T. R. Young
The Red Feather Institute

and

James Yarbrough,
Texas Woman's University

August 11, 1998

This paper is dedicated to James Yarbrough, d. 1997.  James was a most promising grad student at TWU when he died of cancer.  He is greatly missed by family, friends and colleagues.

There are two problematics addressed in this work: first the ontological character of natural and social systems as an empiric referent answering to the concept of 'structure.' Three are analytic choices affect the degree to which a given series of events become a social structure: a) scale of observation, b) region in an outcome basin and c) stage in a bifurcation map. The second problematic in this paper considers the degree to which class structures/processes can occupy the same time/space region. In short, nonlinear feedback processes make it possible for differing structures to occupy the same lived space at the same time. The paper concludes by considering the degree to which class is a structural feature of complex societies.

A Bifurcation Map: The Transition from Order to Disorder

This essay, building on the new science, offers a way of thinking about structure in which the midline between reality and illusion; between actuality and apparition; between noumena and phenomena is reconceptualized. At the same time, the use of a plurality of structures having variable causal efficacy is required. Class structure thus may be determinative or may be subordinate in causal efficacy depending upon the character of feedback between class status and the dynamics of other structures.

Post-Structural Critique In post-structural sensibility, the search a grand theory which brackets all human behavior within one coherent structural system called a 'grand narrative' (Hassan, 1987a) or within a 'master narrative' (Lyotard, 1984) is simply not on. Marxist class analysis, Freudian theory, Islamic or Christian theology as well as Utilitarianism cum Choice theory of modern criminology are, all variously, an artifact of political desire of an 'author' or 'reader' who hide themselves behind, as Richardson (1988:203) puts it, '...the bramble of the passive voice.' In postmodern terms, all theory on nature or society becomes a 'readerly text' which, in its complexity, invites a rewriting at every reading (Rosenau, 1992:35). While accepting most of the post-structural critique, I want to lay out a view of structure which reclaims the concept to social theory. There is a way to read nature and society which helps one recognize the limits on truth saying.

Post-structuralists rightly argue that human beings extract, from a large array of data, just those facts which support their favored theory. Post-structuralists are correct in the assertion that structuralists commit epistemological sin by confusing between their favorite theory and God's Will or the Law of Nature. Post-structurals are correct when they assert that structural analysts subvert the knowledge process when they hide the raw and self-serving politics of human endeavor behind 'objectively' existing and extra-personal forces. Structuralists also abort human agency by pre-empting all possible futures with the one future set by the inexorable Law of that theory at hand. Theories which hold that the source all behavior is located in genes, or in original sin, or in economic formation are equally totalizing and equally appropriate topics for critique.

Postmodern critics are joined by modernist sociologists who still believe they can look at a social formation objectively and make truth statements with a high degree of validity, and in the looking see a decline in class status as a causal nexus in advanced industrialized societies (Nisbet, 1959; Clark and Lipset, 1991; Pakulski, 1993). Opposed to this reading of the data are scholars who see class as a powerful dynamic in such societies (Hout, Brooks and Manza, 1993). However, if, as is the case made here, those structures in nature and society do not fit the assumptions of modern science about structure and dynamics and thus vary in their geometry, in their linearity, in their causal (determinative) efficacy and at times not excluding of other causal agents within the same dynamical field, then postmodern critique becomes irrelevant. Arguments within the modernist critique of class are more difficult to sort out since, in complexity theory, the research design required to catch those varying dynamics has yet to be put in place. It is entirely possible that Marx, Weber, Hout and his associates as well as Nisbet, Clark and Lipset or Pakulski have sampled adequately and have caught the dynamics of class status as it exists in differing scales of analysis, in differing regions of an outcome field or, more likely at different phases of complexity.

