The world is not only stranger
than we believe it to be,
it is stranger than we can
imagine it to be.

...J.S. Haldane

INTRODUCTION Chaos theory is producing a fundamental shift in the knowledge process in all disciplines comparable to the shift in the 16th century from premodern understandings to the missions and methods of modern science. This shift in the knowledge process moves symbolic interactional theory from the periphery of sociology to the deep rich core of it. The ontology and epistemology of nonlinear dynamics subsume the messy, squiggly, squirmy, emergent dynamics of symbolic interaction far better than does the tight, rigid, mechanistic determinism of modern axiomatic theory. 1

The consequences of this conversion of social behavior to the language and logics of chaos theory for a philosophy of science should not be underrated by those in the social sciences. In the first instance, the mission of modern science assumes that there is, in fact, one set of universal and eternal propositions which govern the dynamics of all societies. That mission points all social research toward the discovery of general theory. The assumption of general theory presumes that societies which implement rational, lawlike social processes are higher on the evolutionary ladder than those who use folk methods and social magic in organizing social reality.

In the second instance, the presumed fact of linear dynamics and law-like theories grounds research which is oriented to the discovery of such theory through the method of successive approximations using hypotheses, prediction, quantification, observation and estimates of correlation to confirm or refute the truth value of theoretical statements. The ontology revealed by chaos research does not support the presumption of either linear dynamics nor formal, axiomatic theory. In turn, the method of successive approximations becomes irrelevant to valid knowledge of natural and social systems.

The central feature of the natural systems illuminated by Chaos research is the nonlinearity of their dynamics; while such nonlinearity is well established and well researched in the natural sciences, there are very few people working on nonlinear dynamics in the social sciences. In order to encourage such work, in the next section, I will illuminate the nonlinearity of social dynamics using symbolic interactional processes as the data with which to do so. All this is prelude to the larger task of shifting social science toward postmodern expressions of theory and method.

In all of this, the concept of magic must be carefully understood. By magic, I simply mean the appearance of events which do not follow logically and coherently from that which has gone before. In the kind of social magic of which I speak, the ordinary canons of cause and effect, cherished as the foundation of the modern knowledge process, are not operative. Rather one finds things happening which surprise, astonish and bemuse those of us who are accustomed to orderly and routine consequences in everyday life. The terms we use with which to refer to such nonlinear dynamics include miracle and indeed, the event is so unusual as to be worth looking at; wonder, and indeed the event is a source of constant wonderment; and mystery. However, Chaos theory removes most of the mystery. It is entirely within the logic of natural change patterns that wondrous things happen. This essay offers the reader an alternative to supernatural explanation for magic.

SYMBOLIC INTERACTIONAL THEORY, SOCIAL MAGIC AND NONLINEARITY Symbolic Interaction Theory is a loose set of assumptions about how symbols are used to create a shared frame of meaning which, in turn, is used to organize and to interpret human behavior in loose and everchanging patterns of work, commerce, family, worship and play. This process, symbolic interaction, is the solid empirical basis for a social magic in which that which does not exist and which has no causal precursors, does in fact come into actuality. It is a remarkable and wonderful process yet it happens everywhere two or more human beings define a situation, reify it by means of belief, organize their behavior as if such a social event were real and, in the consequence, create a fractal, intersubjective social fact.

Hope, trust, faith, and belief are nonlinear (and non-material) psychological processes essential to all effective symbolic activity. These psychological processes produce nonlinear effects (and come to be taken-for-granted) in all social life. All social reality requires the same 'leap of faith' that many use to characterize belief in the supernatural. The nonlinearity of the symbol using process draws upon trust, innocence and belief and is sustained by them. Of course, trust, hope, faith and belief, while essential to the production of all forms of social reality may be also used against the social process. And, it may be used up--although human beings have a rare capacity for believing and trusting in spite of all good evidence to the contrary.

Part of the postmodern critique is that, living in an age of modern science and exploitative economic, racial and gender relations, trust converts into cynicism while cynicism bifurcates into raw power on the one side or nihilism on the other. The subtext of this entire work can be read as an effort to reinvent society in such a way as to minimize the sociology of fraud and to enable the reinvestment of desire, trust, faith and belief into ordinary human relations at school, in market, in sports, as well as religion and government. Basic to the task is a knowledge process in which nonlinear transformations in human affairs are understood as neither irrational, imperfection nor deviancy but rather the stuff of which enlivening social relations are made.

The concept of structure is one in great dispute in the social sciences. Chaos theory offers a way to resolve the polemics around which a whole literature called 'post-structural' critique is found 2 . In brief, the argument goes that the very idea of structure is imposed upon an infinitely complex and interconnected whole. Extraction of any given pattern which explains, describes, predicts or otherwise accounts for the vast and variable whole is a political act which privileges such an account. Chapter 9, below, offers the argument in more detail. In social life-worlds, Marxian theory, Christian theology, Gestalt theory, exchange theory, freudian theory or any other such 'totalizing' explanation simply does not/cannot do justice to the messy, fuzzy, contradictory and inexplicable realities one encounters in daily life (Lyotard, 1984). Yet there are sufficient data which form a connected whole from which to generate these 'grand narratives.'

I will make several points from Chaos theory which helps sort out these polemics, coming down on the side of structural analysis for the most part but a very different kind of structure from that presumed by modern science and its post-structural critics.

