T. R. Young

The Red Feather Institute

and

Texas Woman's University

Denton, Tx., 76204

Prepared for the 1995 Meetings of the North Central Sociological Association

and the session on Social Stratification, Wm. Flint, Organizer.

Distributed as part of the Red Feather Institute Transforming Sociology Series.

The Red Feather Institute, 8085 Essex, Weidman, Michigan, 48893.

CHAOS AND THE CONCEPT OF STRUCTURE.

A. THE PROBLEMATIC: Postmodern critiques of structure and 'grand narratives'
are pointed at modernists conceptions of structure and process. The new
sciences of chaos and complexity render such critiques of limited scope.
The geometry of actually existing 'structures' do not fit the tight and
tidy models of structures such that boundaries can be clearly drawn, cases
assigned unambiguously and correlations derived which are always and everywhere
valid.

Instead, we see that in nonlinear social dynamics:

1. Process may or may not become structure

2. There are five dynamical states marked by bifurcations in one or more
key variables producing 'structure;'

3. Complexity increases at each bifurcation;

4. Structure becomes ever more fuzzy and difficult to locate as social
dynamics become ever more complex.

5. New techniques from physics and mathematics allow us to locate 'hidden'
structures in complex social data sets.

B. THE POLEMICS OF STRUCTURE IN MODERN AND POSTMODERN SENSIBILITY.

1. MODERNIST VIEWS ON STRUCTURE and the assignment of cases.

a. Structures have a euclidean geometry.

b. Structures are stable/permanent features of reality

c. Structures are bounded sets of similar events

d. Structures are caused/causal

2. POST-STRUCTURALIST CRITIQUE: HASSAN, LYOTARD, DERRIDA

a. Structure is 'totalizing,' re-representations of reality which fail
to transcend time/place, special pleadings for existing arrangements, one
of many readings which could be made of a socio-historical epoch.

b. Totalizing views of structure are inimical to human agency; individual
or collective. Such views tend to be nihilistic, simplistic, reductionist
reifications of a much more complex process most resistent to research.

3. CHAOTIC VIEWS ON STRUCTURE: From Foundations of Postmodern Science:

a. Structure change as bifurcations unfold [fig. 2]: the mix between
order and disorder increases by orders of magnitude at key bifurcations.

b. Structures are non-euclidean: they have fuzzy boundaries and fractal
'reality.' [fig. 3].

c. More than one structure can occupy the same time/space region [fig.
1]

d. Structures emerge [fig. 3] from feedback loops in which

e. structure is/becomes a 'causal' element as

f. other systems in time/space begin to respond to the mix of order/disorder

B. CLASS STRUCTURE AND NONLINEAR DYNAMICS:

1. The number of classes at each phase in time/space varies with key
parameters [see bifurcation map]; in simple dynamics, there may be but
two classes; with small changes in key parameters, class structures bifurcate.
Complex societies may have four, eight, sixteen or more class strata, each
more difficult to discover using modern techniques of measurement and inference.

2. Causality of class, as structure, varies with the mix of order/disorder;
causality fades and fails as bifurcations progress along a bifurcation
map of a social field.

3. Causality of class varies with the presence of other 'structures' in
the outcome field [Race, Gender, Religion, Ethnicity].

4. Causality of class emerges as 'entrainment' develops. Entrainment refers
to the fact that other systems/organisms in an eco-system __may__ come
to recognize and to exchange energy with newly emergent structures.

5. Primacy/determinacy of class varies with the nature of feedback between
it and other 'structures'

6. The boundaries of class structures become qualitatively less clear,
precise, or discernible with each additional bifurcation. It is possible
for a class stratum to occupy only part of the time/space continua; it
is then said to be a 'fractal.'

7. Classes and class structures may continue to exist and continue to have
'causal efficacy' even in very complex social dynamics.

8. Class, as a fractal structure, may have causal dynamics which change
dramatically at each bifurcation. That is, the effects of class position
may produce one kind of result in one part of an outcome field and another
result in a different part of the outcome field.

9. The concept of a 'feedback loop' is a better term to use to refer to
the causality of class structures. There are three kinds of feedback loops,
each of which produce differing dynamics:

a) Positive feedback. Class dynamics with positive feedback loops tend
to explode, that is, inequality becomes so great that bifurcations occur
after which boundaries are hard to discern. Monopolies are exemplars of
positive feedback and entrainment.

b) Negative feedback. Class inequalities tend to disappear with negative
feedback. Progressive taxation is a form of negative feedback.

c) Nonlinear feedback. Structure can be maintained indefinitely with nonlinear
feedback between class and other structures; race, gender, politics or
religion. Such structures are called, 'solitons' [fig. 1]

10. There are survival advantages to nonlinear feedback loops not well
thought out for social dynamics. In terms of capitalism and class strata,
it may be the case that some inequality, based upon technical divisions
of labor promote economic health. The same feedback, based upon social
divisions of labor [race, gender, ethnicity, nation and international status],
may produce so many complex social problems that whatever short term advantages
to the economic process they entail is lost to the long term de-stabilizing
effects. For example,

11. Social control and human agency becomes ever more difficult as bifurcations
explode to fill the space available to them. Planning and goal attainment
are very difficult in deeply chaotic regimes.

