T. R. Young

The Red Feather Institute

May 25, 1991

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


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A 4-Dimensional Bifurcation Map

INTRODUCTION The central point of this essay is that human understanding of the ontological basis of the knowledge process has been profoundly and irreversibly altered by the findings of chaos theory. Given the nonlinear dynamics and the nonlinear transformations between dynamic states discussed in detail in the literature of chaos, the methods and mission of American sociology are forever changed. 1 I would like to think through with the reader some of the implications of chaos theory for both method and mission of the knowledge process in the social sciences.

Perhaps the most profound and most interesting implication for sociological theory is that, given the propriety of chaos assumptions for social dynamics, the only possible theory that can, henceforth, be change theory. If the dynamics of social systems are, in fact, nonlinear, then axioms, propositions and theoretical models can never be permanently true. More than that, truth statements about relationships take a fractal value; one must learn to think in terms of degrees of facticity as well as truth quotients less than one.

The Scientific Mission The findings of chaos theory, if appropriate to sociology, inform us that the task of the social scientist is not, cannot be, the discovery of the immutable laws of society; it is not, cannot be to build grand theory by means of value-free research designed to approach objective reality through the method of successive approximations, it is not and cannot be the identification of the ideal structures of social organization; if the role of the social scientist is not and cannot be to be the impartial arbiter of that which is natural and normal, of that which is deviant and perverse--then what is it to be?

Before I offer one of many answers to such a question, I want to take the reader through a multi-dimensional critique of the epistemological assumptions which ground the knowledge process in American sociology and in its many reincarnations around the world. Two central problematics fuse to ground the mission of modern science: 1) objectivity as the methodological stance and 2) general theory as goal of social science. I will critique both for their implications in both modern and post-modern methodology. Then, in a companion essay, I will open up the possibility of an inter-subjective model of truth finding as one alternative, among many, for postmodern social science.

I can foreshadow my argument about theory by saying that, in post-modern sociology, praxis displaces theory as the mission of the knowledge process. Theory itself is demoted from the foundational base of post-modern sociology to a convenient stop-over; theory becomes an instrument to be used and discarded as new dynamics replace those of the previous dynamic system. In Seidman's terms (and in the terms of many post-structuralists), theory is reduced to a meta-narrative tied to concrete struggles. These meta-narratives must have reality quotients if they are to serve, but those quotients are fractal rather than binary. In social psychology, in stratification, in religious studies, grand theory is decentered while, in the postmodern vision offered here, praxis is recentered. 2

The theoretical task of postmodern social science will be to generate fractally true statements about the pattern of transformations through which a social system goes. This task will be twofold: to identify that which pushes a social systems through stages of near stability into chaos and that which generates order from disorder. I offer a beginning of the first part of the task in other essays in this collection. The immediate task at hand is to set the conditions under which research ideas and research projects will be pursued.

The ideas that discovery of social laws and grand unified theory is the mission of science; that such laws can be reached through the method of successive approximations; that they will yield superb predictions must be abandoned. Those who seek universal and eternally valid axioms of social life are left, now, without an ontology to justify their missions or their methods.

Exit Order Theories If the data of natural and social systems do not fit the ontology presumed by modern science; if those data are unstable, discontinuous, fractal and qualitatively different in each iteration of the cycles, periods, phases and rhythms of really existing natural and social systems, the question arises, why has order and predictability been presumed as the natural ontology of the cosmos. There are two dimensions to an answer.

Figure 1 Regions of Order; Regions of Chaos


First and foremost were the astonishing successes of prediction of the movement of heavenly bodies; the law-like behavior of atomic and molecular particles, the mathematical patterns of genetic inheritance; the emergence of structure in tosses of a coin or rolls of dice as well as the smooth curves with which bacteria grew--and died. All this seemed proof demonstrative and proof sufficient of the order and rationality of the natural and biological world.

Chaos theory instructs us that there are pockets of order which appear, suddenly and unpredictably in nonlinear dynamics. One can see the regions of order/disorder in Figure 1. Almost all of the ordered area is that of simple systems such as the thermostat (bottom left) or predator-prey dynamics (bottom center). When the periods of a system bifurcate the third time (i.e., it has eight or more periods), chaos sets in--but note the areas of order (white dust) in the region of chaos. All one can expect is near-to-stable chaos; never order of the sort found in some physical systems.

But more than mathematics fueled the rise of modernism and its ontologies marked by order, coherence, connectivity and comprehensivity of interacting laws. There was also the human desire for prediction and control. It has been understood for many years that the knowledge process is shaped by cultural values and by social structures. The earliest work of those in the sociology of knowledge beginning with the work of Tracy de Stutt and the ideologues in pre-revolutionary France and including the works of Marx and Mannheim, has made it clear that the knowledge process is a product of human interests framed within the logics of a given human culture.

If one prefers order theory and runs across these pockets of order in natural systems one is tempted mightily to assert that one's findings are correct and all other findings are error, faulty design, observer bias and such. The reader will note the bias in graduate departments of sociology and other social sciences for findings which yield high measures of correlation and goodness of fit to a normal curve. The bias is in sociology; not in nature or society.