It is the story of these remarkable geometries and nonlinear changes in the nonlinear dynamics of symbolic interaction that Chaos theory can help us understand. In that understanding is the promise of a society in which dynamics are created by intending human beings sufficiently stable to satisfy the human need for continuity and intersubjective agreement yet variable enough to satisfy the human need for change and renewal.

In making the case for nonlinearity, I ask the reader to visualize the actual embodiments of the various social forms to which I refer remembering that each such embodiment is a complex, variable and finely tuned whole that changes from moment to moment, day to day, year to year yet keeps much of its essential characteristics. If one imagines concrete social occasions in which one has been immersed, it will help the reader see the nonlinear, hence chaotic nature of social interaction and the everchanging realities it produces.

Strange Attractors There are several points at which the nonlinearity of symbolic interaction and the theoretical framework of chaos theory are easily connected. A centering concept in Chaos work is that of the 'strange attractor.' Such an attractor gets its name for two reasons; first, it is called an attractor since key parameters in the life of a set of human beings tend to create a pattern in the time-space of such persons. That pattern is called a 'strange' attractor since it does not fit the dynamics expected within the linear mechanics of a newtonian paradigm 3 . Newtonian scientists expect sameness and precision; symbolic interaction produces similarity rather than sameness. Newtonian scientists expect smooth transformations which can be plotted by linear equations; symbolic interaction often leads to nonlinear transformations in human behavior.

A close look at what each of us do every day reveals the nonlinearities and the discontinuities of social discourse.

In everyday life, human beings use four sets of symbols with which to generate quasi-stable embodiments of social reality. Iterations of all such embodiments in phase-space taken together has the self-similarity of a strange attractor.

These four media include voice, body movement, body decoration including clothing, as well as whole lines of behavior. The developing child learns to read each and every symbol in each and every one of these most personal of media. The developing child learns to weigh the harmonious and disjointed meanings embodied in the parallel expressions of symbolic messages by voice, body, clothing and behavior. It is a task that exceeds the capacities of even the most advanced mathematics or the most complex computers. To do symbolic work is to be human and it requires a most remarkable capacity; a capacity to create, store, retrieve and to use an infinite set of meanings.

In learning the use of each common symbol in each of the four linguistic systems mentioned, the child learns to use each such symbol in a variable but similar way. Thus the word, hand can refer to billions of concrete but different objects of which human beings have two each. The word hand has, in terms of meaning, a number of different attractor states; it can refer to a fingered appendage, a worker, a round of bridge, a round of applause, a set of cards, handwriting, assistance, or any number of variations there on. It is important to note that, in the actual use of any such symbol, the concrete object or the specific process to which it refers in never quite the same; it is similar but more--or less--different. Meaning always takes the shape of a strange attractor.

The pattern any given body gesture, any given item of clothing or any given cosmetic display as well as any line of behavior, if assigned meaning in a culture, also takes on the character of a strange attractor. Any embodiment of sound or motion has two components; one stable and one which varies depending upon conditions at hand. The use of signs, symbols and significations resemble the geometry of a mandelbrot set with infinite length, infinite center, and infinite detail. 4

Nonlinearity The actual process by which symbols are called forth is nonlinear; the use of any given word is chosen from among a set of closely related attractor states of meaning. 5 Thus were the next word I use in this passage to be 'passage,' I could have selected other terms including; section, text, paragraph, sentence, story or essay. It is impossible to predict linear causal linkage between the use of one word in a text and the appearance of the next word. Indeed, graceful writing and eloquent speech as well as apt behavior requires both pattern and variety. Writing in which either words or actions are entirely predictable is said to be trite; speech which is entirely familiar is said to be cliche. Surprise and variety is the spice of life in the preparation and presentation of food as in the art of love.

One can make probability statements, indeed authorship of ancient texts is attributed on the basis of habitual usage. However habitual is such usage, even so, it is not deterministic usage given the standards use in modern science. 6

All uses of symbols are nonlinear since different stimuli produce the same symbol; the same symbol produces similar but not identical response.

The human voice has several variable attributes upon which meaning can be assigned: pitch, timbre, volume, pace, harmonics, tone and so on all of which can be modified by use of lungs, larynx, tongue, lips, teeth, nose and other parts of the sound chambers. No one sound is ever exactly like another sound in any given iteration of that sound since body states vary, air quality varies, sound dynamics vary with architecture and since the sound waves from other sources make interference patterns.

No one gesture is ever precisely like another, similar gesture even though the same meaning might be assigned to it. Body position, muscle tone, nerve signals and states of awareness vary and interact in varying ways to produce an ever changing pattern for the same hand shake of welcome, nod of agreement, shrug of contempt or smile of delight. The fact that differences are ignored or that missing data are supplied in any such gesture means that symbolic activity is, again, nonlinear activity.

Hands, face, body posture, body tension, legs, feet as well as arms and shoulders are used to convey meaning. Facial muscles in combination can produce over 100,000 discernible bits of information. When one considers all the possible iterations of all possible embodiments of a single symbolic encoding using just body parts as a linguistic medium, one begins to see that each one can have a veritable mandelbrot set of iterations with infinite length, infinite centers, and infinite detail. No two iterations of a gesture, pose, or stance are ever alike. There is no linearity between the thought and the deed when it comes to body talk yet there is the human capacity to conceptualize any given embodiment as part of a region of meanings in a basin of concepts.

