|The Impact of Chaos on Science and Society (UNU, 1997, 415 pages)|
|16. Chaos in society: Reflections on the impact of chaos theory on sociology|
This paper draws heavily on three previous publications (Mayntz 1988, 1990, 1991), some passages from these publications having been adopted virtually unchanged.
Over the past decades, attention in the natural sciences has increasingly turned to phenomena that defy analysis in terms of the traditional physical world view with its assumptions of linearity and reversibility, i.e., to the behaviour of systems remote from equilibrium and to discontinuous processes resulting from nonlinearity. After the recognition of the stochastic nature of many real processes, the attention paid to nonlinear processes means a further step away from the traditional mechanistic world view. Nonlinear systems display a number of behaviours that can be widely observed in the natural world. Their state variables can change discontinuously, producing phase jumps, i.e., sudden changes of state, as in the phenomenon of ferro-magnetism or in superconductivity. In such discontinuous processes, threshold and critical mass phenomena often play a decisive role. A threshold phenomenon exists where a dependent variable initially does not react at all, or only very little, to continuous changes of an independent variable, but beyond a given point it reacts suddenly and strongly. The threshold may be defined by a critical mass, e.g. the number of particles of a specific kind that must be present before a reaction sets in, but other kinds of threshold also exist. There are phase transitions from order to disorder and in the reverse direction. The behaviour of nonlinear systems can become completely irregular - or "chaotic" - if the values of given parameters move into a particular range. On the other hand, nonlinear systems can also move spontaneously from disorder to order, a stationary state far from equilibrium; this is called a dissipative structure, or self-organization. Furthermore, systems characterized by nonlinear dynamics can display a specific kind of irreversibility, i.e. hysteresis (path dependency of phase jumps), and a specific kind of indeterminateness expressed in the term bifurcation: a point where a trajectory can proceed in different directions. The analysis of nonlinear dynamics has been enhanced by the development of new mathematical methods, as such René Thom's catastrophe theory, and by the computational power of modern EDP,1 which for instance made it possible to discover and formalize the phenomenon of (deterministic) chaos.
The label "chaos theory" is presently being used both in a narrower and a more comprehensive sense. The narrowest interpretation of the term equates it with the mathematical theory of deterministic chaos (and its applications), and hence with the preconditions of a phase transition from order to disorder in nonlinear systems. In a wider interpretation, chaos theory may refer to discontinuous processes moving either from order to chaos or from chaos (or disorder) to order; the term would thus also cover phenomena of self-organization. Sometimes, the term chaos theory seems to be used in an even wider sense, referring to the whole field of research into nonlinear dynamics of non-equilibrium systems. In this paper, the second understanding of the term "chaos theory" is used. I shall be considering discontinuous processes, or phase transitions, going in both directions - from order to chaos and from chaos to order. However, I shall rather use the terms self-organization or nonlinear dynamics except where we deal with phase transitions from order to chaos, the narrowest meaning of "chaos theory."
The following argument can be summarized in the form of a few theses:
1. Natural science theories of nonlinear dynamics were not necessary to turn the attention of social scientists to phenomena of sudden disruptions of order and system breakdown.
2. Natural science theories and models of nonlinear dynamics have nevertheless had an impact both on formal modelling attempts and substantive theorizing in sociology.
3. The potential relevance of natural science theories of nonlinear dynamics lies in the promise to gain a better understanding of discontinuous changes at the macro-level as a consequence of micro-level processes.
4. The nature of social reality nevertheless seriously limits the potential applicability of natural science models of nonlinear dynamics.
Human societies obviously display all the characteristic features of nonlinear non-equilibrium systems: unpredictability due to complex interdependencies and recursive processes, hysteresis, phase transitions, and critical mass phenomena. Even where sociologists have tried to establish and measure causal relations between two phenomena, e.g. between a specific social condition and a specific kind of behaviour, they have at best discovered stochastic regularities, with correlation values that very rarely move into high ranges. As for the phenomenon of chaos, social theory has always started from the (implicit) assumption that due to the existence of human volition, disorder is the hypothetical natural state, and has consequently been concerned primarily with the emergence of social order. This had already been true of social philosophy before the advent of sociology proper; thus, Hobbes explained how the state was created as a means to curb the chaotic war of all against all that characterizes the natural state. Later, the sociologist Emile Durkheim found the basis of social order in the conscience collective, while Max Weber pointed to traditions, values, and interests as the societal factors producing social regularities - without need to refer back to physio-psychological concepts such as fixed, innate reaction tendencies.