Steven Seidman put it nicely when, in a recent Newsletter (V.13, No.2, April 1991) of the Theory Section of the American Sociological Society, he summarized postmodern critique:

As this relentless epistemological suspicion is turned against disciplinary discourses by, say, feminists, and as this same trope is rehearsed among African-American, gays, lesbians, Hispanics, Asians, the differently-abled and so on, no social discourse can escape the doubt that its claims to truth are tied to and yet mask an on-going social interest to shape the course of history. Once the veil of epistemic privilege is torn away, science appears as a social force enmeshed in particular cultures and power struggles. The claim to truth, as Foucault has proposed, is inextricably an act of power--a will to form humanity (1990-2)

Just as postmodernism decenters and delegitimates the quest for the iron laws of nature and society from the perspective of a thorough-going sociology of knowledge, Chaos theory decenters and delegitimates that same quest from the perspective of a thorough-going investigation of the behavior of really existing systems in physics, chemistry, meteorology and biology. The ontology of the cosmos is fractal, non-linear, asymmetrical and discontinuous. Order, prediction and control shrinks to a narrow and temporary cornice of time and space.

Chaos theory underwrites a postmodern science that sweeps across physics, physiology, psychology and sociology with little regard to discipline boundaries. Oriented to infinite variety, infinite and fractal connectedness and to infinite length in the iterations of any given natural or social system, Chaos theory offers an ontological envelope into which to insert postmodern expressions in music, art, poetry, religion, politics and science itself; indeed, the boundaries between poetry and science, religion and science, politics and science become blurred and intertwined as one inquires into the worlds revealed by chaos research. Epistemology and ontology are twinborn at the most basic level of sub-atomic physics as at the largest possible scales of observation and mapping in phase-space.

The Limits of Method The epistemological assumptions made by researchers in the modern epoch of the knowledge process is that they have adopted operational tactics with which they could discover external reality unblinded by culture or by social position. Chaos theory reduces the utility of current methodological assumptions to a small corner of the natural and social-life worlds to which they are addressed.

Thus both ontology and epistemology central to modern science, as a world-view, is discredited as central to the knowledge process. The method of modern science, that of a successive approximation to truth and theory through a differential calculus of trial and observation, fails to find that stable set of laws that encompass and connect all the events at all levels of systems functioning: one cannot predict the fall of the sparrow nor the death of the species.

As Madhi (1989:26) so nicely put it, the emphasis of modern sociology "...on the methodological priority of facts represents a reified approach to social reality--an approach that fails to see the totality of the process with which facts emerge as facts." Chaos theory tells us to watch the whole basin of outcomes for pattern. One does not collect facts, test them against hypotheses and build up theory cumulatively. One maps out the whole basin of outcomes of a system and notes the regions of order and those of disorder. Given the means, if one wishes, desired, prefers order, one notes the initial settings which yield near to stable dynamics, institutes them, and gets the facts one wishes.

Objectivity of truth processes, universality of findings, stability of propositions, falsifiability of truth claims, the successive approximation to general theory and the possibility of prediction are all aspects of modern science which cannot be assumed in postmodern science. Chaos theory confirms what Marx, Mannheim, Madhi, and Seidman have asserted and that which feminists, colonial subjects and excluded minorities have shouted; those who impose order and structure on a society; those who define disorder and deviancy--those persons have a political agenda and use police and science to enforce their own privileged social orders upon others.


The foundational assumption of modern science is the existence of discrete objects of study as well as the possibility of objective study of the natural world. In rejection of the pathways to knowledge of premodern times, an intense and highly personal subjectivity, such claims of objectivity, supported by inter-observer reliability in the study of stars, of the geological record, of biological inheritance as well as the thousands of other scientific researches seemed indisputably better than premodern claims to knowledge.

For such scientists, claims of objectivity can be grounded upon a set of methods which insulate outcomes from the bias of the scientist. Thus objective, value-free, impartial truth statements are possible within the camp of the modern scientist and sociologist. They are not possible in post-modern sociology. The case made in the philosophy of science and in the sociology of knowledge is that one cannot think nor act in ways other than permitted and encouraged by one's culture. A noteworthy counterclaim is that mathematics is a universal language that permits the scientist to transcend culture.

Chaos theory joins with the philosophy of science and the sociology of knowledge to discredit mathematics on several grounds not the least of which is the poorness of fit of linear mathematics to non-linear ontologies. There is a mathematics which resonates with and is useful to deterministic chaos. Briggs and Peat (1989:84) present and apply some of these mathematics chief among which are fractals, Lyapunov numbers, and 'rubber' math. 3 Such a mathematics elide the sharp-edged, clear bounded objects that formal theory assumes and, in their place, offer objects with fuzzy edges, infinite dimensions, varying saturation of the space they occupy as well as infinite variation in form.


The possibility of objective research stands as the central issue to resolve in any adequate knowledge industry. There is much from physical and social science which speaks against that possibility.