Body parts are often shaped by surgery, binding, tattooing or burning to convey information. Some societies file teeth, stretch necks or lips, cut off clitoris, or insert bone, metal or fiber objects into body parts in order to help define social status-role, social occasions or social boundaries. The iteration of body decoration for any given person is unique. Age, height, skin tone, skill, materials available, and all other components of body talk converge to form an infinitely variable universe of symbols. In actual symbolic interaction, both small and large differences in embodiments of body talk symbols are ignored and with that subjective interpretation, nonlinear meaning is taken and returned for validation.

Clothing, cosmetics and body paint, weaponry, tattoos, manicure, and jewelry are used in great array to define social standing, age, occasion, gender, religion, sexual preference, marital status, kinship grouping and other social facts. No one piece of clothing is ever worn exactly as before or as another wears. Body posture, body health, time of day, lighting or humidity affect shade, shape, or other features of display in infinite variety. Those who read such data take an active part in the language process. All symbolic interaction is interactive; that means it is not causal in a linear fashion [i.e., a ® b]; as presumed in most formal theoretical models of social causality.

Runs of behavior, from simple hand motions summoning, greeting or dismissing others to whole cycles of behavior that take years to complete are, also, assigned meaning. Psychiatrists become adept at reading the private meaning of cycles of destructive behavior for their primal meaning of rebellion, resentment, guilt or neurotic compulsion. Psychiatrists are often helpful in teaching patients to sort out the double, triple and quadruple binds in which they are put by differing messages being encoded and communicated in the same phase-space region by parents or other significate persons using voiced expressions to say one thing, body talk to say another, cosmetic and dress to say still a third thing and lines of behavior to confound and negate the other lines of meaning read out by the trying and failing child, wife or friend.

Preparation of a meal may denote an anniversary; the bringing of roses may denote a fine appreciation of a loved one; the re-enactment of the Stations of the Cross at Easter time may denote a re-commitment to private and public redemption of our sins. No one run of behavior is ever just the same as a previous embodiment nor is the meaning of a given run of behavior exactly the same, yet there are common themes which suffuse all such runs of behavior and produce self-similarity sufficient to stabilize meaning and social relationships.

Each of the millions of iterations of Thanksgiving Dinner are centered in terms of date, time, and condiments. One can be pretty certain about the social connections of the celebrants at any given iteration of the holy day; relatives have a high but not perfect certainty. Membership from one year to the next is stable but far from the stability required for modern, linear science. But the very concept of thanksgiving permits a far wider variety of ingredients than those listed here; such variability does not sit comfortably in the citadel of modern science.

Fractal Geometries The reality-creating process involving symbolic interaction thus takes on the fractal geometry of a mandelbrot set; a recognizable configuration of stability of meaning together with an understandable variation of new and unique usage. It is in the fractal nature of language processes as in its nonlinearity that symbolic interaction is most clearly seen to be a chaotic process. 7

A fractal is a measure of the degree to which a system uses the space available to it. In modern science, the geometry of natural and social objects have the usual number of dimensions; one, two or three. Boundaries of objects in modern science are clear and unambiguous. One can discern between point and nonpoint; between line and nonline; between plane and nonplane; between sphere and nonsphere. Not so in the world as revealed by research in Chaotic regimes. 8 In Chaos theory, it is possible to have less than two but more than one dimension; that is to say order and disorder can occupy the same time-space continua.

It is of considerable interest to note that, in the unfilled space of a fractal, still other fractals can be found. The same is true for social realities. More than one social reality can be found in the same social occasion; indeed some of the unit acts in a social occasions are components of two quite differing social facts occurring at the same time in the same space by the same persons. A clerk at a supermarket could be checking out the value of the groceries of a friend and, in the same activity, reaffirm friendliness and embody clerkness.

The boundaries of all social events are fractal; one cannot discern a sharp, discrete boundary between the social event and its larger environment.

One can never identify precisely when an individual social actor, a social relationship, a social occasion or a social system begins or ends. One cannot identify with precision the boundaries of any social fact. For any given social role, social occasion, social establishment or whole society, the boundaries are loose and permeated by other sets of unit acts (some intended; some physiological lapses and some unit acts compatible with other social realities but not compatible with the situation under construction. 9

In boxing, fencing, or basketball, as in conferences, prayer meetings, and festivals there are, as Goffman put it, opening moves that signal the beginning of a contest or a cooperative endeavor. In boxing, contestants touch gloves; in fencing, there is a set of three moves which, if not made, signals a false start. In racing, a shot is fired; in football, a whistle blown, in basketball, a ball tossed in the air. All signal the beginning of the social event. In church, a song or a prayer is used to disperse other competing lines of activity with other, competing interpretations. Yet however precise the effort to distinguish between event and nonevent, there are smaller or larger variations in the begin of play. Sometimes it takes a team several minutes to 'really' get into the game. Sometimes given players are 'out of it' for the whole game. Boundaries are hard to determine.

In many sports events, there are games within games not all of which are 'visible' to the innocent spectator. Sometimes one or more team members will conspire to shave points or subvert victory. Sometimes a player will 'grandstand' for a friend on the sidelines. Sometimes owners will conspire to fix team rosters, rules or outcomes in ways not congenial to the publicly known rules of the game. Possibilities for fraud in religion, market, school and marriage abound. Unit acts which are distinctly outside the logic of the occasion can be reinterpreted by a skilled player to take on the semblance of legitimate action.

The use of multiple, reinforcing symbol sets to constitute the beginning of a social occasion or relationship means that there is no clear and sharp edge to social reality. The initial but decreasing mismatch in meaning and social standing between the person who signifies and the person(s) who interprets the signified also testifies to the loose geometry of the social fact.

