T. R. Young, The Red Feather Institute

Jan. 21, 1997

NON-LINEAR SOCIO-DYNAMICS: blink.gif (995 bytes)Explications blink.gif (995 bytes)Implications blink.gif (995 bytes)Applications


Complexity and Self-Similarity
in Non-Linear Dynamic Regimes


Humanist Sociology in a Postmodern Era

T. R. Young
Virginia Polytechnic and State University
Apr., 1992


Chaos theory has several useful lessons for those who would try to advance a theory of human agency. It sets forth the delicate and shifting geometry of order and disorder and thus signals the fractal boundaries between the realm of necessity and that of agency. It identifies the limits of human agency in differing regions of a causal basin; it marks the points at which human intervention has the greatest effect [and takes the greatest risks]. It thus aids in efforts to stabilize--or perchance-destabilize existing social arrangements. In the world of actual, living, thinking and acting human beings, Chaos theory opens up space for human agency in ways not possible in either God-hewn worlds or in clock-like models of social life. Chaos theory provides empirical grounding for an exercise of human agency in which infinite variety, plurality of centers, and the variability of postmodern sensibility most comfortably rests.


The political agenda which informs this and other work centers around emancipatory uses of postmodern knowledge processes. Postmodern critique questions the grounds for grand unified theory, for sure and certain knowledge as well as for neutrality in the knowledge process (Rosenau 1991). Given the validity of that critique, once again the question of the role for social science in human affairs arises. I want to help fashion a postmodern social science which affirms the possibility of human intervention into the social process but recognizes its politics, its many uncertainties and its limits.


For most of human history, the reach of human agency has been short and feeble. With the advent of hydraulic agricultural societies some 4000 years ago and then industrial capitalism some 400 years ago, human agency has been greatly extended in terms of raw power in many realms of human activity. However, modern science with its penchant for 'totalizing' theory, reduces human agency to compliance with universal laws of nature and society. Much postmodern reflection on human agency accepts the presumptions of modern science about totalizing 'laws' of nature or society and thus, remains pessimist (Rosenau 1992, p.81).

In those postmodern critiques which speak against the possibility of human agency, the data they marshall are convincing. Most human beings were subject to the blind forces of nature: drought, disease, storm, and starvation. For them, life is short, brutal and nasty. Even in the face of the great increase in human agency for those who are captains of industry or leaders or well-armed nations, human agency has been assimilated into elite theory. Some of that elitism focussed upon Natural law as understood by Thomas Aquinas and some focussed upon natural law as understood by Comte, Laplace, Pareto and others. For Aquinas, freedom is collapsed into compliance with divine Law. For Laplace, freedom is encompassed by natural law; in both, structure has precedence over volition.

Structuralism Since the publication of Novum Organum by Bacon in 1620 and Principia Mathematica by Newton in 1687, there has been a quest for the deep and enduring structures which pre-form natural and social behavior. In the Enlightenment, the search entailed discovery of universal laws of biology, physiology, psychology and sociology with which to guide public policy. Rationality and freedom were the icons of modern science but freedom was limited to the use of theory to design society. Rationality meant that, in order to be a fully active subject, one had to confine one's action to that which was compatible with those natural structures as revealed by universal law. To act in ways not compatible with natural structures was to be the fool, the idiot or the psychopath; to waste one's time and that of others.

Structuralists see permanent, natural and universal structures everywhere. Greek and Roman thought began structural analysis with its use of the human body as metaphor for society (Polkenhorne 1983, p.135). Hegel gave structuralism a powerful impetus when he posited and published a coherent map of the structures of history and social life in which a 'Spirit' of orderly Reason emerged to give pattern to art, religion, philosophy and science as well as to mind, soul and society. Movement in history is the movement toward Absolute Spirit by which Hegel meant a state governed by and governing surely and forcibly with knowledge of universal laws of nature and society. This made a lot of sense given a Newtonian world view and a stratified political economy which privileged people and peoples. All else was only 'becoming' and could be dismissed as 'imperfection.'

