PCT-Specific Methodology, and vectors

[From Rick Marken (2006.12.23.0015)]

Martin Taylor (2006.12.22.20.58)--

Bill Powers (2006.12.22.1630 MST)--

I think I've forgotten why we got into this in the first place.

It was triggered by my response to [From Bill Powers (2006.12.16.0555 MST)] in which you were following up on questions of correlation in behaviourist and PCT approaches to data analysis. I thought the analysis of maximum and minimum correlations as a function of control quality might prove useful in the discussion.

And it is an interesting relationship (that the correlation between d and o is directly related to the quality of control). But I can't really see how knowing that could ever be of much use in a behaviorist or PCT approach to data analysis. The concept of control is completely missing from a behaviorist analysis and the correlation between any particular o and d is not of that much interest in a PCT analysis once you have a good idea about what the controlled variable is. So what do you think is useful about knowing maximum and minimum correlations between o and d as a function of control quality?

Best

Rick

···

---
Richard S. Marken Consulting
marken@mindreadings.com
Home 310 474-0313
Cell 310 729-1400

[Martin Taylor 2006.12.23.11.04]

[From Rick Marken (2006.12.23.0015)]

Martin Taylor (2006.12.22.20.58)--

Bill Powers (2006.12.22.1630 MST)--

I think I've forgotten why we got into this in the first place.

It was triggered by my response to [From Bill Powers (2006.12.16.0555 MST)] in which you were following up on questions of correlation in behaviourist and PCT approaches to data analysis. I thought the analysis of maximum and minimum correlations as a function of control quality might prove useful in the discussion.

And it is an interesting relationship (that the correlation between d and o is directly related to the quality of control). But I can't really see how knowing that could ever be of much use in a behaviorist or PCT approach to data analysis. The concept of control is completely missing from a behaviorist analysis and the correlation between any particular o and d is not of that much interest in a PCT analysis once you have a good idea about what the controlled variable is. So what do you think is useful about knowing maximum and minimum correlations between o and d as a function of control quality?

It wasn't my notion. I simply butted in on an ongoing thread in which the question seemed to have some significance, because I thought my result my have some relevance to their discussion. The original reason I wrote the message (March 3, 1998) must have been because there was a discussion about correlation or its limits. So it is something that comes up from time to time, which suggests it must have some value.

On the other hand, I think anything that adds to our understanding of the properties of control systems has the potential to be useful, even if we don't see how right at the moment. The subsequent discussion seems to have been of same personal value to Bill, anyway, and that can't be all bad.

I suspect that the derived issue of how to treat waveforms as vectors might be more useful in the end.

Martin

[From Rick Marken (2006.12.23.1111)]

Martin Taylor (2006.12.23.11.04) --

On the other hand, I think anything that adds to our understanding of the properties of control systems has the potential to be useful, even if we don't see how right at the moment.

One thing that I think would be of actual, rather than potential, value would be to figure out how variance in the reference signal, r, affects the relationship between d and the hypothetical controlled variable, qi. Your analyses of factors that affect the correlation between qi (you call it p) and d assume that r is constant (and zero), which is fine and certainly makes things clear. But we have pretty good evidence that r is never realy constant, even when a person tries to keep it constant.

For example, take my mind reading demo, please!:wink: (http://www.mindreadings.com/ControlDemo/ThreeTrack.html) There you have three hypothetical controlled variables -- call them qi1, qi2, and qi3 -- which are the positions, over time, of the three squares on the screen. The computer determines which of the three is actually controlled by applying different disturbance waveforms -- d1, d2 and d3 -- to each and continuously computing the correlation between each disturbance and the corresponding controlled variable. If the reference for the controlled variable were a constant then (as your analysis shows) the correlation between that variable and the disturbance to that variable would be ~0.0. But when a person is moving the controlled square around the screen in some pattern, the reference for the position of that square is constantly changing. So the reference for the controlled variable is also a time varying waveform which contributes to the value of qi and, thus, affects the correlation between qi and d. But we don't know anything about the form of the r waveform.

My mind reading demo makes the decision about which of the three qi's is controlled using a fixed rule of thumb based on nothing better than my own estimates of what works "pretty darn well": if one of the three correlations between a qi and its corresponding d is .3 less than the absolute values of the other two correlations then take that as the controlled variable, otherwise assume that none of the qi's are controlled. This is obviously a very coarse approach to determining the controlled variable.

What would be nice is for someone (you?) to develop a powerful method for determining a controlled variable using the basic principles of "the test" (looking for _lack of correlation_ between d and hypothetical qi) but taking into account the "wild card" in this research: secular variations in r that are completely unknown. It seems to me that this might require the development of some new statistical analysis (since the r waveform can only be known probabilistically) or, perhaps, some clever mathematical scheme that can factor out possible variations in qi due to variations in r.