The case made here, then, is that the concept of structure has enduring value, both to science as to those who would like to ground progressive social policy on the theory which mirrors structure. Complexity theory allows of truth statements upon which to found policy...however, those truth statements are very different from those grounded in the euclidean, newtonian, leibnizian view of structure and theory. Fractal truth values displace ideas of absolute truth/falsity. Truth values change as dynamics change. Truth values expand and contract as scale of observation enlarges or diminishes. In all this, predictive truth and thus some limited human agency based upon it are possible (Young, 1993). The task of postmodern science as well as postmodern politics is to do the kind of research which gives us a larger, more modest view of that which is and that which is possible.

Then too, this new science of complexity teaches us that the notion of 'fact' itself becomes relative to the scale of analysis. However honest differences in the reading of nature or society is possible since scale of analysis is also a human choice. In brief, what is process of unrelated objects at one scale of observation becomes a structure having depth, breath and height at another scale of observation. Social structures are experienced by individuals and groups as process: one feels the touch of a fist; one hears the music of language; one sees the data on paychecks, bills and one reads the words about one's own life in letters, books and magazines but one never directly experiences the structure of gender relations, of friendship relations, of class relations or of monopoly capital. From this very Humean point, one can question the facticity of such structures. The reality is that human beings cannot infer class, gender, caste or race from and only from the data of individual experience. Yet those who would like to build their own practical action in the world do well to 'read' the patterned behavior of such individuals and groups as 'structure' and to organize every day policy around it.

Finally, the question of structure is shown to be far more complex than modern science, grounded on euclidean geometry and newtonian linearity, permits since the thickness and thinness of a fractal object varies with its dynamical phase (Young, 1994). There are five such phases in a bifurcation map. As a system changes from one pattern of behavior to another, the configuration of that pattern changes dramatically. In terms of the truth value of incompatible findings (say those of Pakulski on the one side and those of Hout, et.al. on the other), it is entirely possible that Pakulski has sampled a passing dynamical phase in which a key parameter has changed enough to force a re-organization of class relationship while Hout and his colleagues are sampling a different run of events which testify to the continuing efficacy of class status as a significant part of social life. Pakulski has mentioned several parameters which might be operative in changing from one dynamical state to another (1993:284).

NONLINEAR DYNAMICS AND FRACTAL STRUCTURES Helpful to a resolution of the issue whether structures exist or not; are totalizing or not; are determinative or not, is the concept of the fractal. In the simplest terms possible, a fractal is an estimate of the degree to which a given object occupies the space available to it in its periodic cycles. This definition would not raise any eyebrows in modern science were it not for the fact that fractals may occupy fractions of a dimension; hence the name. More than that, what appears to be a solid body at one level of observation turns out to be mostly empty space at another level. If these two attributes of complex systems were not enough to create confusion about the facticity of a given collection of events we want to call structure, the fact is that such collections may take on any one of five different dynamical states in which the configurations of events in the slice of nature or society in which we are interested vary dramatically as between dynamical phases in what is called a bifurcation map of its dynamics.

If we take the position that only those objects which are the object of empirical experience exist as 'facts' in the world, the postmodern critique of structural analysis makes great sense. Yet we 'know' that such social structures exist. The question then becomes, How is it possible that we can perceive as structure that which is only process? Chaos theory, using the concept of the fractal, suggests that the boundaries of a social structure system may be too loose and too open for the specific individual to sense them. We are quite able to sense fractal structures in which the boundaries are too small for us to enter but for those in which we are, ourselves member parts, palpable sensory tasks are beyond our capacity. We are quite able to sense and measure atoms, molecules and tissues yet, were we to change scale and observe such entities on their own terms, the open spaces between units would exceed our grasp as direct and tangible perceptors.

