NON-LINEAR SOCIO-DYNAMICS: Explications Implications Applications

CAUSALITY FADES AND FAILS AS BIFURCATIONS IN KEY PARAMETERS OCCUR...NOT NEW OR INTERVENING VARIABLE BUT MORE OF THE SAME PRODUCES ENTIRELY NEW RESULTS!!!

ABSTRACT

The new sciences of Chaos/Complexity provides an structural base for postmodern sociology. In brief, there are five dynamical regimes, each of which has a different 'causal' patterns. As transitions from one regime to a more complex regime occurs, causality loosens while certainty fades. In such dynamics, nonlinear processes transform into fractal structures. Causal connections develop as patterned behavior produces secondary and tertiary effects throughout an eco-system. The paper suggests some implications for social problems, social movements and social policy. Recent work in the quest for hidden attractors serves as a template for postmodern research protocols.

INTRODUCTION

Each epoch in the knowledge process tends to use differing models of causality. For most of human history, causality could be qualitative; i.e., it could leap, twist, reverse and suspend at the whim of the gods or caprice of nature. Looking at the catastrophic and discontinuous changes in their own lives: flood, famine, war, disease and earth-quake, human beings inferred some agent or agency with malice or rare disinterest in their fate. Alternatively, appreciating a sudden stroke of unexpected and undeserved good fortune, human beings came to believe that they, above all others, were blessed by the fates. In this world-view, human beings themselves, purified and dedicated, could enter into the causal matrix and produce effects which, presumably, otherwise would not occur.

In modern times, since the 16th century, a much more tightly knit and impersonal model of causality has been preferred. John Stuart Mill, following David Hume, defined cause as an invariable and unconditioned antecedent of an event. Alfred North Whitehead offered a more subtle and more variable notion of causality in his concepts of multiple causality and negative correlation. Modern science continues to admire a model of causality in which discovery of constant conjunction of events wins fame and fortune. Newton gave us the laws of motion with which one could observe a causality so tightly patterned that prediction on the order of one part in 1014 parts was possible. Penrose, (1992: 152-155) calls the theory which produces this degree of certainty, SUPERB theory; the capitalization is his. Other research, yielding less elegant theory might be USEFUL while still less certain results are only TENTATIVE.

In sociology, Auguste Comte urged positivism upon the behavioral sciences and set, as its mission, the discovery of the universal and coherent laws of social dynamics. In discarding findings which do not fit linear dynamics, much mischief is done to the knowledge process and, more importantly, to social policy and the possibility of human agency (Young, 1992). In Chaos/Complexity, this agency is severely limited but, given a much more sophisticated research capacity than is now in place, it is possible to augment human agency beyond that which we now see in efforts to control crime, to protect health or to mitigate the economic cycles which throw entire societies and blocs of nations into despair and, too often, into warfare.1

As we go into the 21st Century, sociology and other behavioral scientists will face many challenges in the effort to design research protocols appropriate to nonlinear dynamics; to fractal structures and to a changing causality. The most interesting frontiers in the sociology of medicine, law, criminology, religion, education and other such fields await exploration, discovery and explication.

POSTMODERN UNDERSTANDINGS OF CAUSALITY

Postmodern sensibility tends to see social causality as 'inter-textuality, that is, as a complex and variable interweaving of actions and reactions, many of them blind to purpose and destiny; some quite deliberate in both goal and means (Rosenau, 1994). Direct linear causalities are few and, in most research findings, a product of the research design which in using controls, simplifies and reduces complexity to a more linear pattern.2 Causal 'agents' are difficult to locate in that they, themselves are part of a larger, interconnected tapestry of which the 'effects' are part and parcel of the causal complex. For those who need empirical grounding for postmodern respect for variety, difference, otherness, opposites, contradiction or plurality, this new science serves.

I will first present the basic ideas of nonlinear causality, the bifurcations which produce ever more complex causal fields and, in passing, mention some of the implications for postmodern philosophy of science. Then I will suggest some implications for otherwise intractable social problems and, thus, for social policy very different from the usual efforts to solve the problem of order. Indeed, order itself is a problem, since for nonlinear regimes, only chaos can cope with chaos; that is, there is a changing mix of order and disorder which answers to questions of social control and social policy. As an exemplar of sociological research in nonlinear dynamics and fractal facticities, I include a brief report on what may be the first discovery of a hidden attractor in complex social dynamics by a research team lead by Patricia Hamilton at Texas Woman's University.