12. Research by Bryan Berry, U/Texas at Dallas, reports that both Kutznets
cycles and Kondratieff waves exhibit chaotic dynamics.

13. Research by Hübler, U/Illinois and James Yorke suggests that,
even in deep chaos it is possible, by identifying such patterns, to stabilize
social dynamics. Such control efforts, now far removed, require both the
information as well as a very light intervention...often as little as 5%
change will suffice.

Fig. 1. The Soliton | Fig. 2. The changing shape of Structure. | Fig. 3. From Process to Structure. |

**ARTICLES IN PRINT ON CHAOS &
NONLINEAR SOCIAL DYNAMICS**

1991 Change and Chaos Theory. The **Social
Science Journal.** 28(3). Fall.

Chaos theory and Symbolic Interaction. The Journal of **Symbolic Interaction,**
14:3, Fall.

Part I: Chaos and Crime: From Criminal Justice to Social Justice. **The
Critical Criminologist. V. 3., No., 2. **Summer.

Part II: Chaos and Crime: The ABCs of Crime. **The Critical Criminologist.**
V. 3., No.3. Fall.

The Archeology of Human Knowledge: Premodern, Modern and Postmodern Missions
and Methods for the Knowledge Process. **The Michigan Sociologist.**
Fall.

1992 Chaos Theory and Human Agency. **Humanity and Society. **V. 16:
4. November.

1993 The Great Flying Chaos Learning Circus: A Strangely Attractive Way
to Teach Large Sociology Classes. With Anna Zajicek, Jennifer Sult, Tim
Wolfe and with the assistance of Ruan Hoe, Andrew Philaretou and Joanne
Glago. **The Wisconsin Sociologist. **Fall.

1994 Chaos Theory and Social Dynamics: Foundations of Postmodern Social
Science. In Robert Robertson (ed.), **Proceedings of the 2nd Annual Conference
on Chaos theory. **Forthcoming.

ARTICLES IN DRAFT: Available from T. R. Young, Sociology, TWU, Denton,
Tx., 76204.

Chaos Theory and Management Science: Control, Prediction and Nonlinear
Dynamics. With L. Douglas Kiel.

CHAOS, CLASS AND COMPLEX SOCIAL DYNAMICS: Structure and Process in Postmodern
Philosophy of Science.

Chaos and Causality in Complex Social Dynamics.

**STANDARD REFERENCES:**

- Berry, Brian J.L.
- 1991
**Long-Wave Rhythms in Economic Development and Political Behavior.**Baltimore: Johns Hopkins University Press.

- Braudel, Fernand.
- 1980
**On History.**Chicago: U. of Chicago Press.

- Briggs, John and F. David Peat.
- 1989
**Turbulent Mirror:**An Illustrated Guide to Chaos Theory and the Science of Wholeness. New York: Harper and Row.

- Casti, John L.
- 1999
**Searching for Certainty**. New York: Wm. Morrow and Co.

- Ekeland, Ivar.
- 1988.
**Mathematics and the Unexpected.**Chicago: the University of Chicago Press.

- Feigenbaum, Mitchell,
- 1978 Quantitative Universality for a Class of Nonlinear transformations,
in
**the Journal of Statistical Physics**, 19:25-52. Cited in Gleick, p. 157.

- Gleick, James,
- 1988
**Chaos**: Making a New Science. New York: Penguin Books.

- Glass, Leon and Michael Mackey
- 1988 .
**From Clocks to Chaos**, Princeton: Princeton University Press.

- Holden, Arun
- 1986 .
**Chaos**, Princeton: Princeton University Press, 1986 .

- Hübler, A.
- 1992 Modelling and Control of Complex Systems: Paradigms and Applications.
**Modeling Complex Phenomena.**L. Lam, ed. New York: Springer.

- Kahn, Peter B.,
- 1990,
**Mathematical Methods for Scientists & Engineers,**Ch. 16, One-Dimensional Iterative Maps and the Onset of Chaos, p. 421. New York: John Wiley and Son.

- Mandelbrot, Benoit
- 1977
**The Fractal Geometry of Nature**. New York: Freeman.

- Penrose, Roger,
- 1989
**The Emperor's New Mind.**Oxford: Oxford University Press.

- Prigogine, Ilya and Isabelle Stengers,
- 1984
**Order out of Chaos: Man's New Dialogue with Nature.**New York: Bantam Books.

RF
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