[From Rick Marken (931214.0800)]

Me:

What would make you think that

dynamical mathematics would no longer apply?

Martin Taylor (931213 12:50) --

I've been arguing that they [control systems] ARE physically

realizable, and that the mathematics of dynamical systems DOES apply.

Every time I do, I get shot down, or at least shot at.

I think of calculus as the "mathematics of dynamical systems".

Are you saying that there has been a gross misunderstanding --

that all you are saying is that calculus applies to control

system behavior?

Me:

Aren't the variables

involved in perceptual control changing over time? Who disagrees with

the idea that a lot (all?) of dynamical mathematics is useful to to

PCT; how else would you mathematically describe a dynamic phenomenon?

Martin:

Do you, perhaps, own a mirror?

So you think I have been disagreeing with your proposal that calculus

applies to the behavior of control systems? I don't disagree with

this. Let me be very clear: calculus applies to the analysis of

control systems.

In your posts on this subject you mentioned "attractors" and

"attractor basins" which led me to believe that you were talking

about an approach to understanding purposeful systems based on

the idea that their "apparent" goals can be viewed as the "equilibrium

states" of "dynamical", "self- organizing" "complex" systems.

This "complex" or "dynamical" systems approach to understand-

ing living systems has become quite popular in some circles (the

Artificial Life Institute in Santa Fe, for example, is dedicated

to understanding living systems from this point of view). This

"dynamical" approach to living systems is nearly the opposite of

the approach taken by perceptual control theory; this is what I

thought you were referring to when you talked about the potential value

of applying dynamics to behavior: I though you were talking about these

kinds of "dynamical" models -- not calculus. Of course, these

"dynamical" models are completely useless and misleading (as far as

purposeful behavior is concerned) so it was probably silly of me to

think that you were claiming that such models could have much value

for the study of behavior. I should have known that you meant that

"calculus can be usefully applied to the study of behavior" -- a

statement with which I heartily agree.

Best

Rick