CAUSALITY AND DYNAMICAL REGIME

The central point I want to make in this section is that causal connections change as dynamical regimes succeed each other in an elegant parade toward disorder. In the Bifurcation Map presented in Figure 1, we note five dynamical regimes, each produced by the same set of variables; each with a differing geometry, each with differing patterns of causality as small changes in the environment produce large changes in behavior.

For purposes of this exposition, I will define causality as the probability that a given set and only a given set of factors will produce the same behavior in a system or set of similar systems.3 In a work, that a given effect will produce a given result; the operative work is 'will.' Or as David Hume would say, causality involves 'constant' conjunction of events. I will use the test of Roger Penrose (Penrose, 1989: 152) for full and Formal Causality. He sets that probability at better than 1 part in 10 million that a system will be where a theory predicts it will be. I will make a case that causality fades and falls from 'super' status to Useful then to Tentative; again Penrose's categories. Penrose notes that such theories fall are 'rather more untidy than one would wish (p. 154).' There is no set probability statement of how dependable causality is in Penrose. I suspect that Chaos theory will offer a fairly good test. Penrose's third category, Tentative theories 'lack any significant experimental support...' (p.154).

The first two regimes are of little interest to behavioral scientists since they appear so seldom in psychological and sociological dynamics. The middle two regimes subsume behavioral patterns most of the time; they are the central focus for social research in everyday life. The fifth regime displays too much uncertainty for most species, most peoples and most societies, yet it is the regime out of which entirely new forms of life and social innovation come.

Dynamical Regimes The first dynamical regime is called a point attractor since any system displaying such precise dynamics is 'attracted' to the same point in each cycle it makes in time-space. The pendulum is an exemplar for a point attractor. The second dynamical regime is familiar to those who observe the dynamics of thermostats, automobile cruise control or, perchance an automatic light switch which comes on at dusk and turns off at dawn. This dynamical state is called a 'limit' attractor' since there are precise limits above and below which the behavior of a dynamical system does not exceed.

Then there is a series of semi-stable but very different dynamical regimes beginning with the torus in which sameness is replaced by self-similarity. The fourth regime consists of very 'strange' attractors; dynamical patterns which are called strange since they depict behavior which is very different from the neat and orderly behavior presumed to ground the universal laws of nature and society: twists, leaps, reverses, skips and other very strange behaviors are observed. Sometimes there are two very different fates for the very similar systems; sometimes four, eight or sixteen different outcomes are observed among these strange attractors.

Bifurcations

Of considerable interest to social scientists is the third dynamical regime, called a torus, whose dynamics are registered in the third region of the bifurcation map in Figure 1. The torus marks the first appearance of a series of three qualitative changes in causality which confounds and perplexes those who presume that social laws must be neat and stable.

I want to stress the general point that causality changes after each bifurcation (the forking points in Figure 1) of key parameter(s). Nonlinear dynamics displace linear, proportional behavior while uncertainty increase qualitatively at each bifurcation. I will point to three orders of qualitative change and emphasize that the transition from one form of order to another form occurs at very precise points on a bifurcation map. Causality and certainty become more complex and more difficult to trace as bifurcations unfurl but in all this disorder, there is an elegance and a meta-order which challenges the next generation of sociologists. Entirely new epistemological tools must be developed to trace the dynamics of complex socio-cultural systems. Some such tools are applied by the Hamilton team; more have yet to be invented.

Qualitative Change in Causality:

First order change is observed when limit attractors loosen up to become toruses.4 More bifurcations brings second order change; one in which there are two outcome basins in an outcome field. A third order change occurs when deep chaos appears; a regime in which prediction is impossible and human agency very, very difficult. Such changing distributions are not the result of faulty instrumentation, inadequate research design, observer/respondent bias or bad theory, they are intrinsic to the dynamics of complex systems.

