REVIEW FIGURES CHAOS THEORY AND SOCIAL DYNAMICS: FOUNDATIONS OF POSTMODERN SOCIAL SCIENCE** T. R. Young Texas Woman's University and Virginia Polytechnic and State University August 26, 1991 January 3, 1992 April 17, 1993 June 25, 1993 April 14, 1994 _____No. 158____ This essay will appear in Robert Robertson and Alan Combs (eds.), Proceedings of the 2nd Annual Conference on Chaos theory. Forthcoming. It is dedicated to Hubert Blalock [1926-1990], who if he had lived, would lead the way to the research designs so essential to discovery of hidden attractors in complex and fuzzy sets of social data. A good and gentle man who, among other things, taught about racist intolerance in a time of racism. Chaos is ubiquitous, it is stable and it has structure. ...James Yorke CHAOS THEORY AND SOCIAL DYNAMICS: FOUNDATIONS OF POSTMODERN SOCIAL SCIENCE** ABSTRACT Chaos theory provides an elegant mathematical grounding for a postmodern social science which affirms variety and change as entirely natural attributes of social systems. Nonlinear dynamics mark symbolic interaction- -and thus reality construction processes in social life; they reveal patterns in the forms of crime as well as the larger transformations of Law found in human history. Chaos theory has particular impact on deviance theory in that notions of the normal, the natural and the perfect are incompatible with the fractal geometry of complex social dynamics. Among the more profound implications of Chaos theory are: 1) all theories of social dynamics henceforth must be change theories; 2) natural or divine laws oriented to stability or linearity cannot be used to inform moral wisdom nor to ground definitions of normality; 3) postmodern philosophy of science locates knowledge processes in particular human interests variously grounded in patriarchy, in ethnocentric stances, in class privilege, in national pride or other human interests. INTRODUCTION The forms of social order and the sources of disorder have always been a central problematic in the behavioral sciences. For most of human history, the assumption has been that there is but one and only one natural way to organize social relations; a way sanctified by religion and reproduced with rough hewn social skills over the centuries. With the modern concept of evolution, stability in social life worlds has given way to change but, in most theories of social evolution, there is an 'advanced' or final stage of social organization to which all change is directed. Chaos theory forces one to question both the normality of any given social order as well as the presumption of directionality and finality in social evolution. As theory and technology develop by which to explore the infinite variety of social life, even less may one offer privilege to given social forms as a product of the 'iron laws' of nature, society or the gods since human beings increasingly have the knowledge and the means to shape the world as they would have it. In the pages which follow, I want to sketch out the larger transformations of the knowledge process as it wends its way through human history and through the many struggles within and between tribes, ethnic groups, nations and empires. In the doing, I want to stress the complementarity of these many pathways to human knowledge and, in the same moment, place the differences between them in perspective. Each epoch in the forging of human knowledge is essential to the task of building the elegant and fragile forms of social reality in which we all must, perforce, live out our lives. With skill, patience and good will we just might be able to do a bit better in the 21st century than have we in the recent past. Premodern Knowledge Processes Until the scientific revolution, most social philosophy presumed an enduring social life world centered in the present unchanged from millennia past. The mission for pre-modern knowledge processes was to teach the folk methods by which a given social life world could be reproduced while the human interest which organized the knowledge process was sanctification of that social order. Out of the incredibly complex web of events and processes in human societies, premodern thinkers selected, created, celebrated just those variables and just those truisms which helped do that. Premodern knowledge processes required belief, faith, trust and shared engagement in the reality creating process and thus serve as permanent foundation for all modern sociological theories about the character of human societies. The language and practice of moral indignation used in the reality creating process with its concepts of evil, sin, depravity, iniquity, corruption, error and debauchery bring along with them concepts of the good, the right, the correct, the fair, the pure, the true and the upright life served the human interest in sanctifying existing forms of social reality. In such societies, socialization and social control efforts tend to reproduce existing patterns of gender relations, political practices, economic forms and religious understandings. Living at the edge of uncertainty, and equipped with only the most basic of tools, such pre-occupation with reproduction of existing ways to do family, to do economics and to do politics made and still makes good sense. To the extent humans embody belief, faith and trust in their everyday activity, society does reflect a certain stability which defies change and the second law of thermodynamics. The incalculable improbability of even simple and brief social encounters still depends upon these premodern knowledge processes. Modern