Chaos As Social Order


            Chaos is a new way of understanding social order.  Rather than a perverse paradox, this assertion draws on the diverse developments of chaos theory in the natural and mathematical sciences (Barnsley 1988; Crutchfield et al 1986; Dewdney 1985; Gleick 1987; Mandelbrot 1983; Mullin 1993).  Over the past two decades, chaos theory has been applied in many disciplines of theoretical and applied science (Baier and Klein 1991; Cohen and Stewart 1994; Davies and Gribbin 1992; Gleick 1987; Hao 1990; Holden 1986; Moon 1987; Mullin 1993; Rasband 1990; Ruelle 1989), including some areas of social science (Brown 1994; Chen; Dendrinos and Sonis 1990; Gell-Mann 47-48; Goodwin 1990; Hao 573-632; Holton and May; Kiel and Elliott 1996; Lewin 44-62; Nicolis 1991).  The latter applications, however, have used chaos theory as a mathematical tool incorporated into conventional conceptual frameworks rather than as an alternative conceptual framework which could illuminate the very social order from which chaos theory has arisen.  To serve conceptually chaos theory must be understood conceptually.

            In this article, I do not produce mathematical models or computer simulations nor do I offer copious new data.  I also definitely do not use chaos as a metaphor.  This is not a literary exercise designed to decorate the social sciences with yet another image, such as the machine, the organism, the deductive system, or the adversarial debate (Morgan 1986).

            It might seem appropriate to group chaos with such heuristic metaphors.  These metaphors have been used in social science to approach and explore phenomena which were thought to be otherwise intractable to rigorous scientific examination.  However, the success of multiple research efforts in the mathematical, physical, life, and social sciences in identifying various kinds of chaotic dynamics suggests that chaos should be grouped not with metaphors but with known types of order such as linear deterministic, stochastic, and random.

            This grouping emphasizes that I use chaos as a theory not as a model (Harvey and Reed 309).  My use of chaos is therefore theoretic and not semantic (Richards 98).  This grouping also does not deny that the bulk of existing research has regarded chaos as an outcome of changes in parameters of deterministic systems.  Chaos is usually viewed as deterministic chaos.  It affirms, additionally, the discovery of chaotic dynamics in social science data (Kiel and Elliot) where the social situations generating the data cannot be reduced to linear deterministic principles or equations.  From this affirmation seems to flow the possibility that chaos is a kind of order which is not strictly dependent on deterministic systems for its existence.  Indeed, as a type of order, chaos may be the first clear, non-reductionist link between certain specific conditions in numeric and physical systems, such as phase transitions, and a pervasive, spontaneous quality of social reality.  Rather than a fad or a misplaced metaphor, chaos may be a small window into a new and larger way of understanding human life which includes determinism, stochasticity, and randomness.

            Grouping chaos with known types of order frames chaos as a comprehensible form of order rather than as a metaphor for some incomprehensible condition.  Besides being a more useful alignment, this grouping also raises a deeper question for the philosophy or foundations of social science.  This question defines the horizon of my inquiry here:  What properties must the (social) universe have in order to exhibit all four kinds of order?

            Considering chaos as a type of order allows me to use the results of experiments to prepare the conceptual ground for chaos as social order.  I present the established features of chaos which bear on social order.  I highlight the mixing/folding phenomenon characteristic of physical chaotic phenomena (Crutchfield et al 51-4; Gleick 122, 255, 257; Mullin 19-21).  My focus on social power as actions upon actions provides a necessary bridge for understanding chaos as social order.

            After this presentation of chaos theory as a conceptual framework, I then lay out an application of chaos theory to diverse social phenomena–oppression, modernization, language change, moral change, political change, and cyberspace.  In the course of this application, I show that chaos theory can be used conceptually to clarify contemporary social order but that the nature of social phenomena place significant limitations on the mathematical application of chaos theory to social science data.

Social Power

            We begin by reflecting on the fact that others–mother, father, siblings, pets, blankets, rain, sun–have been acting upon us for a long time.  Others, both animate and inanimate, have been acting not only on our bodies as rain acts on tin, water, or sand but more specifically on our bodies’ attempts to act.  These actions include the entire range of qualities–caress and punch, embrace and push, praise and blame, approve and reject, and so on.  These actions upon our actions have induced and introduced social power:  actions upon actions.

            Actions upon actions sounds repetitive.  Not redundant, but repetitive in the sense that something similar is recurring in each action.  Similarity through difference characterizes individual life stories, family histories, and community histories.  Indeed, as historical beings, all of human life is involved in each human action upon an action–patterned, compressed, focused, refracted, fractionated–as much as all of a language is “in” any instance of its use.

            What precisely then is the process of actions upon actions?  We can interpret the phrase as scalar recursion which is the recurrence of similar structure on different scales.  Something is similar in every instance of actions upon actions, whether it is in the relationships between a Supreme Commander and an entire military establishment, a lieutenant and a platoon, or one private and another.

            Paying closer attention to the phrase “actions upon actions” supports such a linking of social power with chaos theory.  The first and third terms–”actions”–are identical but this identity is qualified by the second term–”upon.”  The preposition “upon” is used rather than those which indicate symmetry or equality, such as “with,” “together with,” “beside,” etc.  The verbal sense of “action” is amplified by the dynamic sense of the preposition.  These observations may be provisionally summarized:  the structure of social power as actions upon actions is dynamic asymmetry.

            We next observe the absence of any modifiers of the noun “actions.”  Words such as “all,” “most,” “many,” “some,” etc. could have been used.  But no one can actually count the number of actions upon their body.  This noncountability extends across all human time scales.  This is true whether the time scale of the actions is generations of national patterns mediated by living cohorts, years of family patterns mediated by relatives, years of being a consumer, student, parent, child, or employee, or months of dating, going steady, being engaged, or being married.  It is not possible, therefore, to fit this idea of social power into a quantitative, countability dualism such as finite/infinite.  This impossibility in turn refines the provisional summary in the preceding paragraph:  “upon” is ambivalently or ambiguously asymmetric.  It is not necessarily either symmetric or asymmetric.