Figure 1: From Order to DisOrder: the Natural Transition of Causal Connections

Figure 1, right, shows the transition from the tight, predictable causality so admired by modernist philosophy of science.  But that kind of causality is found in and only in the first region of the bifurcation map depicted in Fig. 1.; that of the straight line...a point attractor.  Causality appears to be tightly joined in Region A, but that is a bit of an illusion...while one can know precisely where a system will be at the upper and lower lines of a limit attractor, one cannot know precisely where the system might be in between the lines. 

First Order Change is found in Region B...that of the Torus;

Second Order Change is found in Region C; that of the Butterfly or Strange Attractor. 

Region C is of particular interest to the social and behavioral scientist since this is the Region where the Dialectics between Order and Change; Dependability and Creativity; Structure and Autonomy; predictability and Surprise are found.  In Region C, the best of all possible worlds exist for human beings;  there is enough order and predictability to ground planning, trust, intentionality and the fulfillment of human desire...all these are possible without either the utter despair of deep chaos or the utter futility of either God-hewn laws or Universal Laws of Nature.

Region D, Figure 1, shows a regime in which causality is almost lost. This is the Region of third Order change in causality...and while predictability is lost; this regime has very interesting implications for a Theory of Social Change since it is in these dynamics that entirely new forms of  social organization appear out of the turbulence of uncertainty. In 1977, Ilya Prigogine took a Nobel prize for his work on emergence of new forms of order. The most general implication for causality is that, when such new systems emerge and survive, other systems in that eco-system adjust their behavior such that new causal connections emerge. Brian Arthur refers to this emerging causal connectivity as 'mode-locking' more about which later.5

Feigenbaum Points

There are specific turning points at which the dynamics of causality are transformed. These change points orchestrate an elegant and very ordered dance toward disorder. Mitchell Feigenbaum (1978) discovered not only the point at which each period-doubling bifurcation in every dynamical regime transformed to more complex causality but he also found that the doubling converged in graceful progression. He calculated a universal constant, 4.66920.6 Every dynamical system studied so far went through the same sequence of bifurcations on the way to deep chaos. This finding and others in the new science of complexity grounds a postmodern science in which the preference given to order in natural and social systems is displaced by an acceptance that there is an enduring tension between order and disorder which marks the dynamics of the world about us.7

This transition to disorder, so orderly in itself, means that the ordinary tools of scientific inference are useful for and only for the first two dynamical regimes in Figure 1.8 Prediction, rejection of the null hypothesis, replication, and tests of significance no longer ground the quest for sure and certain knowledge. Certainty is greatly reduced in its epistemological reach. The binary truth tables of propositional logic give way to concerns with fractal truth values and convergence toward chaos.

In all this, a postmodern philosophy of science emerges in which one looks at the changing relationship between order and disorder; between cause and effect; between certainty and probability; between control and creativity. It is not, as some of the more nihilistic postmodernists assert, impossible to know with certainty; rather the question concerns how much certainty is possible and, more to point, when one level of certainty is replaced by another, lesser level. There are answers forthcoming to both questions in the literature cited at the end of this essay and more to come as this new science is explored in all domains of interest to the human creature.

FIRST ORDER CHANGE The torus in Figure 2 is of special interest to the philosophy of science as to the quest for human agency since it is here that one observes departure from the precise and superb patterns of causality so dear to the heart of the modern scientist. In each of the first two simple attractors mentioned, change is precise. In the torus, a new kind of change with new causal patterns is observed; here sameness is replaced by self-similarity. We can get a closer view of those systems whose dynamics produce a patterned but variable outcome. Note that, in Figure 2, each succeeding cycle in the life of the system at hand is similar to but different from each preceding cycle.

Figure 2. A Torus as process

Process into Structure It is very important to note that, as the behavior of a plant, animal, firm or society is entrained and enters into a complex interdependent feedback process, both structure and causality emerge. More simply, process becomes structure as causality emerges. Looking at the one cycle of a torus in Figure 4, one can see only process; looking at five such cycles, one begins to see structure but the pattern is so loose and so variable that some poetic imagination is required to call it structure...and since it has little systematic impact on other events, its reality quotient is small indeed. Yet after 20, 50, or several thousand such iterations, its dynamics are dependable enough that other energy-using entities come to adapt to it. Figures 3 and 4, above, shows the emergence of structure from process in closer detail. External conditions produce these semi-stable structures, which in turn, produce the objective conditions which shape the behavior of other systems in the environment; causality becomes very complex as such interconnections grow and fade like the grin on a Cheshire cat.