Knowledge Processes Modern science changed belief and faith in stable social relations with the idea that previous societies were flawed, primitive, or 'underdeveloped.' In this knowledge process, science and technology could find the path to truly modern social systems in family, education, economics and transport. The mission of the knowledge process became a circling quest for a stable set of principles which could be welded into an eternally valid theoretical structure upon which to ground social policy and social practice. Modern methods of research set aside folk methods and folk beliefs in favor of a more objective and putatively value free research design which, in turn, could generate knowledge apart from human interests and political agenda. In the name of 'modern science' and modernization, societies which had been stable for millennia were delegitimated and dismissed as part of a primitive past. Such delegitimation cleared the way for the impersonal, desanctified mass societies now emerging in the modern world. In place of a self system anchored in the belief systems of premodern understandings, the problem of social order was given over to science and technology. In factories, workshops, schools, prisons, hospitals and politics, interactively rich interpersonal dynamics were slowly displaced by unilateral application of regulations, rules, statutes, laws, principles and theories of scientific management. Thus, dry and impersonal rules of scientific method replaced wisdom, judgment, insight and poetic genius as the foundation of human knowledge. Out of the incredibly complex and interwoven fabric of social reality, the quest for certainty selected just those variables and those findings which confirmed the use of rules, principles, laws and regulations were included in the body of knowledge called science and used to guide behavior. As these scientific 'principles' re-entered the ever changing social life world from which they came, uniformity and universality displaced variety, creativity, surprise and discontinuity as the tools of scientific management. Human beings, in the guise of scientists, worked assiduously to find and reproduce order in the same moment they disprized and tried to discard variety and dis-order. The very logic of the method of successive approximations presumes a stable set of natural and social laws to which all normal persons subscribe and all modern societies emulate. Modern science, more so even than pre-modern social philosophy, gives preference to stability and control as the natural and normal form of theory and research. In the lived experience of research subjects, deviance from a scientific principle is thought to mark pathology while refusal to accept the inexorable workings of social laws become grounds for therapy, confinement or warfare. Concepts embedded in modern theoretical paradigms depersonalize sources of disorder, change and diversity by attributing variations from putatively normal social relations to genetic inferiority, to birth defects, poor socialization, primitive cultural beliefs, inadequate controls and/or social disorganization. This was the rough beast lumbering toward Bethlehem to be born of which the poet warned; if human agency gave way to scientific fiat about how the world should work, then truly we live in an iron cage; truly freedom is but compliance to that which is written in the textbooks of experts. In the laboratory, faced with research findings each different from the last, modern epistemological paradigms dismissed variations among such findings with reference to faulty research design, inaccurate measurement, missing variables, observer error, poor instrumentation, observer bias or just plain bad theory. This new science of complexity, often called Chaos theory, makes it possible to accept that variety and disorder are a feature of the social life world itself rather than of bad behavior, imperfect social controls or poor research technology. Self-similar findings are common; identical results rare. In this new philosophy of science upon us, even contrary but valid findings are possible. Variations in findings are dependent upon a) the region studied in a complex outcome field, b) upon the dynamical regime at hand and c) upon the scale at which one chooses to do research. The use of replication, statistical inference and falsification as an epistemological tools are thus greatly limited. For point attractors and for limit attractors such tools suffice. When more complex dynamics are at hand, fractal truth values and semi-stable generalizations are the best we can do. Postmodern Social Science Chaos theory and research findings offer a view of the ontology and dynamics of social systems which promise to help build an entirely new paradigm for the understanding of order and disorder. In so doing, Chaos theory provides intellectual and moral space for variety and contrariety. This new science of complexity offers support and direction for postmodern understandings which honor change, variety and disorder. Dramatically changing ratios between order and disorder found as one moves along the bifurcation map in Figure 5 below, resonates with premodern understandings of social change: miracles, magic, and mystery once again become acceptable conceptualizations of the dynamics of social change, of healing and of interpersonal dynamics and even of the evolution of life forms. Quantitative change transforms into qualitative change at each bifurcation. Uncertainty grows and prediction fails with the appearance of each new set of attractors in an