marken rsmarken@gmail.com wrote:

[From Rick Marken (2013.03.02.1000)]

Martin Taylor (2013.03.01.15.14)–

      RM: OK, I can see that our differences run far deeper than a

disagreement about information theory.

MT: I keep hoping our differences will dissipate, but it seems that

whenever I agree with you you find something else to disagree about.
Now it seems to be about the nature of the “Test for the Controlled
Variable”.

I think that The Test has to involve a human subject. You don't.

RM: Not true. Your experiment does involve a human subject: you.

I

think that if “The Test” is to distinguish between two hypothesised
controlled variable, the experimenter arranges a disturbance that
influences the two candidates differently. You don’t.

RM: Again, not true. In your experiment, the two hypothesized controlled variables that I suggested are affected differently by the separation between cursor and target, the disturbance.

I believe that

you used to think “The Test” involved human subjects and a
disturbance that influenced candidate controlled variables
differently. I believe that because you produced a nice Demo that
demonstrated it.

Why have you changed your opinion?

RM: I haven’t. Here’s a diagram that might make it clearer.

I think this is a reasonable representation of one frame of you pursuit tracking task. The subject is to keep the Cursor ellipse aligned with the moving Target ellipse. I proposed two possible controlled variables in this task; vertical separation between Cursor and Target (v in the diagram) or the angular separation between cursor and target (alpha in the diagram). The separation between Cursor and Target (s in the diagram) is different. This variable (s) is a disturbance to alpha but not to v. So if the subject is controlling v then s should have no effect on control; if the subject is controlling alpha then s will have an effect on control (as shown by the model; control will become worse with increases in s).

So your experiment does perform a version of the TCV. It shows control becoming worse with increases in s, suggesting that you (the subject) are controlling alpha rather than v. Of course, this is just one test and more would be needed to show that the decrease in control is due to the fact that you are controlling alpha rather than for some other reason (such as an increase in noise while v is controlled, as you suggested). But that’s what PCT science is about; you keep looking (via experimentation) for the best model of the observed phenomenon.

Best

Rick

---

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

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

[MartinT]

[Martin Taylor 2013.03.02.14.45]

[From Rick Marken (2013.03.02.1000)]

        Martin Taylor

(2013.03.01.15.14)–

          RM: OK, I can see that our

differences run far deeper than a disagreement about
information theory.

        MT: I keep hoping our differences will dissipate, but it

seems that whenever I agree with you you find something else
to disagree about. Now it seems to be about the nature of
the “Test for the Controlled Variable”.

        I think that The Test has to involve a human subject. You

don’t.

      RM: Not true. Your experiment does involve a human subject:

you.

        I think that if "The

Test" is to distinguish between two hypothesised controlled
variable, the experimenter arranges a disturbance that
influences the two candidates differently. You don’t.

      RM: Again, not true. In your experiment, the two hypothesized

controlled variables that I suggested are affected differently
by the separation between cursor and target, the disturbance.

        I believe that you used

to think “The Test” involved human subjects and a
disturbance that influenced candidate controlled variables
differently. I believe that because you produced a nice Demo
that demonstrated it.

        Why have you changed your opinion?

      RM: I haven't. Here's a diagram that might make it clearer. 

      I think this is a reasonable representation of one frame of

you pursuit tracking task. The subject is to keep the Cursor
ellipse aligned with the moving Target ellipse. I proposed two
possible controlled variables in this task; vertical
separation between Cursor and Target (v in the diagram) or the
angular separation between cursor and target (alpha in the
diagram). The separation between Cursor and Target (s in the
diagram) is different. This variable (s) is a disturbance to
alpha but not to v. So if the subject is controlling v then s
should have no effect on control; if the subject is
controlling alpha then s will have an effect on control (as
shown by the model; control will become worse with increases
in s).

OK. I see what you mean, and withdraw my objections as I originally

stated them. But I disagree with your last sentence. It applies only
if the subject perceives the CEV accurately in each case.