We can start with a critique of objectivity with the work on chaos theory and then go on to quantum physics and then come back to the interactive nature of social life. At every turn, we will find that objectivity--as a situation in which the object of study; as a stable object indifferent to the action of the researcher--is unknown. 4 In sociology as in physics, the researchers is an acting subject which affects the field of study and thus, subverts objectivity.

Figure 2 Fractal Geometry

FRACTALGEOMETRY.GIF (45858 bytes) from Sprott's Fractal Gallery


Objectivity, as a methodological stance, requires that discrete objects be found in nature. Objectivity also requires that the observer not intrude to create the object or to affect its dynamics. Part of postmodern science is an understanding that objects are neither whole, discrete, nor bounded in their geometry. Such objects display nonlinear dynamics such that they are not found in a basin of outcomes where linear math would predict. Another part of postmodern science is an understanding that the scientist calls forth the 'object' of research in the measurement of it. A third part, scarcely visible at this writing, is that all parameters and all paradigms are constructed out of an infinite universe of parameters and paradigms. 5

Fractal Objects Chaos research reveals quite a different geometry of the objects of nature and society. Instead of discrete object, bounded and self contained, the geometry of natural systems is more like cantor dust, Koch curves, a sierpenski carpet, a menger sponge or the lovely patterns of a mandelbrot set; such forms are riddled with holes and open to the passage of other systems.

Figure 2 depicts the geometry of a menger sponge. Persons, groups, social occasions, institutions, and whole societies take on a fractal geometry rather than a euclidean geometry. If we think of a person in fractal terms, we find a discrete object answering to the concept of the 'individual' hard to find in nature. Instead, we find what Cooley and Mead said we would find. Self and society are twin born; where a mother ends and a father starts is difficult to know. Where a mind starts and stops or meets another mind is hard to know.

If we observe the self structure, we will find that each of the centering identities of the individual is, in the first instance, a response to a role-other and, in the second, itself a very fractal affair. One is never always, only, fully or uniquely a mother, a Baptist, a Republican or a daughter. Other identities intrude, mediate, displace and unite with any given social identity. The ways social identities merge, separate, and interact is, given the validity of chaos dynamics, nonlinear and qualitatively discontinuous.

Even if one could take the life of a given person and follow it continuously, in the life of even the worst criminal, there would be bursts of kindness, generosity, self sacrifice and admirable restraint in the face of provocation. In like fashion, if one could follow the life career of even the most admirable of people, done would find bursts of selfishness, dishonesty, betrayal of trust and viciousness. To make a call of an end state, i.e, into which analytic category the researcher is to cast the individual concerned as either a criminal or a conformer, depends upon the time scale one uses to study members of the sub-set. 6 Quantification based upon the assumption of such geometries is suspect indeed.

Objectivity and Scale of Observation

Chaos research teaches us that the shape of an object, while similar, is never quite the same as we follow it through the iterations of its cycles of life and death, growth and decline. If we follow the population of storks or trout or gypsy moths, we find the fractals which define and depict its dynamics to change each year. If one were to study the dynamics of the first year in the life of a person, one would get one kind of generalization; if one chose to use the same categories for the same person after the fifth or twentieth or fortieth year or at death, one would still be forcing the object to fit a category and thus do damage to the knowledge process.

In such a distribution of possible end-states, any number of conclusions are possible; no final conclusion is possible. In such an elusive population of objects, no universe can be defined nor can generalizations be made from and to its members. The very object of study has indeterminate dynamics that make its encoding into a social category most problematic. In such a world, objectively true statements are partial, contingent upon scale of time; contingent upon categories of analysis; contingent upon scale of category. As one changes time scale and category scale, one changes the distribution of truth statements; such changes are distinctly human work, not objectively pre:existent attributes of ontologically real objects independent of the research protocol.

One could make the same case for groups, social occasions, and other social forms: their geometry is fractal and their dynamics nonlinear. Given this ontological base from which to work, the quest for hard facts, independent variable, tight causality and final truths is not on.

Jumping Jacks Chaos research reveals a world in which the object of study does not behave linearly. For period two dynamics, there are two causal regions: on-off; high-low; there-not there. Nonlinear dynamics produce a basin in which the object tends to fill up the space provided rather than occupying one and only one point as required by the method of successive approximations or two points as required by Aristotelian logic and Popperian truth models (true or false). The dynamics of such objects create a fractal basin of outcomes which can be very complex (the black portion of the chaotic region in Figure 1).

In any given set of members of such a set of systems (birds, fish, businesses, workers, debtors, patients or whatever), some may exhibit one kind of dynamics and others still other kinds of dynamics. The product of these multiple careers is that there are more; many more than one end state possible for the set as a whole. The distribution of those end states takes the form of a fractal boundary basin. A stable finding in which the truth value of statements about such sets of systems is set at 1.00 is not possible. The objects of study yield more than one true statement; sometimes, no true statement can be made.