In anthropology, Lévi-Strauss posited deep structures in mind and society which preorganized thought and action. Wertheimer, in Gestalt theory, posited four grouping structures which organized human perception. Kant posited 12 natural categories which guided empiric research and did not contaminate pure reason. Husserl posited deep structures which constituted and preshaped human grasp of natural and social 'facts.' For Husserl, human beings did have a creative role in the knowledge process but that role was presumed to be based upon such natural and essential structures (eidos) that objective knowledge was possible (Polkenhorne 1983, p.42). In moral development, six natural stages posited by Kohlberg preëmpted moral theory. In sociology and in economics, a variety of modernists posited a single set of social functions toward which all structural change was a becoming.

Deep structures, if linear in their geometry, are inimical to human agency. Linearity implies that that which exists in the present fully determines that which shall exist in the future. This is a view which informs much neo-fascist social philosophy in that it tends to privilege the present as necessity and the future as inevitable. Chaos theory, of course, delegitimates that view. There are no inevitabilities in nonlinear dynamics of natural and social systems. Instead what is found are three generic forms of change within which there is more, or less, room for human agency. This essay tells the story of these kinds of change and explores their meaning for a theory of human agency in a time of great uncertainty.

Fractal Structures: Natural and Analytic Chaos theory offers a view of 'structure' which reconciles the insistence of reductionists that such totalizing entities do not exist yet accepts the insistence of structuralists that there is a whole from which the behavior of the parts is given both meaning and direction. In Chaos theory, nonlinear dynamics produce natural structures, the fractal geometry of which varies, depending upon their dynamical state; there are five such states discussed below. The geometry of such structures also varies with scale of observation: that which is a solid object from the point of view of a human scale of observation becomes almost completely empty space when viewed at sub-atomic scales. At scales of observation between, there is an interesting self-similarity in structure but there are qualitative differences as well--in the very same object.

In all this Chaos theory grounds a philosophy of science and knowledge very different from that of modern, Newtonian metaphysics and thus renders much of the postmodern critique of modern philosophy of science moot since it decenters modern science and relegates its presumptions to just a small portion of the actually existing natural and social systems. It is not that modern science and its project is to be rejected; only that it is to reserve its claims to those very simple natural and social systems which behave linearly and predictably. There remains much that is valuable in modern science but, as a grounding for a theory of human agency, there is much to criticize. Chaos theory offers a beginning which answers most of the objections of post-structuralism.

HUMAN AGENCY IN MODERN PHILOSOPHY In the Enlightenment version of modernity, in order for human agency to exist, several prerequisites are necessary. For some expressions of the Enlightenment, such as those who follow Nietzsche, only superior individuals have the intelligence and the will to impose their desires on lesser people. For others who follow Hegel, the state is the repository of both Reason and Will. Still others such as Bacon or Comte thought that a collegium of scientists could advise the state. Still others such as Marx thought a far reaching democracy could link reason to otherwise intractable problems of life. More demanding modernist theories of human agency require:

1) an emancipated subject who would have goals above and beyond those activities preprogrammed by genes, or by 'primitive society' or by those mapped by preëxisting norms, laws, customs and morés common to the society in which the person was socialized. To take on preexisting goals is not, in modern understanding of agency, an act of autonomous Will.

2) a knowing subject who would have precise and positive knowledge about the dynamics of that part of the natural and social order s/he wished to shape in their own interest.

3) a creating subject who would be able to provide self with all the tools essential to a task. Use of others as instruments of one's own will is permitted.

4) a rational subject who would have to use instrumental reason with sufficient skill such that the probability with which goals are achieved routinely surpasses chance.

5) A 'principled' subject who would apply scientific or moral principles rigorously and uniformly over the raw material at hand. And finally,

6) a willful subject, some would say ruthless, others would say goal oriented, who would not be deterred by sustained opposition, adversity or defeat.

For many postmodernists, it would be fair of modernists to posit human agency only if the acting person embodied these most stringent standards above. But few can meet these standards. The operative question is whether these standards are fairly set. The argument here is that those who demand these standards for human agency are more interested in control and compliance than in principled behavior founded upon 'rational social philosophy.' As we shall see, Chaos theory instructs us that natural and social systems are stable and survive precisely because they are 'unprincipled,' i.e., they behave nonlinearily. More generally, Chaos theory rejects the clock-like dynamics upon which modern science is based and from which modernist theory of human agency is drawn.

