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Date:         Tue, 22 Dec 1992 10:18:25 -0800
From:         Marken@COURIER4.AERO.ORG
Subject:      Re: Rick on (off) Shannon

Sent this last night but got no ACK from CSG-L and
didn't see it on the net this morning -- pardon me
if this shows up twice; I'm possibly still suffering
from results of bad trip (well, the trip was fine,
actually -- the mail waiting on my arrival left some-
thing to be desired, however).

[From Rick Marken (921221 2000)]

Martin Taylor (921221 18:00)

Thanks for posting the correspondance; now I see what happened.

You said:

>I suppose I would agree that error could be controlled if it were to be
>provided as input to the perceptual input function of a control system that
>maintained the error at some reference level.

I replied:

>As you will see in a reply I plan to make to Greg, there is no
>supposing necessary in this case. The error signal (which is now
>a perceptual input to a control system) would DEFINITELY be
>controlled.

You said:

> But what on earth would that
> do other than enforce a situation in the ECS whose error was being
>controlled
>that would ordinarily arise only through unresolvable conflict.  I can't
>see why any hierarchy would include such a mechanism--but I suppose there
>might be a reason somewhere.

In other words, you were rejecting the idea that perception of error
in the control hierarchy should be the object of control by a reorganizing
control system. But the notion that perceived level of error
is an intrinsic variable controlled in a reorganization loop seems
necessary to explain the many cases of learning where you develop new
control skills even though you still can eat and breath. Dick Robertson
did a nice experiment to show that reorganization can happen for no other
reason than to solve a problem "better" than it's currently being solved;
no obvious "intrinsic" variable is controlled except control skill (low
level of error in the control system) itself.

So the discussion was about whether the reorganization model should
be able to control the quality of control (measured as perceived
level error in one or more control systems) -- and I think it should.
But we seemed to have lost this thread and moved into a discussion of
error and this is where I misinterpreted what you were talking about.
You said:

>Actually, what Bill has done seems to be a little more complex. He has
>found that the derivative of the squared error is a better criterion.

And I said:

>You mean, as the variable controlled by the reorganization system, right?

This was my mistake. When I saw your formula for error, (K1(e^^2)+K2(e*
de/dt), I assumed that this was the PERCEPTUAL FUNCTION,f, which transforms
error in the hierarchical control systems (e) into the perception
controlled by the reorganizing system, P, so that P = f(e). (I will
adopt your convention of using capitol letters to denote variables in
a reorganization loop -- small letters to denote the corresponding
variables in a "regular" control system in the PCT hierarchy). In fact,
your formula is for the OUTPUT function,g, that transforms the error in the
reorganizing control system (E) into the reorganizing system output (O),
so O = g(E). This fooled me because we rarely need to put non-linearities
into the output functions of our models of tracking type data; just
linear amplification. If we did add such non-linearities, they would
be "absorbed" by the control loop (assuming that they are at least
monotonic). But the output of the reorganizing system is not an amount;
rather, like the tumbles of e.coli, the time between reorganizing events
is the output that matters. So a non-linear output function might be just
what the doctor ordered to make reorganization efficient; now I recall
that THIS is what Bill discovered in his studies of reorganization
algorithms that we talked about this summer.

So, Martin, I was not arguing that error is controlled (as you mis-
takenly said in your summary of our exchange -- I'm quite sure,
unintentionally; I don't think you tried to mislead); I just said that one
intrinsic perceptual variable that might be controlled by a reorganizing
system (which is itself a control system controlling perceptions relative
to intrinsic references) is some measure of ambient error in the control
hierarchy itself. So now we can get back to THAT conversation; do
you think that reorganization involves control of perceived error in
the hierarchy (in human control systems)? Why or why not? Can you think
of a behavioral test for such a model? (These are serious questions-- I
don't know the answers but I would appreciate hearing suggestions -- then
maybe we could design some real experiments instead of just blabbering away).

As for Shannon and information theory; could you give me another sample
of this "understanding" of PCT that you get with info theory that you
don't get otherwise? Could it be that info theory is just one of those
comfortable old pieces of wisdom (like reinforcement, statistics,
reflexes, information processing, experimental methodology, decision
theory. etc) that just MUST fit into this (PCT) SOMEWHERE? What if it
doesn't?

Best regards

Rick
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