exploding field of outcomes. In contrast to both pre-modern and modern assumptions, Chaos theory locates the source of social disorder in the nonlinear dynamics of the system itself rather than in evil, sin, error or ignorance of particular persons or outside agents. It provides an elegant theoretical envelop for grounding of postmodern social policy and social practice. It offers a reading of the change process which encompasses both structural determinism as well as, at special moments, human agency since that which is process at one level of observation is structure at another scale. In Chaos theory, most of the dramatic changes observed in nature and society accrue from small changes of system parameters but there is ample room for individual or collective contributions for fundamental change at strategic points in the transformation from near-to-stable equilibria to full blown chaos. Feigenbaum numbers to which much attention is given in the literature, define those points. In Chaos theory, variation around a central tendency as well as qualitative change from one dynamical state to another is to be found in the interactions of members of a set. One can account for first order change by reference to differences among persons. But second and third order change derive from interactions between two or more interacting variables in an outcome basin rather than from differences between members of a set per se. It is not that new variables intervene but rather that small changes in existing variables produce qualitatively new patterns of behavior; some very different from those found in the previous attractor. Water molecules in one equilibrium state are not qualitatively different from water molecules in another, more chaotic state. The same is true of trout, hummingbirds, cicada, heart beats or human beings. It is small changes in key parameters of a larger field which can produce qualitative change; not necessarily the appearance of an outside agent, a new pathogen. Without any change at all in the genetic or psychological organization of such organisms, they may take very different life courses depending upon dynamics of variables external to the individual organism. It is important to keep in mind that postmodern knowledge processes do not replace premodern and modern missions or methods; they supplement them. Premodern knowledge processes are essential to human agency in the reality creating process; modern science and technology are essential to the expansion of human agency in the management of physical and natural systems; postmodern knowledge processes are essential to an increase in moral agency. We cannot appeal to natural or divine agency for the choices we now must make among outcome basins in a complex outcome field. With each increase in knowledge, we become less innocent and more responsible for the fates we meet. This is the lesson of the fruit from this tree of knowledge; we now know of the drama of social change and we become responsible. CHAOS THEORY Chaos theory has developed rapidly in the past 30 years to reorganize theory and research in a wide variety of disciplines. The geometry of nonlinear dynamics came to be formalized in the work of Benoit Mandelbrot (1977). Mandelbrot worked at IBM's Thomas J. Watson Research Center and discovered that patterns of noise (disorder in lay terms and deviancy in more sociological terms) has a fractal geometry. More than that, in the study of daily, monthly and yearly cycles of stock prices, he found that the stock market had similar patterns of disorder at any number of scales of analysis. Using the fractal model he found in stock prices and in bursts of noise in telephonic transmissions, Mandelbrot produced a visual distribution of galaxies in the universe which astronomers have since confirmed. Galaxies are not distributed randomly over space but display patterns which have fractal geometries (Briggs and Peat: 1989:90). In thinking through the implications of Chaos theory for social dynamics, we want to focus upon three forms of nonlinear dynamics revealed by studies of natural systems. There are two linear forms which are common in simple mechanical systems but these are seldom if ever observed in living systems. These three forms entail three different dynamics, each more non-linear than the last. Figure 1 gives two views of both linear systems (Boxes A and B) as well as two views of nonlinear systems (Boxes C and D). Let us look at each form of order and together think about their implications for a postmodern social science. We find first order change in the torus attractor, Fig. 1, Box C (and Figures 2 and 3, below). It embodies first order change by virtue of the self similarity involved in its dynamics rather than the precise sameness of simple dynamical systems. The butterfly attractor, Fig. 1, Box D (and Figure 4, below) displays second order change; qualitatively different pathways arise for natural and social systems which are otherwise very similar. Third order change is found in the last half of the bifurcation map below. Yet even with the great disorder found in third order dynamics, pattern is found and new order emerges. The Feigenbaum bifurcation numbers inform us when if not why such dramatic social change occurs (Figure 5, below). The Torus and Self Similarity In generating postmodern understandings of self and society, of social change and human history, one begins by looking at the nature and sources of self similarity in social systems. Self-similarity, as a concept, means that the behavior of any natural or social system, including