CAUSALITY AND INFERENCE IN COMPLEX SOCIAL DYNAMICS: Fractal Realities and Fractal Truth Values in Postmodern Philosophy of Science T. R. Young The Red Feather Institute April 30, 1994 No. 173 Prepared for the 1994 Stone Symposium of the Society for the Study of Symbolic Interaction at Champagne- Urbana.Distributed as part of the Red Feather Institute Transforming Sociology Series. The Red Feather Institute, 8085 Essex, Weidman, Michigan, 48893. CauseThe word, cause, comes from the Latin, causa, correlative to the term, 'effect.' It refers to that which determines, produces, or conditions an effect. TruthThe word truth comes from a fusion of an old English word, truwa, meaning faith, and another old English word, treowan, meaning to believe. Together, they yield treowa, from whence our words truth, troth, and trow. The post-modern version of truth is much more aligned with the old English usage in that intersubjective truth is a product of believing and vowing to perform truly. The modern use of truth assigns to it an independence of culture, history or political agenda. CAUSALITY AND INFERENCE IN COMPLEX SOCIAL DYNAMICS: Fractal Realities and Fractal Truth Values in Postmodern Philosophy of Science ABSTRACT Three points are made about causality in a distinctly postmodern philosophy of science; 1) causal connections change with dynamical regime; there are five such regimes, three of which have qualitative different causal patterns; 2) causal connections develop as other systems in an energy field adapt their behavior to newly emergent dynamics of still other systems and, 3) human beings enter into the causal matrix as knowledge processes improve and technical means develop. INTRODUCTION Each epoch in the knowledge process tends to prefer differing ways and 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 otherwise would not, presumably, occur. In recent 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 complex and more variable notion of causality in his concepts of multiple causality and negative correlation. Modern science still admires a model of causality in which constant conjunction of events wins fame for its discoverer. When Newton discovered the laws of motion with which one could observe a causality so rigorously patterned that prediction on the order of one part in 1014 parts was possible. Penrose, (1992: 152-155) calls the theory which produces accuracy to this degree of certainty, SUPERB theory; the capitalization is his. Other research, yielding less elegant research might be USEFUL while still less certain results are only TENTATIVE. The long history of human observation and reflection on causality continues to bring new surprises and new insights into the uncertain understanding of we fallible human beings about how nature and society works their ways all around us. Today, the nature of the underlying reality is known to be considerably less obliging to the human interest in knowing the form and tendencies of causal connection. More importantly, arguably, the human interest in controlling nature and society faces a much more complex problem than has heretofore been appreciated. Indeed, that is the topic of this discourse. I want to make a case that, given findings about this underlying ontology from the new science of complexity, causality opens and closes like the grin on a Cheshire cat; comes and goes with an elegant regularity but, in most actually existing systems, truth statements are, as are the reality we seek to say, fractal. I will make that case below but, in all this, I want to say that, in most of the dynamical regimes of interest to the social scientist, there are moments when there is sufficient pattern such that human beings can, indeed, act, plan and control with certainty adequate to the human project. There are, on the other hand, moments when control, certainty and rationality are lost to human agency (Young, 1992). 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 the Bifurcation Map presented in Figure 1, next page, we can note five dynamical regimes. The first two are of great interest to those pre- occupied with certainty but of little interest to the researcher since they appear so seldom in real time and space. 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 the 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 a dynamical system is not allowed to exceed. Both the point and the limit attractor, as models of the dynamics of really existing systems, are rare. Much more common in both physical and social dynamics is the torus whose dynamics are registered in the third region of the bifurcation map in Figure 1. We will re-visit the torus and examine those dynamics later but first, I want to make the general point that causality changes after each bifurcation of key parameters. Nonlinearity displaces linear, proportional behavior while uncertainty increase qualitatively at each bifurcation. I will point to three orders of change and emphasize that the transition from one form of order to another form occurs at very precise points on the bifurcation map. Causality and certainty may become more and more complex and difficult to trace as bifurcations unfurl but in all this disorder, there is an elegance and a meta-order which captures the imagination. Bifurcations It is very important to note that, at each bifurcation in Figure 1, above, causality loosens. What was perfectly ordered behavior in the point and limit attractor transforms into a stable but variable tori after the third bifurcation. We find, in this dynamical regime called a torus, first order change. Variations around a mean are familiar to most readers of scientific literature...these variations 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. Indeed the smug attitude of physical scientists toward the behavioral sciences is misplaced. It is not that social science is a 'soft' science but rather that the subject matter of social science exhibits complex dynamics while, by careful elimination of key parameters, some physical sciences are able to simplify system dynamics to the degree that causal inference appears to be 'superior' to that of those who work