You may say that "information theory spectacles" obscure my vision,

but it remains true that if you can’t perceive something accurately,
you can’t control it accurately. Increasing separation decreases the
accuracy of perceiving the level difference, so increasing
separation would be expected to decrease the accuracy of control if
the subject (me) is controlling level difference. In the case of
angular difference, increasing separation increases the precision of
perceiving the angle, but the magnitude of the disturbance variation
decreases. The ratio of variation to precision of perception is the
same in both cases, so the expected magnitude of the effect of
separation would be expected to be the same for both candidate
controlled perceptions.

Martin

[rsmarken]

[From Rick Marken (2013.03.02.1330)]

Martin Taylor (2013.03.02.14.45)-

      RM: So if the subject is controlling v then s

should have no effect on control; if the subject is
controlling alpha then s will have an effect on control (as
shown by the model; control will become worse with increases
in s).

MT: OK. I see what you mean, and withdraw my objections as I originally

stated them. But I disagree with your last sentence. It applies only
if the subject perceives the CEV accurately in each case.

RM: What do you mean by “accurately”? How does accuracy fit into a PCT model?

MT: You may say that "information theory spectacles" obscure my vision,

but it remains true that if you can’t perceive something accurately,
you can’t control it accurately.

RM: I have to know what accuracy means in terms of how it fits into a model of control before I can agree (or disagree) with this.

MT: Increasing separation decreases the

accuracy of perceiving the level difference, so increasing
separation would be expected to decrease the accuracy of control if
the subject (me) is controlling level difference.

RM: How does increasing separation decrease the accuracy of perceiving the level of separation? Please show me how this works in a PCT (or information theory or whatever) model of your tracking task.

MT: In the case of

angular difference, increasing separation increases the precision of
perceiving the angle, but the magnitude of the disturbance variation
decreases.

RM: Increasing separation has nothing to do with increasing or decreasing the precision of perceiving the angle – at least in my model. Since the angle depends on s, increasing s does influence the perception of the angle; that’s why it’s considered a disturbance; it’s an environmental influence on a controlled variable, alpha.

The influence works by facts of trigonometry. When separation, s, is small the change in alpha per unit change in v is larger than when s is large. The disturbance produces no change in accuracy of perception of alpha; the rate of change in alpha is all that is affected and the model controlling alpha does more poorly as s increases, I believe, because the loop gain decreases (with constant system gain, G) with increasing s.

MT: The ratio of variation to precision of perception is the

same in both cases, so the expected magnitude of the effect of
separation would be expected to be the same for both candidate
controlled perceptions.

RM: I don’t understand this. You’d have to show me in a model.

In my model there is no change in the accuracy of perception with separation, s, for either controlled variable, v or alpha. My model accounts for the data just by assuming that you were controlling alpha rather than v.

Again, if there is some kind of accuracy issue in your model you will have to show me how it works so that I can include it in my future modeling efforts.

Best

Rick

···

–
Richard S. Marken PhD

rsmarken@gmail.com
www.mindreadings.com

[MartinT]

[Martin Taylor 2013.03.02.16.38]

[From Rick Marken (2013.03.02.1330)]

        Martin Taylor

(2013.03.02.14.45)-

          RM: So if the subject is controlling v then

s should have no effect on control; if the subject is
controlling alpha then s will have an effect on control
(as shown by the model; control will become worse with
increases in s).

        MT: OK. I see what you mean, and withdraw my objections as I

originally stated them. But I disagree with your last
sentence. It applies only if the subject perceives the CEV
accurately in each case.

      RM: What do you mean by "accurately"? How does accuracy fit

into a PCT model?

Well, if it doesn't in your version of PCT, then your version of PCT

hasn’t much to do with everyday life. O tyhough the general idea was
that PCT was a theory about how living organisms behave. At least
that’s my idea of it.

  In my model there is no change in the accuracy of

perception with separation, s, for either controlled variable, v
or alpha.

Yes, that IS a problem. It's the problem I identified. If you

actually try to measure it, as I did in the data I provided for you,
you will see that the accuracy of perception does change with
separation.

Martin

[rsmarken]

[From Rick Marken (2013.03.02.1600)]

Martin Taylor (2013.03.02.16.38)–

      RM: What do you mean by "accurately"? How does accuracy fit

into a PCT model?