individual human beings, may be similar from day to day, year to year or generation to generation but no one embodiment in any given cycle or iteration of any given system is precisely like a previous embodiment. Thus variation is the natural state of social forms which take the geometry of a torus; self-similarity comprises first order change found in all symbolic interactional processes, in all cases of crime; in all worship services and in all forms of business activity. The fractal geometry of a torus is seen in more detail in Figure 2; each succeeding cycle builds up a portrait of self- similarity in that there is a loose approximation of one cycle of behavior to the previous cycle. Thus, in a baptism, a marriage, a funeral or a mass, however practiced is the priest; however formal is the ritual, however skilled are the communicants, still no given cycle of religious service is precisely like another. The same is true in any given social act one might wish to examine even in the most stable and enduring of societies. In any given social role; in any given social occasion or in any given embodiment of a class room lecture, self-similarity displaces sameness. Whatever pattern is found in social life, it is there because sentient human beings work hard to create one iteration of an occasion in the image of a previous cycle. Human action entails variety. It is here that individual judgment can cope with exigency; it is here that individual creativity can assert itself within the limits loosely defined by external parameters: food supply, cultural values, social controls, social esteem, and interpersonal dynamics. But do note that while there is uncertainty about the life course of any given marriage in a simple agrarian political economy, all marriages will fall within the boundaries of the torus...in that, there is great certainty. If one doesn't respect the norms of food preparation and usage, hunger awaits. If one doesn't respect the norms of property holding and property transfer in settled agrarian society, poverty awaits. If one doesn't observe the norms of sharing and caring, mutual aid is foresworn. If it is the life course of a single marriage which is modelled in phase space (Fig. 2, top left), one can see process transforming into structure. Each marriage has a similar beginning, weaves loosely around given norms: e.g., norms about how to organize gender relations, child rearing practices, size of family, frequency of visiting kin, fidelity to the spouse, or whatever else is of interest to the researcher and found to be part of the ways of marriage in a culture. Variations outside the fractal boundaries of the torus are damped out by negative feedback in the larger environment. If several such marriages in the same culture are superimposed upon each other (top center), one can begin to see a normative pattern emerge. This is the beginning of customary law. After thousands of iterations of marriage forms over dozens of generations, the idea of the normal and the abnormal emerge (top right). Together, the similar dynamics of a family in a given environment merge to produce structure which in turn shapes the dynamics of other social forms in a field. Ordinarily we do not think in terms of a torus since most research takes slices of the marriage form or of hundreds of marriages at one point in time (called a Poincar section). Figure 3 shows this technique. This practice reduces a three dimensional dynamical form to a two dimensional static form. Ideas of normality and eternality thus come to be, in part, artifacts of research tactic. In brief, self similar systems such as a torus exhibit near to stable dynamics. In the observations of thousands and millions of iterations of natural and social systems, a structure emerges; that structure is a chain of small variations with infinite variety, infinite length, and infinite detail rather than a stable, natural pattern. Modern research designs can pick up distributions around a central norm but, in the sectioning of a much more dynamical process, lose the larger pattern of change and renewal. We will see that larger pattern in the graphics below. Just as no two marriages are identical, no two meetings of a classroom or a conference are precise iterations of each other. This similarity but-not-sameness is of special interest to deviancy theory. It sets variation as the nature of the social process rather than conformity. These small and local variations, under some conditions, amplified and transform into much more complex patterns. I will return to this point in the discussion of even stranger attractors, below. Sources of Sameness: Feedback Most sociological theories of order place great emphasis upon socialization, social controls as well as a magical but quite human process in which things defined as true become true in the consequence; the self-fulfilling prophecy. Again, the process doesn't fulfill itself; sentient human beings do the necessary work of trusting, believing and acting as if something quite problematic would indeed become real. Without denigrating these sources of sameness, we want to look at another very important source. Modern science uses the concept of causality in which one variable changes another; complexity theory makes great use of the concept of feedback to explain system both stable and changing social dynamics. The source of the semi-stable order of a social torus is to be found in nonlinear feedback. Unrestrained positive linear feedback drives systems into deep chaos; negative linear feedback tends to restrict creativity and