We still need DATA

[From Rick Marken (940615.1600)]

Martin Taylor (940615 15:00) --

Just to make it concrete, let M=30, N=3, and the disturbance bandwidth
to each of the M be 1 Hz, and the bandwidth of each of the N outputs
also be 1 Hz. According to Rick, the M angels will naturally dance on
the perceptual control pin-head, without problem. HPCT says so. Good.
Show it.

No experimental data is needed to discover that it is impossible to
_simultaneously_ control 30 perceptual degrees of freedom with 3 output
degrees of freedom. I never asserted that this was possible. What I have
been asking is "what is the alerting phenomenon and why does it need to have
some new feature that switches from control of one perceptual signal to
another"? I want DATA sans model -- not model sans data (all I ever get from
you -- you cad ;-)).

You are assuming that a person is in a situation like this:

p1 c1 o
p2 c2
p3 c3
p4 c4
p5 c5

Here we have 5 perceptual inputs to the comparators of 5 control systems but
we only have one output df. The situation (as you described it) assumes that
the output only affects the perception of the control system to which it is
attached (c1 at the moment). So there must be something that switches the
output to one of the "free" perceptual signals when that signal moves "too
far" from it's reference (ie. there is an "alert").

I could develop some scheme for allocating o to the "free" perceptual signals
when necessary; but how in the world would I know that what I was doing had
anything to do with anything? There is no data against which to check the
model I come up with. This is masturbatory modelling -- fun, but it doesn't
have much hope of accomplishing anything :wink:

I can imagine situations like the one described above; a subject controlling
5 cursors with one mouse cursor, for example. The mouse cursor (o) influences
a controlled cursor (p.i) only when it is within the band of controlled
cursor movement. So the subject has to move the mouse cursor to the
appropriate controlled cursor band in order to control it. We could get
an idea of what constitutes enough of a discrepency in a controlled cursor to
merit movement of the mouse cursor to it.

The model would probably require no new mechanisms; I would imagine that a
higher level system could monitor something about all five controlled cursors
and change the reference position of the mouse cursor as necessary to control
this perception (and, in the process, control the individual controlled
cursor perceptions).

This would be a good experiment to do. It is obviously relevant to some
"process control" issues. Would somebody out there PLEASE do it. Once we
have the data we can start building the PCT model of a person doing it.
Could be VERY interesting. Actually, this is something that Bill P. has
suggested studying for some time. It looks like a perfect way to get a start
at studying "allocation of attention" (or control). Rich Thurman -- how
about you? Seems like something the Air Force might like!

Best

Rick

[Martin Taylor 940616 11:00]

Rick Marken (940615.1600)

No experimental data is needed to discover that it is impossible to
_simultaneously_ control 30 perceptual degrees of freedom with 3 output
degrees of freedom. I never asserted that this was possible.

Good. I've been misunderstanding you. I thought that was what you had
been asserting. By your posting, you have leapfrogged my "plan" for the
next two postings, and we can go on to the meat.

Let's take your proposed experiment, and add one little feature to test
for any possible differences between "alerting" and simply maintaining
a lot of perceptual signals tolerably within bounds. Your experiment,
as described, is just as good for the purpose as the one I had intended
to bring up after I had convinced you of the statement quoted above.

I can imagine situations like the one described above; a subject controlling
5 cursors with one mouse cursor, for example. The mouse cursor (o) influences
a controlled cursor (p.i) only when it is within the band of controlled
cursor movement. So the subject has to move the mouse cursor to the
appropriate controlled cursor band in order to control it. We could get
an idea of what constitutes enough of a discrepency in a controlled cursor to
merit movement of the mouse cursor to it.

The model would probably require no new mechanisms; I would imagine that a
higher level system could monitor something about all five controlled cursors
and change the reference position of the mouse cursor as necessary to control
this perception (and, in the process, control the individual controlled
cursor perceptions).

Right. For this purpose, I'm not sure that 5 is enough, but let's assume
it is for the moment. The experiment can surely be programmed to make 5
easy to change to 50 if necessary.

I imagine that you are correct in general terms in how the model would
work, but I'm not clear in detail about what the model would be, in its
linkages between the higher and lower control systems.