In terms of class structure, when one looks at the lived experience of particular persons, one sees only process; people talking, people working, people buying, people eating and driving. When a worker is laid off, one sees only a person called a supervisor handing a pink slip to someone called a worker. When one steps back, looks at the number of workers laid off, the amount of goods stored in factories or warehouses, the changes in profit and loss over an entire industry or an entire nation, one can 'see' larger patterns emerge. The owning class, having its own pattern of expenditures simply cannot afford to pay workers when production had exceeded demand. And, absent income, workers cannot afford to buy the goods already produced. From all this, one can 'see' the operation of capitalism as structure complete with class relations while, looking at persons two at a time, one can see only quick and connected processes of talking, handing, walking and presumably, feeling. Structure dissolves into process at the scale of lived experience.

Figure 1 shows the evolution of a fractal attractor called a torus as cycles of behavior of some system is mapped in phase-space at given points over a given cycle of its behavior. It shows the emergence of structure from process. Figure 1 could be a mock-up of the cycles of employment/disemployment produced by flucuating market dynamics for a given firm or set of firms. The first cycle in Figure 1 might depict the points at which demand for labor is set at weekly points in a yearly cycle. The second figure might represent the demand for labor for several such firms in a given year while the third figure coming from data collected over a period of say, ten years, displays enough stability to warrant the concept of structure.

The Ontology of Process It is the larger structure of patriarchy while unseen, unheard, ungraspable to human sense of particular men and women, does in fact, shape and preshape gender relations in the single household. Built into the normative structure of religion, business, school, government and family, class dynamics can be seen only by looking at the whole and seeing process. Process is an abstraction of a pattern from all the single separate acts which are the immediate data of experience. Class as process has no separate embodiment apart from the actions of those who live out the norms. In order to treat a process as if it were a concrete thing having its own ontology; its own 'thingness,' it is necessary to abstract, out a billions of unit acts of situated people, some sub-set of unit acts, to grasp the myriad patterns therein, to treat each pattern as if it had a form of its own and then to give it a name. The name we give it is structure.

If we examine class structure in terms of the fractal concept, we understand patriarchy as:

a. a complex set of self similar unit acts

b. over a broad spectrum of institutions

c. emergent anew with each interactional occasion.

Given this definition, patriarchy consists of billions of unit acts within a given society. Each unit act is slightly or greatly different in any given iteration of any given interaction between any two persons defined as man or woman. Units acts can differ greatly across social institutions; thus the nature of the unit acts which embody patriarchy in the home can be very different from the unit acts which embody patriarchical relations in the shop, office, factory, church or school.

If we were to conceptualized patriarchy in the home as fractal, we would see an outcome basin of the sort depicted in Figure 1. We can think of patriarchy as an instruction which mediates each unit act of eating, dressing, talking, making love, rearing children, making decisions or receiving visitors. We can think of eating, for example, as another, different, set of instructions about what kind of food to eat, what time of day to eat, size of portion, rhythms of talk and response as well as seating arrangements.

Patriarchy in the home then is comprised of two complex sets of instructions which mediate any given iteration of any given meal. Patriarchy can be conceived of as a stable set of instructions which mediate another fairly stable set of instructions to produce each and every unit act in a house hold.

Patriarchy at work likewise is comprised of another group of two mediating instruction sets which combine in very differing form to produce unit acts relative to wage determinations, to job assignments, to language usage, to dress code as well as to patterns of deference and other forms of demeanor.

Were we to fashion an outcome field in which the outcomes of two or more groups of unit acts were charted, we would find a very complex outcome field of the sort depicted in Figure 2. Notice each fractal clusters in one region of phase-space yet each set of unit acts are qualitatively different from patriarchical relations in another behavioral domain. At no time is the boundary between any two domains completely and unambiguously separate. Many of the unit acts found in one domain are self-similar to the unit acts found in another domain. Thus in a factory, the clothing women wear might be the same or similar to the clothing worn at home in house or field. The language style might be same or similar to language in shop or market. A woman might say, 'Hello, love' to men in any of several interactional matrices each iteration of which has similar meaning except in the home where its meaning might well be qualitatively different from similar unit acts of greeting elsewhere.