I think developing a rigorous method for estimating the correlation between hypothetical qi and d independent of the effects of variations in r would be a very significant contribution to the advancement (and to the mproved understanding) of PCT methodology.

Best regards

Rick

···

----

Richard S. Marken Consulting
marken@mindreadings.com
Home 310 474-0313
Cell 310 729-1400

Re: PCT-Specific Methodology, and vectors
[Bruce Nevin (2006.12.23 15:29 EST)]

Martin Taylor 2006.12.23.14.24

···

Bill Powers (2006.12.23.0930 MST ) –

It is commonplace in science to organize work by hueristics, informed guesses, and outright hunches, but then to do most of the actual work verifying a valid relationship of hypotheses to data. It is also good practice in many fields to do a “sanity check” to rule out small slips with large consequences, such as sign inversion. I am very familiar with a kind of Pygmalion process where a brilliant weaver of abstractions takes them for the “deep” reality underlying mere observational data. On the other hand, it was Watson & Crick who got the structure of DNA, and not Franklin or Wilkins. The story http://en.wikipedia.org/wiki/King%27s_College_DNA_controversy illustrates the both the difficulty and the importance of collaboration between the two complementary cognitive styles.

/B

[Martin Taylor 2006.12.23.22.51]

[From Rick Marken (2006.12.23.1111)]

What would be nice is for someone (you?) to develop a powerful method for determining a controlled variable using the basic principles of "the test" (looking for _lack of correlation_ between d and hypothetical qi) but taking into account the "wild card" in this research: secular variations in r that are completely unknown.

It's an interesting question, I agree. I went and tried your mind-reading demo, and had a rather difficult time controlling my chosen square. I think that for me at that time (after half a bottle of wine at lunch) there was a certain perceptual lag, which would introduce some transport delay into the equation. That, in turn, makes the analysis quite a bit trickier than it would be with just a leaky (rather than a perfect) integrator. The correlations become rather dependent on the spectrum of the disturbance waveform. There may be some noise, too, which would reduce all the correlations.

It seems to me that this might require the development of some new statistical analysis (since the r waveform can only be known probabilistically) or, perhaps, some clever mathematical scheme that can factor out possible variations in qi due to variations in r.

I'll have a look at it and see if I can think of anything clever. All I've done so far is to find maximum and minimum possible correlations for an ideal case, and to suggest how those limits would change under some well-defined departures from the ideal.

I think developing a rigorous method for estimating the correlation between hypothetical qi and d independent of the effects of variations in r would be a very significant contribution to the advancement (and to the mproved understanding) of PCT methodology.

Worth thinking about, for sure. Maybe Bruce has some ideas, too?

Martin

[Bruce Nevin (2006.12.24 13:34 EST)]

Rick Marken (2006.12.23.1111) --

What would be nice is for someone (you?) to develop a powerful method
for determining a controlled variable using the basic principles of
"the test" (looking for _lack of correlation_ between d and
hypothetical qi) but taking into account the "wild card" in this
research: secular variations in r that are completely unknown.

Hm ... qi by definition as a measured quantity is not hypothetical. It
is necessary to affirm that it is a true measurement of what appears to
the observer to be input to the observed system's sensory organ. It is
the status of qi as a measure of the CV that is hypothetical. In other
words, the relationship of qi to r is hypothetical; and of course r
itself is hypothetical.

Martin Taylor 2006.12.23.22.51 --

Maybe Bruce has some ideas

You flatter me.

The task is one of finding some pattern or other evidence that values of
r are being changed by higher-order control.

All you have to go on is that some variable measured by the observer
(with strong reason to identify that variable with qi at the observed
organism's sensory input) does not respond to measured disturbance d as
predicted by the laws of physics, and that the effect qo of actions by
the organism account for the difference. That's enough to confirm
control of a CV corresponding to qi. If that's all you mean by
"determine a controlled variable," you're done. But taking you at your
word I think you do mean "determine" and not just "identify".

Assume r is a constant. The influence of qo counteracts that of d,
maintaining qi more or less constant, and the remaining variability of
qi is proportionate to loop gain.

But if r varies, then d is permitted to affect the CV somewhat. Changes
in qi by hypothesis mirror changes in r (modulo loop gain as above, and
assuming loop gain constant).

Is this too simplified? I am a bear of very small brain.