MT: Well, if it doesn't in your version of PCT, then your version of PCT

hasn’t much to do with everyday life.

RM: But how does accuracy fit into the model? I want to know the mechanism that is responsible for the varying levels of accuracy of a perception. For example, if your idea is that the model of perception in a tracking task should be:

p = c-t+e

which says that the controlled perception is proportional to the vertical distance between cursor position, c, and target position, t, plus some noise (the random error term e) then I would like to know the mechanism that results in an increase in noise (and thus a decrease in perceptual accuracy) when, for example, s is increased. How does it work? I have to know in order to be able to correctly map the model to the experimental situation.

  RM: In my model there is no change in the accuracy of

perception with separation, s, for either controlled variable, v
or alpha.

MT: Yes, that IS a problem. It's the problem I identified. If you

actually try to measure it, as I did in the data I provided for you,
you will see that the accuracy of perception does change with
separation.

RM: I thought you were treating the decrease in the ability to keep the cursor on target with increased target - cursor separation (s) as the indication of decreased perceptual accuracy with increased s. But I showed that the observed decrease in the ability to control with increasing s could be accounted for by assuming that the controlled variable was angle alpha. The accuracy of the perception of the angle alpha was the same at all values of s. So what is it in the data that you think will let me see that the accuracy of perception does change with separation?

Best

Rick

···

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

[MartinT]

[Martin Taylor 2013.023.03.00.25]

[From Rick Marken (2013.03.02.1600)]

Martin Taylor (2013.03.02.16.38)–

                RM: What do you mean by "accurately"? How does

accuracy fit into a PCT model?

        MT: Well, if it doesn't in your version of PCT, then your

version of PCT hasn’t much to do with everyday life.

      RM: But how does accuracy fit into the model? I want to know

the mechanism that is responsible for the varying levels of
accuracy of a perception.

Do you mean the physical mechanism? Imagine wearing spectacles that

have quite the wrong focal length, so that your vision is quite
blurred. Then try to place a glass as near the edge of a table as
you can, glass and table edge both being quite fuzzy. If you try it
many times, I think you will find that sometimes the glass falls on
the floor, sometimes it doesn’t.

      For example, if your idea is that the model of perception

in a tracking task should be:

      p = c-t+e



      which says that the controlled perception is proportional to

the vertical distance between cursor position, c, and target
position, t, plus some noise (the random error term e)

I don't think you can say it like that. Maybe it would work if you

said

p = c - t +- e

and propagate the plus-minus in the model. I haven't tried it so I'm

not sure.

If you say it as in your equation, the control system would simply

counter the “e” just as though it were added to the disturbance
value.

      then I would like to know the mechanism that results in an

increase in noise

What noise? I guess +-e could be interpreted as noise, but that's

not how I think of it, because if you say it is noise, the
implication is that at any moment the value is precise but it
changes from moment to moment. What you (or at least I) see in the
experiment is the two ellipses and if the vertical distance between
them is too small, I am uncertain about which one is higher. I don’t
see one dancing between clearly higher and clearly lower than the
other, or the angle alpha oscillating between positive and negative
values. I see the angle alpha as being so close to zero that I can’t
tell it isn’t zero, or the two ellipses being so close to the same
height that I can’t tell that they are not.

      (and thus a decrease in perceptual accuracy) when, for

example, s is increased. How does it work? I have to know in
order to be able to correctly map the model to the
experimental situation.

I'm not a neurophysiologist, so I don't know how it works. But when

I looked at a few of the very slow compensatory tracking runs as a
function of separation early in my self-trials, I found that the rms
error was well fitted by a straight line with an intercept of 1
pixel when the two ellipses were touching at their tips. I know that
these measures are numerically wrong, because they include 60 values
of zero that should have been 60 values of tracking data above and
below zero, but that will not affect the trend. You can recompute
those values in the spreadsheets to get them numerically correct.
The wrongly computed values are in the cell labelled “rms static” in
the spreadsheets (E5).

