X-Envelope-to: CSG-L@vmd.cso.uiuc.edu
X-VMS-To: @CSG
MIME-version: 1.0
Content-transfer-encoding: 7BIT
Newsgroups: bit.listserv.csg-l
Date:         Tue, 22 Dec 1992 09:42:15 -0700
From:         "William T. Powers" <POWERS_W%FLC@VAXF.COLORADO.EDU>
Subject:      Misc replies

[From Bill Powers (921222.0800)]

Rick Marken & Martin Taylor (various posts) --

Your argument is based on a misplaced reference. When Rick said
that the squared error was a controlled variable, he was
referring to error signals in the hierarchy being sensed as
intrinsic variables and being controlled by the reorganizing
system. When I corrected Rick, I was influenced by the same
misreading; on hasty reading it was possible to confuse the
squared error in the hierarchy with the reorganizing system's own
error signal. So all this has been just a verbal
misunderstanding. It's made more confusing by the fact that in
the reorganizing system, the rate of reorganization seems best
based on a function of the absolute error and derivative of
absolute error in the reorganizing system (sign of error doesn't
matter when the output is a rate of application of a random
process). Whether this absoluteness is achieved by an absolute
value function or by squaring or by RMSing is a detail; I
happened to use squaring as a way of getting absolute value,
which totally confuses everything.
--------------------------------------------------------------
Greg Williams (921221.1500) --

>I suspect figuring out which types of nonlinearities to try in
>the models might be easier with steps/ramps. Also, be sure to
>look at a broad range of disturbance bandwidths, to make sure
>the "good" models aren't biased for a notch which you are
>gradually moving up the spectrum. I'll be interested to see
>your results.

The problem with using any kind of disturbance with predictable
properties is that higher-level systems get into the act. It's
been known for a long time among engineers and engineering
psychologists that tracking unpredictable waveforms produces
"deterministic" behavior, while tracking any predictable waveform
like a sine wave or square wave or ramp produces
"nondeterministic" behavior. Any regularity YOU can see in the
situation, the person doing the tracking can also see. So you
can't do the standard kinds of tests that are done with an
artificial system that is capable of behaving at only one level.

As I interpret these terms, deterministic behavior involves a
clear lag so that cause and effect can be separated in time. With
deterministic behavior it's possible to derive a transfer
function that fits the behavior quite well. Nondeterministic
behavior, on the other hand, involves spontaneous generation of
output in a way that can lead the disturbances. When a sine-wave
disturbance is used, the skilled participant adjusts a
spontaneously-generated sine wave output so its amplitude,
frequency, and phase match the disturbance (this works best for
pursuit tracking, I presume, where there is a representation of
the disturbance in the form of the target movements). The
movements of the cursor can actually get ahead of the movements
of the target, and there is no longer any simple transfer
function that can express the relationship.
I would not use terms like deterministic and nondeterministic; I
think that the difference is one of level of controlled variable.
One of the portable demonstrations from the 1960 paper by Powers,
Clark, and MacFarland shows this "nondeterministic" kind of
behavior as a demo of control of sequence (as we called it then).
The experimenter moves a finger up and down in a regular sine
wave while the participant tracks it with a finger. The frequency
of the sine wave is made rather fast, around 1 to 2 Hz. At some
unexpected time, the experimenter abruptly stops moving the
finger and holds it still. The participant's finger continues to
move, going almost a foot past the experimenter's finger before
any correction starts even if the halt is at a zero-velocity
point like the peak of the sine wave. This also works for a
continuous movement of the target finger in a circle, or in any
other simple predictable pattern. The reaction time to the sudden
break in the regular pattern is quite long, indicating to me that
higher order control is involved.

Now, of course, we can set up an experiment with continuous
control of such a pattern and measure the parameters. If PCT were
being taught as an experimental science in universities, this
would be a part of a nice experiment for a Master's thesis.
Unfortunately, all the real experimental investigation of control
behavior is being done by a small handful of people with no
funding or assistance, who are either retired and decrepit or
working full time at something else to make a living.

>What's the timetable?

The timetable is the same as always: when the queue gets emptied,
or when someone else decides to take on the project.

The proper way to do this kind of work is to analyze the lowest
levels of control first and get a model to fit them accurately,
then introduce variations on the experiments that supposedly
bring in higher-level variables, and model them USING THE MODEL
FOR LOWER-LEVEL BEHAVIOR OF A PARTICULAR INDIVIDUAL AS PART OF
THE OUTPUT FUNCTION IN A MODEL OF THAT INDIVIDUAL.

I've known for a very long time that this was the way to go, but
it wasn't until 1974 that I had even rudimentary computing
equipment to start doing this, and then it took me years to find
a simple model that really worked (and for the speed of computers
I could afford to increase enough to do the experiments right). I
did everything the hard way first.