Figure 4. Structure Emerges     

In Figure 4, Above, after a few journeys through time/space, structure slowly emerges.  If the system at hand is able to extract order (energy and raw materials) from its environment, it can survive.  If it survives, other systems in the environment begin to adjust to its behavior and its potential for their survival or collapse.  In biology, such emergent structures comprise the content of natural selection...in sociology, such emergent structures comprise the content of social change.   Often such change is dis-continuous...that is to say, there is not historical record for 'intermediate forms.'

All the discussion on the validity of Hegelian, Darwinian and Marxian theories of change simply do not take into account the transition from order to disorder in Fig. 1 above.  Causality skips, twists, fades and re-appears in complex dynamical systems; that is to say, systems experiencing more than three bifurcations.

Marriage forms, child rearing customs, transportation and housing practices, longevity rates, varieties of crime and well as most other human behavior are stabilized within a larger eco-system which, in turn, is affected, is changed and requires still other ways of doing social life. Causality is a never-ending process in this paradigm while the quest for eternal truth is lost to the changing web of nonlinear dynamics.

The fractal character of social structures provides grounds for great debate; postmodern critique includes an anti-structural tendency which rejects all efforts to speak of class structure, patriarchy, Catholicism or any other 'totalizing' model of social life. Such critique is often well placed but the assumption that class, race or gender structure is not entrained in everyday life does not follow. In class analysis for example, the interconnections of key variables may be so loose that they can be found only using very special, and quite new, research tactics. More of that later.

Social Tori

For those of us in Symbolic Interactional theory, exemplars of the tori come readily to mind. Forms of social reality are constructed using four or five sets of symbols: words encoded on voice and print; body talk encoded in gesture and act; body dress encoded in cloth and cosmetic; whole runs of behavior which can be read for their social meaning as well as architecture as well as the larger infra-structure of a society all shape and preshape the behavior of others significant to the occasion and to the social order.

In each of these symbol sets, there is a semi-stable mix of order and disorder so essential to social survival, communication and inter-subjective understanding.9 Consider a voiced word; there are any number of close pronunciations of it which can be understood by a competent adult in a given socio-cultural complex. Each variation in pronunciation implies a slightly different meaning; surprize, delight, anger, doubt or such. Consider the same word; there may be two, four, eight or sixteen quite different meanings in common use but more than sixteen are very, very rare...such variety offers far too much complexity for most of us to track. It would be very unwieldy if there were a word for each and every shoe, finger, or social role. Placement of similar objects in a category is a poetics since the boundaries between each object has varying similarity to the last.

In more complex social dynamics, socialization and social control tend to produce social tori [called norms in social psychology]. For example, in any given set of families located in any given political economy, the number of children produced will cycle around a norm. The number of children in any given family will vary but there are lower and upper limits which restrict family size to but a small portion of the causal space available to such behavior.10 With respect to a wide variety of other familial behaviors; frequency of acts of intimacy; frequency of violent behavior; size of family; patterns of expenditure and debt, if they take the shape of a torus, they present the researcher with pattern and stability such that prediction is possible and planning is feasible.

Figure 5. A Butterfly Attractor with two causal basins

SECOND ORDER CHANGE

At the next bifurcation, an important change occurs in causal dynamics. In the butterfly attractor, Figure 5, one can observe two outcome basins in the causal field defined by the dynamics of any physical, biological or social system. Modern science permits one and only one outcome basin for any given set of variables. Chaos research reveals 2, 4, 8 or more such basins in this region of a bifurcation series. The most interesting point one can take from such complex dynamics, in terms of postmodern understanding of causality is that the same set of variables can produce two or more differing outcomes; contradiction and contrariety displace coherence and conformity. Modern science makes much use of Aristotelian logic and propositional inference in its generation of hypotheses. Chaos/Complexity is congenial to the 'fuzzy logic' of variation and qualitative change. Postmodern science is thus a bit more forgiving of those who find uncertain and varying causal linkages. Those who find different outcomes have more to discuss than whose arguing which is the 'truth' of the matter.

