[From Bill Powers (930905.1000 MDT)]
Gary Cziko (930905.0926 UT) --
... would it not also be of interest to examine tracking during
which the "axis" of the mouse varied smoothly around the clock.
As it moved from 12 o'clock to 3, vertical movements of the
mouse would have less and less effect while horizontal movements
would have more and more. Having the axis move unpredictably in
one direction (e.g., clockwise) for a while and then the other
(e.g., conter-clockwise) at varying speeds would require the
subject to continuously adapt his mouse movements to control the
cursor.
This might be a way to approach a higher level of control. It's
similar to Rick's conflict tracking task in which one axis of the
mouse space is rotated to generate varying degrees of conflict in
a two-dimensional tracking task. What you're talking about is
like a very difficult sort of disturbance, one that rotates the
spatial relationship between the person's output and a one-
dimensional controlled quantity. Since there isn't any direct
indication of the angle of rotation, the only reflection of the
rotation is in the difficulty in control that would be
experienced.
A higher-level system might eventually be learned that would
monitor the relationship between direction of hand movement and
direction of cursor movement, and maintain the perceived
relationship constant by internally rotating the visual field (or
the division of output between x and y axes).
I've tried a tracking task that requires a continuous rotation of
the relationship between the error signal and the direction of
hand movement. Imagine a small circle moving at a slow constant
speed around the periphery of a large stationary circle. The
disturbance is applied radially, and the y-axis (only) of the
mouse also affects the small circle in the radial direction. The
task is to keep the small circle bisected by the arc of the large
circle as the small circle moves steadily around the center of
the large circle. A positive disturbance always makes the small
circle move farther from the center of the large circle, and a
negative-y movement of the mouse always makes the small circle
move radially inward, toward the center of the large circle.
When the small circle is just passing 12:00 o'clock (the top) on
the large circle, a positive disturbance makes the small circle
move up, increasing its radial distance from the center of the
large circle, and is counteracted by pulling the mouse in the
negative y direction. 180 degrees later, as the small circle
passes the 6:00 o'clock position, a positive disturbance moves
the small circle down, still increasing the radius, and the mouse
still has to be pulled down, in the -y direction, to counteract
the disturbance -- but now the small circle moves opposite to the
direction of the mouse. In fact, as the slow rotation proceeds,
the angular relationship between the mouse movement and its
effect on the small circle changes continuously, going around and
around through 360 degrees. The mouse is always moved in the y
direction, but the effect of this movement on the small circle is
always radial to the center of the large circle.
The control experience is interesting. My feeling is one of
rotating my sense of relationship between mouse movements and
small circle continuously -- up to a point. Then there's a sudden
"reset" and I'm rotated the other way by 360 (or 359) degrees.
It's as if my inner perceptual rotation reaches a limit and if I
tried to keep going I'd break something, like my imaginary neck.
This isn't quite the same as your proposal, but I think it gets
into something similar.
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Gary Cziko (930905.0825 UT) --
This is where the teacher (or coach) is needed. He or she will
shout "lower" as you come around the skating rink, and so you
try to get lower without falling on your butt or breaking your
back. You come around again as low as anyone could possibly be
on skates (or so you think), and the coach says, "Better, but
still not quite low enough." You keep working on this (over
weeks, months and perhaps years), until one day you hear "too
low" and you know you are a real speedskater (I never heard "too
low").
If the coach is really providing feedback, it should be feedback
about the state of the controlled variable, not advice about how
to change the output. The coach should should yell "Positive 15
degrees," describing the angle the skater's back is making with
the desired line. The skater must know what the intended angle is
-- zero. If the coach just yells "Lower!", the skater has no idea
whether the actual angle is getting lower, or by how much, or how
much error is left to correct. What the coach must do is provide
information equivalent to what the skater would get if standing
at the side of the track watching a side view of the body, with a
reference-view of the ideal position superimposed.
Feedback is the effect of a variable on itself. The variable the
skater wants to control is the "lowness" however it is defined.
By acting on the basis of the difference between actual and
desired lowness, the skater can control lowness. All the coach
can do is provide a verbal definition of the reference
perception, and a running verbal report on the actual perception.
The skater is controlling for the coach saying "Zero degrees" or
whatever, by varying the perceived body configuration while
skating. At the same time, the skater should be noting and
remembering how the body configuration feels, building up a
kinesthetic reference image of the "proper" configuration for use
when the coach's feedback is no longer present.
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Your application to teaching chords is a little different from
the skating example as you presented it, and a little closer to
my revision.
Now the coach is controlling the perceived center note in a triad
by means of a control handle that disturbs a visual cursor, and
the student is correcting the cursor position by means of playing
different center notes in a triad. The coach's action directly
affects the cursor and the student's action directly affects the
central note, but the coach is controlling the note while the
student is controlling the cursor. Organizationally, this is just
like one of Tom Bourbon's two-person tracking tasks, but two
different modalities of perception are involved.
What makes your suggestion pregnant with teaching possibilities
is the fact that by using one control task, the coach can
demonstrate directly to the student how a different perception is
experienced when being controlled as the coach wants it
controlled. Furthermore, the new perception to be controlled is
actually being altered by the student's actions instead of by the
coach's. The coach isn't just reaching in and pounding on the
right note. So the student is learning the output coordinations
required for controlling the new perception, while experiencing
control of the old perception which is easy to control.
Of course the student must reserve some attention for the new
perception. At first, I suppose, most of the attention will be on
getting the cursor to the target position and keeping it there.
At the same time, however, the sound is being experienced, as
well as the actions being used for control, so experiences of the
right relationship between action and sound are being recorded in
memory. Playing the central note that keeps the cursor on the
target also produces the sound that the coach is trying to get
the student to perceive, as well as the lower-level actions
required to create that sound.
This is the counterpart of Rick Marken's "mind-reading" demos:
it's the transmission side of telepathy. "If you just vary that
middle note until you see the cursor on the target, you'll be
hearing the sound that I'm thinking." The coach never has to emit
the wanted sound out loud: it's always produced by the student.
Is this telling us something about how we learn new control
systems in general? We control one perception by actions that
have side-effects on other perceptions. Eventually we notice
those side-effects, remember them, and try to reproduce them
instead of using the same actions to control the original
perception. Of course the actions are a little different, they're
related a little differently to the side-effects, so we end up
with slightly different patterns of action in controlling the new
perception -- and those different patterns of actions have new
side-effects, and so on ad infinitum.
Looks like your idea might wake us all up. Beautiful.
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Best,
Bill P.