From Detector To Attractor

            This understanding of social power can be used as a power detector.  It can be used in any human situation to bring into view, to outline or highlight, to unmask or reveal, power relations.  This power detector is not like a metal detector that finds a distinct, physical thing nor is it like a thermometer that quantitatively reduces a complex physical condition.  It is a detector of human situations in which people’s actions may be found to be acting upon people’s actions.  It can be used analytically to consider relations of cooperation or collaboration, which are indeed actions upon actions, as well as to consider situations of oppression.  It predicts that social power will be dynamic, ambiguously and fluidly symmetric/asymmetric, and numerically uncountable.

            The condition of uncountability may be understood as meaning that actions can be decomposed and recomposed indefinitely into more and less inclusive patterns.  The oppression of being forcibly confined in a mental institution, for example, can be analyzed in many terms–architectural, political, economic, familial, social, psychiatric, etc.  All the terms are relevant to an analysis aimed at completeness though none of the terms exhausts the entire range of actions upon actions in such a situation.

            We can now consider a smooth social process or the surface of water in laminar flow without turbulence or chaos.  The onset of turbulence or chaos constitutes both a qualitative and a quantitative change from the laminar condition and is not simply an accumulation of prior conditions.  The change introduces a pattern characterized by repetition and similarity across different scales of the pattern.  The detector of social power detects a repeated action upon action among human beings.  The repetition and the similarity indicate a certain attraction of the actors to one another.  The detector indicates an attractor.

            In chaos theory, an attractor is a pattern in space.  The kind of space is state or phase space.  Phase space is a multidimensional space inclusive of the Cartesian coordinates and the momentum of a system, i.e., the attractor.  There are many definitions of attractors in the literature (Cohen and Stewart 204-7; Coveney and Highfield 166-75; Gleick 150, 232-6; Hao 16-18, 51-63; Kiel and Elliott 26, 54-5, 172; Mainzer 4-7, 58-9; Mullin x-xii; etc.).  Moon’s definition is simple and useful:  An attractor is a “set of points or a subspace in phase space toward which a time history approaches after transients die out.  For example, equilibrium points or fixed points in maps, limit cycles, or a toroidal surface for quasiperiodic motions, are all classical dynamical attractors” (261).  The attractor pattern is an equilibrium state or set of states to which a dynamical system converges.  An attractor is not necessarily either one or many states exclusively.

            The verbal phrase “to which…converges” conveys this non-dualistic quality and also points toward the quality of an attractor that makes it strange:  a final equilibrium is never reached–symmetry is never reached, nor is a “stable” asymmetry reached.  The pattern shows self-similarity across scales but it never reaches an identity, or, equilibrium condition.  Using Moon again, a strange attractor is “the attracting set in phase space on which chaotic orbits move.  An attractor that is not an equilibrium point nor a limit cycle, nor a quasiperiodic attractor.  An attractor in phase space with fractal dimension” (267).

            A strongly defining characteristic of a strange attractor, moreover, is sensitive dependence on initial conditions.  The pattern of a strange attractor may be taken as the pathways of points that begin at arbitrarily small distances from each other.  Over time, those distances change so much and so quickly that at a later time in the pattern the initial conditions are no longer observable.  The later state of the pattern or system cannot therefore be connected deterministically with the beginning state.

            It has been proven repeatedly in both numerical and physical experiments that such a pattern must involve simultaneous folding and stretching.  For example, you put a spot of dark blue dye on the surface of a large lump of white bread dough.  You then knead the dough.  Kneading folds and stretches the dough.  Folding and stretching mixes the blue dye through the dough until it is distributed throughout the dough.  The entire mass of dough is pale blue.  It is physically or mathematically impossible to determine from the final state of mixed dye where in the dough the spot was in the beginning.  The sensitivity of the system to its initial conditions thus means that, regardless of how close to each other the elements are initially, stretching and folding results in the initial conditions no longer being observable or deterministically relevant.  Such mixing involves simultaneous expansion and contraction.  As this happens, old or earlier information is destroyed and new or later information is created.

Chaos And Oppression

            When introduced into a consideration of oppression, this approach illuminates some crucial aspects.  First, oppression works on the human body in two distinct ways–one by removing the body from home and two by covering the body with non-indigenous, uniform clothes.  Examples of both operations can be found with prisoners of war, convicted criminals, committed mental patients, military personnel, and students in compulsory education.

            Second, oppression works on human structures and on the earth.  Imperialism, whether religious, political, military, or ecological, has repeatedly involved the destruction of buildings and of parts of the earth such as groves, crops, livestock, fields, and species.  Examples are the destruction of groves of trees in the Old Testament, the burning of manuscripts in China in 212 BC and the burning of the library in Alexandria, in 525 AD.  More currently, the destruction of human living spaces and places, from rain forests, to living sites, to old sections of cities, involves the destruction of old information and the creation of new information.

            Combining these two operations of oppression, we see the human bodies of survivors, born and bred close together, then moved, mixed, and clothed so that, when observed later, no traces of their initial conditions–their indigenous or native states–remain.  The old information about the former identity of the displaced persons or of the destroyed places is replaced by new information resulting from actions upon the persons and the places.  If we add to this the repression, disuse and disappearance of unprivileged languages and customs, then the image of uniform mixing, or, mixing for uniformity, becomes clearer.

            Third, sensitive dependence on initial conditions in both numerical and physical experiments involves amplification of small initial differences into larger differences later.  Twins, siblings, and neighborhood or village cohorts often develop lifeways that not only put out of focus their initial conditions but also differ from one another in ways that are not susceptible to deterministic, linear calculation.  In the case of groups of ethnically homogeneous refugees crossing a border into another country, individual lifeways can diverge beyond linear reckoning over time.

