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.

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