Tom Bourbon [931214.1217]

More on words, confusion and confused again.

[Martin Taylor 931210 12:10]

(Tom Bourbon 931209.1320)

I had posted in reply to Bob Clark.

Martin:

Thanks, Tom. Now I have a much better appreciation of what it is that

raises antennae when you hear the word "dynamics." I dissociate what I

have been talking about from the kind of thing you present. It's not

the same objective or even domain of thought, despite perhaps using

methods with the same mathematical background. As Bill P says, having

a common mathematical background doesn't give things equal validity.I guess I have to be more careful about what I presuppose in respect of

how people will interpret stuff. You have explained some reactions I

have up to now considered quite bizarre.

After that exchange, Rick and Martin began an exchange under the heading,

"confused again," which seems to oscillate around the idea that calculus can

be applied to the description and analysis of control systems, which

comprise a subset of dynamic systems.

## ยทยทยท

On my side, I am still trying to learn how Martin, and others, conceive of the relationships among PCT, information theory and the study of nonlinear dynamical systems. In a reply to Rick, Martin [Martin Taylor 931210 14:45] said:

"Before

joining CSG-L, I and some others here had been developing our own dynamical

approach to cognition, but it wasn't at all like what Tom quoted. We

were dealing with interacting physical systems, using as a text a set

of introductory books in what is called The Visual Mathematics Library.

They are called, misleadingly, "Dynamics: The Geometry of Behavior" by

Abraham and Shaw, Aerial Press 1984. I say misleadingly because the

behaviour in question has nothing to do with biological behaviour. It

is the behaviour of equations, and relates to all physical systems."

And he continued:

"The "dynamicists" I

referred to in my postings were people like Abraham and Shaw, probably

Prigogine and Nicolis, and people like that. Not people who look at the

various approaches to a human goal as defining an attractor dynamic (which

they do, in a loose sort of way) and treating that fact as an explanation

(which it isn't)."

I have not gotten hold of a copy of Abraham and Shaw, but I have seen, a

couple of years ago, Nicolis and Prigogine (_Exploring complexity_, 1989).

The dynamical psychologists I quoted also cite the people (A&S, N&P) cited

by Martin. The psychological dynamicists obviously see their work as an

extension or facet of mainstream dynamical analysis. I grow more confused!

In my search for more clues about possible connections among information

theory, dynamical analysis and PCT, I came across the following brief

article, from which I will quote a few passages. Martin, can you try to help

me see how the author's ideas might differ from yours, or resemble yours?

JAS Kelso (1992) "Theoretical concepts and strategies for understanding

perceptual-motor skill: From information capacity in closed systems to

self-organization in open, non-equilibrium systems," J. Exptl. Psy: General,

121, 260-261.

This was published as part of the APA centennial celebration last year. It

is Kelso's invited "brief impression" of a "classic" paper published nearly

40 years ago:

PM Fitts (1954) The information capacity of the human motor system in

controlling the amplitide of movement. Journal of Experimental Psychology,

47, 381-391.

Fitts's article is often cited as containing the first recognition of the

idea that movement time is "affected by" both the distance and the required

precision of the movement. The article is often said to be the first, or

one of the first, to bring information theory, a la Shannon, into psychology.

In the article, Fitts stated what has come to be known as Fitts's Law:

Movement Time = a + (b * [log base 2] of 2D/W),

where D = distance from starting position to center of target and W = width

of target.

In contrasting Fitts's article with recent work, Kelso writes about

recent conceptions of people as systems more complex than those studied

by Fitts. Recently, psychologists have "identified synergies and

coordinative structures" as solutions to the problem of coordination in

complex biological systems. To quote Kelso:

============================================

"This does not necessarily mean informational complexity as found in the

Shannonian view, which stems from the statistical mechanics of closed

systems. Rather, the existence of synergies in open, nonequilibrium systems

implies a smaller set of informationally simple but functionally meaningful

chunks. Their representational structure may be said to correspond to

attractive collective states of a dissipative dynamical system. Semantic

information appears to be created in dynamical systems by a cooperativity

among participating elements."

. . .

"How might Fitts (1954) see the field now, nearly 40 years after his seminal

paper? On the information-theoretic side he would see several important

developments. Among these are efforts to extend information theory into

nonequilibrium systems by Haken (1988) in Stuttgart (TB: see the note below)

and explicit attempts along similar lines to incorporate semantic

information into computational theory and computer design by Shimizu's

group in Tokyo."

============

Kelso's Note: "Haken (1988) developed the maximum entropy principle of

Jaynes. The latter has a nice ring to it for psychologists: 'If any

macrophenomenon is found to be reproducible, then it follows that all

microscopic details that were not under the experimenter's control must

be irrelevant for understanding and predicting it'" (Jaynes, 1985, p. 256).

H Haken (1988) _Information and self-organization_, Berlin:

Springer-Verlag.

# ET Jaynes (1985) Macroscopic prediction. In H Haken (Ed) _Complex systems:

operational approaches in neurobiology, physics and computers_ (pp.

254-269). Berlin: Springer-Verlag.

Back to Kelso's text:

# "Some years ago . . . I suggested that the reason for the *lawfulness*, or

regularity, evident in Fitts's Law was because the surface relation between

movement time and amplitude emerges from harmonic basis functions (e.g.,

mass-spring dynamics) tailored by boundary conditions (e.g., spatial

accuracy requirements). Guiard (in press) has recently produced quite

compelling evidence along this line. In particular, he observed deviations

from linearity (simple harmonic motion) in a cyclical aiming task as the

tolerance or accuracy requirements were systematically increased. The

relation identified by Fitts is lawlike, one assumes, because of the

ubiquity of periodic motion (regular and irregular) in nature and the

corresponding role of the (nonlinear) oscillator as an archetype of

time-varying behavior. It is important to note that whether such a

dynamical system exhibits postural states or discrete, rhythmical (or even

chaotic) behavior depends solely on its parameters. In this view, Fitts's

Law itself arises as a consequence of applying parameters to an underlying

dynamical law created by the nervous system for a specific goal-directed

action."

These brief quotes from a short commentary by Kelso provide some glimpses

of how closely the psychological dynamicists believe their work meshes

with that of information theorists and nonlinear systems dynamicists. For

example, twice Kelso cited the work of Hermann Haken. Haken has published

extensively on information theory and dynamical systems analysis, and on how

those areas are related. Kelso, Mandell and Schlesinger (1988) did a

Festschrift in his honor at the Center for Complex Systems, at Florida

Atlantic University. The papers are published as, _Dynamical patterns in

complex systems_, which is not readily available here.

All I have to show for my exploration is a clearer idea of the historical

links between information theory and nonlinear dynamical systems analysis,

and a greater sense of confusion over how either of those fields might apply

to PCT, other than at the level of abstract *descriptions* of the

superficial *appearances* produced by control systems as dynamic systems.

My faiure to see more to it than that does not mean there is nothing more,

only that I haven't been able to find it.

Martin, or anyone else, can you give me some help?

Until later,

Tom