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