Footnotes
The history of the false scientization of social dynamics began with Auguste Comte, Vilfredo Pareto and George Lundberg among many others. At first, Comte called his new science social physics. Pareto said: "My wish is to construct a system of sociology on the model of celestial mechanics, physics, and chemistry." Lundberg was even more explicit when he said, "The social sciences are concerned with the behaviors of those electron-proton configurations called social groups....It is sometimes convenient to use different words to designate behavior mechanisms of different systems or levels of electron-proton configuration. But certain basic concepts of proton energy and force are equally applicable to all behavior...from the point of view we have adopted, any situation in which we choose to observe association or dissociation is regarded as a field of force..." (Cited in Rickman, p. 299). Any such use of the concepts from one field of endeavor to the dynamics of another field is, technically, poetics. However, the choice of terms is more than mere poetics, it is political; the structure of bureaucratically organized work, politics, military, and school makes any theory using the concepts of force, power, and object and objectivity preferable to one using concepts of prophecy, definition, subjectivity and coercive sanction. The idea of a objective science of human behavior complete with universal laws and deductive predictions, which must be verified in the quest for truth, is a process which helps depoliticize the struggles of workers, colonial subjects, women, or students--anyone who challenges the putatively natural order of the social world dramaturgically embodied by mechanistic models of society. Return
Pauline Rosenau, (1992) offers a fine overview of postmodern critique generally and post-structuralism in particular. Those who find themselves mystified by the language and the esoteric examples will appreciate the lucidity and simplicity of her expositions. Return
A strange attractor is simply the pattern of the pathway, in visual form, produced by graphing the behavior of a system. Since many, if not most, nonlinear systems are unpredictable and yet patterned, it is called strange and since it tends to produce a fractal geometric shape, it is said to be attracted to that shape. The first such shape identified took the form of a butterfly; it arose from graphing the changes in weather systems modelled by Lorenz. The operative term here is self-similarity. Each event, each process, each period, each end-state in phase-space is never precisely identical to another; similar but not identical. Return
A mandelbrot set is an attractor with a geometric configuration in which the harmonious arrangement of order and disorder produce variations on a theme. These sets appeal to our aesthetic sense in that there is surprise and delight within pattern and contentment. Such figures appeal to our epistemological concern for insight based upon integration of the familiar with the strange. These sets embody the possibilities of change without end. They represent a universe that is not frozen in structure nor featureless. Echoing from each part of a speech act is a new sound; each new sound is full of potential for new meaning. Such sets are named after Benoit Mandelbrot who developed the mathematics to describe them. Mandelbrot sets adorn the covers and pages of every book on Chaos. Return
I want to be very precise here. If I were to point of a street light and say, that is a street light at one time, and then do the very same thing without pausing for breath, both the words given off and the street light itself would have changed; the electrons then present are now gone; the oxygen content of the surface of the metal would have changed; the amount of lumens given off would have fluctuated and the total amount of light in the area would have changed as cloud formation, moon phase, and proximity of the sun would have changed. The words used the second time would have changed as well since lung capacity, muscle tone and sound expulsion always differs; since body posture would have changed and thus resonance; since the micro-climate below the light would have changed thus affecting the speed and quality of sound waves. It is human convention to ignore such changes; not ontological necessary. Return
Roger Penrose, in his excellent opus, The Emperor's New Mind (Oxford: Oxford University Press, 1989), rates theories as Superb, Useful, and Tentative. He notes (p. 153) that Einstein's General Theory is accurate to about one part in 1014. By these standards, social sciences are next to useless. Marx, Durkheim, Spencer, Weber, Mead, Cooley, Blumer, Goffman and Garfinkel are seen as casual, intuitive, armchair amateurs rather than as foundational and seminal analysts. However, one would not impose Penrose's standards, given actual, nonlinear, dynamics of really existing systems. Invidious comparisons between social science and the 'hard' sciences are, thus, exercises in status politics. Return
Some will see the use of Chaos concepts as a poetic device by which to illuminate the dynamic and mysterious character of social reality. Some will see Chaos theory as a solid body of theory complete will numbers, principles, predictions and separate disciplines for each domain of dynamics. In the curious world of the postmodern, both can be right since each is using the symbols differently, and correctly, in each their own domain. A theory can be both a poem and a prediction in the postmodern sociology that I am trying to map out; they can be such in way that is more than poetry and less than science. Return
Gleick (1987:83 et passim) has a very readable section on the fractal geometry of nature. Mandelbrot presents his original work in more technical terms. See especially the use of Hausdroff equations to estimate fractal geometries (1977 [1982]: 361-366). There is also a discuss of the fractal and measurement early on in Chapter 1. Return