Social order, moreover, has always been considered precarious, not only in sociology but in age old practice. Transitions, and often very sudden transitions from order to disorder are ubiquitous in social life. From time immemorial, man could not fail to see that social order is permanently in danger of collapse. Rapid and radical losses of a state of order can be found at every level of social reality - from marriage disruptions over company failures to the destruction of political regimes. In contrast to gradual transformations, such a sudden collapse of social order is followed by a period of turbulence. Social processes become erratic, patterns of conventional behaviour dissolve, latent forces become manifest, and mass behaviour reigns where social interactions used to be normatively controlled; in such a turbulent state, future developments are largely undetermined and subject to the influence of accidental events. This insecurity of social order has not only motivated attempts to control disorder and turbulence. The ubiquitous experience of social discontinuities has also meant that the world view of Newtonian mechanics has never been an accepted model for the representation of social reality.
The dominant concern of sociologists with the problem of social order has indeed meant that they have often focused on the preconditions of stable social states. Nevertheless, they have also dealt with many instances where a state of order suddenly breaks down. At the macro or societal level, the outbreak of revolutions has attracted the attention of sociologists - whose very discipline, sociology, is rooted historically in the French Revolution, an event that most of the first generation of sociologists explicitly dealt with. More recently, political scientists have studied the breakdown of democratic regimes (Linz 1978). Simple social discontinuities, i.e. the irregular change or sudden break in one particular variable, have been the object of research on various kinds of collective behaviour - panics, mass mobilization in political campaigns, social movements, and the outbreak of violence (see Tilly 1978). At the social meso-level, the breakdown of organizations, man-made disasters and catastrophic disruptions in the functioning of large socio-technical systems have been analysed (see for instance Turner 1978; Perrow 1984). The extensive literature on such phenomena, however, is largely qualitative, inquiring into the causes of such events and the basic social mechanisms underlying them. It is therefore an open question to what extent natural science models of discontinuous processes in nonlinear systems can be used to describe the kind of social processes alluded to.
In the development of modern science, the dominant paradigm of Newtonian mechanics was first challenged by classical thermodynamics, which introduced the notion of basically irreversible processes. The theory of dynamic non-equilibrium systems has in turn superseded classical thermodynamics. This second paradigmatic revolution started with many initially separate developments in different disciplines, including the mathematics of nonlinear dynamics - catastrophe theory and deterministic chaos. These theoretical developments in the natural sciences have increased the potential relevance of physical theories for sociology.
In sociology, borrowing from the natural sciences has a long tradition. Particularly common were attempts to picture society as an organism. Organismic analogies inspired Herbert Spencer in his analysis of social differentiation. From there, an unbroken line of sociological theorizing about the structure and development of social systems can be traced to the very present. Physical analogies have had a much weaker impact on sociology until recently. When sociology developed as a new discipline, there were occasional references to "social physics," but the mechanical world view with its assumptions of reversibility and linearity limited the potential relevance of the physical sciences to sociology. This changed first with the ascendance of general systems theory, cybernetics, and information theory. In sociology, it is particularly the systems theory of Talcott Parsons that reflects these influences. The growing interest of natural scientists in the analysis of nonlinear dynamic systems has recently stimulated a new wave of borrowing from the physical sciences. This influence has been twofold. On the one hand, the mathematics used to analyse and represent nonlinear, discontinuous processes have influenced sociological efforts to model social processes formally; on the other hand, substantive theories of the behaviour of natural non-equilibrium systems have stimulated social science theorizing.