            From the standpoint of social power, the actions of such people are worked on by the actions of social operations that “mix,” “fold,” and “stretch” everyone.  At one and the same time, contemporary, industrial, urban society functions to stereotype everyone while making available the physical and mental means for individual differentiation.  From the standpoint of chaos theory, this allows for indefinitely small and large distances between points, or subjects, in the pattern of the strange attractor.  It also allows for signs and signals, such as hair styles, clothing, gestures and jewelry, web pages, and c(i)ber(dentities), increasingly bereft of any anchorings in known, traditional societies–traditional initial human conditions.  Instead, these signs and signals increasingly occur in production, consumption and communication patterns that transcend national, linguistic, and ethnic differences or origins.

            Such uniformity of pattern and signal leads, fourthly, to another illuminating characteristic of strange attractors also repeatedly proven by physical experiments.  This is a continuous power spectrum.  When a mutable medium, a fluid for example, is excited beyond a certain threshold, its measurable signals change sharply from continuous to discontinuous to continuous.  At the extreme level of excitation, the signals are continuous.  Rather than showing discrete peaks and valleys throughout the signal, the bulk of the signal is continuous, undifferentiated “noise” (Brown 135; McBurnett (2) 43-5).  Urban areas where waking human activities go on twenty-four hours a day are examples of such social “white noise.”  This noise has the power to eclipse bird-songs, wind sounds, and much of human speech.  In urban areas, everyone’s and everything’s sounds and noises are folded upon one another and mixed into collective sound.  This mixing produces a variety of aural experiences which cannot be predicted from knowing the origin and quality of any particular sound–emergence and synergy–and which blur into white noise in which no one sound dominates although any one sound may be momentarily more or less distinct.  In fact, the blur of urban noise obscures not only origins but also dynamics (Brown 123; Dendrinos 241; McBurnett (1)171-5, 185, 190).  Is the dynamics of urban “white noise” random, stochastic, chaotic or yet another type of order which a conceptual use of chaos theory can illuminate better than other kinds of order concepts?  I will return to this question in my conclusion.

            A continuous power spectrum connects with sensitive dependence on initial conditions in describing, at the onset of chaos, the destruction of old information and the creation of new information.  Pre-chaotic signals literally disappear and are replaced by erratically punctuated broadband noise.  This characteristic connects with oppression in that the latter always involves the injection of new energy into an existing system.  Destroying living sites, destroying some bodies and moving others, burying the dead and clothing the living then resocializing the survivors injects new energy into the bodies and into their relations with others.

            Oppression not only subjects bodies to new forms of energy but also makes new energy available to those bodies.  It should be emphasized here that this use of chaos theory does not lead to any simple, reductionist view of social power or of social order.  Social power may constrain or it may liberate or it may do both in the same situation and through the same person.  Declines in the hegemony of white, American, heterosexual, Christian males, books and chainsaws coupled with empowerment of women, children, homosexuals, non-whites, non-Christians, non-Euroamericans, hard drives, and endangered species show oscillations of social power in contemporary social order.

            Some further examples of this mixing and folding are Gandhi learning English and English law which he used to drive the British from India, Crazy Horse learning to use a rifle with which he killed invading soldiers, prisoners using weapons taken from guards against guards in prison riots, and students using computers to attack the military-industrial complex, university regulations, or high school dress codes.  This variable characteristic of energy-induced continuous power spectra–as though the law of the conservation of energy were functioning socially to preserve social power regardless of who has it or what its change of hands does to existing social order–shows that some kinds of social power persist through interruption.

            Two examples of persistent social power are the physical structure of a modern prison and the legal and temporal structure of modern mass education.  In the former, a prisoner’s body is disciplined twenty-four hours a day by its environment of bars, walls, locked doors, and fences with or without other individual human presence.  In the latter, people from six to sixteen years of age are persistently disciplined by a system that linearly encloses every day of the calendar year with its own significant events, such as the beginnings and endings of classes, quarters, terms, and semesters.

            A closer look at an excited fluid will strengthen the connections just mentioned.  When heat is applied to water in an open container the water moves gradually until there is a sharp transition to boiling.  Boiling may be understood as the creation of infinite surface in finite volume.  The water occupies a finite space.  The elements of the water, the water molecules, remain forever separate but move more and more rapidly.  Since the molecules cannot turn into each other and since they cannot stop moving, they must have infinite surface.  They get infinite surface by the rolling of the water which is a process of stretching and folding the fluid medium.

            The water mixes, folds and stretches indefinitely and unpredictably.  Boiling may be further understood as releasing thermal energy to air.  The more heated water is exposed on the surface to air, the more heat is released.  If the heat is stopped the water will cease boiling and return to its pre-chaotic, quiescent regime.  If the heat is continued the water will slowly vaporize until the container is empty.

            There are two phases of this event in which old, earlier information is destroyed and new, later information is created.  The first is the transition from quiescence to boiling.  The second is the transition from boiling to vapor.  All information about quiescent positions of water molecules disappears in boiling.  All information about boiling positions of water molecules disappears in vaporization.  It is impossible to ascertain by observing atmospheric water molecules when and where those molecules were parts of a fluid body of water, either boiling or quiescent.

            Many individuals and groups of individuals may be seen as culturally vaporized.  It is impossible from observing people on city streets to ascertain when or where those people, or their ancestors, were members of groups that could have been considered ethnically homogenous tribes, clans, or cultures.  As the borders of the world’s nations change, as data transfer technologies dissolve the barriers of time, space, and place, as war and environmental degradation persist, as droughts, floods, and volcanoes displace people, more and more human beings are culturally vaporized.

            The condition of cultural vaporization, moreover, involves three simultaneous expansions–the increase in human population, the increase in urban dwellers, and the increase in standardization by the extension of centralized, bureaucratic control over larger and larger numbers of people and into more and more details of human life.  Coincident with these expansions is the contraction of total per capita living space and within that contraction a further contraction of unstandardized living space.