        RM: In my model there is no change in

the accuracy of perception with separation, s, for either
controlled variable, v or alpha.

        MT: Yes, that IS a

problem. It’s the problem I identified. If you actually try
to measure it, as I did in the data I provided for you, you
will see that the accuracy of perception does change with
separation.

  RM: I thought you were treating the decrease in the ability to

keep the cursor on target with increased target - cursor
separation (s) as the indication of decreased perceptual accuracy
with increased s.

Conceptually, it was the reverse, but I guess the relationship is

reversible.

  But I showed that the observed decrease in the

ability to control with increasing s could be accounted for by
assuming that the controlled variable was angle alpha. The
accuracy of the perception of the angle alpha was the same at all
values of s.

That seems strange. My data (the same ones) suggest that the

precision of perception of angle alpha increases with separation.
Intuitively, that makes sense to me, because it is easier to
perceive the off-horizontal of a long line than of a short one. It’s
why you ordinarily would use a spirit-level when installing a shelf,
but “by eye” is usually good enough when hanging a picture.

  So what is it in the data that you think will let me

see that the accuracy of perception does change with separation?

The RMS variation of cursor position with very slow disturbance in

the compensatory tracking part of the run (the last 10 seconds). You
can use the same data to estimate the accuracy of perception of the
angle alpha.

Martin

[rsmarken]

[From Rick Marken (2013.03.03.0930)]

Martin Taylor (2013.023.03.00.25)–

      RM: But how does accuracy fit into the model? I want to know

the mechanism that is responsible for the varying levels of
accuracy of a perception.

MT: Do you mean the physical mechanism?

RM: Yes, And in particular how that would be represented mathematically in a working model. The focusing analogy you gave is fine; now the question is how do you put that into a computer model of your tracking task?

      RM: For example, if your idea is that the model of perception

in a tracking task should be:

      p = c-t+e



      which says that the controlled perception is proportional to

the vertical distance between cursor position, c, and target
position, t, plus some noise (the random error term e)

MT: If you say it as in your equation, the control system would simply

counter the “e” just as though it were added to the disturbance
value.

RM: Yes, of course e is a random variable with a probability distribution. So you don’t really need to write ±e; it’s understood that the error term is a random variable that can range over any real space you choose.

      RM: then I would like to know the mechanism that results in an

increase in noise

MT: What noise? I guess +-e could be interpreted as noise, but that's

not how I think of it, because if you say it is noise, the
implication is that at any moment the value is precise but it
changes from moment to moment…

RM: OK, but you have to include that in the model in some way in order to simulate the behavior. I would include it as a time varying random variable; if you have some other idea just let me know. The goal here, I think, should be to get to a working model of the behavior in this task so we can figure out what might be going on. A working model is what I think of as the PCT “gold standard” for evaluating the results of any experiment.

      RM: (and thus a decrease in perceptual accuracy) when, for

example, s is increased. How does it work? I have to know in
order to be able to correctly map the model to the
experimental situation.

MT: I’m not a neurophysiologist, so I don’t know how it works…

RM: When I ask about how it works I’m just asking for a plausible suggestion about how to put the effects of separation on accuracy into the model. This doesn’t require knowing the neurological details of how it works. But it does require proposing a plausible process that can be put into the working model as a set of quantitative relationships. This is what we do when we model the perceptual function in our models. When I suggest that the controlled variable is p = atan(v/s) I am not proposing that the visual system computes the arc tangent of the tangent v/s the way Excel does it; I am just proposing that somehow the visual system does some kind of computation that produces a neural signal, p, that is proportional to the arc tangent of v/s, which is the angle alpha in my diagram. I know from the neurophysiology that the visual system is capable of computing an analog of the angle somehow so I put it into the model in mathematical form. That’s all I’m asking from you – a plausible equation that includes s that will lead the working model to have poorer control as s increases.

  RM: I thought you were treating the decrease in the ability to

keep the cursor on target with increased target - cursor
separation (s) as the indication of decreased perceptual accuracy
with increased s.

MT: Conceptually, it was the reverse, but I guess the relationship is

reversible.