If we were to peer closely inside any given social occasion, social institution or social formation, we would find that only a small part of the activity going on is relevant for the symbolic integrity of the occasion under construction. Speech acts, to begin with, are full of belches, grunts, pauses, mispronunciations and other 'errors' which lay there ignored by the symbolic using, making parties. Body motions; squirms, scratching, picking, plucking, pulling and squinting are in the phase-space of the social occasion are treated as if they were not there.

If we were to look closely at a shop, store, office, or even whole society that pronounces itself to have a capitalist system under symbolic construction, we would find within the same time-space continua, whole lines of activity that have nothing at all to do with capitalism. Production and distribution in homes, churches, schools and many government agencies are based upon need rather than profit. Charities, auctions, garage sales, church bazaars and thrift shops do not follow the symbolic logic of capitalism in any linear way. Crime in all its variety is outside the logic, understood as linear aristotlean logic, of free market capitalism. In any store, factory or society that defines itself as a capitalism form, perhaps as much as 50% to 95% of the unit acts actually observable, lay outside the situation as defined.

One could make similar analyses of sports events, religious occasions, electoral politics or any complex social process. Those who work in hospitals know of its many non-medical activities. Those in police work know the many parallel but non-game activities engaged in by police and public alike. Marriage itself is a very loose and very fractal social form. All attest to the fractal geometries of social reality rather than the euclidean geometry presupposed by linear models of social realities.

Structure and Region When looking at an entire basin of outcomes of any given instance of reality making in symbolic interaction, that part of an outcome basin which shows sufficient self-similarity in iterations of a unit act across time-space can be, properly, conceived as one kind of structure while those occupying another region of in a basin outcomes may, properly, be identified as another, qualitatively different structure. 10

The emergence of social structure does not depend upon the behavior of any one member of a set; rather structure is an attribute of a large set of interactive events.

It is most certainly true that the single individual is itself a 'structure.' It has parts which work together to constitute a whole. It is certainly the case the behavior of a given individual takes on the character of a 'structure.' If we followed the behavior of such a person over days, months and years, we would see regularities of sufficient coherence to call the patterns found, structure. Yet, if we are speaking of social structure, then we must speak of the interaction of two or more persons--even, strangely enough, when but one person is within view.

If we observe a single individual going to work (or to class or to dinner) with regularity day after day, we can focus on the motives, needs, urges, proclivities, values, and drives of that individual in order to explain that behavior. Or we can focus upon the expectations, reactions, orders, commands, or requests of others significant to the acting individual. If we do the former, we are said to be psychologists. If we do the latter, we are said to be social psychologists. Yet we could focus upon rules, norms, laws, morés, customs, traditions, sanctions, or status-roles with which to explicate the very same behavior. If so, we are said to be sociologists.

But that is not the end of the elements which go into the production of strange attractors. We could look at the way architecture limits and directs human behavior; if so, we take the point of view of the urban ecologist in explanation of the same phenomena. We could look at more macro-structural features of the eco-system in which that behavior is found. Capitalism offers opportunities and limitations not found in socialist economics. Patriarchy limits and prefigures gender relations. Racism is a distinctly macro-social process in which physical features, otherwise trivial, are singled out with which to discriminate in favor or against social discourse.

One can see the grounds for the post-structuralist critique of 'totalizing' structural theories. Yet there is merit to such theorizing. Chaos theory introduces the concept of scale with which to sort out such interconnected and complex dynamics. In order to do social science, one must specify the scale upon which one focusses and, in order to do macro-analysis, one must be ready to look for varying connections between dynamical structures. As we shall see, sometimes it is appropriate to speak of a totalizing system (as in the case of the single physiological entity we call the human animal. Yet sometimes, a system can occupy the same time-space continuum and not at all be a part of the whole. The concept of the soliton is explicated below.

Scale and Structure. The concept of scale is, then, of epistemological importance in ways not known in modern science. In modern science, phenomena at all scales of observation are coherently connected. Some modern scientists, most notably astrophysicists, await the time when all dynamics from sub-atomic particles to the creation of whole cosmos can be written in tidy fashion with one equation which will fit on the front of a tee shirt. In Chaos theory, there are intractable and untrackable discontinuities as one changes scale of observation. Yet, self-similarity reappears unpredictably at differing magnitudes of observation.

The nonlinearity of social dynamics take on even greater clarity when we observe the behavior of whole societies over generations, centuries and millennia. Given human scales of observation and understanding, history seems to stand still and social forms seem forever. If we would speed up the time dimension of phase space, we could see the nonlinearity of economics, religion and politics with startling vision. Two societies with about the same resources, with the same religion, with the same population dynamics would diverge greatly were they isolated from each other for a few centuries.

If we were to open up the space dimension of phase space, we would see, in the one direction, an infinite number of self similar social structures answering to the name of family, tribe, clan, friend, or firm. In the other direction in phase space, we would see infinite detail in the dynamics of actual families, each embodiment of, say, a dinner or a caress, similar but different from all previous and all future such events.

Scales of space and time, thus, open up our understanding of the nonlinear nature of social action. We see social reality as a seething cauldron of coalescing, changing, diverging, emerging and reuniting patterns of speech, worship, gender forms, marriage forms and political forms.