more complex fields. The fourth bifurcation (really a set of coterminous bifurcations) brings second order change; one in which there are two outcome basins in an outcome field. This fact has profound meaning for a postmodern philosophy of science since small changes in the very same set of variables produce not one but two different outcomes. In modern science, a given set of variables produces one and only one outcome; not so in this new science. Qualitative analysis displaces quantitative analysis. A whole new mathematics is required in order to deal with the changing complexities of nonlinear dynamics in any field. Figure 1 shows a fifth dynamical regime, region 5, in which causality is casualty to complexity. This regime, called deep chaos, has very interesting implications for any understanding of causality since it is in this regime that entirely new forms of life and 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. Feigenbaum Points Happily, there are specific turning points at which the dynamics of causality are transformed. Mitchell Feigenbaum is credited with identification of these points; he 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 process converged. He calculated a universal constant, 4.66920. Every dynamical system 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. 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. 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 new 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 two simple attractors discussed, 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. In physics, the behavior of an electron around the nucleus of an atom traces a fairly tight torus. In biology, the rise and fall of trout, moth, or deer populations produce tori providing that food, temperature and predators stay within given limits. If one of those key parameters should change, then entirely new dynamical patterns are observed. I shall return to this remarkable fact shortly. Right now, I would like to flesh out the concept of the torus for the social scientist. Social Tori For those of us in Symbolic Interactional theory, exemplars of the tori come readily to mind. First there is the very sound of a word...if we were to trace the waves which make up any given word on a graph, we would see that each iteration of that word is slightly different from every preceding enunciation. Try saying the word, 'Yes' exactly the same way twice. Depending on scale of observation, we could observe greater or lesser difference but never, never an identical graphing. Changes in body position, in lung capacity, in position of the neck, in placement of the tongue, in formation of the lip as well as changes in direction of the sound all affect the wave pattern. If we turn our heads even slightly, differing bodies in a room absorb sound at different levels and thus affect that which is heard; that which is recorded as the 'actual' behavior of the speaking person. In more complex social dynamics, say that of a marriage, social mor‚s, socialization and social control activities tend to produce social tori [we call them norms in social psychology]. In any given set of families in any given political economy, the number of children will cycle around a norm as will the age at which one enters into a marriage process. With respect to a wide variety of other behaviors; frequency of acts of intimacy; frequency of violent behavior; size of family; patterns of expenditure and debt, all these present the researcher with cycles which have pattern and stability such that prediction is possible and control is feasible. Second Order Change At the next bifurcation, an interesting change occurs in causal dynamics. In the butterfly attractor, Figure 3, next page, one can observe two outcome basins in the 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. Complexity theory reveals 2, 4, 8 or more such basins. 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 aristotlean logic and propositional inference in its quest for truth statements. Postmodern science is a bit more forgiving of those who find uncertain causal linkages. Figure 3 offers two views of the butterfly attractor; the top view is the well known time series. The bottom view shows the geometry of a butterfly attractor. A butterfly attractor can be viewed as two linked tori which define a 2n outcome field; in like fashion 4n, 8n, and 16n outcome fields can be viewed as multiples of a butterfly attractor for purposes of postmodern understanding of causality. One can get some idea of the degree to which a given system or set of systems occupies the causal space available to it in the bottom view. A point attractor occupies a tiny fraction of such causal space; in deep chaos, Regime 5 in Figure 1, almost all causal space is used. In the attractors found in Regions 4 and 4 of Figure 1, there is a varying but semi-stable outcome basin. These 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 environment itself in continuous change. And too, in the postmodern philosophy of science unfolding in this research, weak and fractal patterns of causality are not to be dismissed. In research on the linkage between smoking and lung cancer; on the linkage between micro-waves and leukemia; on the linkage between crime and television programming, one is too expect and consider the implications of such dynamics for social policy and social programs. These regimes have sufficient order to serve the human interest in regularity, dependability and planning on the one side along with variability, creativity and innovation on the other. Within the limits of second order change and the strange attractors found in region 4, 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. I will discuss some of the advantages of disorder and nonlinearity at the conclusion of the paper since it has so much meaning for political life and social policy. Third Order Change A third turning point in nonlinear dynamics important to a theory of causality occurs when key parameters reach a specific Feigenbaum point. 