            Unstandardized, unoppressed living space can be a space of resistance, armed or unarmed, written or unwritten.  In the US, for example, where the rhetoric of individuality is continually encased in the gestures of conformity, the only unoppressed living space many people have is their bodies.  Thus, resistance to oppression as forced uniformity, as the constraint of standardization without the liberation of individualization–standardization as erasure of difference–appears as tattoos, body piercings, jewelry, hair-do’s, make-up, cars, clothing, music, dialects, food, and gestures.  But the information conveyed by such diversity has no clear or deterministic relation to the initial conditions of the resistors, that is, to their ancestors, their indigenous groups, or their homes.  Resistance by differentiating the appearance of one’s body is a response to anonymity and depersonalization.  It folds the person even further into the strange attractor of change.

            At the same time, however, that modern power is “uniforming” and standardizing all of us, the modern industrial economy is diversifying and differentiating us.  If twenty different kinds of modem, thirty different makes of athletic shoe, fifty different kinds of car, or several hundred different shades of lipstick are not enough, more can be invented and produced.  The operations of modern social power upon humans thus move contemporary social order in two opposite directions simultaneously:  toward greater uniformity and toward greater diversity.

            Expansion of individualized treatments and options occurs with contraction of per capita living space and per capita unoppressed living space.  The operations of oppression may therefore be said to have two asymptotic limits.  In one direction, oppression tends to make everyone the same; in the other direction, it tends to make everyone different.  For example, short hair, low-heeled leather shoes, pants, a shirt, and a windbreaker could describe a male or female from almost any society on earth.  But in the US, where the unisex look is common, everyone of age has a unique social security number, a unique driver’s license number, and many people also have unique phone numbers and addresses.

Transients and Trajectories

            We may further this approach of chaos to social order with work in chaos theory applied to mathematical and physical phenomena that echoes the simultaneous interpenetration of contexts in social life.  We take contexts to be attractors and the habitual practices of contexts to be basins of attraction.  A basin of attraction is a set of initial conditions in phase space which leads to a particular attractor or context.  These initial conditions are usually connected, such as the practices of a group, and form a continuous subspace in some larger cultural phase space.

            Reported by Peter Yam in the March, 1994 issue of Scientific American, numerical experiments conducted by Edward Ott and John C. Sommerer, in which a particle in motion on a “frictional surface is occasionally pushed,” led to indeterminacy as to which of two attractors “the particle would chase, because one basin is riddled with pieces of the other basin.”  According to Yam, the researchers found that, so far from basins simply overlapping each other at their edges or occasionally penetrating each other’s space, “every area in one basin, no matter how small, contained pieces of the other basin within it.”

            This research supports chaos theory as a good representation not only of particular practices but also of contexts which interpenetrate by mixing and folding.  All human practices are accumulations of other practices.  Any one practice can be either decomposed into smaller practices with varying histories or recomposed into larger practices with varying histories.  For example, learning to use a computer keyboard involves the fine coordinations of using different fingers separately as well as the gross skills of using equipment powered by electricity, such as plugging in a plug and turning on a switch.  What we mean by tradition, custom and habit is precisely a layering–mixing/folding–process by which information is compressed and through repeated use and application eroded into shapes and forms that are usable–reproducible–over long periods of time and in different spaces.  The different spaces of guard and prisoner, patient and doctor, or consumer and producer are thus different contexts–attractors–which continuously operate upon and within each other.

            Paradoxically, the decomposability of human practices reflects the nondecomposability criterion of chaotic systems:  “Chaotic systems are indecomposable because they cannot be broken down into two subsystems that do not interact; this arises because of topological transitivity” (Richards 96).  This point can be understood mathematically as the requirement that “[n]onlinear differential equations, and the phenomena or problems they describe, must be seen as a totality, that is, as nondecomposable” (Kiel and Elliott 4; see also, Jaditz 69).  For example, riding a bicycle can be viewed as a combination of large muscle skills using legs and arms, or of small muscle skills using hands, feet, and eyes, or of social sensitivities involving posture, appearance, and style.  Each of these three combinations can be viewed separately as a verbal or even quantitative event.  However, none of them can be lived, experienced, or learned separately.  They all come with each other; they all interact with, impact, and are impacted by each other.  However finely the “subsystem” involved in bicycle riding–or using a computer, singing, swimming, painting, riveting–is described as a separate coherent skill or ability, it is always (already) interacting with all of the other systems.  Indeed, the growing popularity during recent decades of terms such as “interpersonal,” “interaction,” “interconnection,” and “interpenetration” suggests that chaos theory, at least to a contemporary mind and imagination, is a fully credible way to approach understanding social phenomena.

            Viewing both oral and written traditions as different contexts–as interpenetrating sites, as interacting systems–suggests that the subject-matter of social science, whether diachronically elongated or synchronically stacked, can be viewed as dissipative systems.  The continual maintenance, repair, and rebuilding required from bodily cells to clothing to transit systems to software configurations seems to leave little doubt that human living arrangements are predominantly dissipative rather than conservative systems.  In considering challenges to the management of complex systems, De Greene asserts that

            A sociotechnical or techno-economic macrosystem is a dissipative             structure in the sense that high-quality inputs (energy and matter)             are converted to low-quality outputs like heat and waste, with an             increase in disorder and entropy.  Within this overall process, of             course, low-quality raw materials are converted into high-quality             finished products, but these eventually break down, yielding further             entropy. (287)

            If this is reasonable, then it further clarifies the attempt to approach social order conceptually with chaos theory.  As Hao Bai-Lin explains in Chaos II, “it is dissipation that realizes the contraction [compression] of description [information] in a natural way: a vast number of modes die out due to dissipation; only those spanning the attractors need be taken into account in modelling[sic] the system”(6).  Dissipation–depreciation, degeneration, degradation, die-off, extinction–may be seen as the means by which normally and naturally functioning social and natural systems stabilize long-term function against short-term instability caused by proliferation of divergences.  Dissipation, in this sense, according to Hao, “causes the volume representing the initial states in phase space to contract in the process of evolution”(19).