  /B

[From Rick Marken (2006.12.24.2220)]

I rechecked my "Mind Reading" demo at http://www.mindreadings.com/ControlDemo/ThreeTrack.html and found that there was a mistake in the algorithm. I've now fixed it up a bit. The correlations you now see are the absolute correlations between disturbance and hypothetical qi. I'm trying to think of ways of making this algorithm more powerful, accurate and rapid.

Bruce Nevin (2006.12.24 13:34 EST)--

Rick Marken (2006.12.23.1111) --

What would be nice is for someone (you?) to develop a powerful method
for determining a controlled variable using the basic principles of
"the test" (looking for _lack of correlation_ between d and
hypothetical qi) but taking into account the "wild card" in this
research: secular variations in r that are completely unknown.

Hm ... qi by definition as a measured quantity is not hypothetical.

Yes, of course. What is hypothetical about any particular qi it is whether it is controlled or not.

It is the status of qi as a measure of the CV that is hypothetical.

Right! Though I think it's better to just say that it's the status of qi as a controlled variable (CV) that is hypothetical. qi isn't really a potential _measure_ of a controlled variable because qi _is_ already a measured variable. qi is like the temporal variations in the position of one of the squares in the Mind Reading demo. The question is not whether the position of, say, the largest square (call it qi3) is a measure of the CV; the question is whether qi3 _is_ a controlled variable.

In other words, the relationship of qi to r is hypothetical; and of course r
itself is hypothetical.

Again, I think this is kind of an awkward way of conceiving of it. I just conceive of it this way: there are all kinds of variables (qi's) that I can measure: some (like the vertical optical velocity of a fly ball) are controlled in certain circumstances (like when a person is trying to catch a ball) and some (like the shape of the optical trajectory of that same fly ball) aren't. The goal of PCT research is to determine what qi's are being controlled when we see people carrying out various kinds of skilled behaviors.

Merry Christmas!

Rick

···

---

Richard S. Marken Consulting
marken@mindreadings.com
Home 310 474-0313
Cell 310 729-1400

[From Bruce Nevin (2006.12.25 09:56 EST)]

Rick Marken (2006.12.24.2220)--

Yes, that is a simpler way to put it. What I am bearing in mind is that
the loop is closed through the environment, the CV is modeled as being
in the environment between the observed organism and the observer,
disturbances typically affect the CV in the environment and not at the
observed system's sensory input, and so on. There are always at least
those two perceivers, the observer and the observed organism, and for
each perceiver there is a qi that corresponds (we believe) to the CV in
the environment. There is no other way to model interactions of two
organisms around one CV. Indeed, coordinated control with another is our
confirmation that what we perceive exists and is as we perceive it. To
identify the CV with qi is to leap past that on wings of assumption.
That is why I say that qi as a measure of input to the observed system
is one measure of the CV. What I think that in fact a measure of the
observer's sensory input is taken to be a measure of the CV, which rests
on the assumption that the two systems (observer and observed) are
controlling the same CV, and indeed that is one way of stating the Test:
are we controlling the same CV?

  /Bruce

···

-----Original Message-----
From: Control Systems Group Network (CSGnet)
[mailto:CSGNET@LISTSERV.UIUC.EDU] On Behalf Of Rick Marken
Sent: Monday, December 25, 2006 1:20 AM
To: CSGNET@LISTSERV.UIUC.EDU
Subject: Re: PCT-Specific Methodology, and vectors

[From Rick Marken (2006.12.24.2220)]

I rechecked my "Mind Reading" demo at
http://www.mindreadings.com/ControlDemo/ThreeTrack.html and found that
there was a mistake in the algorithm. I've now fixed it up a bit. The
correlations you now see are the absolute correlations between
disturbance and hypothetical qi. I'm trying to think of ways of making
this algorithm more powerful, accurate and rapid.

Bruce Nevin (2006.12.24 13:34 EST)--

Rick Marken (2006.12.23.1111) --

What would be nice is for someone (you?) to develop a powerful method

for determining a controlled variable using the basic principles of
"the test" (looking for _lack of correlation_ between d and
hypothetical qi) but taking into account the "wild card" in this
research: secular variations in r that are completely unknown.

Hm ... qi by definition as a measured quantity is not hypothetical.

Yes, of course. What is hypothetical about any particular qi it is
whether it is controlled or not.

It is the status of qi as a measure of the CV that is hypothetical.

Right! Though I think it's better to just say that it's the status of qi
as a controlled variable (CV) that is hypothetical. qi isn't really a
potential _measure_ of a controlled variable because qi _is_ already a
measured variable. qi is like the temporal variations in the position
of one of the squares in the Mind Reading demo. The question is not
whether the position of, say, the largest square (call it qi3) is a
measure of the CV; the question is whether qi3 _is_ a controlled
variable.