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 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 has many virtues; social control becomes progressively less effective. There are 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 education, in politics and in religion most congenial to the human estate. More about the potential for human choice and human agency in the last section but I want to draw attention to a most challenging task for those who work the field of postmodern science; pursuit of questions about the entrainment of causality when and if a new life form does appear out of the turbulence of deep chaos. Entraining 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 event 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. Once a given invention or social form has been 'lock-ed,' secondary adjustments occur which make it difficult for competing forms to thrive. When a city is geared to private automobile transport, public transport is in trouble. Once mechanics have learned one form of engine, getting service on a new form is risky. 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 while still more animals and plants come to depend upon those, ad infinitum. We, each of us, is a walking eco-system the health of which depends upon the health of each. Pathogenic organisms have a hard time expanding in a niche when it is already occupied by a benign organism. In more social terms, one could think about the entrainment of patriarchy, slavery, feudalism and capitalism. All developed practices which, entrained, had secondary effects which re- enforced the original set of norms. As women adjust to patriarchy, whole sets of understandings, values and practices emerge which accommodate it and make it just that much harder to institute new 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. Slavery, feudalism and Patriarchy are all being dis- entrained by capitalism since the profit motive tends to ignore social standing and non-economic forms of power. Law, religion and science, now adapted to capitalism, further stabilizes and institutionalizes it. Still 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 workers who, on the face of it, are better and should receive, in a free market, higher wages, then sexism, racism, and other forms of status privilege can survive as causal fractals. Causal Complexity As a system changes from one pattern of behavior to another, the configuration of that pattern thus changes dramatically. In a distinctly postmodern philosophy of science, causality varies with dynamical state but it also varies with the scale of observation. I offer two quick examples, the first dealing with incompatible findings varying by dynamical regime and the second dealing with causal outcomes which differ by scale. In thinking about the first example, keep in mind the central dynamical regimes in Figure 1; Regions 3 and 4. One gets quite different findings depending upon which region of the butterfly attractor one is studying. In thinking about the second example, it is useful to keep in mind the Butterfly attractor; one can generalize from one wing or one can change scales and generalize about the transformations from on causal regime to another. Regions of Differing Causality 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 a passing dynamical phase in which a key parameter has changed enough to force a re- organization of class fractals while Hout and his colleagues are sampling a different run of events which testify to the continuing efficacy of class status as a significant part of social life. Pakulski has mentioned several parameters which might be operative in changing from one dynamical state to another (1993:284). Hout and his associates (1993) may well be looking at a much larger pattern from which they extract quite different, and quite valid conclusions. There are more examples one could adduce to make the point; the great variety of findings about the connection of crime to jobs; of crime to ethnicity; of crime to gender deserve a research design to ascertain whether a finding is dead wrong or is valid for a given region in a larger outcome basin. I want to reiterate the point that differences in outcome are not the result of new, unmeasured, unknown intervening variable but rather the result of small changes in an existing parameter(s). The same set of variables can, in postmodern science, produce quite different results. Causality is far more complex than Aristotle, Hume, Kant or Carnap thought. Scale of Observation and Causal Complexity The immiseration thesis of Marx is a case in point about how causality varies with scale of observation. Marx held that, as capitalism proceeds to commodify production and change the ratio of variable capital (workers, labor power) to constant capital (machines, buildings, fuel, raw materials), workers as a class would find themselves in progressively more difficult straits. If one looks only at American and European workers between 1945 and 1980, the immiseration thesis looks untenable. Yet as more and more nations were drawn into a globalized economy and more and more of their production commodified, the working class expanded to include more than American or European workers. If one counts the fate of former peasants in the urban ghettos of Africa, Asia, South America and the MidEast along with workers in core capitalist nations in the weighing of the immiseration thesis, then it looks much more tenable. Both Nisbet, Clark and Lipset as well as Pakulski select the class patterns in North America and Europe to support their case while Clark, Lipset and Rempel (1993) and his associates use data from the USA, Australia, Canada, Japan and France. Class structure seems to be disappearing or at least more fragmented if one reads only the data selected in one part of a connected outcome field. Reading the larger field, one could, reasonably, offer a different and very different conclusion. Fractal Truth Values 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 truth value of prediction. In Newton's universe, the future was knowable with a truth value of approaching 1.0. 