For example, given the same set of variables, a small change in profit may produce a large change in corporate crime; or a small change in unemployment rates may produce a large increase in divorce or child abuse. If, for example, doctors are faced with a small change in expense or income, large increases in medical crime might ensue. It is not that X, Y, Z, and G produce corporate crime but rather that X, Y, Z and G' may produce entirely different behaviors for the same set of doctors. Then too, looking at Figure 3, one basin might consist of all those doctors who continue to engage in quite ethical behavior while the other wing might consist of all those who have begun to cheat on medicare and medicaid. For both groups, behavior is predictable; prosocial and criminal behavior, once adopted tends to become entrained. However, for those at the margins of the wings of the butterfly attractor, it is impossible to predict which doctor would move to which basin.

These complex regimes are far the most common of dynamical regimes found in nature and society; indeed, if multiple causal basins were not available, the flexibility and creativity essential to speech acts, art, music and work would not be available. 2n marriage forms, 4n business practices, 8n forms of religion appear and embodied precisely because they permit adaptation to the larger uncertainty in an environment itself in continuous change. Too much order or too much disorder becomes hostile to survival. Those who demand a completely free market do no service to the business in which they find themselves; nor will those who demand strict controls and detailed planning take much comfort from the lessons to be found in Chaos/Complexity theory.

Within the limits of second order change and the very complex attractors found in Region 4 of Figure 1, human life can survive and thrive; indeed all life can survive and thrive. It turns out that disorder is to be greatly valued while pre-occupation with order and conformity an asset to human endeavor in and only in a very stable environment. Regimes with 2n, 4n, or 16n outcome basins have sufficient order to serve the human interest in regularity, dependability and planning on the one side along with enough variability, creativity and innovation to serve the human interest in change and renewal.

THIRD ORDER CHANGE

A third turning point in nonlinear dynamics important to a theory of causality occurs when key parameter[s] reach a specific Feigenbaum point (1978).11 This new regime is found in Region 5 of Figure 1, above. In Region 5, the number of end-states to which any dynamical system might go reaches toward infinity, i.e., a system fills all the causal space available to it. Instead of one natural end-state toward which all normal systems go, the more likely pattern of causality is one in which a variety of end-states are possible. This fact has profound meaning for theories of deviancy and for theories of social control. In brief, 'deviancy' may have many virtues; social control efforts become progressively less effective.12

Algorithms

The complex structures found in deterministic chaos are produced by the interactions of key parameters. These interactions take the form of an algorithm. Without being too technical, an algorithm is an interactional process or procedure in which feedback loops produce ever differing patterns (Penrose, 1989: 17,30-35). The task of the researcher in Chaos/Complexity is, first to find the fractal structures hidden in complex data sets; second to identify the key parameters which drive them and third, to determine the algorithm which produces these patterns. The Hamilton research, discussed below, reports on the first phase of such research--the first ever in sociology.

Feedback Loops

In complex, non-linear social dynamics, feedback is a better concept with with to grasp the sources and patterns of change than is causality.  For Hegelians and Marxists, it is interesting to note that the concept of the Dialectic is very, very similar to that of non-linear feedback loops...and, curiously enough, thesis, anti-thesis and synthesis are not incompatible with first, second and third order change of the sort described above.  It is the particular poetic genius of both Hegel and Marx...and their followers on Right and Left, that they could grasp the non-linear interconnections between key variables long before the formal proof that Feigenbaum (1978) gave was available.

Negative feedback loops tend to shrink a fractal to the smallest possible region in causal space;

Positive feedback loops tend to explode the fractal to fill up all the causal space available to it.

Nonlinear feedback loops tend to preserve a fractal in a semi-stable configuration.

For those who wish to conserve given social structures, attention should be given over to the character of nonlinear feedback. While there is much to explore in this field, I tend to think that, when the dust settles, those nonlinear response which entail mercy rather than justice, forgiveness rather than vengeance, tolerance rather than conformity will offer the greatest stability. Careful and precise application of rules, laws, policies and standards defeat the quest for stability.