If the object of study does not behave the same way, if it does not do predictable things, if it does not exhibit the same behavior across dynamic states, one may ask how then, is objective research possible. If the end state of any one member of a many-membered system cannot be determined; if the process by which that system attains a given end-state cannot be followed, then upon what grounds may we make objective statements about the behavior of any one such system in a set; upon what grounds may we generalize from the behavior of any give subset to the universe of all such systems? Objective statements, valid statements about the object of study are not possible when the putative object of study undergoes transitions from stable to near-to-stable to far-from-stable dynamics. Verification and falsification are diminished greatly as knowledge aids.

In their study of the outcomes of the beer game, Mosekilde and others (1990) show that there are regions of stability of outcomes. Those playing the beer game can create a steady state between brewery, distributor, wholesaler and retailer. But, as the dynamics of the beer game change, the interaction of the periods (cycles of orders and shipments) of each player interact to send the game into an unstable amplification of periods. A three dimensional phase-space graph of the outcomes of thousands of those games reveal regions of stability and regions of chaos similar to that of Figure 1, above. In the phase-space basin in which the outcomes of those games are distributed (and by extension, all social encounters), there are regions of stability and of instability. The important thing to note is, that as any given game/system approaches the boundary of the regions in that phase-space, it is impossible to predict whether the game goes into stable dynamics or into chaos. The fate of such boundary games is non-linear; small differences produce large outcomes.

Take as a thought experiment, the present set of infants born in the United States. Then take as a more manageable subset, the cohort of Afro-American children born in 1990. Let us consider whether it is possible to follow the physiological cum social-psychological entity, the social object which we have identified as a Black infant. Could we possibly follow the progress of that one child through all the transformations in her/his social life? Were we to have the technical research capacity to do so, could we generalize from the pathway that one of these children take to the entire subset of Afro-American children with like initial conditions at the beginning of their life?

Fractal Outcome Basins Chaos theory would suggest that the end states of all such children taken together would fit the form of a fractal boundary basin in which the end state of some black children would end up in steady work in stable marriages culminating in dignified retirement. The end state of others would be an early and violent death. For others in conditions very similar to any given subset on any given parameter, it would be increasingly impossible to predict their fate. Just as Mandelbrot found bursts of static in any given subset of information bits in his work on fractal communication, a demographer would find subsets of chaotic lives in any given subset of children born under the most favorable of social conditions; would find subsets of stable, productive lives of persons born in the most unfavorable of conditions. Studies of concentration camps, of institutionalized children, of Hutterite communities or of Swiss villages should reveal the same fractal character of life courses.

One will observe that, as one goes from period one to period two to period four dynamics above, prediction remains possible even if precision is lost in period four dynamics. As James Yorke put it, Period three implies chaos. Mitchell Feigenbaum found that all systems, whatever their nature, tumbled into chaos after 4.6 bifurcations. The changing dynamics as systems bifurcate are of monumental import to the philosophy of science as well as social policy The same system will display different causal models depending upon the number of attractor states available to it; causality tightens and loosens depending upon how many attractors are present. With two, four, or even eight options, causality is tight enough to justify statements of central tendency. After that, predictability is decentered as an epistemological tool.

The implications for social policy are also profound. Control is impossible as causality loosens while too much choice implies chaos. This implication will haunt both conservatives and liberals all the days of their life.

Elusive Universes and Samples

Mandelbrot was assigned by IBM to help eliminate noise on telephone lines. It was well known that noise came in bursts and that there were periods of error free transmission followed by periods of static. In trying to sort it out, Mandelbrot found that one could never find a time during which errors were scattered continuously. Within any burst of errors, no matter how short a time slice one took of the universe of static bursts, one could always find a periods of completely error-free transmission. No matter which time scale one used, an hour or a second or a nanosecond, the same ratio of error to error free transmission one found. 7 In chaotic processes, a universe of a given population is impossible to define; a sample of such a universe equally impossible to define. All such 'samples' are fractal and, more importantly, their parameters vary depending upon which region of phase-space one is sampling. Efforts to generalize across a universe or from a sample becomes questionable in such an ontology.

If this is also true of any given set or sub-sub-set of children in the USA, then prediction of a single case from general 'laws' of the encompassing universe is always impossible no matter how good the research design, the research instrument, the research team and the propriety of the mathematical tools. The system in question as a whole does not stand still for the researcher. Still less does the life of a given system follow a stable pathway answerable to the analytic categories of the social scientist.


Quantum physics offers its own doubts about objectivity. There is a question whether objects exist as discrete entities. Objectivity as a process in which particles exist as entities to be studied as discrete objects being acted upon by external forces--as independent or dependent particles--is called into question. More than that, for some, quantum physics implies that observation calls forth the 'objects' of observation.

In his discussion of the Pauli Principle, Ian Barbour (1966) notes that, in newtonian physics, the individual part could be considered on its own and that the laws of nature did not change when parts were assembled in a new configuration. However in post-modern physics, it is frequently necessary to study the behavior of the whole as an emergent, transcendent entity not derivative from a complete knowledge of its parts. In quantum physics, physical particles appear to be intersections of indivisible waves. These emergent 'particles' are stable for a while and then dissolve and recombine to create new entities.