innovation. If we want to maintain the integrity of any given social form, then, there must be some form of social response with which to defeat the transformation of the torus into a butterfly attractor. In human affairs, this requires a forgiving, a forgetting, a treating of incompatible events as if they had never happened and in general, a continuous and expert editing of the reality process as it unfolds. In everyday interaction burps, belches, grunts, sneers, and shrugs are treated as if they did not occur. More serious delicts are registered on human consciousness but defined as 'not really' there. Infidelity in marriage, dishonesty of employees, contempt of students, dis-obedience of soldiers and heresy in the priesthood are usually defined nonlinearily...as noise in the system. The curious thing is that, if we want to resist change, we must couple one kind of change with another (Briggs and Peat: 37). With recourse to nonlinear and qualitative change, it is possible to institute a stability which relies upon instability. This curious feature of ultra-stable systems depends upon nonlinear change. Ultra-stability The effort to conserve traditional structures in times of great uncertainty depends more heavily upon change than upon repressive social control tactics since, to paraphrase H. Ross Ashby, only Chaos can cope with Chaos. In a concrete case, if we want to maintain the integrity of the nuclear family in the social, cultural and economic conditions of the 1990s, we must innovate. New ways of doing child care, new ways of doing food preparation and new ways of organizing education and religion are required. Instead of health care, child care or housing apportioned to each family in terms linear to their income; poor families having poor housing, health care or child care while rich families have interactionally rich child care, informationally rich health care or just plain rich housing, nonlinear processes of distribution must occur for the poor family else the family fall apart. Children wander off; spouses separate and landlords evict. In similar fashion, if we want to design a low crime society, then we may have to make qualitative change in quite ordinary practices. Corporate crime, white collar crime, organized crime as well as street crime explode when key variables exceed given limits. In other work, I have suggested that the key variables include inequalities in class, race and gender relations, more about which later. It well may be the case that some inequality in wealth is helpful to the economic life of a nation, Plato suggested a four to one ratio, but it is likely that larger ratios set up the stage for a wide variety of corporate and political crime for those at the top of the pyramids of power while street crime and organized crime become attractive for those at the bottom of such pyramids. White collar crime may begin to be interesting to rich and poor alike who live on the cusp of financial uncertainty. There are any number of nonlinear ways to discourage the positive feedback found in laissez faire market societies which produces great inequalities and thus perchance the potential for great crime. Progressive taxation is a well known social policy. Programs of social justice by which access to education, health care and decent housing are found in low crime societies. Deuteronomic Law required the forgiveness of debts every seven years and forbade usury as a violation of God's Law. Indeed, the mercy, forgiveness and charity found in many religious are exemplars of nonlinearity. In modernist views of causality, globalization of the economy threatens to eliminate diverse cultures and religions. Some have looked at that process and have despaired of the possibility of diversity. They see one global culture marked by uniformity, rationality and finality of social change. Chaos theory is more reassuring; mutually exclusive religions can exist side by side; rationality is reduced in importance as a social tool; the end of history is never, never near. Again, it is nonlinearity which makes such variety possible even in the largest, most totalizing process one could imagine. The psychological processes of compartmentalization have their counterpart in nonlinear social processes. Social controls work to minimize entropy of a social torus yet no set of social controls can generate that precise behavior favored by modern science and intrinsic to its assumptions of linear causality. And, as we shall see in the anatomy of a butterfly attractor, when a system parameter changes beyond a given value, that system goes from self-similarity to contrariety in outcomes and increase in uncertainty between the wings of such attractors. In each more chaotic dynamical regime, social controls lose efficacy; indeed, causality, prediction, and control become casualties to the knowledge process. The Butterfly Attractor Under specific conditions, a small change in a key parameter can force a stable torus to break up into two or more tori. Such change produces an tongue as in Fig. 3 [arrow] which expands such that a system might end up in either one of two wings, as in Figure 4. below, the butterfly attractor. The first such attractor was identified by Edward Lorenz in his modelling of a weather system with twelve variables in the early 1960s. Since then, butterfly attractors have been found in a wide variety of natural and social data sets. In social terms, small differences in initial conditions between, for example, similarly situated children can be amplified to produce two entirely different life courses. Howard