Causality, Inference and Outcome Basins

In any complex dynamical regime with two or more outcome basins, causal connections vary with the region in the larger field in which the basins are found. In, for example, a butterfly attractor, there are two outcome basins. Correlations from which causality is inferred will vary with the region one happens to sample. Four such sampling regions are marked in Figure 5.

If one should have to catch one's sample in time-space denoted by 'B,' one would be forced to conclude that there was a fairly tight and positive correlation between the variables which produced the behavior in that area. If one should happen to take a sample at a different time-space marked by 'D' on the right, one would be happy to report that there is a definite negative correlation between the variables in question. If one sampled at a time close to a bifurcation point, denoted by 'C' in Figure 6, one would not find strong correlations and thus 'accept the null hypothesis.' Only by taking the field, 'A' as a whole and displaying it in the analytic geometrical form shown in Figure 6, would one see that there is indeed a two basin outcome field.

Figure 6. Variations in Causality in Nonlinear Dynamics

Incompatible findings about class dynamics (say those of Pakulski on the one side and those of Hout, et.al. on the other) are possible. It is entirely possible that Pakulski (1993) has sampled one part of the total field in Figure 6 while Hout and his colleagues are sampling a different run of events in the same field. Hout and his associates (1993) may well be looking at a much larger pattern from which they extract quite different, and quite valid conclusions. Pakulski has mentioned several parameters which might be operative in changing from one dynamical state to another (1993:284).

EMERGING CAUSALITY

Given the appearance of a new structure, existing systems adapt to it. This simple fact means that an entirely an new causal factor enters into the fabric of life and living for all creatures and for all societies in a given time-space continua. The process by which causal efficacy develops has yet to be clarified. Yet one can, intuitively, understand that when a new species, say Homo sapiens, appears on the scene, both plant and animal species are affected. Some species are exterminated; some adapt to the new fact and, in that adaptation, entrain a mutual causal dependency which lasts until some other, extraneous change occurs to re-inforce or to diminish causal connectivity.

I have mentioned the work of Brian Arthur on mode-locking. The point to take is that a new species or new social group may (or may not) carve out a niche of its own in a eco-system. If it does, a complex interdependence develops as other systems 'read' its behavior and adjust their energy acquisition, energy using habits to it. If the dynamics of the system are stable enough, orderly enough, then other sentient systems in the eco-system can use/feed on that energy or avoid losing energy to it.

Arthur gives several examples of mode locking from industry and commerce (Waldorp, 1992:36 ff). He notes that it not the technical virtues of, say, Beta-versus VHS which determined the success of VHS. A small advantage in the market place 'lock-in' the VHS---consumers didn't want to take the risk of having a lot of obsolete Beta-tapes or an obsolete VCR. VHS has a slight advantage, so more and more customers bought it giving it still greater advantage. Another example is the QWERTY keyboard. Other, better keyboards were developed but since a lot of typists knew QWERTY, it was difficult to dis-entrain it. Arthur also mentions such entrained items as the clock-wise face of a clock, the gasoline engine and light-water nuclear reactor...entrained since, in the environment of the time, it had a slight head start on gas-cooled reactors and on heavy-water reactors.

In more sociological terms, once a given marriage form develops, it is locked in by any number of subsidiary behaviors. When a city is designed for private automobile transport, public transport is in trouble. Once a library has adopted one system to catalog, introduction of another is costly. In the case of new life forms, animals and plants come to depend upon it or develop ways to avoid it while still more animals and plants come to depend upon those, ad infinitum. In all this, new factors enter which change the patterns of those parameters which mark the coming and going of a dynamical regime. Causal relations are ever-changing as in this elaborate dance of life and death.

In more social terms, one could think about the entrainment of patriarchy, slavery, feudalism and capitalism. All developed social practices which, entrained, had secondary effects which re-enforced the original set of norms. As each new generation of women and men adjust to patriarchy, whole sets of understandings, values and practices emerge which accommodate it and make it just that much harder to institute new or different gender relations. It takes a much larger change to dis-entrain causality once other systems in the same time/space region has adapted to it.