In topological mathematics, the smaller the value of a fractal, the more sharply delineated are its boundardies. Thus the behavior of a pendulum describes a very tight point in a portrait of its dynamics in phase space. A torus has a slightly looser portrait while a butterfly fractal occupies a lot of the phase-space available to it. We would have little trouble treating the portrait of a point attractor as an unity rightly reified but we would have a great deal of trouble making and sustaining a claim that a butterfly attractor had unity. We can see space within and between any two iterations of any given unit act. We are tempted to deny thingness to such shapes since they do not have clear and definite boundaries.

However, the purist of pure empiricists would have no trouble counting a tree or a bird or a human as a thing but, if one were to change scale of observation, the thingness of the tree or bird would be lost to sensibility and thus to facticity. As one changes scale of observation from organic to molecular to atomic to quantum scales, things lose their boundaries and exist only as process. An electron is the process that energy waves makes when they intersect; an atom is the process that electrons and other particles make when they go about their separate business. A molecule is a process of atoms always changing, always vibrating, always in semi-stable exchange of parts. A tissue is even more a process as electrons, atoms, molecules and cells come and go; in the course of a month or so, the entire set of atoms which make up a tissue may be exchanged for another entirely different set yet the tissue remains as an empirical fact.

Absent sharp boundaries, any slippage in causal efficacy has to be explained, in the modern science paradigm, by intervening variables not yet conceptualized, measured and correlated to the dynamics of a system. Chaos theory does not require recourse to missing variables; nonlinearity is a feature of the whole system. There are no missing variables to seek since causality is not linear.

When one accepts that process converts into ontos as one changes scale, one concedes that there is a great deal of latitude in selecting out of an infinitude of unit acts at the human level of perception, one, two or ten groups of units acts; giving each one a name and treating it as a structural feature of a society. Those in the postmodern camp appreciate the subjectivity in such selection and assign the human hand and wit great responsibility for all the conceptual categories used by science or poet.

Resolution of the dilemma is possible. One such resolve is offered here and in other related work. In brief, Chaos theory, with its concept of the fractal and its emphasis upon scale offers the physical scientists an entirely new vision of natural and social systems. In that science, distinctly postmodern, iterations of a system over time take on a fractal facticity. That facticity begins to affect other systems in the mediate time-space region and, at quite specific points, produces nonlinear change in an outcome field. Those moments of qualitative change, entirely foreign to modernist visions of system dynamics, entail the generation of new outcome basins within an outcome field for similarly situated systems (Young, 1991a). Causality thus fades, blooms, fails and transposes within the logic of nonlinearity.

Concommittant with Chaos theory and its nonlinear dynamics and expanding outcome basins, Symbolic interaction Theory retains the human hand to the constitution of social facts. In this theory, social facts emerge out of a self-fulfilling prophecy in which an idea of a social fact is set forth by means of any number of symbol sets: voice, clothing, body talk and behavior. Shared understandings about the meaning of symbols permit the coordination of behavior such that an idea pronounced as a social fact, takes on a varied facticity. That which is a distinctly personal creation at the human level of action and preception becomes a distinctly social creation at the level of groups, institutions, and societies.

Symbolic interaction as theory has been around for a long time in various forms. What is new is that the iterations of reality creating interactional processes produces social ontos with fractal geometry (Young, 1992b). Those who look for clear and unambiguous boundaries for social structures do not find them and, not finding them, are reduced to appeal to those entities which, at the human scale of observation, do in fact have sharp and distinct boundaries and thus can enter into a causal scheme of explanation. There is another way to view the location and efficacy of causality.

The Location of Causality When one insists that there is a unitary process which takes definite shape, form and substance, one joins with the structuralists and reifies structure. In such reifications, causal agency is assigned. In arguing for the factual existence of the class structure of the structure of patriarchy, one sets up an entity which can enter into a causal field and, in its own right, affect outcomes. Thus patriarchy is said to produce battering men or class is said to immiserate workers. In so doing, human subjectivity appears to disappear from the creation of fact and the story of history.