Becker (1963) picked up on this fact in his development of labelling theory. Small differences in processing and labelling inside the criminal justice system can produce large differences in the fate of children otherwise very similar in demographic conditions. One congery of children in a city such as Chicago or Dallas might end up in college; one batch might end up in prison. The differences between members of both sets might be so small all would take pretty much the same pathway (that of a torus) were it not for the labelling process; a small change at a crucial point in the moral career of a child. Such labels become locked in for the child when school, police, court, and other authorities utter and publish such labels to peers, family and neighbors. Likewise, small reductions in income (or increase in expenses) can trigger qualitative change among white collar professionals in tactics to generate income. In a given society at one point in time, most if not all physicians might behave pretty much the same toward their patients in terms of diagnoses and prescriptions for tests, medications and surgery. Given small changes in certain parameters of income and/or living expense, some number of physicians might begin to over-prescribe for patients and over-bill third party carriers. Of the universe of all doctors, each with very similar socialization, personalities and life styles, a small change at a change point might send one into embezzlement, stock fraud, medicare fraud or income tax evasion while the other might make adjustments in life style (moving to a smaller house, selling a second home or third car, borrowing from family or friends). The operative point upon which to focus is that it would be impossible to predict which of that universe of doctors would engage in deviant behavior. All that the deviancy theorist could be certain of is that, given small changes in key parameters, even larger numbers of doctors will defraud or mistreat their patients. The Butterfly Attractor can be viewed as comprised of two tori; each of which is a qualitatively different outcome basin for very similar systems. This is the essence of Second Order change; similar systems will have different fates depending upon their journey through uncertainty. Under some social conditions, an outcome basin in which each set of persons has a different fate could be, in human terms, desirable. In mapping the socialization of children, there comes a time when most societies track one set of children into one set of status-roles and another set(s) into other status roles. Gender differentiations, occupational differentiation, ethnic and religious differentiations are examples of normative bifurcations in outcome states between persons with but small differences in initial states. Such differentiations serve as reservoirs of variety from which nonlinear transformations to new states are possible thus increasing survival chances in an ever changing macro-environment. Differentiations may be helpful also in that specialization occurs and experience is augmented. Yet the continuing sub-division of labor may be inimical to both quantity and quality of work. Stratification, as mentioned also may have limits beyond which so much uncertainty accumulation for those at both the top and bottom that the pattern and predictability so essential to social processes fail. Third Order Change There is a third kind of change of interest to those in the social sciences. Chaos theory offers an explanation and description of the transformation of social tori and other strange attractors from quasi-stability toward deep chaos. The short version is that when the periods of a system bifurcate the third time, they are in a situation where another very small change can produce great numbers of possible endstates toward which a person, a group, a business or a society might go. The operative point to keep in mind for a theory of deviancy is that this great increase in alternative ways to behave is a feature of the whole system not just the single, acting person; punishment of individuals for trying to cope with such emergent conditions is an exercise in folly if not in mean-spirited vengeance. And, for those in social philosophy generally, it is good to remember that even in deep chaos there is a great deal of order. And, even in deep chaos, it is possible to obtain an uncertain stability. A. Hbler (1992), of the University of Illinois, Urbana, has shown that, if one can model the key rhythms of chaotic displays, one can control chaos even in the most uncertain regions of a bifurcation map. Figure 5, below, shows faint tracks in deep chaos at which very gentle intrusions can stabilize system dynamics. While this ability to control in deep chaos is now limited very simple systems [in this case, a laser beam], still we see that, in principle, control of key parameters is possible. For those who like minimal intrusion by the state into public discourse, this fact is interesting. In a great many different kinds of systems, a similar pathway toward full chaos is observed. As one can see in Figure 5, the bifurcation map below, after the first bifurcation (or forking), a system has but one loose endstate in which it might be found (Region 2), its dynamics describes a limit attractor. After the second forking (Region 3), it loops around and within that fractal geometric figure called the torus. After three bifurcations, there are two possible destinies which any normal system may take (Region 4). The pattern observed is called a Butterfly Attractor. Then there is a