Many would argue that these criteria are too stringent; that the test of human agency is met when one acts with insight and enthusiasm in the embodiment of existing norms; that human agency is found when one is creative and innovative in existing institutions and that human agency can be seen in efforts to reform and extend foundational concepts and practices in an otherwise good and decent society. There is much merit to this position but I am considering the ways in which Chaos theory speaks to a theory of human agency which meets even these most rigorous tests.

Post-structuralist Critique Skeptics in the postmodern camp take their lead from Nietzsche who questioned the facticity of these deep structures. They question the preoccupation of modern science with truth, natural law and objective theory without a human author immersed in a political, constitutive process. For postmodernists, all knowledge about structure is a quest for power more than for truth (Foucault, Derrida). Saussure, in his work on general linguistics, 1915, led critique at the level of thinking and knowing (Polkenhorne 1983, p. 152). Lyotard and Hassan gave the same treatment to the grand narratives of modern science and modern religion. When one deconstructs any such narrative about language, mind, perception or politics, one finds a politics and a poetry which presents itself as universal truth.


Human agency has a more optimistic future in both critical theory and in American social psychology. Predecessors of critical theory in Europe, Vico, Droysen, Windelband, Rickert, Dilthey, Wundt, Husserl, and especially Weber set the human sciences outside the reach of natural law and thus provided space for human action. Marx had insisted that, in capitalism, one could see the possibility of collective human agency; of the end of the 'idiocy' of prehistory. Given good theory and good politics, a universal subject could be brought into being. Critical theorists today argue that there is a shifting and complex connection between economics on the one side and ideological hegemony on the other which, along with other structural constraints such as patriarchy and racism, shapes the possibility of human emancipation (Held 1980).

In America, social psychologists from Mead to Cooley to Blumer saw the possibility of human agency even against the putatively iron laws of nature and society. In their reading of the social process, human agency was not captive to natural law. Rather human beings constructed the social life worlds in which they lived out their lives. Given the human hand in such construction, there are any number of ways to create social realities. Anthropology confirmed the great variety of social forms by reporting data on the 3 to 4000 societies which sentient human beings, collectively, in their wisdom and with their own agency have constructed.

Postmodern Phenomenology The postmodern phenomenology offered here differs greatly from Husserlian phenomenology. In it, there are no preëxisting and natural categories which shape thought and action. There are, however, linguistic categories which do preshape thought and action but these do not predate culture nor are they located exclusively in the mind of the single acting individual. Mind, self and society emerge continuously within an ever-changing symbolic envelope. Foucault has laid out, in a wide-ranging series of books, the changing categories with which we grasp the dynamics of madness, crime and human sexuality. Marx has laid out the changing principles with which one can grasp the larger economic factors which preshape thought and action. Gilligan showed the political nature of Kohlberg's rendition of moral development and its preference for linearity. Feminist theologians and others have noted changes in the god concept in religion.

In all this, the human being is very visible as author of the categories of thought and action. In all this, one can see political agendas, legitimated as universal truth, inside the knowledge process. Postmodern phenomenology building upon the work of Husserl, Sussure, Wittgenstein and others offers a much broader field to human agency in the invention of reality and all sciences which purport to describe that reality than do modernist phenomenologists who follow Husserl and assert universal and natural categories of experience or analysis (Young, 1992b). Postmodern phenomenology grounded upon the new sciences of chaos and complexity, offers a view of human agency which concedes that there are 'structures' in the human mind and human culture which preshape thought and action but insist that these structures are themselves historical and ever-changing.

Whatever one's views on human agency, Chaos theory offers insight and guidance into the delicate and shifting relationship between order and disorder in ways not permitted in modern science nor imagined in more traditional knowledge processes. It is in those dynamics that one can find a theory of human agency which is at once, affirmative and realistic. The realm of necessity and the realm of freedom are not mutually exclusive nor does the dominate the other in all dynamical states; they are always found together. There is never a time in a nonlinear system in which there is no order; never a time in a stable system when there is not disorder. Human agency and human determinism dwell in the same theoretical house.