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). The question of what is an acceptable truth value for any given correlation is, at its most profound reaches, a question of moral philosophy. If the quest for objective truth is not, can not be the mission of science, once again we return to the moral question, What should be the role of science in the quest for truth? In post-modern sociology, the task of the researcher could change from generation of absolute truth the stabilization of a truth value of a correlation around a value that is acceptable to those who live it. In praxical terms, this means that the truth value of any statement about social relations can be set by policy processes. At time one, the correlation between class, race, gender and crime could be hard and close. At time two, given better politics and better policy, the correlation could disappear or reverse itself. Since the futures of science are open in terms of both method and content; since the potentialities of social science constitute a fractal basin of infinite variety, since quest for absolute truth has both technical and moral deficiencies, let us survey alternative repositories of truth that we may widen our choices and thus, widen our freedom. KNOWLEDGE AND HUMAN AGENCY For most of human history, the place to look for truth and the true meaning of a thing was in the temple, in the priest and in Holy writings and stories of the time. With the advent of newtonian physics and baconian optimism, the repository of truth shifted from religion to science while scientific truth resided in the scientific community and in the research institute. The scientist and the body of Science displaced the priest and the Body of Christ as the repository of truth. However, both priest and scientist are inextricably linked to the quest for social justice. The long history of clerics in working toward the Peaceable Kingdom needs no apology. As for scientists, Loren Eiseley pointed out that Bacon's vision was a world in which people would be transformed. Humans were beastly in the baconian world but need not be. They could however, with the aid of science, expand their ethical and creative powers. Bacon's work lead to the founding of the Royal Academy in Britain as the repository of truth for European versions of modern science. Ostensibly that academy was founded on the Enlightenment assumption that alienation involved the separation of subjective understanding and objective truth. However, its more practical impetus came from Bacon's assumption, widely shared, that knowledge was the fuel that ran an industrial machine, which properly guided, could save us from the short, brutal and savage ways of life attributed to 'primitive' societies. With objective knowledge about health, transport, manufacture, agriculture and communication, human agency could be expanded. Expanding Human Agency and Human Knowledge A central form of alienation in modern society is a certain sociology of fraud in which the technologies of theatre, psychology, mass electronics communication together with the forms of art combine to create the dramaturgical semblance of honesty, agency, quality, service and necessity (Young, 1989). Intersubjective methodology (Comstock, 1980) in all realms of social life, the antidote for this form of alienation. Human beings can enter into a given causal matrix in a number of ways, not least of which is a choice among which of two or three dynamical regimes to entertain. Given the possibility of generating deep chaos in selected situations, whole new options are available. The only interesting question becomes who is to make such decisions; who is to benefit; who is to carry the burden of risk and failure. Bacon had the idea of 'Solomon's House' a collegium of experts who would advise the king on such questions. Yet, Eiseley notes, Bacon went "...beyond the aristocratic humanism of the Florentines" which lead to elitist production and use of knowledge to a "...wholly new social order" in which the scientific habit of mind is universal, the production of the humanly useful is a society-wide preoccupation in a socio- cultural world which expressed both rationality and charity (Gerber and McFadden, p. 107). Whatever the view of the Church fathers, the Florentines, Plato, Euro-centric males or any other custodian of knowledge, the fact of the matter is that a well designed knowledge process is not beyond the reach of the vast majority people. In their everyday life, people calculate equations far more complex than those handled by the most sophisticated mathematicians using number systems. In the calculation of the health of her child, the mother weighs more variables with more sensitivity than the best physician. In his calculation of the flight of a football, the quarterback uses a computer more sophisticated than the space flight engineers at Houston. In her quest for just the right word, a six year old scans and selects words using a computational method far more sophisticated than that used by any computer engineer. A navajo woman, weaving a two grey hills rug or blanket, builds a complex equation comparable to a Bach sonata or the algorithm of a mandelbrot set. Folk methods of producing practical knowledge existed long before number systems were invented to truncate and to distort the incredible richness of everyday life (1983). What is missing today is access to the production and distribution of knowledge; that access is subverted by a politics of knowledge which removes the knowledge process from the practical needs of such people and deposits it in secret places or in expensive markets. The democratic character of science and human knowledge can be expanded greatly in the next 200 years. An interactive methodology is possible in the generation of new social and natural structures as in questions of choice as between them. REFERENCES 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. Clark, Terry Nichols, Seymour Martin Lipset and Michael Rempel. The Declining Political Significance of Social Class. International Sociology. 3:293-316. September. Clark, Terry Nichols and Seymour Martin Lipset.1993 Are Social Classes Dying? International Sociology. 4:397-410. December. 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