Efforts to construct formal, particularly mathematical, models of social processes have always been stimulated by the availability of analytical methods, quite apart from the influence of any substantive natural science theories. Thus in the 1950s and 1960s, the development of mathematical graph theory and the mathematical theory of higher transition probabilities characteristic of Markov chains have stimulated social scientists (e.g. Harary 1959). There have also been attempts to develop formal models of discontinuous processes that were quite independent of any influence from natural science theories. In the simplest case, a discontinuous social process involves the irregular change of a single-state variable, which may suddenly escalate or plummet, or display "chaotic" changes without any visible pattern. There are numerous societal characteristics that develop discontinuously - the crime rate, the number of cases of collective violence registered annually, the divorce rate or the frequency of strikes. However, sociologists have been less interested to construct formal models generating such fluctuations than they were to develop theories explaining the occurrence of crime, divorce, or violence in qualitative terms. In contrast, formal modelling has been variously applied to mass behaviour (McPhee 1963). The diffusion processes that characterize mass behaviour can be continuous as well as discontinuous. Continuous diffusion models were especially applied to the spreading of various kinds of innovation, while discontinuous diffusion processes are typical of epidemics, social and political mobilization, and the development of riots and panic (for an overview see Mayntz 1988). In such processes, the incidence of specific types of behaviour (throwing stones, running away, etc.) changes irregularly, displaying sudden take-offs, escalating, or coming to an abrupt halt. The corresponding modelling attempts were independent of any influence from natural science theories.
This is no longer true of recent efforts to model discontinuous social processes with the help of mathematical catastrophe theory. Developed by René Thom (1972) and elaborated by Zeeman (1977), this theory was meant to provide a mathematical instrument for dealing with situations where the continuous variation of one or more parameters leads to sudden changes in the behavioural (or outcome) variable. More specifically, catastrophe theory is concerned with the classification of singularities of smooth functions. Within a given family of functions that differ in the values of the parameters, each function can be characterized by the singularities (minima, maxima, saddle points) it displays and can be categorized accordingly. For certain types of functions it has been observed that with incremental changes in the value of one or more parameters, the functions in a family "jump" from one category to another; they are therefore discontinuous in terms of a specific property (i.e., the number and characteristics of singularities).
Obviously, the sociological application of catastrophe theory must have been very tempting in view of the observation that seemingly small disturbances will often cause a social or an economic system to enter into a state of instantaneous, radical change, or even to collapse. In fact there have been attempts to develop social science applications immediately after the publication of the theory. However, it is obvious that a catastrophe in the mathematical sense just spelled out bears only a superficial resemblance to catastrophes in the colloquial sense - system breakdowns with severe consequences for people directly or indirectly affected. Above all, it would be erroneous to believe that the mathematical formalisms of Thom's catastrophe theory could directly help us to understand the causalities underlying social catastrophes. Before the mathematical theory can be applied, a number of assumptions must be made that are highly technical and difficult to translate into properties of real phenomena and their interrelationship. The utility of catastrophe theory hinges on the possibility to give a precise empirical meaning to the control and behavioural variables and their interactions. In attempts to apply catastrophe theory to social or economic phenomena, this is often not possible, so that the model transfer remains at the level of a mere analogy, which, moreover, is highly speculative as far as the underlying causal theory is concerned - a practice harshly criticized already by Sussmann and Zahler (1978). Some authors have rightly stressed that catastrophe theory is nothing but a mathematical method of analysing and representing a specific type of mathematical function, and have admittedly used Thom's topological models in a merely illustrative way (e.g. Bühl 1984). Others, however, have used the graphic (topological) representations that Thom uses to represent the singularity profiles of a family of mathematical functions with incrementally changing parameter values, by attributing directly some specific empirical meaning not only to the parametric dimension, but to all dimensions of the geometrical plane - in spite of the fact that in Thom's theory the geometrical plane does not display changes in a state variable of the underlying function directly, but only changes in the categorical property of functions in a family. One example is Brian R. Flay (1978), who interprets Thom's geometrical models in terms of attitude change. What results from such attempts at application are hardly more than metaphorical curve-fittings at the level of aggregate or outcome variables that do not explain why and at what point a threshold is passed and a phase transition occurs in reality.