In the case of symbols and symbolic interaction, if we listen to one word or one tone at a time, neither meaning nor music emerges. In order to generate meaning, we must specify which of many possible scales of observation it is to which we refer. If we want to know the meaning of a word, we must locate it in its larger context. If we want to know the meaning of a book, we must locate it in its cultural context. If we want to know the meaning of a war, we must locate the war in the grand sweep of history; in predatory economics, in feudalism, in colonial conquest or in capitalist requirements for oil, metals, markets and surplus labor reserves.

Deep Structures When a lot of people orient themselves in a systematic way across a variety of social occasions without much reflection or overt discussion, the patterns of meaning and action which emerge are the deep structures of society; age grades, gender differentiations, class relations, race and ethnic, religious and nationalistic orientations, as well as other 'structures' including whole economic formations, multinational coalitions, and transgenerational programs.

The degree of facticity of such structures vary with the scale with which they are observed. Norbert Elias (1983) thought the term, Pattern, was too strong a term to use for the degree of facticity involved in such deep structures; he preferred the concept of 'figuration.' From the point of view of the single individual life-time, figurations tend to be a fixed part of human nature but from the point of view of a generation, there is glacial change; from the point of view of the whole society, figurations change with bewildering speed much as the figurations of clouds in fast motion film.

Fernand Braudel (1980), a historian, was more systematic in his approach the to use of scale in conceptualizing social facticity. Braudel saw time flowing in three time scales: the short time span of a single event, say a party or a confirmation; the conjuncture or medium time span, say an epoch in science or economics; and the long duration of time (longue duree) of a historical span that bridges several epochs in geology, biological evolution or social knowledge. Politics operate in the short time frame, economics on the medium time scale and geo-physical factors in the long term to produce the deep structures and preshape the observable structures. For Braudel, the longer the time span the more clearly the structure emerges as a bounded fact.

Of Reduction and Reification The ancient quarrel between process and structure, between hasty reductionism on the one side and false reification on the other is partly resolved by Chaos theory. What is process at one scale of observation is structure at a different scale. The argument between free will and necessity also yields to the concept of scale and nonlinearity: what is freedom of choice at one scale of observation is fractal (and changing) probability at another. Polemics about boundary, individuality and autonomy are clarified by concepts of scale and by nonlinear dynamics. What is the operative, autonomous unit of functioning at one level of observation is part of a larger interacting and interdependent whole at another level. Thus contrarieties are accommodated within the logics of Chaos theory.

At the same time, such co-existent contrarieties have the double hazard of artificial freezing of deep structures as a fact of nature or necessity on the one side and a danger for attribution of their authorship to non-human agency on the other hand. Without the concept of the fractal, it is easy to reify these deep structures and to assign them a linear (and supra-natural) determinism that does not respect the probabilistic, hence openness, of the ontology at hand. 11

The opposite conceptual error is also made easy by our propensity to think in terms of continuous or discrete facticity rather than fractal facticity. When one looks at a forest and sees only trees, one at a time, one is prone to reduce to the individual tree. When one looks at a high crime society and sees only the individual criminal acting as an autonomous individual, one is prone to support policy which speaks to the behavior of individuals taken one at a time. This reductionist point of view is opposite of the false reification of structure. With the concept of the fractal applied to emergent social structures, we can walk the fine line between over-generalization on the one hand and concrete thinking that is limited by personal interests and politics on the other.

With the concept of the fractal in combination with the concept of scale, one can accept understandings that forests and human families have fractal facticity, fractal dynamics as well as discontinuity in causality; a fractal and changing causality if you will. This understanding does not set well at all with modernist assumptions of thingness, causality and change. Yet if we see the individual criminal as a whole person whose criminal behavior is a soliton that sweeps through larger solitons of prosocial behavior, we might take a different policy stance. If we see a criminal as a nonlinear product of a similarly situated population in a larger soliton that is criminogenic, we might focus on the attractors and feedback patterns that produce the soliton rather than try to punish or rehabilitate the individual criminal since we would understand that there, but for the grace of small differences of chance or luck, go each of us.

Chaos and Connectedness In choosing to focus upon one region of a complex connected whole, we often make arbitrary judgments about the degree to which each region is autonomous from other close or remote regions. In some regions of phase space, causal connections are tight enough to speak of a dynamic system; in other regions of phase-space, connections are loose enough to judge that region a separate autonomous entity. In fact, all such connections are constantly changing and the fate of any given system is now self determined and now part of a larger dynamic whole.

The nonlinear character of social dynamics can be observed as between levels of systems organization; symbolic interaction produces mind, self and society, each of which has fractal boundaries and each of which is part of and dependent upon the other levels of system functioning.

In the same moment of defining meaning and creating social reality by the use of symbols, several nonlinear but interacting levels of social fact are created. Mind, self and society are born in the instant one reaches toward another person with a set of symbols. Mind, self and society are destroyed in the same instant one turns away--ceases to express and embody information in a symbol set--from a friend, a spouse, or a student. The human mind consists of shared meanings in personal expression of a symbol or set of symbols. We cannot think without symbols; and when using symbols in the algorithms of speech, then and only then do we have a mind. 12

For the most part or at least a large part of cognitive activity of a human being, before, during and sometimes after an actual social engagement, that cognitive activity is oriented to trying to share mind; understood as symbolic activity with other persons. In that respect, it makes considerable sense to say that mind and society are twinborn; the intersubjectivity of shared meaning and activity parallels the subjectivity of each mind taken separately. We often use symbols when alone; however most of that use, that calling forth of mind, is oriented to rehearsal, to reflection, to self critique or to remembrance of or in anticipation of agency in designing and building the specific form of social reality one desires.