In other words, the relationship of qi to r is hypothetical; and of
course r itself is hypothetical.

Again, I think this is kind of an awkward way of conceiving of it. I
just conceive of it this way: there are all kinds of variables (qi's)
that I can measure: some (like the vertical optical velocity of a fly
ball) are controlled in certain circumstances (like when a person is
trying to catch a ball) and some (like the shape of the optical
trajectory of that same fly ball) aren't. The goal of PCT research is to
determine what qi's are being controlled when we see people carrying out
various kinds of skilled behaviors.

Merry Christmas!

Rick
---

Richard S. Marken Consulting
marken@mindreadings.com
Home 310 474-0313
Cell 310 729-1400

[From Rick Marken (2006.12.25.1200)]

Bruce Nevin (2006.12.25 09:56 EST)--

Rick Marken (2006.12.24.2220)--

Yes, that is a simpler way to put it. What I am bearing in mind is that
the loop is closed through the environment, the CV is modeled as being
in the environment between the observed organism and the observer,

Actually, that's not quite true. The CV is a perceptual variable; a _function_ of certain environmental variables.

disturbances typically affect the CV in the environment and not at the
observed system's sensory input, and so on.

I would say that a disturbance is an environmental variable that influences the state of sensory variables of which the CV is a function. Consider a possible CV when catching a ball: vertical optical velocity. This CV is a function of the optical projection of the ball on the retina (a sensory variable) that is a function of the actual trajectory of the ball in the environment (one of the disturbances to the CV).

There are always at least
those two perceivers, the observer and the observed organism, and for
each perceiver there is a qi that corresponds (we believe) to the CV in
the environment.

Yes, of course. But as the observer, my hypothesis is about the CV controlled by the observed organism. So I formulate hypotheses about the CV in terms of qi as perceived from the organism's perspective. So my hypotheses about the qi controlled when catching are formulated in terms of what the fielder sees, not in terms of what I see while watching the fielder catch the ball. So one hypothesis about the variable controlled by the fielder (that is, one hypothesis about a qi controlled when catching a ball) is that it is (d alpha/dt) where alpha is the vertical optical angle between the ball and some reference point, like home plate, as seen from the point of view of the fielder -- not of an observer in the stands.

There is no other way to model interactions of two
organisms around one CV.

This is a whole different question. And I don't think you can model interactions of two organisms around one CV. Each organism controls its own CV, of course. What you must be talking about is modeling interactions between organisms controlling CVs that are the same function of the same environmental variables. For example, person 1 might be controlling qi1, which is f(i1, i2..in) and person 2 might be controlling qi2, which is also f(i1,i2...in). But the inputs, i, for person 1 are seen from a different perspective than the same inputs for person 2. So even though the two CVs, qi1 and qi2, are functionally the same, the value of these CVs will always be different for person 1 and 2. This "control parallax" must, indeed, be taken into account when modeling interactions between two or more organisms.

Indeed, coordinated control with another is our
confirmation that what we perceive exists and is as we perceive it. To
identify the CV with qi is to leap past that on wings of assumption.

We only identify qi as a CV when it has passed the test for the controlled variable. We don't simply assume that any particular qi is a CV.

That is why I say that qi as a measure of input to the observed system
is one measure of the CV.

This sounds very strange to me. How can qi -- which is a hypothesis about a perceptual variable that is controlled -- be anything other than the CV, if it passes the test. qi is a guess about a measure of the organism's sensory environment that it is controlling. So qi is a measure of what _may_ be the variable that is controlled: the CV. For example, (d alpha/dt) is one qi that might be controlled when catching a ball. Suppose we do the test and find that (d alpha/dt) is controlled. Can't we then say that (d alpha/dt) _is_ a CV? It's not really a measure of the CV; it _is_ the CV.

What I think that in fact a measure of the
observer's sensory input is taken to be a measure of the CV, which rests
on the assumption that the two systems (observer and observed) are
controlling the same CV, and indeed that is one way of stating the Test:
are we controlling the same CV?

I don't see this at all. When I do the test I don't have to be controlling a variable in order to determine that another person is controlling it. All you have to do is hypothesize a CV (some variable qi) and see if it is protected from disturbance by actions of the organism. You don't even have to be able to directly perceive qi yourself (as in hypothesis about the very high frequency sounds echos controlled by bats) or even be there doing the testing (as in my Mind Reading demo) where the computer does the test automatically.

Best

Rick

···

---
Richard S. Marken Consulting
marken@mindreadings.com
Home 310 474-0313
Cell 310 729-1400