CHAOS AND NONLINEAR DYNAMICS Edward Lorenz, James Yorke, Mitchell Feigenbaum, Stephen Smale, Benoit Mandelbrot and many others developed the theory, math and the sequences of nonlinear dynamics in natural systems (Gleick, 1988). The work of Mandelbrot is central. Mandelbrot worked for the Thomas Watson laboratory of IBM and was charged with solving the problem of interference in electronic transmission of signals. Mandelbrot found that, at all scales of observations, electromagnetic dynamics were fractal rather than integral. From that insight, Mandelbrot (1977) went on to generalize that the ontology of all natural systems was fractal rather than integral.

Given the nonlinear behavior and fractal geometry of almost all natural and social systems, one might first think that, in such an irrational world, human effort and human purpose is pointless. Nothing could be further from the truth. Human agency is possible; the operative question is when and what is possible. It is the changing ratio between order and disorder; between harmony and disharmony; between linearity and nonlinearity which answers such questions. At time, human interests warrant a preference for order but for most human purpose varying degrees of disorder are most helpful.

Human Action in a NonLinear Social Life-World In this section, I invite the reader to look at the various dynamic states which social systems can take and to think with me about the degree to which human action and agency is possible within each and between all of them. We will look at the first four dynamical states in some detail and explore the fifth state a bit later. Figure 1 offers two views of four equilibrium regimes. One view is that of the familiar time-series; the second is that of the fractal geometry of systems dynamics in phase-space. It is explication of this fractal geometry which opens up profound implications for the philosophy of science and, in this application, human agency.

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The first form, 'A,'  in Figure 1 is called a point attractor and the second is called a limit attractor. These two forms describe a dynamics in which there is little space for human agency. There are also two semi-stable attractors; the torus and the butterfly attractor. The latter two are called 'strange' attractors since a system is attracted to a particular region of phase space. These attractors provide space for human agency in ways not possible in those dynamics privileged by Newtonian physics, Aristotelian logic, Euclidean geometry and the linear causality they presume.

For Box A in Figure 1, the realm of freedom collapses into a single point. For Box B in Figure 1, the realm of freedom is tightly confined to a single repeating curve. If one were to base a theory of political agency upon these linear dynamics, one would hold that rational human agency involves the discovery of necessity and compliance to that which is necessary. However, nonlinear dynamics are far more common and far more open to choice among uncertain futures. The first such attractor, Box C, is called the torus. Social dynamics which take the form of a torus have some limited room for human agency. It is Box D, the butterfly attractor and its close cousins (with 4n, 8n, and 16n outcome basins) in which one finds significant human agency possible. A fifth kind of dynamics, full chaos, is discussed later since the human agency it offers is qualitatively different.


Figure 2: First Order Change: The Torus

For all such systems whose key parameters produce a torus, human agency is limited but it is there. In this first order trans-formation, the regularity found in the point attractor or limit attractor gives way to some uncertainty. We know that a given system will end up some where within the torus but we do not know just where to find it.

Think of the single line in Figure 2 as the dynamics of a family, a firm, a fellowship or a college class over the course of some given time period, say a year, on any given variable of interest to the researcher. If one is interested in say, number of children, employees, members, or attendance patterns, one would see that such values would stay within given limits over the course of a year but do vary. If a couple needs at least ten children to be certain that five would live to provide social and economic security in old age, human agency is a complex process limited by such exogenous factors as food supply, health care practices, religious values and personal vigor.

If the third set of lines in Figure 2 were, say, a large set of families, firms, fellowships or classes, one might see sufficient pattern to call that behavior a 'structure.' However similar, no iteration of a family or a firm is ever precisely the same as that of another family or firm. Similarity-but-not-sameness is the quintessence of the torus and of first order change. In any environment in which the key parameters produce a torus, one has latitude to move within the confines of the torus. Larger freedoms are difficult. For instance, one does not have the 'freedom' to choose to produce no children else one is bereft in one's old age. Nor may one choose to have ten healthy children if such numbers exceed the carrying capacity of the political economy at hand.