From the perspective of quantum physics, particles do not exist, objectively, as separate entities but rather as interdependent parts of a greater whole (Barbour:298 et passim).

In quantum physics, it is a human choice about which research technique to use. The choice determines whether one finds waves or finds particles in the 'natural' ontology. The object of study varies according to the methodology used to look for it.

With these reservations about the existence of a distinct object of study in even the purest of the pure sciences, claims of objectivity are weakened. There may be no object as such. However, objectivity in social research could not be grounded on the objectivity of physics and chemistry even if such objectivity were possible since the units which comprise social reality are far more complex, far more interdependent and far more competent to affect their surroundings through sentient activity than are photons, quarks, charms, colors, leptons, muons, ups, downs, tops, bottoms, heavy or light 4th generation neutrinos if they exist.

If the particles which make up the physical world are not ontologically, separate objects, the whole notion of discrete objects which grounds the methodology of science and after which social science is modeled, calls into question whether the scientist can separate themselves as persons from the roles, societies and other objects of study or from their larger historical and sociological field. 8

The methodological question reduces to doubts about whether the social scientist, per se, can distance self from the object studied. More precisely, is not the scientist an indivisible part of the field which is studied? Can claims of objectivity be sustained if, in fact, the scientist is shaped and shapes the world in which the knowledge process is located? 9

Indeterminacy For physicists, the epistemological adequacy of the truth process also centers around indeterminacy; the inability of physicists to know fully and thus predict precisely, the behavior of particle/waves. One can ask from what sources does the inability of physicists to achieve absolute truth about the behavior of wave/particles arise. There are four general explanations for the inability of science to determine, precisely, the behavior of such wave/particles.

First, for many in modern physics, indeterminacy is said to arise from the ignorance of the scientist about all the variables at play. In principle, all such variables can be measured at the same time and therefore, in principle, precise prediction is possible. In a letter to a colleague, Einstein put it thusly for all such partisans:

The great initial success of quantum physics does not convert me to believe in that fundamental game of dice...I am absolutely convinced that one will eventually arrive at a theory in which the objects connected by laws are not probabilities but conceived facts.

With perfect knowledge of all existing variables, one could predict, perfectly, the end state of a particle. For Einstein as form most sociologists today, a fact is possible. 10 In this explanation of the source of undetermined facticity it is from ignorance rather than from nature whence comes indeterminacy.

A second view, that of the observer inadequacy, is a bit more subtle. This view holds that nature is a seamless totality and that selection of only part of it to study necessarily results in partial knowledge. If we want to know how a particle or a system will behave, we must expand our research design to measure everything; to record more and more of reality until we have it all on paper. The interconnectedness of the universe extends to include the observer and thus, we must measure the effect produced by measurement. In principle, certainty is possible given a research design adequate to cover the cosmos and, as well, include itself. 11

A third explanation is called, generically, the Heisenberg effect, explains uncertainty as a result of the experimental activity of the researcher. Nils Bohr explained the Heisenberg effect by saying that when we study an electron or any other particle, we bombard it with a quantum of light which makes it behave differently than it normally does when not studied. There is, still, an objective world that behaves coherently but we introduce a new coherency, a new result when we study the world; an end-state that we, being part of the field in which the electron is studied, help determine. For Bohr, the result of research is a stable fact but one has no way of knowing what fact would have emerged had not the quantum of light been introduced at that moment into the field under study.

In the Heisenberg principle of indeterminacy, it is intrinsic that objectivity is impossible since the researcher "...forces one of the many existing potentialities into being, into actuality." As Heisenberg put it, the transition from the possible to the actual takes place during the act of observation. 12 The event studied actually occurs and it occurs as measured but it would have occurred differently or not at all had it not been studied. We can never be certain how the world would have worked had we not chosen this potentiality to measure and thus to create.

In the views above, that of the observer intruding to produce effects, that of the ignorance and inadequacy of the research act as well as that of observer inability to measure everything, perfect knowledge is not possible but there is still a stable cosmos that exists out there; that is linear and coherent even if no knowledge process exists or could exist that describes it fully.

A fourth view, from chaos theory, used in the sections above as in other essays in this series, says that nature is, ontologically, unknowable. When in a chaotic modality, the path of any given event is non-linear, hence unpredictable, unknowable. This understanding is developed at length in the research reported by Gleick and reviewed in Part I of this article. The behavior of a chaotic system in near-to-stable equilibrium describes a trajectory in a pattern called a 'strange attractor.' The pattern is fairly stable, the path of the system is generally, but not precisely, predictable. However, when the periods of the system bifurcate beyond the 4th bifurcation, then the bifurcations cascade, i.e., periods enter into completely unpredictable, unpatterned behavior. This cascade of bifurcations spell the end of whatever degree of facticity one might have safely specified in describing the behavior of a system.