region in which several outcome states are routinely visited. However, after four bifurcations, the number of endstates possible for similar members of a set are progressively short lived (Region 5). Feigenbaum (1978), has found that a system with three bifurcations is fairly stable but one with four quickly tumbles into full chaos. The Feigenbaum constant, 3.5699, gives us the possibility of making a prediction of the onset of full chaos when the first few period doubling parameters are known. There are many features of the sequence shown in the bifurcation map depicted in Figure 5 which are of interest to the behavioral scientist. In the first instance, the choice of which basin to set as the normative and which others to define as abnormality, deviancy, error, sin, or crime is shown to be a human, thus a political, act. In all societies, in some fields of human endeavor, of some number of outcome basins, one such basin ordinarily, and quite reasonably, is set as normative. In the pronunciation of a word, in the counting of bricks, in the naming of flowers, communication and interpersonal understanding depends upon pattern and consistency. However, in such matters as gender socialization, many societies set one and only one pair of gender orientations as normative. In other societies, three, four or more genders are possible, each with varying patterns of sexuality and intimacy. Second, in the immediate vicinity of such change points, human agency is greatly augmented (Young, 1992). Small adjustments of key parameters can prevent a great increase in the number of basins to which a system will go or, alternatively, facilitate change. It is a human choice to make and a human responsibility to make such choices. Social control tactics work fairly well until one gets to such points but, without changes in the larger parameters, control fails (Briggs and Peat, 1989; Young and Deal, 1994). Third, at the boundaries between any two outcome basins, small untrackable differences push a system into deep chaos. In the case of economic dynamics, well run businesses might not survive a great depression while other poorly run businesses might not fail (Young and Kiel, 1992). A small difference in location, in customer traffic, in profit margin might catapult even well run businesses into bankruptcy. Nonlinear feedback from their failings might trigger other bankruptcies of well run companies or, perchance, help other poorly run firms survive. In the boundaries between stable regions of such an outcome basin, the fate of any given business in quite unpredictable. An important point to note is that, in a sea of disorder, there are pockets of order. The emergence of such pockets of order is entirely unpredictable. Ilya Prigogine (1984) won a Nobel prize for setting forth the principles by which new order emerges out of disorder. If we look at the Left side of a Bifurcation Map, we see the order which warms the heart of a Conservative. If we look at the right side of Figure 5, it is easy to see the 2nd law of thermodynamics at work; things do tend to their most probable state. But if we look more closely, we see pockets of order which ground the insight that new order is always emerging out of chaos. Such new forms do come; come what may. And they do come when linearity in feedback pushes system dynamics beyond the fourth bifurcation. For those in public policy as in social philosophy, the operative question becomes how and whether human agency can be deployed to provoke dramatically new forms of social life. POSTMODERN PHILOSOPHY OF SCIENCE: Conclusion. Chaos theory reveals an ontological grounding for the knowledge process very different from that of modern science and strangely akin to some premodern presumptions. Prediction, replication and falsification lose efficacy as the tools of the knowledge process as physical, biological and social systems move from stable to unstable dynamics along a bifurcation track. In the new science of complexity, order occupies a small niche while the changing ratio between order and disorder fills the geography available to it with emergent macro-structures whose geometry becomes so complex that research designs cannot encompass them. Chaos theory requires an entirely new way of thinking: one in which fractal geometries replace neat and tidy euclidean forms; in which the excluded middle discarded by Aristotle is reclaimed; in which truth values of propositions change with region in a complex basin of outcomes; in which newtonian physics is displaced by discontinuity and qualitative change; in which newtonian calculus gives way to qualitative mathematics and in which the second law of thermodynamics is seen to describe but half of the fate of natural and social systems. Out of the other half emerges entirely new and unpredictable forms of social order. Most troubling to modern sensibility is that fact that two similar systems can met very different fates; that contradictory results are found in the same complex causal basin and that causal relationships change as a system leaves one dynamical field for another. The geometry of social and natural systems seem bizarre in this new understanding; they turn, twist, fold and occupy the same time space continua as do other such systems. Even simple systems can display complex behavior. What is true at one scale of observation can be very wrong at another. What is true for the dynamics of natural and social systems in one region of phase space is not true in another. Truth values themselves are fractals in such a science. This opening in the truth table