infomystery, research proposal

[Marken_Richard_S1]

[From (the indefatiguable) Rick Marken (930317.1400)]

Avery Andrews (930318.0700)--

In general, you still seem to be ignoring the point that there are two
senses of the term `information' floating around, the `technical'
sense of information in `information theory' ...
and the ordinary sense, which nobody has any real theories about

In the ordinary sense p(t) alone does not provide info
about d(t), but there seems to be a more mysterious and technical
sense in which the information is `there'.

I think this is a bluff. I have asked for an explanation of how, in
the "techical" sense, information about d(t) is "there" in p(t).
I have not heard anything technically convincing. In a private
post, Martin Taylor gave the following techical definition of
information:

the magnitude of change in uncertainty, and
uncertainty is a property of a subjective probability distribution at
a location.

Based on this definition I proposed the following approach to
measuring the information about d(t) communicated in p(t):

I would say that the location of
uncertainty about the disturbance is "inside the control system".
I'll assume that inside the control system is a subjective probability
distribution characterizing the probability that a particular value
of the disturbance will occur at any time, t. So at each time, t,
the subjective probability distribution at t defines the control
system's uncertainly about which value of d(t) will occur at that
time. This uncertainty is changed (hopefully reduced) by the
the perception at time t (p(t)) which presumably contains information
about d(t).

It should be a pretty easy matter to make some
assumptions about the subjective probability distribution of d(t) at
each instant (my guess is that it would always be normal about the
mean expected disturbance value) and then compute the gain in
information that results from being given p(t) at each instant.

I think, from here, I could write a program to compute the information
about d(t) communicated to the destination by p(t). But there are
some details still needed -- I could make some reasonable assumptions,
but one man's reasonable assumptions are another's "see, you don't
understand information theory". So I am asking the information theory
experts to bless, improve or reject (with clearly explained
reasons why) the approach to measuring the information about d(t)
in p(t) that I described above. OK.

Richard Thurman (930317.1400) --

I may have a (partial) solution for you concerning people to help you
setup and run the experiment(s). This summer Dr. Tom Hancock will be
a visiting professor at this lab. He is under contract to research
"adaptive feedback based on Perceptual Control Theory" from mid April
to the end of August. I think that the kinds of experiments and
and modeling you are describing would fit in with what he has in mind.

The only stipulation I think I would need to put on the Lab doing this
type of research is that it needs to be couched in terms of training
and education. That is, any technical reports or published papers would
need to have a training spin to them.

Interested?

Sold.

And I think the training emphasis would be great. The idea
would be to show that training is largely a matter of learning
which perceptions to control, not which "outputs" to generate.

Keep in touch on this. If we do it over CSG-L (instead of
in private) maybe we can benefit from the advice of others.

Best

Rick

[_Martin_Taylor]

[Martin Taylor 930318 15:20]
(Rick Marken and Bill Powers, various messages 930317)

Let's look at the mechanics of what happens in a control loop, taking
Bill's example as a starting point.

In the following, B represents a CEV, in the specific example an object
connected by springs to A and C. The movements of A and C affect the
movement of B in opposing directions.

          A --- /////////// --- B --- \\\\\\\\\\ --- C

A control system has sensory input representing the position of B (and
nothing else). The position of C (or, equivalently, a force applied to
C) is the output of the control system. (The "equivalence" statement is
there to point out that the output is normally of a kind quite different
from the sensed variable, and there is a functional relation, perhaps
stochastic, between the output and its effect on the CEV.)

When we draw a disturbing variable in a control-system diagram,
we are drawing something analogous to A. The output is analogous
to C.

    Disturbing
     Variable ----////////--- CEV ---- \\\\\\\\ --- Output

Without knowing anything about the state of the CEV, we can
specify the state of the disturbing variable. If the units
involved are distances, we can specify the location of the
disturbing variable. If we observe the system for a while with
the disturbing variable in the position that has no effect on the
CEV, then suddenly move the disturbing variable to a new position
and keep it there, we may well observe something like this:

---------------------T----------------------------------------

                      **************************

Disturbing variable

*********************

---------------------T--------------------------------------
                      *
                       *
CEV *
                          *
*********************** * ************
                                 * *

---------------------T---------------------------------------

                                 * *
                             * *************
                          *
(Opposing) Output *
                       *
                      *
**********************
----------------------T---------------------------------------

(I have inserted time markers "T" in Bill's diagram axes).

At this point, my interpretation of the situation differs from Bill's,
at least I think it does. The following is a little obscure.

It makes no
sense to say that the control system's perceptual signal contains
no information about the CEV. That is why it has seemed so self-
evidently true to you that a disturbance (meaning an actual
change in the CEV) conveys information to the control system --
and so stupid of us to claim that it does not.

In the diagrams, at the moment the disturbance step occurs, it is fully
and completely represented in the CEV (and, by hypothesis, in the
perceptual signal, though that is a point we will wish to dispute in
later postings). As the effect of the disturbance is used by the
ECS, through changes in its output, the representation of the disturbance
is, so to speak, "bled off" the perceptual signal, to find representation
in the output signal. To the extent that the effect of the disturbance
remains in the perceptual signal, it is not in the output signal. To
the extent that it has been used to affect the output, it is no longer
in the perceptual signal.

Now consider the same situation, except that the ECS is blinded for a
period, so that even though A is moving, and thus affecting B, the ECS
does not move C to compensate. A moves left and right, slowly and smoothly,
so that B also moves in a continuous fashion (as only a third party could
see, the ECS being blinded). At time T in the diagram, the ECS is again
sighted, to detect that during the blinded time B has moved to the position
noted. This is not the result of a step disturbance introduced by a step
movement of A, but is the integral of all the effects of A's movement
during the blinded period. It is the integral of micro-steps that would
have appeared momentarily in the perceptual signal before being "bled off"
into the output, had the ECS not been blinded. To a first approximation,
it might well have seemed that those smooth changes in A would have had
NO effect on the perceptual signal, if (1) the gain were high, and (2)
the transport lag were low.

The point of all this is to try to demystify the "magical" fact that
there is no representation of the disturbance in the perceptual signal,
although there is an almost perfect representation of it in the output
signal. Given this way of looking at the situation, one can see there
is no reason at all to expect that the momentary control actions will
be the same on successive trials using the same disturbance pattern.
Near identity of that pattern would, as Rick has pointed out, be evidence
that the disturbance is in some way represented in the perceptual signal,
but unless the disturbance has components faster than the possibility of
control, that won't happen. Unless the disturbance has some macro-step
events (which have high-frequency components) that are not quickly
compensated by the output actions, the micro-step actions would be in
quadrature on successive runs. (By micro-step, I mean the results one
might get in sampling a continuous motion of a low enough bandwidth).

Is this an agreeable reformulation of what Bill wrote a couple of days
ago explaining the events going on around a real loop with finite transport
lag?

Martin