This world view grounds a post-modern social philosophy which transcends the closed, coherent, mechanical view of social and physical reality to include ceaseless variation in the career of all events, produces the surprise of discontinuity as well as the transformations found in dialectic models of causality. 13

All of these views taken individually, have merit. Taken together they bring objectivity, as a process that distances the subjectively observing scientist from the objectively existing particle, into question. Taken together, intersubjectivity at all levels of physical and social dynamics is given credibility.

Post-modern physics does not, can not speak for post-modern social phenomena. The dynamics are different; the units of social organization can think, can intend, can refuse to comply to the laws of nature while atoms and stars must follow the mechanics and thermodynamics of their kind. Post-modern physics can, however, discredit and disenfranchise the hegemony of objectivity as a grounding assumption in social research. Without the cachet of the hard sciences to justify objectivity, theoretic room for reflecting upon the relationship between observer and observed can be found.

Fractal Concepts In addition to the difficulty with which social scientists have in adopting the putative objective character of the ontological entities from physical science, there are also problems of conceptualization and utilization which subvert claims of objectivity. Let us think about the fractal nature of concepts with which we slice up reality in order to study it.

From the very act of thinking about nature and society to the selection of concepts with which to grasp their features to the choice of research topics to the adoption and integration of findings, every scientist works within a socio-cultural formation. Those who do research on weather would have a much richer inventory of concepts with which to analyze solid state H2O were they to work out of the conceptual richness of Eskimo culture. Those who research physics would have a very different set of concepts with which to grasp physical reality were they to speak Navajo. The space in between concepts of snow or molecules or citizens or Black children takes discrete intervals in modern science and modern sociology.

If a meteorologist were Inuit, s/he would design research to examine the dynamics of some 20 different kinds of snow. If a meteorologist were European, s/he would use five or six such concepts. An Inuit meteorologist would be horrified at the ways in which European meteorologists collapse categories. In order to study the 'real' climate, the Inuit would insist that the conceptual tools of the European be junked and those of the Inuit be adopted. Just as we disaggregate data to ascertain offsetting trends, such a meteorologist would insist that the concept of snow be disaggregated.

In chaos studies, fractal concepts are possible. Cantor dust, Sierpienski carpets, Koch curves and Mandelbrot sets have fractal dimensions. In postmodern sociology, the integral concepts of social research have to give way to fractal concepts which intersect topologically and interactively rather than being pure independent or intervening or dependent variables.

In the case of the Afro-American children above, if the concept of race is seen to be a biological fact, the researcher has serious problems. S/he must disaggregate the concept. If there are 100 billion four-part terms in the DNA molecules of 23 chromosomes of the human species and if 99,999,990,000 such terms are identical as between those conceptualized as Anglo and those conceptualized by the social scientists as Afro-American, then it is appropriate to ask about the boundaries of the concept...does one use the genes for pigmentation, muscle articulation, cross section of hair, attachment of ear lobes to skull or what? Do these aggregate in sets uniquely and significantly different for groups we label races? Do these unique sets have any bearing on the behavioral end state toward which one of the other of the objects of study move? If, out of 64, one has 53 grandparents who migrated from Europe and 11 who came from Africa, how is one to be unilaterally defined as Anglo or Black? If the genetic distribution is worth anything at all, its worth is registered in fractals rather than integers.

More than that, is the distribution of all relevant genes which make up a individual person the same for all persons conceptualized as Anglos or Afro-Americans? The more likely case is that in any given population of 250,000,000 people, the distribution of genes takes such a wide variety of combinations that one is using one's own subjective understanding in making a call about whether each person is white or black, yellow or brown, black or yellow, yellow or white. Subjective understanding of a concept is not shaped by the ontological features of the research object; it is shaped by the socio-cultural complex in which one lives and learns.

If such conceptualization of membership in race, or gender, or social class or ethnicity has variable validity, then the research based upon putative membership is unreliable; that is unless, one takes the position that such 'scientific' work is part of the process by which social status categories are created, called race, and used to include or exclude people from jobs, housing, health care, compassion or other similar constructs. The term used to refer to such a construct is racism; not race while the process used to generate such concepts is better called symbolic interaction than scientific endeavor. Science is, then, part of the self-fulfilling process nowise different from that which ordinary people do in ordinary life in the reality-creating process. 14

The Poetics of Language

Postmodern sociology takes the position that all social research operationalism is, in an important sense, more poetics than empirics. Since our concepts are buried in the long history of our language and our interest is in surviving an often hostile world, those concepts are just one set with which sociologists could slice up social reality and make visible some of its workings. The essence of poetics is that it uses an analogous set of concepts from one behavioral domain to explore and to explain another domain of activity. Modern sociology uses the same poetics in its research categories.

Thus the language of war is used to make clear the dynamics of politics; or the language of sport is used to garner insight into the dynamics of sexual encounters just as the language and dynamics of theatre are helpful to verbalize the dynamics of the marketplace. In sociology, the languages of Southern Europe are used as a poetics with which to operationalize social phenomena. As does the medical system, we use Latin, Sanskrit and Greek to create the dramaturgical impression of objectivity; of the correspondence of concept to empiric reality. 15 Everywhere Greek and Latin combining forms are used to discuss social dynamics as if basic Anglo-saxon, Swahili, Ainu or Hopi terminology were, somehow, less scientific.