This does not mean that catastrophe theory cannot be applied to social and particularly to economic phenomena, provided the system variables and parameters as well as the formal mode of their relationship can be given strict empirical meaning. This presupposes the existence of a substantive theory of the underlying empirical relationships linking control and behavioural variables, which can be transformed into a quantitative model. Thus, Zahn (1979) has tried to apply catastrophe theory to economic phenomena such as instabilities in financial markets or discontinuities in consumer behaviour, but he emphasizes the difficulties of going, on the basis of existing empirical knowledge, beyond a vaguely illustrative use of the models. Casti (1982) succeeds in developing a formal model of changes in the growth rate of housing units in an area over time in a mathematical equation containing two (empirically interpreted) parameters. He can show mathematically that for specific combinations of parameter values, the development of the growth rate, i.e. the mathematical function governing it will enter into a non-equilibrium state, either increasing suddenly or crashing. In a second application, Casti takes military action as the behavioural output variable; here functions that do not lead to an equilibrium state represent conflict erupting into war.
The theory of deterministic chaos has so far been used less often to model social processes. Chaos, i.e. irregular, unpatterned change in a state variable, has normally been interpreted as the consequence of uncontrolled or random external disturbances or as the consequence of a high degree of complexity (very large number of variables and parameters) in nonlinear systems. These two categories of explanations for social irregularities seem implicitly to dominate in sociological discourse. Essentially by using computers to solve nonlinear equations, it was discovered that irregular (or "chaotic") behaviour can also occur if the parameter values in a relatively simple nonlinear system fall into a specific range (Schuster 1987). These processes are deterministic in so far as no random external event is assumed to intervene; instead, there exists a well-defined set of equations generating the development over time.2
One of the few examples of social scientists attempting to apply chaos theory is Albach (1988), who has used it to model the "death" of firms by insolvency or bankruptcy. In the model, real turnover is assumed to depend on research intensity and the desired growth rate. Albach shows that for specific combinations of research rate and growth rate, the economic development of firms will result in either continuous growth or contraction, in various patterns of decreasing oscillations, and - for a small range in the combined values - in a completely chaotic movement that eventually passes the insolvency limit. With a continuous, incremental change of the decisive variables, the mathematical system representing a firm will thus go through a pattern from continuous over periodic oscillations to chaotic, irregular movement. It is surely of great importance for social scientists to understand the nature of such deterministically chaotic systems, especially where chaos might spell system collapse or war (Grossmann 1989). It is doubtful, however, that many observable social processes are amenable to be modelled as a nonlinear system that generates chaotic change of a focal state variable; we shall return to this point later.
In addition to natural science (and mathematical) theories of discontinuous change from order, or patterned movement, to disorder or chaotic movement, the mathematics developed to analyse self-organization phenomena in nonlinear non-equilibrium systems have been used in attempts to model social processes. Of particular importance in this connection has been Haken's synergetics (Haken 1978). Weidlich, himself a physicist, has for instance worked on the formal analysis of migration (Weidlich and Haag 1988; see also Weidlich and Haag 1983); in fact, the development of spatial structures as studied by human geography seems particularly amenable to this kind of analysis. Another example is the work of Gierer, who has modelled the development of economic inequalities as an autonomously generated structure in a social system (Gierer 1981). Erdmann and Fritsch (1989) have modelled processes of political opinion formation and of electoral behaviour. Erdmann explicitly connects his work to Haken's general principle of synergetics, which treats collective phenomena in multi-component systems whose elements produce emergent effects through their interactions. This "basic behavioural axiom" of synergetics applies in a general sense to many social phenomena, which can thus be studied and modelled with the help of the mathematical theory of certain nonlinear systems used by Haken for the formal description of a broad range of natural phenomena (Erdmann 1986).