Yet social reality is comprised of two or more persons interacting within status-role sets. A status-role exists when two or more persons organize their behavior in ways compatible with the cultural definition of an occasion. Thus the husband-wife relationship--or any social relationship--exists only when symbols are shared and embodied by at least two human beings defining themselves as spouse and acting in ways congenial to that definition. 13

Many of the symbols used are symbols denoting and hence calling forth social identities. The symbols embodied by 'wife' call forth 'husband' and the symbols used by 'husband' call forth wifehood. The facticity of each social identity depends sensitively, upon the degree to which symbols arouse the same meanings, feelings, and complementary actions in both parties. That sensitive responsivity illuminates the feedback loops and the connectivity of mind, self and society.

For any given person there is a set of mutually created social identities (wife, mother, Catholic, friend and so forth) making up core of the self system; thus it is appropriate to say that mind, self, and society are trineborn. That core of self could not exist, ontologically, by itself. The idea of a wife without a husband, a mother without a child, a priest without a parishioner or a friend without another; these are nonsense ideas without flesh and bones in actual life. The same geometry of symbol sets, mentioned above, are found in the geometries of mind, self and society; the boundaries are fractal, the degrees of facticity variable, and the strange attractors of self, society and mind infinite in their variation.

Bifurcations and Social Change Perhaps the most challenging implication of Chaos theory to a full understanding of social dynamics is the finding that systems change from near-to-stable dynamics to far-from-stable dynamics when they undergo bifurcations in their parameters of rhythm, period and cycle. 14 Although the reason is not clear, dynamic systems undergoing four or more bifurcations tend to break apart and to use all the time-space available to it, thus lose much of the order and pattern they have.

Qualitative social change arises from bifurcations in the dynamics of social life. 15

Cheryl We can get an idea of how bifurcations in social rhythms produce far from stable dynamics by looking at the life space of Cheryl J. Cheryl is a bright young woman who, at the age of 22, has written two books, several songs and many poems...all unpublished but still indicative of the level of her talent and ambition. In the next year, she will have married, left her home town and enrolled in college while taking on a job at a local Red Lobster restaurant. Cheryl is full of energy, full of confidence and full of plans; she wants to teach.

In many respects, her life is typical of that for which many young women plan and work. Each line of activity; work, marriage, and school takes on a routine each with its own cycles and rhythms. Work and school have the least forgiving cycles; if Cheryl is to succeed, it is the marriage which will have to adjust. One must attend work if one is to be paid; one must attend class if one is to pass. Yet marriage is an interactively rich and informationally rich social form that requires a lot of time and energy; especially in the first years as newly married persons get to know what to expect and how to interpret a move, a mood, a word or a glance.

If chaos theory and its findings for nonlinear dynamics is relevant, then we can expect the bifurcations in time, finances, and energy resources between work, school and marriage to produce a fractal basin of outcomes for persons in Cheryl's position; we will not be able to predict which activity will end in far from stable dynamics but we can predict that, as a class, some unknown number of students will fail and some unknowable number of marriages will fail.

Each line of her activity has its own economics; the expenditures of marriage on food, shelter and clothing must compete with the expenditures of school on tuition, books, computer hardware and software. Work has its own costs; transport, clothing, and food. Many young people try to support several forms of recreation, each with their own economic demands. If the pattern of income bifurcates from the pattern of expense, one can expect the onset of chaos. 16 In the case at hand, the epistemic correlate of far-from-stable dynamics for Cheryl and her new husband would be divorce; for Cheryl and her classmates would be dropping out; for Cheryl and her workmates, unemployment.

There are nonlinear feedback loops which may stabilize her three (or four) lines of reality creating; her professors may not count her absences for work as significant to the grading process. Her parents may count her debts as their debts. Her husband may count her work and school as part of marriage situation. State and/or federal legislators may create student aid programs and award funds nonlinearily on the bases of merit, gender, ethnicity or age. Cheryl may work out some feedback loops that integrate work and school or work and marriage. But, given three parallel reality processes to create; the bifurcations in energy, funds and time may just explode to shatter her life. 17

Chaos and Creativity The work of researchers on chaos and creativity show that nonlinear systems do not tend toward entropy (as the laws of thermodynamics require) nor do they tend toward point attractors (as formal models of social organization require). Instead, social forms take the shape of limit attractors and torus attractors until bifurcations occurs to fill the time space available to a group. Instead of remaining in disorder, chaos work reveals that interactions occur in the soupy murk of disordered dynamics that produce new and quite unpredictable forms.

What one can expect for Cheryl and her small family, and many of the millions of new families similarly situated, is the development entirely new marriage forms; living arrangements, job forms and child care forms. The present situation is so uncertain that, while one cannot predict what will emerge, one can predict with great certainty that the causal basin in which such couple reside will add new outcome basins.

Agency for Cheryl and her husband is very tenuous. She might do just the right thing at the right moment to make a great change in her life. She may write a song, a book or a play which will move her from the downward spiral which most young families face in a declining economy. Or, she may say the wrong thing at work and lose a job at just the wrong moment. Then several possibilities await; Michael or she could become part of organized crime marketing drugs, sex and violence as have so many young people. She could return home to live with her parents whose economic future itself is sensitively dependent upon the automobile market. Caught as they are between outcome basins; one in which traditional family forms are found and many others, there is little which traditional science can say.