            Oscillations in practices of all kinds are well known and extensively documented (Shils).  Oscillations are identified as such in a field of possibilities whose limits are defined by the tolerance of the practitioners for divergence.  A tolerable range of difference exists, as I describe in detail elsewhere (Cornberg (1)), not as a statistical array or generalization, unless quantification of actions is specifically sought, but as a range of preferences enacted and reenacted in contexts.  The tolerable range of difference defines a phase or state space in social life; enactment and reenactment of preferences constitute trajectories of practice.  When a trajectory does not span the attractor, it dies out.

            The research of Ott and Sommerer also encourages us to seek what we have already found in other ways–nested, embedded, and encaptic contexts or attractors.  The critical attractor of every human group is reproduction.  Examples of human groups are families, tribes, nations, and corporations.  All living things must reproduce for their species to survive but humans have the additional task of reproducing practices not just progeny.  Reproduction, such as human progeny, language transmission, and continuity of traditions, all display information compression.  The information that is needed to complete the practice repeats and varies through completions of the practice both as enactments and as learning events for others.  At any identifiable moment of a practice variation may take place and may be taken up in place of the preceding version.  What has gone before is accessible to the present only through the memory devices of the group.  There is no guarantee from any such memory device, oral, written, or electronic, that other versions have not existed.  Human living groups resist the infinitization of preferences with the compressions of tradition.

            A tolerable range of difference is discernible in all such situations.  Intolerable variations bring various other behaviors which are also practices such as indifference, correction, ridicule, criticism, rejection, denial, censure, repression, censorship, punishment, banishment, conflict and war.  If a practice, regardless of how momentary, and regardless of where it falls within the tolerable range of difference, does not entrain a group’s reproductive energy then it becomes a transient and dies out.  A transient is a trajectory that does not span the attractor long or far enough to repeat or to reproduce.  As Farmer, Ott, and Yorke assert, in an article on the dimension of chaotic attractors, “Loosely speaking, an attractor is something that ‘attracts’ initial conditions from a region around it once transients have died out” (154).  Small towns in industrialized nations typically have a variety of private businesses and public services.  Parameters such as location, economy, tax base, climate, and ethnicity form the basins of attraction which layer–interpenetrate or intersect–each other as determinants of what kinds of activities appear and continue or appear then disappear in such contexts.

            A case study or in-depth interview sample of such a location would constitute a phase portrait of the attractor.  Contained in any particular piece of information in such a portrait would be information about other aspects of the social situation.  We know, for example, that personal interviews about such preferences as political candidates or bond issues can also give us information about language use, gestures, and aspects of social life such as class relations and discrimination.  According to Hao, the “basic idea is: due to nonlinear interactions in the system these [information samples taken at different times] contain information on other variables as well and one should be able to extract this information” from such a series of samples (53).  Such co-presence, simultaneity, or interpenetration of data further illustrates that social power combines compression and persistence in social order.

            Homelessness is a powerful contemporary example and indicator of human living regimes which, with increasing regularity, distinguish between transients and non-transients.  The fact that smaller communities have less incidence of lasting homelessness in comparison with larger towns, cities, and metropolitan areas suggests that the trajectories of homeless people are attracted to basins of human living within which multiple basins–e.g. Ott and Sommerer–contain enough pieces of each other to allow–to tolerate in their range of differences–strongly divergent living arrangements.

            But containing pieces of each other then implies substantial rather than cosmetic discontinuities in social process and structure.  Strongly divergent practices in turn form smaller attractors within the larger attractor of the metropolis.  Patterns of homeness and homelessness would then be expected to show a variety of trajectories of practice, such as correlations between incidence of homelessness and existence of soup kitchens, availability of free shelter, locking of house doors, fencing of land, discriminatory zoning, ownership of small arms, or ownership of guard dogs.  On these social sites, the dying out of a transient can be the death of a person, as the dying out of a practice can be the death of a practitioner.  But given that a transient is a trajectory that does not span the attractor long enough or far enough to repeat, then how long or far is enough?  What causes one practice to persist and another to desist?

Prediction and Social Change

            Stating this question in terms of causation hastens the appearance of the issue of prediction which naturally arises in any attempt to apply to social issues a theory grounded and elaborated in numeric and physical experiments.  It is a fact of increasing significance for all branches of science that most of the systems we encounter are non-linear.  The non-linearity of social order may be understood as the interpenetration of contexts discussed in connection with the research of Ott and Sommerer.  This characteristic of interpenetration bears directly and profoundly on the possibility of using chaos theory mathematically to describe social science data.

            Social science data are derived from social phenomena and social phenomena are contextual.  If contexts interpenetrate, then social science phenomena have always already begun, in multiple non-trivial senses, before they are observed, recorded, and quantified in any particular social science sample.  The starting and ending periods of observations are dictated to the social scientist by the available data.  Assumptions can be made about how a particular person or situation got to where it is when observed, but those assumptions cannot give us precise, unique, quantitative conditions.  Since this situation obtains throughout the analysis of social science data, it is impossible to determine initial conditions of such phenomena with the uniqueness and precision necessary to use the established mathematical measures of chaos, such as spectral analysis, Lyapunov exponents, autocorrelation functions, power law distributions, and others (Kiel and Elliot 8-10, 51, 53).  If these calculations are not possible then it is impossible to assert with mathematical certainty and clarity that chaos exists in any particular set of social science data.

            Besides this limitation on the calculability of chaos measures, chaos theory has one other feature which strongly limits its quantitative applicability to social science data:  homogeneity.

            Contained perturbed fluids, amplified electrical charges, atmospheric gases, and chemicals in liquid mixtures all display a homogeneity which is precisely amenable to mathematical description but which is found nowhere in social life.  Mathematical manipulations, such as the construction of the Mandelbrot set and the generation of the Feigenbaum number, also have homogeneity as variations of the symbol system of mathematics.  However, “very rarely, if ever, are social systems comprised of identical components with highly homogeneous behavior” (Dendrinos 240-1).  The only way in which a comparable homogeneity can be obtained in social science data is to quantify some aspect of social life such as divorce rates, voter choices, and incidences of disease.  Once specific quantities are obtained then simulations can be constructed which show characteristics of chaos.