It's been less than two years since I ceased to have to earn a
living by doing rather demanding things of no interest except to
my employers. Remember that since 1960 I have produced major
advances in low-light-level television astronomy including
designing and building three generations of astronomical
television cameras and a whole semi-automated observatory to do a
supernova search, a control system for ruling the best
diffraction gratings in the world, and numerous microcomputer  projects for a
 newspaper including one that took stock market
data off a satellite signal, organized it, typeset it, and sent
it to the APS typesetter to produce camera-ready copy in time for
the Bulldog edition (which went to press 15 minutes after the
last table was transmitted). The time and mental energy available
for developing PCT in the laboratory has been very limited. Now I
have time, but less mental energy (whatever that is, but you know
it when you see it).

The timetable depends, therefore, on the person-hours available
and the facilities for doing the research, including availability
of human subjects. As long as the list of people actually
devising and carrying out experiments and modeling is limited to
Rick Marken, Tom Bourbon, and me, the queue of possible
experiments with HPCT is going to grow while the actual work done
trudges along at a slow pace.

When I last looked, there were 132 subscribers to this list.
Permit me a moment of impatience: when are some of you people
going to get out of your armchairs?
--------------------------------------------------------------
Gary Cziko (921222.0430) --

>I don't think I did a very good job at trying to explain how
>tracking patterns can be seen as controlling a higher-level
>perceptual variable. Perhaps someone can help could help me out
>with this.  It is also related, I believe, to the discussion
>between Taylor and Powers concerning what a control systems has
>to be able to "predict" in order to maintain good control.

Literal prediction doesn't happen at the lower levels. When I
referred to "predictable" waveforms in the reply to Greg, above,
I didn't mean that the control systems themselves do any literal
predicting. It's just that waveforms with enough regularity for a
bystander to predict them can be perceived directly and
controlled. A frequency detector can put out a signal
representing the mean frequency of a sine wave without looking
ahead to compute sine(now + tau).

Think of "prediction" as a proposal for a model. It is always
possible to fit some mathematical form to a process, and compute
its value for some time in the future. The question is whether we
are to propose that the real system actually does it that way.
The equivalent of prediction can often be carried out by a simple
analogue process. For example, a sensor that strongly exaggerates
changes in stimulation produces a first-derivative component of
perceptual signal, which permits the action of the control system
to slow down before the error is actually corrected fully. This
can be interpreted as a prediction that if the present speed of
change kept up, the target would be overshot. But no such
cognitive process is really going on -- to carry it out that way,
literally, would require tons of machinery to do what a single
neuron easily does without any thought or "looking ahead" at all.
You have to ask whether the term prediction is meant literally or
metaphorically.
Maybe my remarks to Greg above will help.
--------------------------------------------------------------
Martin Taylor (921221.2000) --

>If a generative model does predict reality well, without
>excessive use of parameters, then it produces strong evidence
>of the plausibility of the theory that underlies it.

The control system model we use predicts detailed handle
movements within 5 to 10 percent with a single adjustable
parameter, the integration constant. By adding a transport lag,
we can approximately halve that error. So at most we need two
parameters to reduce prediction error to 2.5 to 5 percent. If we
introduce nonlinearities, we might get that down to 2 to 4
percent. But diminishing returns will set in pretty quickly. I
figure that we are pretty near the noise level set by the
discrete nature of neural impulses.
---------------------------
>In this case, the reference signal and the perceptual signal
>are both known within the ECS.  If you remember a long way
>back, this came up.  There is no need for an external
>evaluation of the probability distribution, any more than there
>is a need for an evaluation of a neural current that is based
>on a rate of neural impulses.

I think you're going to have to take us back to a more elementary
level. I still don't understand why a perceptual signal that is
maintained in a match with a changing reference signal is said to
have a LOW information content.

>The information arriving at a receiving point depends on the
>probabilities of the received pattern as believed by the
>receiver, which are unknown to any other party.

What does a simple comparator, which subtracts the perceptual
signal's magnitude from that of the reference signal "believe"
about either signal? What does "believe" mean in this context?

>The information the originator thinks is being sent is based >on
the originator's beliefs as to the probabilities held by the
>receiver.

What does a sensor "believe" about the probabilities held by a
comparator?

>In the 2Hz case, the presumption is that all these
>probabilities are flat (actually Gaussian) distributions,
>maximizing the information that could be transmitted.

Who is doing this presuming in the system? I asked why the
perceptual and reference signals should not both be considered to
carry an information flow appropriate to a signal varying within
a 2Hz bandwidth. You didn't answer that.
--------------------------------------------------------------  Best to all,

Bill P.