requires much thought while it permits more human intervention than modern science thought possible. At the edges of a causal field, small differences in ways of acting, ways of thinking, and ways of feeling interact to propel a person or a set of persons into a very uncertain fate. In complex causal fields, those with 16 or more outcome basins toward which a member of a society might go, idiosyncratic interactions can create entirely new forms of order and certainty. The more complex the system, the more likely it is to become irrational in the technical sense. It is the story of this contest between order and disorder; between precision and pattern; between certainty and possibility; between fate and chance; between truth and fiction to which Chaos findings speak so well. Chaos theory offers a series of insights about the origins and patterns of variation and change most useful to theories of change and deviancy. As such it creates and defines a postmodern science in which disorder has equal standing to order as a feature of natural and social systems. Those who prefer order and view the bureaucracy as the central organizing tool in modernized society have much to consider. In decentering stability and monolithic social forms, it provides an elegant theoretical envelope with which to ground postmodern explorations in art, music, dance, drama, religion, health care, education and other cultural forms heretofore deemed repugnant, unnatural or evidence of pathology. Chaos theory thus forces a comprehensive review and an extensive revision of the basic assumptions which guide the knowledge process in research and theory. It retains and respects the many contributions made by pre-modern contributions to inter-subjective understanding. Trust, belief, faith, hope and love all increase the possibility that one human being will take the role of the other and in the doing, the geometry of self expands to create a 'We.' Feeling, thinking and acting then become shared processes. If such processes are wide and deep, the boundaries of the localized 'we' can expand to create a more Universal We. Thinking, feeling and acting become a much more collective endeavor. The division of labor as well as ancient divisions of gender, race and ethnicity tend to restrict the knowledge process but, knowing that, human beings have a moral choice in domains of life not possible in either pre-modern or modern knowledge processes. Modern science continues to be basic to the knowledge process but is modified to be far more concerned with the entirety of the causal field in which a system is found...the epistemological utility of analysis is greatly augmented by that of totality and synthesis. Simple systems do exhibit the precision and predictability which the early founders of empirical science sought. However, truth values of real existing dynamics were subverted by research designs which isolated, which controlled, which restricted the interaction to some two or three interacting variables. It little serves the knowledge process to find certainty unconnected to the practical interests in health, safety, economy or efficiency which inform most research most of the time. Indeed, pure research is for the most part, irrelevant research. It is real praxis which drives the modern knowledge process. Chaos theory thus offers a version of the dynamics of nature and society in which there is room for human agency as never found in the god hewn worlds of premodernity or the iron bound laws of modern science. What we do with the vast genius and the great knowledge which we inherit from premodern and modern knowledge processes is, in postmodern social science, our own responsibility. We cannot appeal to nature or to the gods for direction nor may we assign blame to devils and genes when things go wrong. In that loss of innocence resides our dignity as architects of our own fate. REFERENCES Becker, Howard. 1963. Outsiders: Studies in the Sociology of Deviance. New York: Free 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 1987 Chaos: Making a New Science N.Y.: Penguin Books. Hbler, A. 1992 Modelling and Control of Complex Systems: Paradigms and Applications. Modeling Complex Phenomena. L. Lam, ed. New York: Springer. Kerbo, Harold. 1991. Social Stratification and Inequality. New York: McGraw-Hill. Mandelbrot, Benoit 1977 The Fractal Geometry of Nature. New York: Freeman. Prigogine, Ilya and Isabelle Stengers 1984 Order out of Chaos: Man's New Dialogue with Nature. New York: Bantam Books. Rosenau, Pauline. 1992 Post-modernism and the Social Sciences. Princeton: Princeton University Press. Waldorp, M. Mitchell 1992 Complexity: the Emerging Science at the Edge of Order and Chaos. New York: Touchstone Books; Simon & Schuster. Young, T. R. 1991a. Part I. Crime and Chaos. In The Critical Criminologist. Vol. 3, No. 2. Summer. Young, T. R. 1991b. Part II. The ABCs of Crime: Attractors, Bifurcations, Basins and Chaos. In The Critical Criminologist. Vol. 3, No. 3. Fall. Young, T. R. 1991a Chaos theory and Symbolic Interaction: Nonlinear Social Dynamics. The Journal of Symbolic Interaction, 14:3, Fall. Young, T. R. 1991b Change and Chaos Theory: Metaphysics of the Postmodern. The Social Science Journal. 28(3). Fall. Young, T. R. 1992. Chaos Theory and Human Agency. In Humanity and Society. November. 16:4. Pp. 441-460. Young, T. R. and L. Douglas Kiel. 1992. Chaos and Management Science. Under review. Young, T. R. and Anthony Deal. 1994. Law and Social Control in Complex Societies. Copies available from the Red Feather Institute, 8085 Essex, Weidman, Mi., 48893.