Chaos research can gauge the new tongues at the margins of social tori, and it can tell us quite precisely when a new wing of an outcome basin will appear but it cannot tell us which of the millions of young families will move toward which outcome basin. Chaos research can tell us when intervention is the most efficacious and requires the least input into the damping or the amplification of new social forms but it cannot tell us what those new forms might be.

Fractal Basins of Outcomes Modern science understandings of the dynamics of social systems, if predicated on the newtonian paradigm, would presume a basin of outcomes for a person or a process in which all such outcomes would be identical. Chaos research reveals a basin of outcomes in which there are qualitatively different outcomes for the same initial conditions.

For any given population of persons, groups or societies, given the same initial conditions, one may expect a basin of outcomes with qualitatively different regions with fractal boundaries between regions.

The fractal nature of outcomes of any given social form can be seen in divorce cases, bankruptcy cases or criminal cases as well. Given some number of marriages in a population, we don't know how many will last three years; how many will last seven years or how many will last until death. But we do know that the basin of outcomes of such marriages is fractal; there are no clear and predictable boundaries separating the conditions that produce marriages which last from those that fail. Again, small differences in the dynamics of such marriages will produce large and unpredictable outcomes. The same is true of businesses, juvenile delinquents and humming birds.

When a person or a group goes through any cycle of behavior (destructive or constructive), each person modifies tactics from past confrontations, from past errors, from present conditions and from future expectations. Over time, if we were to map out the differences and similarities of such runs of behavior, we would see a fractal basin of outcomes. Some part of that basin of outcomes would be recognizable, predictable, understandable but some part would be surprising, contradictory, qualitatively different. In gender struggles, economic machinations, political infighting or religious conversions, there is pattern with dis-continuous change.

Although persons who are seriously ill can still be effective persons in the sociological sense; the basin of outcomes of such performances is fractal; we can't predict how many or who of all such ill persons will function within the confines of a given normative structure. Given limited access to resources, we can't predict the effects of any given sub-system or mega-system on the basin of outcomes of any given effort to be a wife or a friend or a Catholic; we can only see the changing patterns of outcomes over time.

Solitons and Symbols The fractal geometry of social realities make it possible for whole sets of social interaction can pass through a given social form without affecting the integrity of the social form at hand. One can use waves in a lake as a rough metaphor for the nature of social solitons. 18 Waves from passing boats pass through each other with minimal effect. In like manner, such social structures as friendships, kinships, or clans keep their identity and integrity even though successive waves of warfare, economic forms, political regimes or religious institutions occupy the same time-space territory.

The ontologies created by symbol using humans takes the form of a soliton, a coherent and connected dynamical pattern of interaction between members of a social occasion.

If we were to observe closely the dynamics of any given social occasion, we would observe several different sets of activities ongoing at the same. Each set of activity might take on the dynamics of a soliton. If so, then each set of activity would keep its own integrity apart from what happens in the other solitons through which it passes.

We can take the life of Cheryl J., above to make the point. Cheryl is now involved in a marriage; it is possible that her husband might come into the restaurant in which she works. The two dynamical systems, marriage and restaurant occupy the same time space continua but may (or may not) interact. If they do not interact, than each preserves its integrity. As an example, if Cheryl were to give her husband food without charging him for it, then the systems would be interconnected and the restaurant system changed (at least for that event). Or, were Cheryl to take her husband to class, the dynamics of the class and the dynamics of husband-wife would, likely, remain intact; solitons in the classroom can meet and pass through each other without changing form.

Fractal Causality It is an attribute of nonlinear systems that small differences can produce very different outcomes. 19 It is an important attribute of chaotic systems that one is unable to predict which small changes will be absorbed and which will produce large changes; thus, the basin of outcomes of any such sets of nonlinear, chaotic social systems will consist of some, unpredictable portion of outcomes that are expected and some, unpredictable part of outcomes that are new and very different.

All social reality has a fractal causality that varies nonlinearily according to the quality of the symbolic interactional process.

The transformation of individuals to personhood is a non-linear event. Across a basin of outcomes of parenting, for example, there are regions of mechanistic predictability and regions of far from stable outcomes. When a women gives birth to a child, we can predict with some certainty that she will embody the status-role of mother, yet there are times when the biological mother does not take that role. In the universe of all biological mothers, some small differences will produce a deterministic pattern toward parenting while for other mothers, the same small differences will defeat the parenting process.

The nonlinear character of parenting can be seen in adoption cases. At time one, the individual is not a son or daughter; at time two, the individual is a son or daughter complete with mother and father. In like fashion, a court order can remove or reallocate parenting. All that is required to initiate or defeat either social reality process is a few words pronounced by a Judge and a piece of paper with symbols written on it.

In postmodern expressions of science and human knowledge, it becomes incumbent upon the social scientist to give fractal truth values rather than absolute, binary (there-not there) truth values. There is, in chaos theory, same work that helps one to generate fractal truth values. The next generation of symbolic interactionists will have to master and modify that work to their own. 20

Praxis and Rationality The assumption of modern science about rationality is a great obstacle to postmodern praxis and to its ideas of praxis societies. Reason and rationality are, for the modern scientist, the discovery and reporting of a final set of laws which subsume linear dynamics while, for the putatively rational citizen of a putatively modern society, reasonable action consists in compliance with those iron laws. For the bureaucrat oriented to modernity, it is reasonable to use rules to shape the behavior of all who come before the bureau while reason is, for the state, the use of force to ensure compliance with its rules.

