[Allan Randall (930317.1200 EST)]
Bill Powers (930315.0700)
This posting deals with the challenge, not the information
in disturbance or definitional stuff - I will probably
not have time to get back to that until I return from my
trip early next week.
Okay, this challenge thing. I decided from your last response
not to formally accept your challenge, since it seemed
directed at Martin specifically, and not at myself or other
Ashby-type information theorists. The reason is that you
pretty clearly stated that information theory would have to
supply a prediction that control would occur, from information
theory and Ashby's diagrams alone. If this is your position,
then I have no disagreement with you.
However, Martin has encouraged me to try one more time to
arrive at a mutually agreeable form for the challenge, as
he suggested I may be misinterpreting you. So here goes.
>You seem to be admitting here that information theory might
>have something useful to say about control systems.
Insofar as information theory could predict the limits of
performance given signals and signal-handling devices with
certain characteristics and in a known organization, sure.
Hmmm, again maybe we have no argument. Anything that does what
you just described sounds pretty darn relevant and applicable
to me. Perhaps we just value different things. It would seem
hard to believe that something that could tell you about limits
of performance would not also be useful in designing a control
system. Ashby's Law could be viewed as a statement about limits
of performance. Statements about such limits can be quite
fundamental. So if this is your position, then we differ only
in the degree to which we think information theory is relevant.
This is hardly a fundamental disagreement, and so the challenge
is indeed not directed at me, but solely at Martin.
>So I guess I still don't understand exactly where you stand. Is
>information theory completely wrong-headed or is it correct,
>but of little use to PCT?
Information theory rests on definitions and mathematical
manipulations...It's unlikely to be "incorrect" in those
terms... I don't yet see how IT is
actually linked in any rigorous way to specific physical
Oops. Now you seem to question its validity again (at least as
something that can be applied to physical situations). Is it
valid to talk about information transmission in a control
system as the mathematical measure called entropy? That is
the question. If using information theory in this sense is
not valid in the first place, then any "limits of performance"
measures you get will be utterly useless. So I am *still*
confused as to where you stand.
The prediction I'm asking for is
not how much control is required, but how much control there will
be in the two situations. To use a theory to derive the fact that
control will result from either arrangement means to make
predictions by manipulations that follow the rules of the theory.
What information theory will actually tell you is that there is
*more* control in the compensatory system. In fact, there is so
much control going on in the compensatory system that it would
be ludicrous to even suggest a real device or organism achieving
it. Information theory could tell you that the compensatory system
will do very poorly because it cannot be given the output
capacity or the processing power it requires. This kind of
prediction is what I think you have ruled out by saying:
> ... from Ashby's diagrams + information theory, one cannot
>predict what exactly R, the regulator, is doing. You cannot
>predict that R is going to oppose the disturbance. Whether this
>will meet your requirements for the challenge is the main point
>I'd like clarified before accepting.
If you stick with these conclusions, the challenge is unnecessary
because you have agreed to my original claim. You are agreeing
that information theory can't provide the predictions of behavior
that control theory provides, but can only be applied once those
predictions are known and verified.
Not quite. It can be applied before anything is verified. But it
cannot be applied to predict that control *will* happen - only
that it could (or could not).
So my version of the challenge would take Ashby's compensatory
and error-driven control systems and, assuming they were both
designed to control, make a prediction concerning which would
control better. I would not be able to say that either system,
from Ashby's diagrams alone, *would* control. Maybe they will
both play "Mary Had A Little Lamb," and completely ignore their
inputs, for all I know. But I *can* tell you which is more *capable*
If this does not satisfy your requirements for the challenge,
then I think we can all agree that you are specifically
challenging Martin's derivation claim and *not* Ashby's
quantification claim. However, I will do my version of the
challenge all the same, as I think it could be useful. I'm just
trying to determine here whether I can give you a formal
acceptance or not.
Allan Randall, firstname.lastname@example.org
NTT Systems, Inc.