If we changed our view of causality to entertain the idea of fractal causality, it would be possible to accept that structures do emerge out of a set of unit acts, take on causal efficacy of their own but do not exhaust a causal matrix. In fact, a view of patriarchy as a 'system' with partial causal efficiency would permit one to retain causal agency for situated human beings in producing their own social life worlds. In a concrete situation, situated men and women reproduce the structure of patriarchy by their unit acts while their units acts, taken as a collective, affect the probability that still other people can do still other things in still other domains of life. Thus, given a well institutionalized patriarchy, the possibility of a set of employers drawing on the female population to expand their workforce or to drive down wages is sharply curtailed.

As new domains of life appear, patriarchy as system, preshapes the outcomes of interacting human beings who, absent patriarchy, might well fashion a differing set of outcomes through interaction. As hospitals appears, patriarchy assigns some people as nurse and some as doctor. Even through both men and women are perfectly competant to nurse or to doctor, still patriarchy as system, mediates role allocation. As primary school appear on the horizon of history, the same causal efficacy of patriarchy as system affects role allocation and interactional matrices in school: women become teachers, men administrators. When factory replaced cottage as the location of manufacture, patriarchy sent men out to wage labor and keep women at home.

As long as people lived in agriculture societies, someone had to stay home, tend the animals and crops as well as supervise the children. Given patriarchy and given a cash economy, it was likely that someone would enter the paid labor workforce; patriarchy gave preference to men. One should note that such paid labor was no great benefit over which men and women might struggle. Working hours were long and working conditions dangerous and hard. Patriarchy, then, has causal efficacy at the scale of the whole system while individuals retain their own causal agency in the production of household or other activities.

The causal efficacy of patriarchy itself can vary. Given new technologies and new economic conditions, situated men and women as couples, might well change the weight assigned to the set of instructions reproducing patriarchy and decide, one couple at a time, that a women might try to enter the paid labor force. Figure 3 depicts a tongue on a torus in which some couples move toward a new gender relationship in which women gain economic power by virtue of the wages they earn in shop, office, factory, hospital or classroom.

Given a slow increase in the number of couples who so decide, there may come a time when new, more democratic domestic arrangements emerge and are institutionalized. Chaos theory sets such bifurcations points very precisely. A set of numbers called the Feigenbaum numbers encompass the fact that, at a specific point, a small change will produce a large effect. In the theory of causality set forth here, both small and large changes are absorbed by patriarchy as a instructions for interaction. Such dynamics are, in causal terms, nonlinear. Then, at specific Feigenbaum points, qualitative change occurs, a new causal matrix appears and, in this instance, patriarchy loses causal efficacy.

In Figure 2, above, one can see distinct groups of unit acts in which one set of instructions, here called patriarchy, mediates behavior along with another set of instructions to produce situated human activity via symbolic interaction. Really existing systems are still more complex. If we return to the factory or shop wherein men and women work together in patriarchical relations brought over from domestic gender relations and informing economic relations, we must note that there is still another set of instructions which mediate the behavior of bosses, managers, owners, stock-holders and whole economies. Profit is the name of the game for modern economic activity. Patriarchy is an obstruction to profit maximization in every store, shop, factory, office or market.

If we are to apply the ideas of Chaos theory to such social situations, it is necessary to account for the continuing presence of both patriarchy and capitalism in the same social occasion. It is immediately clear to any manager or owner that profit is served by anything which will lower wages. Given patriarchy, it is sensible to hire women on two counts; first patriarchy justifies lower wages and secondly, any thing which expands the labor forces reduces the social power of organized labor. A surplus labor force can be used to drive down wages and to defeat labor actions. Women, children, migrants or machines can be used against efforts on the part of workers to organize and demand higher wages, safer working conditions, retirement plans or vacation benefits. In these days, foreign labor markets are used to force unions to give back benefits won when labor was scarce.