Dis-Entraining Causality

Yet causality patterns are dis-entrained. Slavery, feudalism and Patriarchy were dis-entrained by capitalism. The profit motive tends to ignore social standing and non-economic forms of power. Law, religion and science, adapting to and adapting of capitalism, further stabilizes and institutionalizes it. Some aspects of patriarchy survive; those aspects which lend themselves to the quest for profit have a slight advantage over 'pure' market considerations. If a company can profit from low wages of female, Black or third-world workers then sexism, racism, and other forms of status privilege can survive as causal fractals in a larger, more complex economic system.

Again, entirely new research protocols are required to find out just how much race, gender and class structures do in fact exist. Again, it is necessary to consider the possibility that such research samples different dynamical regimes, different regions in a complex dynamical field or simply is too narrow in focus to pick up the larger structures which have varying causal efficacy in a globalizing economy. Again, it is necessary to consider the possibility that nonlinear feedback loops may just make it possible for very different religions, economics, politics and teaching formats to occupy the same behavior space.

Figure 7. Time Series Display of Teenage Pregnancies

Research and Hidden Attractors.

If the quest for universal truth is not, can not be the mission of the research act, the question arises as to that mission in postmodern science. The first step, as noted earlier, is to discover whether or not there are attractors hidden in complex data sets. Patricia Hamilton (1994) and her associates at Texas Woman's University are leading the way in this phase. They report what may be the first ever discovery of a 'hidden 'attractor' in a complex social data base. Using new analytic techniques from mathematics and physics to explore complex nonlinear social dynamics, they examined 1.2 million births to teenage mothers in Texas between 1964 and 1990. Ordinary research tactics have to deal with a time-series display (Fig. 7) which is so 'noisy' that patterns within it would have been missed.

However, Figure 8 shows us that, hidden in those very complex data on teenage pregnancies, there is an order not discernible by conventional methods. The next step is to identify the key variables which produce this fractal and, then, to map out the algorithm which maps out the process by which these variables work. The Hamilton team is working on that phase now.

Those in social problems might want to consider the implications for the relationship between cancer and smoking; between low level radiation and leukemia; between unemployment and crime; between interest rates and the construction of homes. Consider the possibility that there are nonlinear relationships between economic variables and, say, the resurgence of racism or domestic violence.

Figure 8. The Geometry of Teenage Pregnancy. From Hamilton

Those in class analysis will be interested that, given nonlinear dynamics, class structures may be so deeply interconnected that conventional methods are blind to them. This paradigm suggests that class dynamics may be more, or less, causal. Class can remain a causally dormant structure until feedback loops between, say, race, gender or religion change to increase causality. All this is very interesting to postmodern sociology with its concern with truth claims, ontology, plurality, and the philosophy of science.

Social Movements Theory

Social movements theory has come a long way since the early days in which 'race,' 'blood,' genetics and 'pathology' were used to explain resistance and rebellion. Constructionist theory was a great improvement as was resource mobilization theory. Then too, the new social movement theory (Gamson, 1992) adds important cultural elements to those theories which explain social movements in terms of the larger political economy in which they located.

Chaos/Complexity theory has something to add to social movement theory. The concept of the bifurcation is most important to an understanding of why traditional structures fail; why peoples rebel within the very same structures within which untold generations have fitted more or less comfortably. Slavery, Feudalism, Patriarchy and capitalism all give rise to social movements where before, compliance and conformity were the rule.

There is, of course, no good data to the point since the research act is not designed to look for it, but it well may be the case that social movements arise when the ratio between wealth, status and power exceed that ratio marked by the third order change. It well may be the case that both men and women seek new social gender identities when bifurcations in social or economic power render ancient binary identifications untenable. It well may be the case that bifurcations which increase the relative power of the state also increase the chances of rebellion. Bifurcation theory offers a powerful analytic tool in that these bifurcations are triggered by small changes in key parameters and they follow a very predictable pathway to deep chaos.