Second Order Change There is one feature of the torus in Figure 2 which does not sit well within the logic of modern science. It has great import for a theory of human agency. Chaos research shows when an attractor is about to bifurcate into two (or more) outcome basins. If parameters increase linearly, outcomes change linearly. Not so in Chaos dynamics. Figure 3 shows a Poincaré section of a torus in which a small change might make a large difference. Figure 4 show that cross section in more detail.

Figure 3: Poincare' Section of a Torus

If one looks carefully at the cross section of the torus, Figure 4, one can see two tongues; the first at the extreme left which if expanded more, would expand human agency. This feature of a torus tells us that a new attractor is about to be born. Something is going on with the key parameters in a dynamical field which makes existing ways to do family (or business, religion or education) difficult or undesirable for some portion of the families (or firms, churches or schools) at hand. That tongue alerts us to the nonlinear emergence of, say, new gender relations or new opportunities for business expansion or to imminent sectarian schisms in a fellowship or new programs in a university.

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Figure 4: Second Order Change

In modern science, there is one and only one outcome basin in an outcome field; all systems of a kind are required to behave alike for a given set of conditions (or at least remain inside the geometry of a torus). All else is random error, faulty research design, inadequate instrumentation or just bad theory. Modern science tolerates variation around a mean with the concept of the well known 'normal' distribution for 'adequate' theory. Penrose (1989) uses the term, 'superb' for theories which have a precision approaching 1014. In Chaos theory there can be two or more outcome basins to which similar systems with similar initial conditions can go. The precision with which one can chart those outcomes varies depending upon the complexity of the outcome basin. Weak correlations may be not a product of weak theory or of poor instrumentation but of actual indeterminate dynamics. Moreover, what is a strong correlation in one region of phase-space may be a weak correlation in another for such similarly situated systems.

Postmodern science grounded upon Chaos theory conceives of structure as a loose and everchanging form, the solidity and reality of which is variable depending upon scale of observation and upon dynamical state. In that difference is a major insight for a theory of human agency. Social structures have a fractal value which might be very loose or very tight depending upon the key parameters above. There is never a time in which causality is so tight in Chaotic regimes that human agency is impossible. There is always some room for Will and Desire to combine to move to a different region in an outcome basin, even in a torus.

What is process at one scale of observation can be seen as structure at another scale. It is the pattern of social action which, over countless iterations, produces structure as Figure 2, above suggests. It is the changing ratio between order and disorder in a given outcome field which is so very different from the ontologies of modern science. These differences force rethinking of our idea of structure and, indeed, of our philosophies of human agency. In brief, for any nonlinear system, there is space for human agency. That space opens up as a torus expands into phase space. At crucial points, key parameters change and new attractors can be and are invented by human agency. In their wisdom or folly, human beings act and in that action expand the causal field into two, four, eight or more outcome basins. In any semi-stable field under stress, a causal basin can explode to fill the space available and thus expand the scope of human agency.

The generic point is that small changes in key parameters can force open a monolithic causal basin to accommodate still more outcome basins thus increasing both the range of choices and the regions of uncertainty in which human agency might play. The term used in Chaos theory to denote such moments at which causal basins expand is bifurcation. The first bifurcation produces a butterfly attractor.

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Butterflies, Bifurcations and Human Agency

Figure 5a,  upper right, presents a very puzzling view of the butterfly attractor shown in Figure 1, in the first section, above.

One will note that, in Figure 5b lower right, there is an 2n outcome basin rather than the unitary basin in the torus shown in the Poincaré section in Figure 4, above.

Near the center of each region of a 2n attractor, outcomes are pretty certain and, thus, human agency is limited as it was in the Torus (in fact, a butterfly attractor can be understood to be comprised of two connected tori). At the edge of each causal basin and between the two basins, certainty is lost; a moth or a marriage might end up in either basin or drift endlessly back and forth between two outcome states. To the degree that a family or a firm has control over key parameters, there are quite specific points at which small adjustments can produce large changes. Human agency is greatly expanded given such conditions.