            However, the simulations all posit arbitrary, artificial initial conditions which do not correspond to or represent the ongoingness, the historicity, or the livingness of the phenomena from which the quantitative data are extracted.  For example, in a presentation of his universal map for studying the dynamics of human settlement activity, Dendrinos points out that “a change in parameter values or initial conditions can result in a new frame, m, potentially characterized by a qualitatively different dynamic…” (253).  No doubt there is no end to the abstract possibilities in such a model.  Indeed, according to Dendrinos, “one of the weaknesses” in current uses of chaos theory for mathematical modeling in economics is “that under slight but proper modifications in specification, these models can reproduce almost anything that the analyst wishes to produce through theoretical deduction” (238)!

            But what constitutes the initial conditions of human settlement or even of human action in the first place?  Is an initial condition the fact that a shaman read a bird’s entrails and directed a group to settle in a certain cave?  Or was it the fact that the group had only two days of food left and winter was coming on?  Or was it the appearance of a familiar star in a strange area of the night sky?  Or was it competition between a chief and a sub-chief over who was the best provider for the group?  Suppose that the latter was taken as the initial condition that accounted for the group settling in a particular cave.  In what sense, then, was that the initial condition?  Does calling it an “initial condition” imply that it had no history?  Isn’t it possible that the chief allowed the sub-chief to select that particular cave at that particular time because the chief had already decided to retire from active leadership, or because the sub-chief had promised certain material rewards?  In either case, there is another condition behind, before, prior to, or folded into the initial one.  Indeed, how is it possible to give any kind of precise meaning to the term “initial” in such a situation?

            There is a pervasive silence in the literature on the fundamental question of how to adequately and effectively translate the notion of initial conditions from physical and numeric experiments to social science observation, sampling, and description.  The appearance of chaos in mathematical simulations using quantitative social science data must therefore be viewed with extreme caution.  Certainly dynamics with chaotic characteristics can be generated from many different kinds of quantified social science data.  But is the chaos an artifact of the simulation or is it an explanation of the lived reality of social life from which the quantitative data are extracted?

            This kind of consideration has led Harvey and Reed to assert the following rule as their number one caveat about applying chaos theory to social science:

            1.  Predictive, statistical, and iconological modes of chaos modeling             should be restricted to those ontological levels in which collective             social phenomena can be legitimately treated as a statistically             aggregated phenomenon, that is, as being composed of additive,             numerable, and interchangeable individual units. (314)

            Indeed, since improvements in concrete social forecasting have not yet been achieved using chaos theory (Berry and Kim 216; Brown 128; Jaditz 86; Rosser 209), I am inclined to agree at this time with Dendrinos summary comment that the “single most important contribution mathematical chaos has made [to social science] is to demonstrate the possible presence of new dynamical features in social systems that theoreticians had never addressed before” (238).  Hence my purpose here in showing the radical utility of chaos theory for understanding social order rather than for describing social science data mathematically.

Extended Applications

            Social order which involves mixing and folding and goes in the extreme to cultural vaporization fits the definition of non-linearity and illustrates interpenetration of contexts.  Social order viewed in this way is chaotic.  Chaos as social order also provides a way of understanding the infinite degrees of freedom that characterize human actions.

            The infinitization of human freedom is not due only to some inherent characteristic of human nature, character or personality.  It is a function of the fact that human choices are always situated in contexts which interpenetrate to indefinitely large and complicated extents in time and space.  Each piece of another context or basin of attraction provides more scope for choice and each different piece brings more pieces with it.  Moreover, it seems clear that the only linear systems in social life are those like railroad tracks and contracts that require human will and energy in an attempt to establish and maintain order without variation, that is, without mixing and folding.  Boycotts, strikes, renegotiations of contracts and collusions between prisoners and guards show, however, that even in these high stakes’ social contexts there is no guarantee of linearity.

            When we leave the regimes of established and enforced lines, channels, and hallways and enter edges, transition zones, and liminal spaces, moreover, initial conditions of human trajectories cannot be determined with any certainty.  If they are, then there has been a deliberate and arbitrary reduction–collapse, renormalization–of degrees of freedom experienced socially as options.  Even with such a reduction, the infinities of preference open to humans throughout society reintroduce uncertainties which must again be reduced in order to satisfy the requirements of linearity.  This rhythmic layering of recursive oscillations, of mixing and folding operations, and of deliberate attempts at reductive linearization can be seen in four concrete social situations:  1.  Endangered Tongues; 2.  Moral Basins; 3.  Assassination; and, 4.  Cyberspace.

1.  Endangered Tongues.  Off and on since the late 70′s, I have done various kinds of projects with the Athabascan Indians in Interior Alaska.  One of these projects involved constructing a survey to gather the opinions of Tribal members on questions of indigenous language preservation.              There are nine different Athabascan tongues still in use in some form in the Interior of Alaska.  As a land area, the Interior is slightly smaller than the state of Texas, contains the major drainages of the Yukon, Tanana, Koyukuk, Porcupine, and Chandalar Rivers, and supports over forty villages–Tribes–whose inhabitants derive ethnically from earlier Athabascan peoples with mixtures of Inupiat and Yupik Eskimo, and Aleut Indian.  Most of the villages are accessible only by air, water, or snow covered ice.  The villages range in population from under fifty to nearly a thousand.  All of them have some kind of electronic communication with other villages and with towns and cities on the state road system and in other parts of the world.

            All of them have some kind of public school facility in which the official language is English.  English is also the official language of commerce, public affairs, and most recreational activities such as basketball and bingo.  In most Interior villages, only a small number of older people retain anything like fluency in a Native language, with a larger number being partial speakers some of whom have learned the language not in a natural family interaction but in some kind of classroom setting.

