From Tom Bourbon [931202.0909]
(Once again, my dateline is correct, but for how long?)
[Martin Taylor 931201 15:30]
(Tom Bourbon 931201.0927)
I always cringe when I see mail from Tom that starts something like:
I have a question for Martin about one part of his recent reply to Rick.
Tom knows!... Yes Tom, Mea culpa, mea maxima culpa.
I have a question for Martin about part of his repentant reply. But I will
save it until the end of my reply to him.
Martin:
. . . And when you have
two or more interacting control systems that do not have a hierarchic
relationship, you have to use dynamical analysis beyond simple control.
Tom:
You have made this remark, or others very much like it, many times on the
net. Specifically, why do you believe this is so?
Martin:
As stated, it's obviously wrong. And stupid. As soon as I saw your
posting, I could see that I had been taking a viewpoint that excluded
the one you are using, and had blinded myself to the obvious fact that
one CAN simulate and model as many interacting control systems as one
has compute power for. I was thinking analytically, and even there I
was wrong for small numbers of linear control systems.
I *thought* your earlier remarks might have been oversights. I am pleased
to know that was the case.
In context of the rest of what you call my "frequent assertions about the
necessity of using dynamical analysis," I plead mitigation in that I have
always pointed out that dynamical analysis is the general case, and control
analysis the specific. When the specific can be applied, as I have said,
it is more precise and better to use it. So although I may have used language
that could be so interpreted, I have not been of the opinion that dynamical
(general) analysis is better used where control system analysis is available.
Understood, but the language in many of your posts sometimes gives the
opposite impression. A few years ago, at a CSG meeting in Kenosha,
Wisconsin, Wayne Hershberger talked about the need for PCT theorists to use
"radical" language, meaning that we should be diligent in our efforts to
state the differences between PCT and other theories as clearly and
consistently as possible. We all agreed, but Wayne's injunction is easier
in the saying than the doing. There is no need for one of us to cringe when
reminded by another (or several others) that we have slipped up.
But there is a difference, as I posted to Bill P. Control analysis
describes process, dynamical analysis describes a space of behaviours.
They may often be two views of the same thing, which are in no conflict.
Whether or not there is conflict depends on the ends toward which the
various parties direct their analyses. I have no reason to question most
of the ends to which I see people applying dynamical systems analysis (DSA).
(I am not competent to question most of those applications.) However, when
psychologists claim that DSA adequately explains behavior and that PCT does
not, I am interested. When the models offered by DSA people as explanations
of a particular kind of behavior do not behave, but PCT models of the same
kind of behavior do behave very nearly the same way as people behave, then I
believe the DSA models are wrong, or irrelevant. I feel perfectly justified
in so saying -- in those particular instances, but such a comment implies
nothing at all about applications of DSA in other areas.
So, Martin, your frequent posts asserting the importance of dynamical
systems science are expressions of pure faith? ;->
I've never been sure of the position of "pure faith" in science. My position
is that we have a body of mixed fact and assumption that we take as true,
though that body does change over time. At present, we take as true
Einstein's laws of General Relativity, the laws of thermodynamics (in
particular, for PCT, Boltzmann entropy), the standard model of quantum physics
and stuff like that. We use, as if they were true, Newton's laws of
mechanics, because we are dealing with things whose size and velocity
do not require us to use either General Relativity or quantum physics.
Agreed, but in all of the instances you cited, I am certain that you can
provide specific illustrations of how and why those "laws," models and
"principles" merit our faith. In the case of "using" DSA to explain the
phenomenon of control, when Rick asked for examples, you said you
couldn't think of any. Perhaps I should have said *blind* faith, rather
than *pure* faith. ;-))
. . .
Another thing to consider is the question of generic versus non-generic
dynamics. Your helping studies are generic, whereas at least some of
Kent's demonstrations are non-generic in that the results depend on the
two control systems having the same dynamical parameters. Two parallel
control systems DO help one another when their references and dynamics
are the same, but not, as you have in many ways demonstrated, when they
are different. The dynamical concept of genericity is a useful one.