The Butterfly Attractor has, then, at least three major implications for a theory of human agency. In the first instance, there are two options between which, as mentioned, a firm or couple could chose given resources where before there was but one. Today, many couples live childless without social onus or legal sanction and then, after some variable number of years, may separate without legal obligation. The possibility of new forms of intimacy with or without children opens up the realm of freedom, If one were to calculate the portion of phase space in which human agency were possible, one would find that a Butterfly Attractor has more potential available for individual action than does a torus.

A second theoretical point upon which to focus is that there is an area between outcome basins in which dynamics and thus prediction is fractal. There is considerable stability, pattern and predictability for, say, couples which dwell within either basin of a butterfly attractor; for those couples at the margins, they may enter into a fairly stable relationship--or may not. This region of uncertainty is a goodly portion of the total basin of outcomes and greatly expands human choice if not human problems. If certainty is enemy to choice and human agency requires uncertainty, one can determine with considerable precision what ratio exists and thus have a reading on the room for agency.

Loye and Eisler have picked up on still another theoretical point. If one wishes to intervene in near to stable social dynamics (in order to expand or reduce a range of options), one has the benefit of improved forecasting which helps identify points of transition. As they put it (1987, p. 57), Chaos theory can be used to develop 'early warning systems' which can help forestall crises or identify newly emerging routes out of disorder. When human agency requires both pattern and variation, such warnings are most useful.

A fourth point upon which one might focus is that, in such a causal field human agency, hence moral agency, changes its location from the individual acting firm, family or person, in part, to the whole causal basin. Again, Chaos theory offers a most important point for a theory of human agency since some of the parameters which structure the ratio between certainty and uncertainty involves collective agreement as much as individual volition. There are grounds for democratic political theory in this point.

2N+ Outcome Fields

If one bifurcation alters the ratio between freedom and necessity, the question becomes what meaning do two, three, four and more bifurcations have for a theory of human agency. The most general point one can make is that, up to a point, an increase in the number of attractors increases potential for human agency. However, there is a caveat: while uncertainty may be essential to agency, several overlapping uncertainties might lead to chaos. For example, a couple might have the resources to handle one uncertainty or perhaps two uncertainties (say about income or about work schedule) in their lives but three or more uncertain parameters (say health, income, or work schedule) could push that couple into a chaotic dynamics.

The realm of human agency grows discontinuously as ever more outcome basins are produced yet there is a very regular procession toward a fully chaotic regime. This procession is very precisely choreographed by the Feigenbaum numbers below. We will find that freedom expands up to a point, often enabling persons sufficient options with which to adjust to the disorder in the larger society then, suddenly, freedom overwhelms human agency...and in the same instant that coherence is lost, qualitatively new forms of order emerge. Those who cry freedom too loudly call forth enough chaos to destroy the delicate balance between creativity and rationality.

Figure 6: Creation out of Chaos

Figure 6 sets forth the entire series of transformations from order to disorder across the five dynamical states found in Chaos research. At each of four points (identified by 'Feigenbaum numbers'), more bifurcations produce more outcome basins in regular succession--until the fourth bifurcation. It is a remarkable feature of nonlinear dynamics that 2n, 4n, and 8n outcome basins are relatively stable, given nonlinear feedback loops, but with the next small change in a key parameter, full chaos sets in.

One will note that stability and certainty are fairly tight in region A (that of the butterfly attractor). In region C, that is the region in phase-space where 2n, 4n, 8n and 16n outcome basins are found, there are variable ratios of necessity and freedom. In Region D, full chaos reigns. One cannot predict the fate of a student, a family, a firm or a society in such a social milieu. However, one will note that, in Region D, there are bars and spots of white  interspersed in the darker region of fully chaotic dynamics. These white regions are regions of order; entirely new forms of order emerge out of chaos.

Chaos is a source of discontinuous change and renewal in both natural and social systems.  As bifurcations proceed toward deep chaos; the illusion of freedom increases...yet paradoxically, human agency dimenishes with each bifurcation beyond the fourth bifurcation.

A fourth source of freedom has to do with the contest between order and disorder in these new regions.