            On the basis of this situation, Michael Krauss, who has directed the Alaska Native Language Center at the University of Alaska Fairbanks, in Fairbanks, Alaska, for the past two decades, predicts that all of these languages will be extinct by 2055.  Krauss qualifies this prediction by the inclusion of only native speakers, that is, those who have learned the language as their first language from birth.  This qualification takes into account the fact well-attested by older Athabascan speakers that sounds once used in these highly agglutinative, rhythmical, and guttural languages have already disappeared or are too difficult for contemporary speakers to reproduce.  Along with a dying out of vocal ranges, the disappearance of a once well-marked distinction between a formal style of oratory and ceremony, and a vernacular style of everyday affairs, is affirmed by the same speakers.  The appearance of a “village English” further attests to the mixing ground with English in which the Athabascan languages are fading into a silent hue of memory.

            It is instructive, before trying to tie any of this to chaos theory, to note that the Interior Athabascans used to make rope from spruce roots, and heavy sewing twine–babiche–from moose skin.  They also used to catch fish in bent willow traps, shoot birds with bows and arrows, and kill charging bears on wooden spears with fire-hardened points.  Most of the older, non-metal technology has either completely disappeared or become pastime, show-piece, museum piece, or story line.  The newer technology, based on the metal, chemical, and plastic industries, has made all of the older tasks much safer in terms of risk to life and limb, easier and more efficient in terms of human exertion, more reliable in terms of success per attempt, and more productive in terms of quantities gained.  The newer Athabascan languages, derived from the older ones and adapted to a context in which information processing and transfer are far more important than reverence, ceremony, and maintenance of taboo, seem also to be becoming easier to learn and simpler in use.

            The attractor of Athabascan culture has changed.  Its phase space now includes multi-story office buildings with advanced electronic equipment in Fairbanks, satellite dishes with color TVs, and the latest in snowmachines and outboard motors in the villages.  The trajectories of an older, slower, more complicated language, and an older, slower, less reliable material technology, with hunting and gathering as their basin of attraction, do not span the new attractor.  The result is that they become transients with varying degrees and kinds of “death.”

            Languages that span the national and international artistic, political, economic, and military attractors are English, French, German, Spanish, Mandarin Chinese, Russian, Arabic, and Japanese.  The history of each language shows a contraction of state space with a subsequent decrease in diversity.  A contraction decreases diversity because, as transients die out, there are fewer possible trajectories on a particular attractor.  The unification of the Chinese language, for example, began over two thousand years ago.  The creation of a standard English, French, and Spanish was also achieved at the expense of many local variations some of which, like the Catalan and Basque languages, became smaller attractors with sufficient local energy to survive, but many of which have long since ceased to exist.  It is only in the last decade, according to my own sources in the region, that Athabascans of Interior Alaska have begun to consider unification as a language preservation strategy.

2.  Moral Basins.  Features of linguistic basins are displayed by moral basins.  The last century of life in Taipei, Taiwan provides a stunning example of cross-cultural contact and mixing.  The moral experience of young people in Taipei was the subject of my dissertation as well as of two articles ((2) and (3)) which condensed the content of the dissertation for a wider audience.  I take the position that the moral experience of young people in contemporary urban Taiwan–Taipei–can best be understood in terms of three interacting sites:  the family, the street, and the school.  On the basis of historical considerations that include the perdurant streams of classical Chinese and the intervening streams of European, Japanese, and American civilizations, the moral basin of each context or attractor can be characterized as family/hierarchy, street/fluidity, and school/competition.

            When young people in Taipei traverse, inhabit, and (re)create each site in the course of a day, they are the bearers of the pieces of each basin that recursively layer one another in ongoing oscillations of attitude and behavior.  They carry from the family a hierarchically ordered deference to older siblings and adults into the street and the school.  They carry from the school an egalitarian competition into the school and the family.  From the street they carry a fluid, individualizing sense of freedom and responsibility into both the family and the school.  As layered, recursive carriers of practices who are continually impacted by their peers and by adults, young people live social reality as porous.

            Porosity can be understood as a metric on the state space of society.  The degree of porosity–interpenetration, mixing/folding– is a good index of the degree of chaos in social life.

            The porosity of the space, moreover, makes it holographic in the sense indicated by Ott and Sommerer’s research showing that every basin contained pieces of other basins.  Connecting trails to other attractors in the social order of Taipei can be found in a small portion of that order, e.g., a classroom, a living room, or a bus stop.  For example, while bus riders in Taipei usually do not line up for the bus door, students in school uniforms, although off school grounds and out of the jurisdiction of school disciplinarians, often do line up.  However, relations among attractors and pieces of attractors are rarely linear; they are fractal in the sense of having fractured or fractional relations among parts rather than being integrally related in linear dimensions.  Porous social space is holofractic.  The possibility of prediction within a particular basin of attraction, such as a family or a school, decreases with the increase in porosity of the social life in which the smaller basin is embedded.

            Taipei has been one of the most cosmopolitan cities in Asia for almost a century.  A decrease in older indigenous Taiwanese or imported Chinese patterns has been happening simultaneously with an increase in patterns from other ethnic sources, whether these be technology, language, dress, dance, manners, religion, or marriage customs.  In language, for example, the written Chinese used in Taipei has become more complicated both because of the differing kinds of characters used there and on the mainland and because of the accretion of elements from other languages.  Again, as in Interior Alaska, a contraction of phase space, which signals the dying out of certain trajectories of practice that do not span the attractor of social change, happens together with an expansion of phase space as a birth in new contexts of new trajectories of practice representing various mixtures of the exogenous and the indigenous.

            An application of chaos theory to social issues, as exemplified by Taiwan and Interior Alaska, supports the findings of historical linguistics that there is no simple, inevitable path from older, more complex to newer simpler languages, or vice versa.  It also supports the findings of social science research that the increase in options for attitude and behavior is one of the main events in the complex changes in social order of the last century collectively known as modernization.  This is not a linear decrease in options until some point after which new, more plentiful options can be and are introduced.  Rather, there is a decrease in certain kinds of options which releases cultural energy for a simultaneous increase in other kinds.

