<Bob Clark (940421.2155 EDT)>

Bill Powers (940416.0930 MDT) Subject: CONFLICTS

Thanks for the "appreciation."

It's not quite as serious a conflict as it seems on the surface, and
it's not entirely about mathematics.

I realized this as I read the extensive posts from you and Martin.

It occurred to me that this interchange could be used to illustrate
the development of a conflict from a friendly discussion of an
intellectual subject. This never really became a full-fledged
conflict, although the strength of the underlying emotions came
through to me very clearly.

Using a change of viewpoint to "move up a level" seemed to offer a
different approach to conflict resolution. The User's viewpoint
seems particularly appropriate here.

As I expected, you have now found ways to resolve your differences.
I was afraid you would succeed too soon -- making my remarks moot!

Perhaps you were not surprised, as I was, by the implications of the
poor, that is, discontinuous, control of the usual residential
thermostatic system. I have, in the past, thoughtlessly used this
system to illustrate the operation of the generalized, ideal control
system. However, the discontinuities, both in temperature and in
time, make this system far from ideal.

Another "quick comment." As I recall some of our early discussions,
we observed that effective control systems are ordinarily remain
close to their reference values. Thus the small displacement
approximation is appropriate for many situations. This, in effect,
is one justification for using minimal, linear systems as the ideal
systems. Anything beyond this can lead to many complex questions of
physics, engineering and mathematics.

In developing and exploring new concepts and approaches it seems best
to begin with a simplified, linear, idealized approximation, with
adjustments to be made as discrepancies and omissions become apparent.

Indeed, that has been the history of the development of the physical

I don't, by the way, put a lot of stock in the simple canonical
control system model.

Pretty hard to improve on it. Any suggestions?

I had expected that we would need nonlinear functions, on-off
control, control by parameters, and multilevel models even to handle
simple behaviors.

The Observer describes idealized living systems in terms of variables
that are continuous in both space and time. The Observer converts
seeming discontinuities into continuous form by changing scales -- of
space and time or both. Anything else rapidly becomes unmanageable!

I don't make any predictions as to what model will be needed to deal
with higher levels, except that it will bear a strong family
resemblance to the canonical model.

If you want a "prediction," I guess that's as good as any. More
important, perhaps, is _where_ is the ability to "predict" included
in PCT? And _who_, or _what_ does the "predicting?"

We need to discover omissions and discrepancies in the current
version of PCT. Items that are simply omitted are the hardest to

Regards, Bob Clark