It was Prigogine's explanation of how order emerged out of disorder which won him a Nobel prize in 1977 (Prigogine and Stengers 1984). Prigogine and countless others knew that the basic assumption of thermodynamics was in error; there is no tendency for the universe to disassemble into 'its most probable state' as the second 'Law' demands. More complex forms of organization have developed in both natural and social systems; the question is how? The answer Prigogine gave was that energy dissipated from disintegrating systems can be used to build new systems from the parts discarded. Out of the turbulence of change and disorder come new forms of order.


The most encompassing point with which to fashion a theory of human agency and thus a humanist sociology is that transformations from one chaotic regime to another arise from changes in parameters of the whole system. It is bifurcations in key parameters of the whole system which drive it toward an expansion of its outcome field. In studies of weather systems, of gypsy moths, of heart muscles, of DNA or of molecular crystallization, the 'structure' of cells, birds, insects, water or molecules do not change as phase transitions follow upon one another (Holden 1986) but the structures qua patterns of dynamics most certainly do change. One cannot appeal, in the first instance, to the characteristics of the parts with which to explain the changing pattern of the whole. As Briggs and Peat note in their work, Chaos is a science of the whole. In short, one cannot explain transformations in wealth, weather, bankruptcy, biology, economic, medical or marriage forms by appeal to and only to the personal characteristics of the persons affected. Given this insight, the first and most encompassing policy implication is:

I. Preservation of near-to-stable social dynamics requires identification of key parameters in the whole system at hand and careful modulation of those parameters such that they do not cycle beyond the Feigenbaum point of full chaos.

Discussion: The Feigenbaum numbers suggest that there is some ratio of variety in income, social status or social power which a creative society must exceed and another ratio beyond which a just society (and thus stable) does not exceed. Chaos theory implies that when effective income inequalities remains but 2, 4, or 8 times that of one sector of the population over another sector, a society can be stable. If effective income bifurcates beyond 8, 16, and 32 times, the secondary and tertiary needs of the first group tend to drive the economy and to price the poorer group out of the market for primary goods. In such a case, one can expect human agency of those excluded to create new outcome basins; some of which may be most congenial to the human project and some more hostile. In like fashion, given a group with 8, 16, or 32 times as much political power as another group, the more powerful group tends to make social policy in public and private sectors which give preference to its own welfare at the expense of minorities.

II. Nonlinear feedback prevents destabilizing amplification of system periods and cycles.

Discussion: Only Chaos can cope with Chaos. Conferral of social status may be the most significant stabilizing tactic with which to limit the amplification of deviation in the parameters above. The essence of social status is that the person to whom it is awarded may participate in the construction of all relevant kinds of social reality and that the person has access to the resources with which to do so apart from merit or income. One gets what one needs to be a full person irrespective of any linear, quantifiable input the person makes to the occasion at hand. Market dynamics tend to be rational; hence ultimately destabilizing as wealth and power amplify. Social justice, in its irrationality, tends to be stabilizing. Absent status, even social justice programs tend to be cheap, mean-spirited and degrading...this form of social justice amplifies the very bifurcations meant to be constrained by policy. Absent status, the giving group tends to intrude into the personal life of the recipient group exacerbating resentment and escalating costs.

III. Efficacy of social control institutions as well as the utility of cybernetics varies with equilibrium state.

Discussion: Social justice is preferable to criminal justice as a solution to the problem of order. Pattern and predictability fade as phase transitions cascade toward full chaos. In social terms, if a system passes the fourth Feigenbaum number, social control tactics fail entirely. Policies oriented to law and order; recourse to criminal justice, civil suits, monitoring and sanctioning, private security systems and other control systems tend to become ineffective as uncertainties escalate. Criminal justice tends to be counter-productive on several scores; it tends to increase the amount of pain and resentment in a society and thus encourages conflict. It tends to be linear while social justice tends to be nonlinear. Being linear, criminal justice amplifies status inequalities; being nonlinear, social justice tends to damp inequality.