RM: I thought the graph you posted showed that your ability to control the distance between cursor and target, measured in bits, decreased as s increased. I don’t know what to reverse conceptually here.

I’ve actually lost that graph as well as the raw data (when I decided to give up on this project). But maybe I’ll stick with it because I’m starting to see that your little experiment might be a good basis for teaching PCT modeling and the TCV. So could you send me the graph and data again, please. Thanks.

  RM: But I showed that the observed decrease in the

ability to control with increasing s could be accounted for by
assuming that the controlled variable was angle alpha. The
accuracy of the perception of the angle alpha was the same at all
values of s.

MT: That seems strange. My data (the same ones) suggest that the

precision of perception of angle alpha increases with separation.

RM: I don’t understand this. You really have to send me that graph again; I thought it showed control ability falling off with an increase in s. My model shows that this is expected if what is controlled is angle alpha, suggesting that the poorer control as a function of increased s that is observed in your study may not be due to any decrease in accuracy but, rather to a decrease in loop gain resulting from the much smaller change in alpha per unit change in v as s increases.

  RM: So what is it in the data that you think will let me

see that the accuracy of perception does change with separation?

MT: The RMS variation of cursor position with very slow disturbance in

the compensatory tracking part of the run (the last 10 seconds). You
can use the same data to estimate the accuracy of perception of the
angle alpha.

RM: But that is basically what you showed in the graph of your data that you posted. The RMS deviation of cursor from target (measured in bits) increases (control becomes poorer) as s increases. But I showed that this could be the result of controlling alpha, with a decrease in accuracy of perception having nothing to do with it. In other words,observed variations in the accuracy of control (seen as variations in RMS variation in cursor position, as you call it) do not necessarily reflect variations in the accuracy of perception.

Best

Rick

···

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

[Bill_Powers1]

[From Bill Powers (2013.03.03.10.03 MST)]

Rick Marken (2013.02.22.1900) (To Martin Taylor) –

RM: I accept the fact that all
of your math is correct. What I still don’t accept is that information
theory has anything to contribute to an understanding of control. I wish
I could get you to give up on information theory and just stick to PCT.
But I know I can’t so I won’t try. If you want to show that there is
information about the disturbance in perception, that’s fine with me. But
I’ll keep trying to show that this is just not the case.

BP: The exhibition of professional jealousy and defense of entrenched
positions in this interchange could hardly get more boring. Martin has
already admitted that a control system cannot use the information about
the disturbance that calculations suggest is in the perceptual signal,
and that an observer has no way to see it, either (unless the values of
all other variables involved are known). Martin would not say that
knowing only the value of the perceptual signal would suffice to let the
control system deduce the value of the disturbing variable to help in
producing a countering output. He is talking about calculations and
measurements peculiar to information theory, which as far as I can see is
similar to talking to an astronomer about epicycles, or to Ptolemy about
orbits and diurnal spin. So you are not arguing against anything he
says.
All that is being communicated right now by either side is ill
will.
My house is not yet completely back in order, and I hate to admit it but
the state of my mind depends in some vital ways on the state of my house.
I am, however, forming some notions about a writing project for
Science magazine to be titled “Perceptual Control Theory at
60.” This is an echo of Skinner’s “Behaviorism at 50” and
my own “Perceptual Control Theory at 40” in Volume 4, Number 1
of Closed Loop (see link).

http://www.livingcontrolsystems.com/journals/closed_loop.pdf

I hope to enlist a lot of help from coauthors who will look up references
and contribute their own observations about where we are and how we got
here. I will, for example, request participation by both Martin Taylor
and Rick Marken, as well as Greg Williams, Tom Bourbon, and others from
whom we don’t often hear. But not yet. First, the house.

Then, a working paper to kick off this effort, should anyone prove
interested in it. Target date for submission is the end of 2013. The
working paper will outline what I think is important but of course will
also be open to anyone’s suggestions.

I will not attempt to reply to the 198 posts that have accumulated since
I got involved in moving back and forth and ending up where I started.
Maybe a general remark now and then, but you’re all doing fine by
yourselves.

Best,

Bill P.