The foreign policy of many nations, informed by the logics of modern science and taking itself to be the embodiment of reason and rationality, use force, guile and bribery to modernize third world nations after their own images of modernity. All management science presumes the utility of operant conditioning, the linearity of financial incentives and the necessity of stratification to the success of a firm. Nonlinear dynamics mediate all these presumptions in support of postmodern understandings.

Rationality, informed by linear logic, sets one and only one outcome basin in an outcome field as the preferred, normal, politically correct basin while rational judgment concludes that all other outcome basins (and the people who therein dwell) are abnormal requiring either the services of a psychiatrist or the benefit of a penitentiary where the deviant can reflect upon his/her irrationality and chose to be rational.

Postmodernism, as a science and as a generic world-view, de-legitimates all claims of normality, perfection, progress, or preference. Rather than explaining variation from theory, hypothesis, or social form as observer error, substandard theory, faulty instrumentation, inadequate operationalization or more simply as deviancy, postmodern sensibility treats such differences as, simply, different regions in an infinitely large basin of possible outcomes.

Postmodern views of the natural world, including social forms, are very different from modernist views: there is no one preferred form of plant or animal life, of personal or social organization. All scientific endeavor and preference are informed by human desire and human interest; all efforts at control as well as all claims of psychiatric pathology are equally political endeavor. One cannot appeal to nature or to theology for legitimacy in such endeavor, one can only deconstruct the human desires and human interests in the explanation of such activity.

Opposed to the view that society is shaped by natural, eternal and law-like forces is the view that social relations are the product of struggling, seething human beings using power, deceit, anxiety and hope to solve the problem of order in the drama of social life. Opposed to the view that there is one final social formation toward which all societies evolve is the view that no one form of social life is natural and normal; that all are equally possible, equally normal. A survey of deep phase-space reveals only infinite variety, infinite centers, infinite detail and infinite length of the structures found there.

In postmodern science, contraries can be true; causes can emerge and fade; prediction and control are possible but limited to small regions of phase-space; there are a plurality of natural and normal social orders rather than a series of stages evolving toward rationality and perfection. As tools of enquiry, postmodern science demotes prediction, rational numbering systems, euclidean algebra, aristotlean logic, differential equations as well as distributive and symmetrical mathematics. These are useful for relatively small regions in any universe of real systems. Prediction and replication are equally limited as tools for verification while truth statements become fractal truth quotients.

In its more emancipatory moments, postmodern social psychology helps illuminate the variability of the reality constituting process in symbol using creatures and thus legitimates spontaneity, variety, authenticity and democratic participation in the reality process. 21 Modern science, on the other hand with its assumptions of external, universal and pre-existing laws of social development and social organization; with its directive to social scientists to discover and to validate these laws, and with its notions of perfection and deviancy, helps justify partisan forms of social action as right, normal, universal and necessary.

CONCLUSION The dynamics of social processes, when in near-to-stable equilibrium, take the form of a strange attractor exhibiting self-similarity in phase-space but never moving on exactly the same pathway. All social processes, social facts and social forms founded upon symbolic interaction, are nonlinear. Social forms have fractal facticity while social interactions produce fractally true (or fraudulent) fulfillments of given social prophecies.

Chaos theory offers an empirically solid and conceptually elegant envelop in which to insert postmodern expressions of art, music, family, religion, politics, economics and science itself. As such, it forces social science to reconsider both its commitment to the missions of modern science as well as to its methods of enquiry. The preferred tools of enquiry now used in American social science have limited utility for nonlinear dynamics. Replication is impossible while falsification is a nonsense concept for systems displaying nonlinear dynamics. Given the role of symbolic interaction in all knowledge processes and given the options to select regions in phase-space for analyses and for generalization, all efforts to build general theory or universal laws are shown to be both a poetics and a politics.

Part of the postmodern project is to emphasize the human authorship of both reality and theories of reality. Chaos theory and nonlinear dynamics, implicit in symbolic interaction ground that effort. It is that very interactivity between object of knowledge and subject of knowing that means that science, religion and sociology are but different names for different aspects of the same reality process. The boundaries between such knowledge processes are fractal and everchanging. Understanding that, we can begin to institutionalized the many connections between science, symbolic interaction, social structure, truth, and social justice.

References and Bibliography

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.

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.

Lyotard, J.-F. 1984 The Postmodern Condition. Minneapolis: the University of Minneapolis Press.

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

Norris, C. 1987 Derrida. Cambridge: Harvard University Press.

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.

Rickman, H. P., 1990 "Science and Hermeneutics" in Phil. of the Social Sciences, V. 20, No. 3. Sept. 295-316.

Rosenau, Pauline. 1992 Postmodernism and the Social Sciences. Princeton: Princeton University Press.

Walliman, Isidor, ed., 1989 Research in Inequality and Social Conflict. Volume 1. Greenwich, Connecticut: JAI Press.

Weaver, Jefferson, ed., 1987 The World of Physics, Vol. I: the Aristotlean Cosmos and the Newtonian System. New York: Simon and Schuster.

Young, T. R. 1989 The Drama of Social Life. New Brunswick, N.J.: Transaction Books.

Young, T. R. 1991 Change and Chaos Theory, in the Social Science Journal. 28(3). Fall.

Young, T. R. 1991 Chaos theory and Symbolic Interaction, in the Journal of Symbolic Interaction, 14:3, Fall. [An earlier version of this chapter].