Yet patriarchy is, in many respects, inimical to profit. Any system of preference in which men and only men can buy, sell, use or own a produce restricts the market. A firm can sell twice as many cigarettes, cars or homes if women can be brought into the market place. Marriage itself is an unnecessary constraint on the market. If men and women stay single and, at the same time, leave their family of origin, they will need twice as many dwellings, refrigerations, stoves, televisions, cars and other household goods.

The question becomes, how can patriarchy survive inside a capitalist system since the instructions set by the profit motive are qualitatively different from those set by the structure of male preference. From Chaos theory comes the idea of the soliton in which one structure maintains its integrity within or while passing through another different structure.

Solitons and Social Structure The fractal nature of system boundaries makes it possible for more than one social structure to occupy the same time-space continua. Thus in a supermarket, a factory, an insurance office or a classroom, differing structures, given open and semi-stable boundaries, may be found. If one thinks of class, racism, patriarchy, and bureaucracy along with religion and ethnicity each as separate solitons occupying the same social space, then the picture one has of causality is one in which one or more such solitons maintain integrity even though logically incompatible and dynamically incoherent. Those in the postmodern camp who oppose 'totalizing theories' such as the work of Comte, Spencer, Marx, Parsons or Homans will find much of interest in the concept of the soliton.

Those who write of the multiplicity of factors which give structure, pattern and causality to human behavior such as Weber, are given support by the fractal geometry of nonlinear regimes. More concretely, there may be several social structures which co-exist side by side in the complex dynamics of work, school, church and play. For our purposes, class struggle, patriarchy, ethnicity, protestantism, capitalism, and bureaucratic state welfare may occupy the same time-space continua. It is not a matter of chosing as between them to generate a coherent and parsimonious theory of human behavior but accepting that all these and more can exist together in a behavioral framework such as a school, a factory, a church or an entire society.

If one uses the concept of the fractal to sort out the causal dynamics of a behavior framework, one need not participate in an argument between a marxist and a weberian over which 'structure' is determinative...it is entirely possible, given each as a fractal for each to be a product of sentient human beings and, in turn, affect the behavior of other sentient human beings as a structure.

If one use the concept of the fractal, one can accept that there may well be varying causal efficacy of one's favorite structure (class, race, gender, bureau or religion] depending upon the nature of the feedback loops between them. Indeed a particular kind of a fractal, the soliton permits a given structure to pass through another structure with little or no reciprocal causal efficacy.

Status bound social identities may exist coterminously with occupational identities, religious identities and/or ethnic identities. The integrity of such social forms depends upon the nature of the feedback loops between them. If the feedback loops are negative, one social form will tend to displace a second form; thus gendered social identities and the normative behavior required by them can be smothered by an occupational identities if the feedback between the gender identity and the occupational identity is negative and linear.

In a particular case, a male employee of a bureaucracy may be required to set aside the normative structure of his gender when working with females. If the administrative structure of the bureau does, in fact, apply the rules with rigorous rationality, any effort on the part of the male to exercise authority by virtue of his status as a male will be damped. In prisons, schools, marketplace, and government agencies, given a goal; given a set of rationally coherent rules with which to achieve those goals and given the rational implementation of those rules in every case which comes before a bureucratic employee, status based social identities cannot, will not be permitted to intrude into the dynamical field at hand. Teachers may not act upon their gender identity with students; police may not act upon their kinship identity with offenders; cashiers may not act upon their religious identities with respect to the commodities sold. All this, if and only if interaction is, in fact, rational.

On the other hand, religious, gender or kinship identities, if allowed to fill the space available to them, can and would affect the integrity of the social form we call a bureaucracy.

An enterprize would become bankrupt if employees shared out the resources of the firm with their relatives as required by the normative structure of family.

Given the goal of retribution and status degradation, a prison would lose its character of a punitive and shameful place to go were guards, wardens, and counsellors insist upon using a religious social identity upon which to ground daily interaction.

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