While the formal models of discontinuous social processes deal with phase transitions from order to disorder at least as frequently as with transitions in the reverse direction, sociological theory has been mainly influenced by natural science theories of spontaneous self-organization. As Krohn et al. (1987) point out, several parallel but independent research developments in the natural sciences have merged in the paradigm of self-organization. A major contribution came from Ilya Prigogine who, under the heading of dissipative structuring, analysed spontaneous ordering processes in physical and chemical systems far from equilibrium (Prigogine 1980). The physicist Hermann Haken discovered analogous ordering processes and coined the term "synergetics" to describe them (Haken 1978). Manfred Eigen contributed the concept of hypercycle, an autocatalytic process composed of linked autocatalytic sub-processes (Eigen and Schuster 1979). The neuro-scientists Maturana and Varela, finally, treat self-reproduction (autopoiesis) as one form in which the self-organization of non-equilibrium systems can manifest itself (Maturana and Varela 1975). Self-organizing natural systems are typically composed of a very large number of elements; they are in a state far from equilibrium. In the process of self-organization (self-structuring or self-reproduction), the system consumes energy, but the emergent order that is generated in the process is a consequence of the interactions and interrelations among the elements of the system. The equations governing this process are intrinsically nonlinear.
For more than 10 years now, this self-organization paradigm has stimulated sociologists. Often, key concepts of the paradigm have been applied to social phenomena at the macro or meso level, i.e. societies and organizations, in the form of verbal analogies, emphasizing the similarity between the social and the natural phenomena involved. This kind of theory transfer, however, hardly generates new insights. Whether the analogy is drawn directly or used in a wide, metaphorical sense, such attempts hardly amount to more than a kind of verbal "curve-fitting."
There have, however, also been more ambitious attempts to make use of the self-organization, and particularly the autopoiesis paradigm in sociological theorizing. These transfer attempts stand in the tradition of sociological systems theory, and they can be found more frequently among German than among American authors. This difference has to do with the fact that in the United States, the focus of social science theorizing after Parsons has shifted away from systems theory, while in Germany with the work of Niklas Luhmann a theoretically very ambitious form of sociological systems theory was developed (Luhmann 1984) and has influenced both the major theoretical debates and a whole generation of younger scholars. These scholars have applied the paradigm of self-organization and especially of autopoiesis for instance to the analysis of the legal system and of the system of science and research (e.g. Teubner 1989; Krohn and Küppers 1989). The various applications of the paradigm of self-organization and autopoiesis have often met with harsh criticism. However, even the critics sometimes found them stimulating.
In view of the fact that social discontinuities are a familiar phenomenon and have been widely analysed in sociology without any recourse to natural science theories, we may at this point ask what we have gained so far from the more recent theory transfer attempts. To answer this question, it is important to distinguish between the transfer of methods, of concepts, and of whole theories.
Theory transfer in the strict sense has not taken place, nor has it been seriously attempted. Theory transfer in a strict sense presupposes isomorphism between the empirical phenomena in two different areas, i.e., a 1:1 relationship between the elements, the elementary properties, and the relationships that govern the dynamics in two different phenomenal fields. There are strong a priori doubts, however, about the possible existence of a basic isomorphism between the physical and the social world. In fact, together with the humanities, the social sciences have again and again emphasized their distinctiveness, which is presumably related to the ontological character of their object of cognition. With respect to natural science theories of nonlinear dynamics, it is for instance quite obvious that their physical, chemical, and biological core mechanisms have no exact counterpart in society. While formal analogies may exist, e.g. with respect to the importance of recursive mechanisms, or the interaction of reinforcing and damping micro processes that operate on different time-scales, such formal analyses need to be given substantive meaning in order to acquire explanatory power for specific social events.
It is here that attempts to apply formal (mathematical) models of natural processes to social phenomena have their place. These modelling attempts may not provide sociology with new substantive insights, but the gain in terms of precision in spelling out interdependencies is considerable. There is also an indirect effect on theory building, since the attempt to model an empirical process formally forces sociologists to complete and round off their theoretical assumptions about the underlying dynamic mechanisms.
Aside from the borrowing of mathematical methods and models, the transfer efforts we have reviewed are basically of two kinds: they either remain largely at the level of verbal analogies, or they are cases of an indirect or mediated theory transfer that proceeds through the generalization and a successive re-specification of natural science theories. Both may be considered as a kind of conceptual borrowing.
