<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

sciences.

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

find.

Regards, Bob Clark