There are many more linguistic practices that serve to create a false impression of neutrality; of the correspondence between the ontological fact and the epistemological construct. Putting a statement into the passive form instead of an active voice helps create the impression of eternality and objectivity. The use of dry and dusty language styles with which to report horrible things or delightful events gives a false impression of impartiality. The use of recipes and formulae in reporting research makes it appear that one has transcended one's own creativity and intentionality.

We cannot think without concepts and we must either use the concepts given to us over our social history or we must make up new concepts. If we make up concepts, we have to endow them with meaning. The endowment of meaning arise from our location in the social order and from our cultural heritage in the anthropological order. The endowment of meaning arises from the web of group relationships we sustain and the stability of terminology we learn to respect in the socialization process. Out of these relationships and heritages come the range of desires which impel our quest for knowledge and concept; security, status, service, or whatever the culture values.

What is missing in modern sociology is the understanding that it is inevitable that epistemology and ontology will, whatever linguistic system we use, collapse into each other. The very choice of terms; the very selection of topics, the very use of results all enter back into the ontological base to shift it, to move it, to shape it or to defeat it. The respectable thing to do is to accept the interconnection between epistemology and ontology and, thus, accept our moral responsibility for the world we shape and misshape.

Parables, metaphors, similes, and allusions all enrich and extend the knowledge process. In the denial of such borrowings and such transfers, the knowledge process is mystified and occluded. In that denial, the dynamics of the world we overlay upon empiric reality are denied and thus we deny our own agency.

The most bizarre of such alienated uses of language is, of course, the use to numbers to benumb the richness and complexity of social life. Once again, such a use of concepts from one domain to another is often helpful but denial of the transfer always alienative. Numbering systems can parallel the richness of social life in some rough and imprecise way but in the confounding of social dynamics with the transformations of numbers in equations and formulae lay much mischief.

Quantification is, itself, just another poetic into which the language of life may be fitted. When the poetics of mathematics are confused with empirics of actuality, a major political prolapse occurs which gives a false sense of objectivity. Objective science becomes a self-fulfilling prophecy in which the subjective capacity of both researcher and researched is minimized and thus, alienated from both. To be fully human is to be fully involved in the creation of the social life world in which one must live out one's days. To be fully human is to accept moral responsibility for the world one helps create. 16


Chaos theory offers a through-going critique of modern science and that sociology which models itself after newtonian physics, euclidean geometry, Aristotelian logic and the logical positivism. Inference about the truth value of formal systems based upon consistency, sufficiency and necessity are left without an ontological base given fractal outcome basins. Propositional calculus is limited in its purview to some small niches in phase-space. I conclude this essay with a look at some of the problems entailed in using such tests of truth.

Consistency Problems

Heretofore the mission has been to generate axiomatic theory coalescing into a formal theoretical structure having the attributes of consistency, sufficiency, necessity, and independence (Gibbs:1972:220). 17

The assumption of consistency is primal in formal theory building--the possibility that inconsistent axioms or propositions could be true would be considered outrageous to a formal logician. The theory should contain sufficient coverage of causes to account for all the variations in a dependent variable. The causal variables themselves should be independent; they stand as first cause in formal theory. The postulate of necessity means that there can be no slippage between cause and effect in the theory. One must, necessarily, follow the first: if A, then B. B cannot arise if A is not present; A cannot be present without contributing to the probability that B ensue. A could exist without B if there are other independent variables which must appear before B can appear.

The dynamics of chaos systems do not sustain the requirements of formal theory. The consequences of chaotic systems are not consistent with the prior dynamics; qualitative changes occur which are far different from the dynamics of the initial conditions and cannot be predicted from a complete knowledge of those prior conditions. In revolutions, sit-ins, demonstrations and parades, consistency fails. Some may be orderly and some may become chaotic; there is no consistent connection between initial conditions and sequelae.

The postulate of independence falls in social dynamics. Instead of independence and causal priority of one variable in relation to other variables, chaotic systems (and social systems) are characterized by feed-back loops which determine the behavior and integrity of the system. In other essays in this collection, the feed-back loops between trout and pike are discussed which interface with other feedback loops including those of frogs and insects to join in a complex interdependent matrix of causality. For human beings in social matrices, any number of feed-back loops displace the model of causality which mark formal theory construction in sociology; the self fulfilling prophecy concept encompasses the wisdom of this view.

In human affairs as, perhaps in the case of planaria, anticipation of behavior B may invoke behavior A which, in turn, only affects indeterminate probabilities of B. The dynamics of the economic system affects the ratio of jobs to the surplus labor pool. In hard times, jobs are relatively scarce; some persons defined as White may anticipate that they will be laid off and that persons defined as Black may compete with them for the dwindling jobs in the job pool. If so, ethnic/racial animosity increases; in other narratives about job-loss, racial solidarity may increase as workers across racial, religious and national boundaries join in other politics. The effects of racism and ethnic struggles feedback to affect the dynamics of the economic system; to open or to close off more jobs. The situation in the Union of South Africa serves as an exemplar to the point.