Examples of a merely metaphorical use of natural science theories, sometimes presented with the claim of being a fullfledged theory transfer, abound. A considerable part of what might pass as an application of "chaos theory" in the wide sense of nonlinear dynamics is thus nothing but the translation of already well-established parts of a social science theory into the conceptual language used in a natural science theory. Terms like self-organization, feedback, bifurcation, critical mass, phase transition, and turbulence can be applied, in a general descriptive sense, to a large number of social phenomena. But the similarity with the natural phenomena for which they were coined remains quite superficial. The result is therefore a mere semantic innovation that adds nothing to our substantive knowledge.
It is probably not surprising that a merely metaphorical use of natural science concepts to describe social phenomena is often made by authors who are themselves natural scientists. For example, Haken (1984) himself has drawn suggestive verbal analogies between synergetics and organizational processes, analogies that presuppose a certain familiarity with organizational phenomena but do not add anything to our knowledge about them. But there is at least an equal number of social scientists who, having familiarized themselves with the corresponding natural science theories, engage in the same kind of effort with the same result. Thus Michelitsch (1987) describes basically well-known economic processes in the terminology of Prigogine and Haken. In this and most similar cases, the "applied" statements are not "wrong"; they simply do not carry new information.
To present a merely metaphorical use of natural science concepts as genuine theory transfer is relatively rare among social scientists who have themselves made substantive contributions to social theory. Instead we find here - if substantive borrowing from the natural sciences takes place at all - a kind of mediated theory transfer. Such transfer implies the sociological re-specification of a previously generalized version (possibly, but not necessarily in a mathematical form) of an empirical, i.e. field-specific natural science theory.3 In fact, without such generalization of the original theory, social scientists might rarely be tempted to borrow from the natural sciences; this underlines the importance of generalization (and popularization) for theory transfer. In the process of generalization, which always implies abstraction, important parts of the original theories are lost. In theories of self-organization, this is typically the notion that these processes take place far from thermodynamic equilibrium. The same holds for the energy input (in a literal, physical sense) that dissipative structuring presupposes.4 As already stated, there is also no possibility to apply the mechanisms that produce higher level order phenomena in physical and chemical systems, such as chemical auto- and cross-catalysis, to social systems except in a formal analogy. If, however, the paradigm of self-organization is reduced to a few basic principles, such as the coexistence of operational closure and sensitivity to external perturbations, and the emergence of quasi-stationary states through internal dynamic mechanisms of a nonlinear kind, these notions, when specified for social systems, can prove quite fruitful.
The process of generalization and re-specification has been described very well by Druwe (1988), though it often remains implicit in the writing of social scientists.5 This holds particularly for applications of the self-organization paradigm. One of the few explicit attempts to move from Maturana's biological theory of cognition to a general theory of self-referential systems has been undertaken by Hejl, who, though he does not get very far in developing it, claims that such a theory might provide a new theoretical foundation for the social sciences (Hejl 1982: 191).6 Luhmann, on the other hand, starts immediately by specifying the sociological meaning of an already generalized analytical paradigm. The (relative) openness characteristic of self-organizing and autopoietic systems for instance is re-specified by Luhmann to refer to informational inputs, or observations. Krohn and Küppers (1989: 127) even emphasize that it is this informational openness characteristic of social systems that lies at the base of their specific dynamics, if compared to that of biological systems. A similarly important re-specification takes place with respect to the notion of autopoiesis, which Luhmann, as it were, de-materializes. The potential fruitfulness of such transfer efforts rests in the explicit re-specification - and hence authentic theory building - that they can involve. In the case of sociological systems theory, the notions of self-referentiality, operational closure, etc., have led to a new perspective on societies and social subsystems that in many respects can be considered to be not only more congruent with actual experience and observation, but also more satisfactory in an explanatory way.