The perceptual signal of the higher one(s?) presumably is a function of the
set of discrepancies between the lower target and cursor values (i.e.
the higher has ERROR signals as input rather than perceptual signals,
which is a bit of a deviation from the normal model.) But I assume I
am misunderstanding the model you have in mind.

Be that as it may, my variant on the experiment is to have two different
conditions, one that should show an alerting effect and one that should not.
Both have exactly the same spatial display, as described by Rick (making
sure that the target locations for the 5 cursors are not colinear or
related in any visually obvious way). The difference is in an anciliary
display that affects a DIFFERENT perceptual signal than the target/cursor
location perceptual signals. The anciliary display should affect something
we (some of us) think of as suited for alerting, such as visual flicker
or movement, colour change, acoustic events or the like. The everyday
description of the anticipated effect of the anciliary display is to
draw attention to some condition in the main display that requires "attention"
(i.e. a large and increasing deviation between cursor and target).

Let's get specific, and talk about something that can be programmed in
HyperCard, because Rick is quick and good at that.

Divide the screen (card) into N vertical strips, where N is a setup parameter.
At a random height within the middle 1/3 of the card, on each strip, place
a target line. Within each strip, put another mark (cursor) that drifts at
some velocity. This velocity is what mouse movements will affect when the
mouse-cursor (arrow) is within the particular strip. Each velocity is
also affected by random disturbances. There, within each strip, we
have an ordinary control problem. The subject has to keep the drifitng
cursor as close to the target mark as possible, while its velocity is
being affected by random acceleration imposed from outside plus acceleration
derived from the position of the mouse within the strip. For a single strip,
we can obtain model parameters for a best-fit single-level control system.

When we change N, the number of vertical strips, we can model with a single
control system per strip the performance on that strip. I assume that
one more parameter is needed, related to whether the mouse-cursor is on
that strip, because if it isn't, the gain of the control system for that
strip must be zero (not reference of zero, because if the perceptual signal
in question is the target-cursor difference, the reference is always zero).
During periods in which the gain is zero, the behaviour will not be well
fitted by a model in which the gain is non-zero.

That's condition 1--no alerting.

In condition 2, everything is the same, except that for each strip we
define (but do not display) a set of distances away from the target.
Call these distances d1, d2, d3... We use the distances as follows:
For each strip, specify a pitch of a tone, progressing as on a piano
from low at the left to high on the right. If the cursor for a strip
crosses a distance dn going away from the target, emit a string of n beeps
at the pitch associated with that strip.

That's condition 2, with alerting.

The question of the experiment is whether there is any difference between
conditions in the likelihood of large excursions. I anticipate that
there will be differences, more so if N (the number of strips) is large,
and less so if dn is so small that there are differently pitched beeps
going off all over the place. The optimum value of dn should increase
as N increases, but I don't intuit a reason for the form of that relationship.

I don't think that one can say that condition 2 is one in which the subject
controls for a different perception (no beep), because the beep occurs only
in imagination until one of the spatial controlled perceptions gets too
far out of control, and when it has occurred, it will not recur unless
the spatial variable's error is reduced in the interim across the d1
threshold. Of course, if that spatial variable is not controlled, a
double (and later a triple) beep might occur, but they, too, would occur
only in imagination until they actually happen, and then there would be
no action on the part of the subject that would alter the fact that they
had occurred. So I think one can say that the controlled perceptions are
the same under both conditions.

Rick, can you program this?

ยทยทยท

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Rick Marken (940615.0900) to Bob Clark

If YOU perceive a mismatch, there is an error, YOU perceive a "disturbance,"

You are making "Martin's mistake".

I don't understand what is my mistake here. I have never, so far as I am
aware, talked about perceiving a disturbance. I have always talked about
the effect of the disturbance on the perception of a CEV. And that, one
does perceive, to the extent that it is not countered by the effect of
the output of the control system. Bob is talking about a condition in
which the output has failed (so far) to counter the disturbance.

However, that aside, I find that every time you deal with the program-level
control of perception, it becomes a little clearer to me. Maybe I will
wind up seeing it as you do, maybe not. But at least it becomes less
confusing and vague in my mind. Thank you for that.

Martin