There are human-made deviation amplifying and deviation damping feedback loops in all social encounters which make it necessary to the treat the system as an interconnected whole rather than as a system with external and independent causal patterns. The ability of social systems to displace the consequences of their dynamics on external systems changes the rigid pattern of causality set forth by formal and linear models of causality.

Causality in crime, disemployment, health parameters and other significant social facts shifts as the political dynamics of the global economic system shift.

Sufficiency dissipates as an attribute of theory in chaos theory as well. What is sufficient to produce crime or poverty or to increase the mortality rate of infants at time one becomes irrelevant or reversible at time two. In one economic formation, the laws of demand and supply may create more jobs while, in another, demand and supply may lead to the loss of jobs as automation, speed-up, and capital flight occur. In one cultural setting, poverty may be connected to crime while in another, poverty is connected with sharing and mutual aid. New forms of causality arise in chaotic dynamics which require more than the axioms and propositions of linear theoretical models. Most of the systems in the social realm take on nonlinear dynamics thus rendering formal theory of very limited utility.

These attributes, taken together, falsify falsifiability as the maker and breaker of theory. In modern science, if the data do not confirm the axioms and propositions of modern theory, the theory must be reconstructed. If the data do not conform to the predictions and patterns of given chaos findings, then one assumes that bifurcations have occurred to change the dynamics without falsifying the previous findings--or that one is sampling a differing segment of a fractal outcome basin. Falsifiability is dethroned by chaos theory.


Popper (1965) made much of falsifiability as the ultimate test of formal theory. Social systems with the ontological features of chaotic systems cannot be falsified. It is an ordinary feature of such systems that causal connections are unstable for chaotic systems.

The model of theory building currently in vogue in American sociology takes the form of an endless circle in which theory sets at the top from which hypotheses are generated. The hypotheses are operationalized and data collected by direct observation in the field to which the theory speaks. From the data, empirical generalizations are made which, by induction build and rebuild the theory (Wallace:1969:ix). With such a theory, one can deduce lower order statements from higher order statements. The lower order statements have epistemic correlates in the real world which, when examined, serve to verify the truth value of the connection between explanadum and explanans (Wallace:1969:4).

In chaotic systems, however long one might observe a field, it would not reveal stable connections between explanadum and explanans--yet statements about the field would not be false even if one were never to find the same connections again. A second, fourth or tenth replication of the study would produce other results and the research scientist, operating within the logics of linear dynamics would declare previous studies invalid and her/his own findings the true state of the system.


In the same moment that falsifiability is removed as the ultimate test of the soundness of a theory, the importance of replicability is seen to be misplaced. One can never replicate a given study; one can only trace, in panel analysis, the ever-changing dynamics of a system.

There is a limited place for replication--and falsification. In those systems which operate within the phase-space of a torus, there is sufficient recurrence; sufficient pattern to speak of causality in fairly confident terms. But one should always keep in mind that the same system, subjected to another bifurcation, may force open the phase-space which it occupies and fill it in a pattern that utterly defies prediction even in fractal probabilities.


Given the elusive and fractal nature of the objects of social research; given the interaction between subject and object of research; given the shifting patterns of causality as system boundaries change; given the fact of feed back loops which change the nature of causality; given the nonlinear attributes of chaotic systems, the question then arises as to the nature of the research mission in American Sociology.

If modern sociology and its claims of objectivity are insupportable, the task of some postmodern sociologists is to frame a sociology that is value-full. By value-full, I simply mean that the researcher acknowledges the value agenda from which concepts are selected and research is done. We may not share the same set of values in every sociological enterprize; indeed it would be most surprising were that the case, however, in the postmodern epoch, sociology must face up to its partisan and its creative nature.

The attempt to hold on to modernist assumptions, and to organize social research as if its findings were universal in time and space means that such social scientists who use them are engaged in an effort to create a social life world in which such assumptions are valid--rather than merely to report upon it. Any research effort, in its wide-spread reach and in its most profound depths, which helps develop theory that describes a fixed, linear, coherent set of social laws transforms modern sociology into a political tool by which the managerial needs of its sponsors, the legitimacy needs of its home society, the preferences of its leading figures comprise the agenda of sociology. This agenda bespeaks a political goal not a quest for objective truth. In such an enterprize, knowledge and science are harnessed to the ideological needs of an era.

Post-modern sociologies offer alternative ways to harness the scientific process; some hostile to the human condition, some more supportive. 18 What these very different sociologies have in common is that they assume the infinite variety of social forms as end-states of social processes. They do not assume the closed, stratified, unilateral evolution of society toward pure form nor do they assume the functional necessity of any given set of social structures for that pure form. They do not privilege a given social form as natural across all societies. They do not label alternative social life forms as deviant, primitive, disorganized or degenerate. Post-modern sociology recognizes the political character of social theory.

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