[Bill_Powers1]

From Bill Powers (2013.03.03.1120 MST)]

Martin Taylor 2013.023.03.00.25

[From Rick Marken
(2013.03.02.160)

RM:

For example, if your idea is
that the model of perception in a tracking task should be:

p = c-t+e

which says that the controlled perception is proportional to the vertical
distance between cursor position, c, and target position, t,
plus some noise (the random error term e)

MT: I don’t think you can say it like that. Maybe it would work if you
said

p = c - t ± e

and propagate the plus-minus in the model. I haven’t tried it so I’m not
sure.

If you say it as in your equation, the control system would simply
counter the “e” just as though it were added to the disturbance
value.

BP: This is the crucial point. A control system can counteract
uncertainty or unpredicted variation in the perceptual signal by
adjusting the output as required to keep p near in value to r. It can’t
know whether the cause of the variations is inside itself or in the
environment. To know that it would need a way to see the environment
without relying on p.

RM: then I would like to know
the mechanism that results in an increase in noise

MT: What noise? I guess ±e could be interpreted as noise, but that’s not
how I think of it, because if you say it is noise, the implication is
that at any moment the value is precise but it changes from moment to
moment.

BP: That, too, depends on whether it originates in the perceptual
function, output function, or environment, which the control system
can’t determine. It also depends on the averaging time you use. The
result of the averaging is always perfectly precise, being a single
number. The real “accuracy” question is how that number
corresponds to some potential measurement of the environment.

You can refer in general to the “real” effects of external
variables on intrinsic variables, but since we can’t say what they are,
either, that doesn’t help much. I wonder whether “accuracy”
isn’t another red herring.

Best,

Bill P.

···

What you (or at least I)
see in the experiment is the two ellipses and if the vertical distance
between them is too small, I am uncertain about which one is higher. I
don’t see one dancing between clearly higher and clearly lower than the
other, or the angle alpha oscillating between positive and negative
values. I see the angle alpha as being so close to zero that I can’t tell
it isn’t zero, or the two ellipses being so close to the same height that
I can’t tell that they are not.

(and thus a decrease in
perceptual accuracy) when, for example, s is increased. How does it work?
I have to know in order to be able to correctly map the model to the
experimental situation.

I’m not a neurophysiologist, so I don’t know how it works. But when I
looked at a few of the very slow compensatory tracking runs as a function
of separation early in my self-trials, I found that the rms error was
well fitted by a straight line with an intercept of 1 pixel when the two
ellipses were touching at their tips. I know that these measures are
numerically wrong, because they include 60 values of zero that should
have been 60 values of tracking data above and below zero, but that will
not affect the trend. You can recompute those values in the spreadsheets
to get them numerically correct. The wrongly computed values are in the
cell labelled “rms static” in the spreadsheets (E5).

RM: In my model there is no
change in the accuracy of perception with separation, s, for either
controlled variable, v or alpha.

MT: Yes, that IS a problem. It’s the problem I identified. If you
actually try to measure it, as I did in the data I provided for you, you
will see that the accuracy of perception does change with
separation.

RM: I thought you were treating the decrease in the ability to keep the
cursor on target with increased target - cursor separation (s) as the
indication of decreased perceptual accuracy with increased
s.

Conceptually, it was the reverse, but I guess the relationship is
reversible.

But I showed that the observed
decrease in the ability to control with increasing s could be accounted
for by assuming that the controlled variable was angle alpha. The
accuracy of the perception of the angle alpha was the same at all values
of s.

That seems strange. My data (the same ones) suggest that the precision of
perception of angle alpha increases with separation. Intuitively, that
makes sense to me, because it is easier to perceive the off-horizontal of
a long line than of a short one. It’s why you ordinarily would use a
spirit-level when installing a shelf, but “by eye” is usually
good enough when hanging a picture.

So what is it in the data that
you think will let me see that the accuracy of perception does change
with separation?
The RMS variation of cursor position with very slow
disturbance in the compensatory tracking part of the run (the last 10
seconds). You can use the same data to estimate the accuracy of
perception of the angle alpha.

Martin