From Tom Bourbon [931209.1530]
Earlier, [Tom Bourbon 931209.1320], I posted a reply to Bob Clark's
inquiry [931208.1410 EST] about the meaning(s) of "dynamics" in recent posts
on csg-l. I am preparing a paper about using PCT to model several kinds of
coordination. The project requires that I refresh my memories for what the
dynamicists in psychology say about coordination. For Bob's sake, and that
of anyone else who is not familiar with how behavioral scientists use
nonlinear dynamical systems analysis, I thought the titles of a few articles
in that area might be informative. (My earlier post was about an article on
learning, behavioral attractors and phase transitions.)
GP Bingham, RC Schmidt, MT Turvey, LD Rosenblum (1991) Task
dynamics and resource dynamics in the assembly of a coordinated
rhythmic activity. Journal of Experimental Psychology: Human
Perception and Performance, 17, 359-381.
BA Kay, EL Saltzman, JAS Kelso (1991) Steady-state and perturbed
rhythmical movements: A dynamical analysis. Journal of
Experimental Psychology: Human Perception and Performance, 17,
183-197.
RC Schmidt, PJ Beek, PJ Treffner, MT Turvey (1991) Dynamical
substructure of coordinated rhythmic movements. Journal of
Experimental Psychology: Human Perception and Performance, 17,
635-651.
Each article contains lengthy, detailed dynamical analyses and explanations
of phenomena that are defined in terms of group statistics. In each case,
the authors rely on relationships for which the statistically significant
R-squared ranges all the way from .050 to .964. Far and away the majority
of the R-squares are near .3, so most of the analyses and explanations are on
pretty shaky ground -- the coefficients of alienation are very high for most
of the data.
For me, the clearest review of behavior as a dynamicist sees it
is in the following article:
MT Turvey (1990) Coordination. American Psychologist, 45, 938-
953.
This article demonstrates, rather clearly, some of the major points to which
PCT modelers object the most in the literature on dynamical systems analysis
in psychology. The article includes a brief history of work by Turvey,
Kelso, Kugler, and their associates. That history is divided into Round 1
and Round 2 of their research on coordination. Topics of interest to PCTers
seem to fall into the defunct Round 1. The following brief selection,
quoted from the article, is a good example.
"It is fairly obvious to all of us that any given coordination will exhibit
variations that depend on the context. Yet at the same time, it is clear
that the coordination from context to context has a certain sameness about
it. Consider reaching for an object on a table. Very many reaching
movements, starting at very many different places within the vicinity of
the object, can converge on the object. Any reachable object is like a
point capable of attracting a multiplicity of different limb trajectories.
In dynamical terms one would say that reaching -- regardless of when, where,
and with which parts of the body it is conducted -- has the features of a
system governed by a point attractor. If reaching is a task whose dynamics
are those of a point attrractor, then the challenge is to understand the
embodiment of this unvarying task dynamic in variable movement patterns.
Clearly, reaching admits of several alternative descriptions, of which the
point attractor dynamics is the most abstract, and a description of the
changes in joints and distance from the object is the most concrete.
There are two major challenges facing this style of analysis. One
challenge, obviously, is mapping the functional descriptions onto
qualitative dynamics, that is, identifying the attractor layouts. The othe
challenge is to identify the coordinate system in which the invariance of
the dynamics is revealed. In Round 1, an effort was made to give accounts
of coordination in terms of invariant parameters defined at the descriptive
level of muscles and joints. . . ." (pages 951-952).
In Round 2 the effort is directed away from the primitive level of muscles
and joints and toward the more abstract level of attractors, trajectories
and patterns averaged across the performance of several subjects.
I believe a fair reading of this literature reveals that the authors are
trying to create an abstract description of idealized (averaged) patterns of
appearances. They are trying to account for the outward appearances of
actions -- behavior as seen by an outside observer, hence their interest in
trajectories, averaged patterns, and the comparative styles of different
kinds of descriptions.
Turvey's uses of "attractor" seem a little slippery to me -- the problem is
probably in me. My interpretation of each usage is shown as [TB: ]. In
just the short the passage I quoted, Turvey speaks (1) of how any reachable
point is "like a point capable of attracting" [TB: point (e.g., object on
table) is capable of attracting a hand (causing reaching)], (2) of how
reaching "has the features of a system governed by a point attractor" [TB:
point attractor (e,g, object on table) governs reaching], (3) of reaching as
"a task whose dynamics are those of a point attractor" [TB: a task, such as
reaching, has the dynamics of an attractor -- the task possesses or shows
the dynamics], (4) of "point attractor dynamics" as an abstract description
of reaching [TB: the dynamics of an attractor (e.g., object on table), not
of reaching, describe reaching, which is the task], and (5) of attractor
layouts as mappings of functional descriptions onto qualitative dynamics
[TB: I can't decide what to say about this one -- attractors conceived as
layouts which are mappings of descriptions onto dynamics?].
The remainder of Turvey's article is equally rich as a source of material on
the new (nonlinear) dynamics in psychology. There are some pretty clear
differences between PCTers and behavioral nonlinear systems dynamicists.
Until later,
Tom