Grunts, sighs, belches, farts, and sneezes are physiological unit acts which are occupy some of the phase-space of a social event; scratching, rubbing, and doodling are non-game events of a behavioral sort. When one says something that is stupid, irrelevant or tactless, one excises that unit act by mutual agreement simply by saying, excuse (treat the act as if it did not occur) me. Whole runs of intentional behavior can be eliminated by the same social magic that produces social reality in the first place; simply by mutual, intersubjective agreement that such behavior did not occur or is irrelevant. Yet some runs of behavior have permanent, uneraseable effects. Return
The astute methodologist will appreciate that this point is a grounding for qualitative analysis--and a critique of quantification. See also the essay on Paradigm Theory in this series. Return
It does not take much imagination to guess that such deep structures provide a grounding for the god concept for those who have the genius to embrace such figurations. Without the tools of modern science and mathematics, understandings of deep structures in phase-space are a source of wonder and awe. Now they are a source of wonder, awe and empirical study. Return
See Roger Penrose (1989), The Emperor's New Mind, Chapter 2 on Algorithms, Chapter 9 on Real Brains and Model Brains as well as Chapter 10 on the Physics of the Mind. Return
One must be very careful to distinguish between Intersubjective social occasions in which personhood is accorded to each other and, far differently, objective action in which one being is treated as an object to be used, managed, manipulated or ignored. Much of the marxist critique of work; the feminist critique of patriarchy; the Black Power movement is predicated upon that difference. What goes on in a factory or marriage may or may not be symbolic interaction although words are used and behavior is shaped. The necessary reciprocity and mutuality of symbol use is lacking. See the several essays on the sociology of fraud in T. R. Young, The Drama of Social Life, for a systematic exploration of false dramaturgies in sports, politics, and marketplace. Return
In chaos work, there are four possible dynamic states: point attractors with linear dynamics; strange attractors and tori with nonlinear but fairly stable dynamics and a fourth state of far-from-stable dynamics in which prediction is impossible with even a complete knowledge of initial conditions and an infinitely powerful computer. James Gleick (1988: 73 et passim) has a nice explanation of bifurcations and the slow realization that bifurcations produced a patterned transition toward far-from-stable chaos. The definitive work showing the generality of bifurcations to qualitative change was done by Mitchell Feigenbaum. Whatever the system, when it reached the third bifurcation of a parameter, it began to explode into unstable dynamics at a point that is now called the Feigenbaum number, 4.669 (Gleick, pp. 171 et passim). See also Ch. 4, Iterative Magic in Briggs and Peat. Return
In this section, I emphasize the loss of order due to bifurcations. What is omitted here is the most exciting idea that the second law of thermodynamics does not hold for social dynamics; that new order emerges out of disorder. Rather than the bland emptiness of brownian motion or apocalyptic assertions of the dire consequences of disorder, much research in chaos has established that nonlinear interactions give rise to new and qualitatively different strange attractors. Ilya Prigogine took the Nobel prize for his work on the emergence of order from disorder. In social terms, disorder is prelude to change and renewal while resistance and rebellion are often helpful to the human project understood as praxis and community. Return
The onset of chaos has a very technical meaning; it means that two or more systems with the same initial conditions drift apart in ways that cannot be predicted; two or more molecules in a body of water; two or more populations in a food chain, two or more persons in a social system. In fixed point cycles, the behavior of members of a system can be predicted with precision; in chaotic systems, two parts track each other with greater--or lesser--similarity. In near to stable chaos (tori and strange attractors), prediction is possible but fractal. In more turbulent chaos, the distance between two or more such systems is progressively nonlinear; they diverge in ways that cannot be modelled. Return
Since writing this, Cheryl has foregone her education. Last month, she gave birth to a baby, Nathan. The marriage is intact. Her parents are in process of selling their cabin cruiser in order to help buy her a house. Her husband is marginally employed. Chances are good that Nathan's grandmother will soon be taking care of the child and Cheryl will go back to work at the Red Lobster. The economic position of young people like Cheryl and her husband, Michael, is too precarious to predict; they live close the cusp of catastrophe. Catastrophe, in this context means that the marriage will fail, jobs will fail and/or her college education will be postponed indefinitely. Their situation is the same as that of millions of other young married people living in a bifurcating society. Return
See Briggs and Peat, 1989, p. 119, for a discussion of the soliton and the nonlinear dynamics that produce it. Return
This is a very different attribute from linear systems where small differences in initial conditions produce small changes in some precise ratio to previous unit changes while large differences produce large and linear changes in outcome. Return
I refer to Lyapunov numbers. A Lyapunov number is an estimate of how fast neighboring points, variables, events in a river, highway or other dynamical system diverge from each other. Consequently, such numbers estimate how quickly correlations break down and how fast perturbations spread in a system. See Briggs and Peat, 1989: 87. Return
There are, to be sure, ugly and alienating uses to which postmodern expressions of art, science, music, architecture and medicine are often put. In other essays, I have listed and interpreted these negativities; the point here is to help create an emancipatory postmodern sociology as well a mandelbrot set of social forms that such a sociology describes and creates. Return