Multiple Uncertainties and Social Movements

It is also distinctly possible that the concatenation of three or more stress factors in the lives of people may interact to create social problems which lead to social movements. For example, a student may have financial troubles, health problems and family problems; while she might be able to cope with two uncertainties in her life, a third one might put her in a situation that a bit more uncertainty could adversely affect her behavior as a mother, a student or a wife. In like fashion, a worker might well have uncertainty about a job, uncertainty about health and uncertainty about family relations. In such complex dynamics, that worker might given the right situation, engage in either creative or destructive behavior; it would be impossible to predict since a small event could turn him one way or the other.

Chaos and Social Control

It is very important to understand that coercion and social control are inimical to social life when they proscribe creativity, variation, plurality and surprize...all these are

not solutions to the problem of order when the fourth feigenbaum point is reached. Uncertainty becomes so much a part of social dynamics that ordinary control tactics fail. Socialization, role expectations, rewards and obligations begin to fail as a society reaches the point of deep chaos. Penalties, prisons and capital punishment lose whatever causal efficacy they might have had in times of great disorder. In those cases, the quest for order has to come out of the social justice movements rather than social control technologies.

POSTMODERN MISSIONS FOR SOCIAL RESEARCH.

As I have noted in the first part of this work, in nonlinear dynamics, ability to predict the future varies. In modern science, the standards of truth center around the success of prediction. In Newton's universe, the future was knowable with a truth value of approaching 1.0.13 In a chaotic universe, the truth value of a prediction (hence social policy based upon prediction) varies from 0.0 to -1.0 but is never one (except in the special and unlikely case of a perfectly stable state for any given system).

In Postmodern philosophy of science, grounded upon the fractal structures and nonlinear dynamics of Chaos/Complexity theory, the quest of the knowledge process is not the discovery of stable truth values predicated upon tightly knit and stable causal connections. Rather, one seeks those clusters of behavior in a complex data set, tries to locate the factors which produce such fuzzy clusters and, in the interest of social policy, attempts to locate the change points at which entirely new patterns of behavior develop.

In principle, the truth value of any statement about causal connections in a wide variety of social behaviors could be set by policy processes. Correlations between age, pregnancy and marital status; between smoking and cancer; between 'race' and crime; between class and health thus become much more a matter of public policy.14 Given better politics and better policy, unwanted correlation could disappear or reverse itself. It is important to note that, since social realities are constructed by the people who live them, good politics here means a much more radical democracy in policy formation than is now the case. Legislative fiat with legalistic regulations simply do not work as the ratio between order and disorder increases.

James Yarbrough and I have developed this section in more detail for those who might be interested.  That paper is at: RE-INVENTING SOCIOLOGY: Missions and Methods for Postmodern Science.  One can double-click on the address above to scan that article.

CONCLUSION

The new sciences of Chaos and Complexity offer quite a different understanding of the 'realities' with which research must work if human knowledge and human agency is to be augmented. Entirely new research designs, new research tools, and new research projects are required in health and medicine, in crime and justice, in family and child development, in business and economics. Much is at stake in the health and welfare of peoples and ecological biomes around the world. Much is at stake in the making and watching of public policy. An entirely new phase in the knowledge process is upon us and it will take a lot of effort and genius to explore it.

Small adjustments to key variables at key times permits effective public control of events which, given less sensitive and less timely interventions are likely to fail. The implications of this fact for social policy are great indeed. Economists, political scientists and clinical sociologists must begin to master this new body of science and the techniques only now emerging to permit description and inference.

There are at least two more items of interest for those who want to understand causality in all its complexity. In the first instance, entirely new and entirely unpredictable structures emerge out of deep chaos. The second Law of Thermodynamics is greatly modified to accommodate ever changing patterns of order and disorder. In biology and in sociology, evolution continues to be an open ended process. Claims that there is an end to history are set aside by such infinitely rich and unpredictably creative dynamics.

If the future is open and if we know how to locate those points at which qualitative change occurs, then we have the potential for deciding to expand or to retain existing patterns of causality. Moving to a new dynamical regime might be risky in any number of ways but that move also might open up choices in economics, in medicine and education, in politics and in religion most congenial to the human need for order, predictability, accountability and reliability. Wisdom and compassion join hands with reason and rationality in this quest for those fractal facticities which answer to the human project.

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