IV. Small changes in key parameters can prevent large changes later on.

Discussion This point will be very welcome to the ears of those who like minimal intrusion of the state into the economy and private life. Small changes in rental rates, interest rates or tax rates can produce large increases in affordable housing, sustainable agriculture or energy effective transport if made at strategic points. These strategic points are given by the Feigenbaum numbers; if one wishes to double affordable housing, the Feigenbaum number for the ratio between income and housing costs must be at least 3.0; if one wishes to quadruple affordable housing, the Feigenbaum number is 3.5. At both these points, a small increase will push the system into the next phase transition while a small decrease in that ratio (by taxation or adjustment in interest rates, for example) will, if Chaos dynamics are instructive, pull it back from the abyss.

V. Personal freedom on the one hand and social order on the other can be harmonized by some attention to the number of outcome basins offered in any given sector of the social order.

Discussion: From the sections above, one can see that differing configurations of outcome basins affect human agency. There are many important dimensions of personal choice in all near to stable outcome fields; the torus, the butterfly attractor as well as 4n, 8n, and 16n basin fields. The costs and risks of 32n outcome basins may not be worth the gain in personal freedom for some few persons, given the loss of pattern and coherency for the whole system. Chaos theory thus suggests that social policy can be formed which satisfies our interest in stability and continuity on the one hand together with creativity, spontaneity and flexibility on the other.

VI. Full Chaos tends to produce new order; not complete disorder.

Discussion: This is that third order change within which human agency is severely limited. The task for a democratic political philosophy is to observe new forms of politics, new forms of economics, new forms of religion or family and explore their potential for the human project. The events in Eastern Europe lends itself to this kind of research.

There well may be times and realms of social life in which full chaos is beneficial to the system. Given unresponsive institutionalization of social practices which amplify inequalities, full blown chaos with its destructive/creative dialectics may serve to unfreeze existing power/class configurations while producing innovations, some of which may be most congenial to the human project. There may be times when revolution is more congenial to the human project than is the slow and gentle evolution of mediated social change.

I would be remiss if I were to fail to point out that it is precisely in such situations one finds both the ugliest as well as the most emancipatory social engagements. This is the time when wisdom and judgment is best deployed and when the ancient teachings of the Buddha, the Christ and Mohammed remain most valuable to the human enterprize.


There is an emerging literature in both natural and social science about the tactics by which low order chaos can be managed. A. Hübler (1992) of the Beckman Institute at University of Illinois, and Stephen Guastello, (1992) Psychology, Marquette University offer papers to that possibility. In brief, one manages chaos by determining its dominant chaotic regime and adding enough matching chaos to maintain the desired balance between order and disorder. There are several advantages to nonlinear regimes for ordinary biological, physiological, psychological and sociological processes. The fact that Chaos can cope with chaos is embedded in all these advantages. In population dynamics, in heartbeat, in thinking and in talking, nonlinearity permits at once of pattern and predictability and, in the same moment, of flexibility and creativity. Without nonlinearity, life would be chancy indeed and communication most primitive.

CONCLUSION As we expand from a knowledge process oriented solely to the linear dynamics of newtonian mechanics, space is opened for reconsideration of the nature of human agency, the concept of deviancy, the utility of stability and the efficacy of authoritarian structures such as bureaucracies and centrally planned economies. Political and ethical implications of Chaos theory await exploration as do its implications for the philosophy of science and the development of the research tools with which to pursue the knowledge process and to evaluate the validity of what we discover.

It is good to keep in mind, in all of this, that the scope of human agency varies with scale; at the scale of direct, real time interpersonal interaction, there is never a time when one cannot change one's own immediate journey through life. One is always responsible for what one does; given 2n+ attractors, one has more choice and becomes more responsible. It is true that there are larger social processes within which one must live and within which one must fit oneself if one is to survive the moment, however variation, change, creativity and surprise are always found in nonlinear social dynamics; the operative questions are how much change and surprise is available and how such whatever agency available contributes to equity and social justice. A central point in this essay is that, at every level of social organization, there is some level of freedom; with that freedom comes responsibility. Unless we develop a politics with which to constrain that science to human values which transcend a given moment or a given class or a given society, human agency might not always be congenial to the human condition.


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