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Date:         Mon, 4 Jan 1993 10:02:02 -0700
From:         "William T. Powers" <POWERS_W%FLC@VAXF.COLORADO.EDU>
Subject:      Dag's points; qualitative explanation

[From Bill Powers (930104.0900)]

Today, Jan. 4, is the day of latest sunrise; the earliest sunset
occurred way back on Dec. 7. We got an elliptical orbit.

Dag Forssell (930103.1200) --

As Ray Jackson pointed out, what you do in seminars adds a lot to
what is in the printed material. I was trying to point out that a
person reading the material you posted might well take it in just
the way you don't want it taken: as a prescription for what to
DO. I think it's important to keep asking, as you read your own
writing, "Is this the sort of thing anyone could say no matter
what theory they believed in?" Making good use of resources (for
example), it seems to me, is something I have heard before ad
nauseum. Even when you do say things that are commonplace, the
point should be to explain WHY these things are beneficial. Your
students come out of the seminar understanding a lot more of the
"why." Can't more of that get into the printed matter?

I do agree with you that there are situations in which
anticipating a disturbance can help control. These tend to be
those involving higher-level variables for which control is slow.
But anticipation alone is never enough.
---------------------------------------------------------------
Rick Marken, Gary Cziko, Greg Williams (930103-4) --

It strikes me that all of the ways in which Skinnerians and other
dismiss PCT ideas treat a quantitative theory as if it's a
qualitative theory. Rick said this, but it's a point that bears
elaboration.

Even trying to play Devil's Advocate pushes one into the
qualitative mode. Greg said that it is possible to detect the
disturbance through its effect on the cursor. That is true,
qualitativly. Everyone can tell immediately THAT there is a
disturbance, because the cursor doesn't behave as they expect it
to under the hypothesis that they have the sole means of
affecting it. But nobody can tell, on that qualitative basis
alone, WHAT THE DISTURBANCE IS.

I should also point out that no matter what method a person uses,
there is no way of telling HOW MANY disturbing variables are
acting at the same time, or what their individual magnitudes and
directions are.

Given enough practice, people will realize that there is
information about the details of the disturbing variable. It's in
their own handle movements. In either compensatory or pursuit
tracking, an experienced subject will have a pretty good idea of
how the handle should move, on the average, to keep the cursor on
target. In compensatory tracking it should be centered; in
pursuit tracking it should move in proportion to target
movements. The disturbance results in the handle moving in other
ways, and the deviation of handle movements from the expected  movements (or
 position) is direct information about the direction
and magnitude of the invisible disturbance. But of course you
don't have this information available until AFTER you've achieved
good control.

Greg caught on to this in showing how, by looking at the
relationship between the handle and the cursor, the participant
could get more information about the disturbance. What you
missed, Greg (possibly) is that this information can't be used to
ACHIEVE good control, because if you don't already have good
control, the information isn't available.

Greg asks "HAS ANYONE ACTUALLY LOOKED AT THE CORRELATIONS BETWEEN
CURSOR POSITION AND VELOCITY, AND HANDLE VELOCITY, RATHER THAN
HANDLE POSITION?" The answer is yes. The correlation increases
somewhat -- say from 0.1 to 0.3. Rick, maybe you have some more
exact numbers on this. The reason, as I was guessing yesterday,
is that either noise or chaotic effects come to dominate the
error signal. I think that people keep improving their control
until there is no further systematic error perceivable by them.
This means that the signal in the error signal will be just
barely discernible amid the noise in the error signal. When a
person has learned to control in a given situation as well as
that person is going to control, most of the error signal will be
unsystematic.

Rick just called, and is going to handle some more aspects of
these questions by running a simulation.

Just one more point. In a real experiment, although not in
ordinary simulations, the HANDLE movement is not perfectly
smooth. It wobbles relative to the correct position by a few
percent of its range. This makes only a small difference in the
match between handle and disturbance, and indeed accounts for
most of the difference between the observed handle-disturbance
correlation and -1.0000. But that same small wobble in handle
position becomes a very large relative wobble in cursor position,
because we are subtracting two large numbers from each other,
disturbance magnitude and handle position. There's no telling
where this randomness enters the loop -- it could even be in the
reference signal -- but it's that randomness that drastically
lowers the handle-cursor correlation. In a simulation containing
no noise, that correlation can become quite high if you correlate
error signal with handle velocity. In fact there's no reason it
shouldn't be perfect, in a simulation. But the real system does
contain noise, and that is why the _measured_ correlation is so
low. Injecting noise into the simulation would produce the same
low correlation, approaching zero.
--------------------------------------------------------------
Best to all,


Bill P.


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