Agreed. In the various cases of two interacting elementary PCT models
that I have examined, the interactions *we* see, and the name we give them,
depend on the reference signals and the gains of the two models. And, of
course, on the couplings between environmental variables. The models are
the same, in their organization, but can differ in reference signals and
gains. Given only those differences, and the same environmental couplings,
two models, or two people, can create the impression that there is a large
array of "attractor basins."
. . .
The kind of thought I had in mind when talking about two or more interacting
control system was the approach to an attractor, which will be exhibited
not by either control system individually, but by the behaviour of the
interacting pair. Maybe the (externally observed) state of the doubly
influenced CEV approaches a steady state, maybe it oscillates, maybe it
goes chaotic, but the joint system exhibits some kind of dynamic. That
dynamic and its corresponding attractor-repellor structure describes how
the control group performs when the CEV is disturbed.
It describes **the state of the CEV** when the control group performs. It
says nothing at all about *how* the group performs, in terms of mechanisms
or their functions. What PCTers disagreee with is the assertion by some DSA
psychologists that they can explain *how* and that PCT cannot. You also
expressed this idea:
. . . As I wrote to Bill P. (was it in the post
I repeated to the net?), a dynamical analysis describes the overall
situation, control analysis the process that makes the situation be what
is described.
Pleae tell me, (1) specifically, *why* do
you say "you have to use dynamical analysis" in that instance, and (2)
specifically *how* how would you use dynamical analysis to improve on the
accuracy of re-constructions and predictions that I achieve with two
independent PCT models? I would appreciate thorough answers, on the net, to
both parts of my question; I have long been puzzled by your frequent
assertions about the necessity of "using" dynamical analysis any time there
are more than two non-hierarchic control systems.
(1) I misspoke. As to "*why*" I said that "have to" rather than "may,"
I don't have an answer.
OK, for now. But "we" will be watching! :-)))
(2) I don't believe that anything I wrote, considered in context of the
net interactions, could easily be taken to say that dynamical analysis
would
improve on the
accuracy of re-constructions and predictions that I achieve with two
independent PCT models
Neither do I (think you said that). That was why I wondered what point
you were trying to make in the original post, and in others like it in the
past, when you said we "have to use" DSA.
Any analysis tuned to the specific will always (if correctly done) achieve
better results than an analysis based on the more general case. But if
any specific analysis produces results that are inconsistent with the
general case, it is the specific that must be examined for unwarranted
assumptions or incorrect execution.
PCT modeling of an instance of control by a living system recreates the
phenomenon of control *and* it incidentally produces the side effects that
so fascinate DSA people. In contrast, the DSA models and analyses we have
seen all provide descriptions of the side effects, but they do not produce
control behavior. Applying your argument, I believe we can conclude that
the general analysis produces results that are inconsistent with nearly all
specific analyses and that it is the general that must be examined for
unwarranted assumptions or incorrect execution.
Eager to see your reply,
I don't know whether this is enough to satisfy your eagerness.
Much of it. Thanks.
. . . Before
learning of PCT, I did indeed approach the questions of thought from a
more general dynamical viewpoint. I wrote (for Behavioural and Brain
Sciences) a rather critical review of "The Emperor's New Mind" based on
this view as opposed to the algorithmic view of thought, and I would
change none of it now. I think that my exposure to the dynamical view
is one reason I found PCT so immediately congenial. Perceptual Control
is the special kind of dynamics that works for living systems.
So, DSA was one of the rafts that brought you to PCT. Was it Lao tzu who
spoke of people who so love the raft that carried them safely across a
river that they struggle to continue carrying it, long after their path has
taken them into the high mountains? (It can be difficult indeed to let go
some of the traditional baggage -- or to step out onto the unseen bridge.)
(Relocated from the beginning of the paragraph above)
Incidentally, you, Rick, and Bill all have put me into some kind of
"dynamicist" camp, when all I have tried to do is to show that a dynamical
viewpoint need not be inconsistent with a control viewpoint.
My question to you is this: Why do you say I have put you into a
"dynamicist" camp? All I asked was why you said:
. . . And when you have
two or more interacting control systems that do not have a hierarchic
relationship, you have to use dynamical analysis beyond simple control.
Until later,
Tom