            This crucible of contact with exogenous power which constrains and liberates, represses and releases, and destroys and amplifies indigenous power contains the interactions whose unraveling in theory will determine what kinds of predictability, if any, are possible in such spaces.  It seems unquestionable that a strong correlation exists between the availability of culturally unbound or unencumbered power, either coming in from outside sources or released from inside sources, and the appearance of chaotic cultural regimes.  Whether the culturally free power takes the form of guns, drugs and money, or communication, transportation and production technologies, it does not automatically and smoothly reproduce indigenous practices and patterns.  Its introduction becomes an intervention that induces interference patterns.  The interference patterns fold, bifurcate, and diverge into multiple orders or basins which, in a city such as Taiwan, can include new millionaires, depression and suicide, new environmental activism, unprecedented street crime, a clean, quiet electrorail system, and some of the worst air pollution in the world.  As the unprecedented, the novel, the new, and the unheard of increase in extent and frequency, complexity becomes chaos.

3.  Assassination.  A brief example from another country comes from Mexico, shortly after the assassination of PRI Presidential Candidate Luis Donaldo Colosio, in Tijuana.  Interviewed for the New York Times, March 27th issue, by Tim Golden, Jesús Cantú, “an editor whose independent newspaper” had been “firebombed two weeks” previously, shared a widespread feeling that the assassination had shown weakness in Mexico’s political system “that once seemed indestructible.”  In terms of chaos, such a change is emergent porosity.  The laminar state space of Mexico has articulated into turbulence with a dramatic increase in possible trajectories of social and political practice.  It is no accident or surprise, from the standpoint of chaos theory, that the Mayan uprising in the south happened shortly before the assassination.  As Cantú remarked, “You feel now like anything could happen” (Golden 3).

4.  Cyberspace.  The electronic trip is a dependent phenomenon–when the power goes out the trip stops.  As a dependent phenomenon it must constantly be recreated.  The qualities it has are the qualities given it by those who take, make, and use it–Aryans make it Aryan, environmentalists make it environmental, investors make it investing.  It does not have the independent existence of the natural, hardwired software known as imagination.  Why then does cyberspace exist at all?

            This question is easier to answer on the streets of Taipei than on the tundra of Alaska.  Taiwan has the second highest population density in the world.  When population density combines with multiple, flexible, increasing avenues of expression, new human spaces result.  When population density combines with limited physical space, such as an island like Taiwan, a nation like the United States, or a planet like the earth, compression takes place.

            Compression involves a multitude of actions upon actions, of foldings and mixings.  Compression destroys information and creates information.  In both processes, certain kinds of space are created in order not only to accommodate the destructive and creative processes but also to contain the destroyed and created information.  Where does a document go when it is trashed?  Where does a document go when it is cached?  Where does a document go when it is stored or saved?  Where does a document go when it is emailed, faxed, printed, or mailed?  Each process requires a certain kind of space.

            Compression creates space by contracting quantity.  Compression of human beings creates more and more finely faceted human spaces.  Simultaneously, the increase in human beings, the expansion of their personal spatial horizons, and the increase in their physical possessions create needs for more living space.  Humans now need more living space.  Many people are responding to compression by moving to more and more remote land areas, to outer space, and to the bottoms of oceans.

            Cyberspace is a new kind of living space which combines the remoteness of satellite transmission with the intimacy of home computers, and the standardization of hardware and software with the individualization of preferences in nearly every aspect of the medium.  It is continuous with play space, art space, recreational space, and ceremonial space.  Certainly cyberspace is a medium of communication.  Email is continuous with other communication media such as speaking, singing, dancing, signal fires, drums, letters, messengers, telephones, microwave, and fax.  But email is only a small part of cyberspace.  Impersonal, privately controlled, data transmission and self-stimulating cyberplay are two other major uses which show that cyberspace grows from a need for new kinds of unoppressed living space.  Indeed, the resistance of cyberusers to formal regulation shows how continuous cyberspace is with the traditional individual spaces of play, recreation, and expression.

The changes described above in languages, morals, politics, and human space are not linear, laminar, and sequential.  They are like a quiver of arrows being shot in all directions at once.  The basic attractor of reproduction in a cross-cultural context illuminates this phenomenon because people must continue to speak, dress, marry and so forth in order to survive regardless of the precise ethnic stamp of the language, clothing, or customs.  But if in the process of reproduction, available power increases at an increasing speed and available options multiply more quickly than older options can transform, then the phase space contracts and expands simultaneously with some trajectories dying out and others spanning the new attractor.

The older practices whose enactment connects indigenous power with exogenous power span the new attractor.  Those which do not, not even as museum or tourism curiosities, die out.  The newer practices whose enactment connects exogenous power with indigenous power span the new attractor.  Those which do not are resisted and excluded.  How long is long enough and how far is far enough?  In terms of human living arrangements it is a question of how people use the various kinds of power that are available to them.

            In physical terms, the onset of chaos in physical experiments is reached by means of adding certain kinds of energy to systems–chemical, mechanical, electrical, etc.–that are capable of different regimes of behavior.  These physical systems do not get to chaos by themselves.  They get there by way of receiving and processing energy as the quiescent water described above gets to boiling by receiving and processing thermal energy.  They are physically driven, deterministic systems.  They have regimes of behavior whose characteristics, including transitions to turbulence and to chaos, are determined by manipulation of certain parameters such as temperature, speed of rotation, and voltage.

            Numeric systems are more difficult to describe in concrete terms but they too are deterministic.  In processes such as the generation of the Mandelbrot set or of Feigenbaum’s constant, a finite numerical entity is subjected to repeated recursive layerings or foldings until typically bifurcatory oscillatory behavior occurs.  Again, the numbers do not get to chaos by themselves.  The “energy” of manipu

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