If so far the most coherent attempts to apply basic concepts of a theory of nonlinear non-equilibrium systems to social phenomena had their specific point of reference in the notion of autopoiesis, a self-organizing mechanism rather than a process leading from order to chaos, we may now consider in more general terms the theoretical promise that chaos theory (both in the wider and the narrower sense) holds for sociology. Walter Bühl (1990) argues that the sociological relevance of natural science theories of nonlinear dynamics rests in particular in their application to the analysis of discontinuous social change - of fluctuations, catastrophes, and chaos, as the subtitle of his book reads. According to Bühl, such change processes have been neglected in the recently dominating sociological theories, which have rather been concerned with problems of social order, social differentiation, and patterned structural change. As we have seen in section 1 of this paper, this diagnosis is correct if we think of explicit post - World War II macro theories. It is not quite correct with respect to the broad mass of sociological work; nor does it apply to such classical theorists as Karl Marx. We do, however, lack an integrated, modern sociological theory of discontinous social processes that might provide a general framework for the wide variety of specific cases that have been analysed by sociologists - from riots and mass violence to revolutions and other forms of structural disruption. The question is to what extent natural science models of nonlinear dynamics in general and chaos theory in particular would be helpful in the development of such a sociological theory. Doubtless natural science theories and mathematical models of nonlinear dynamics may help us to get a better understanding, or at least a better formal grasp, of certain kinds of social discontinuities. However, keeping in mind what has been said earlier about fruitful and abortive forms of theory transfer, what is needed in any case is the development of a genuinely sociological theory, instead of a mere reformulation of existing insights in the fashionable terminology of "chaos."
Theories and models of nonlinear dynamics hold still another, even more general theoretical promise for sociology, over and beyond their ability to direct sociological theory building to the mechanisms underlying various forms of discontinuous processes. This promise derives from a feature that all of the natural science theories and mathematical models that come under the heading of nonlinear dynamics have in common: they all deal with the generation of macro events or macro patterns from micro processes. By virtue of their dealing with the micro - macro link in systems behaviour, these models also contribute to a better understanding of the hierarchy problem. Hierarchy in this connection does not refer to vertical control relationships, but to a succession of different levels where the phenomena at each higher level have properties that cannot be derived by summation from the properties of the lower level phenomena. To the extent that the natural science models can be applied to social reality, they might help to clarify the micro - macro link, i.e. what is probably the most crucial general problem in present social theorizing. This special theoretical relevance may have been most evident in the case of the self-organization paradigm, but it holds in principle for all models of nonlinear dynamics that generate macro events from the uncoordinated (though interdependent) micro behaviour of the system elements, whether these macro events are phase transitions to chaos or to new stationary states far from equilibrium.
That a theory of self-organization should be able to contribute to a specification of the famous micro - macro link is explicitly recognized by its natural science proponents. The point they all emphasize is that self-organization produces qualities at the macro level of the systems considered that cannot be derived from, or explained by, reference to the measurable properties of the elements. With reference to ferromagnetism and the laser, Haken for instance states: "Thus the order on the microscopic level is a cause of a new feature of the material on the macroscopic level" (Haken 1978: 3). In the case of iron, it is the quality of magnetism, in the case of the laser, a light beam of particular intensity that is generated. Similarly, in the case of the Bénard instability, the macro quality is a pattern of fluid motion that obviously cannot be derived directly from the qualities of the H2O molecules. Since, in Haken's words, "to describe collective behavior we need entirely new concepts compared to the microscopic description" (Haken 1978: 13), he introduces the term "order parameters" to refer to such macro-features. An order parameter represents a macroscopic property emergent from interactions at the microscopic level.7 Of course the properties of the elements are important because they imply specific capacities for influencing each other and being influenced, but it is their interaction that produces the new structure. It is evident that these formulations can also be applied to the relationship between micro behaviour (individual behaviour) and macro properties of social systems. The promise to gain a better understanding of emergent effects in social systems resulting from the behaviour and interactions of the system members is probably the main reason for the attractiveness of the self-organization paradigm to social scientists, and it plays a focal role also in the transfer of mathematical models of nonlinear processes.
Though micro - macro relations have been a perennial theoretical problem in sociology, this problem seems to have special salience in present-day sociological discourse. This special salience has to do with the renaissance of action (or agency) theory in today's macro sociology. As long as structural change at the systems level is explained by reference to functional imperatives, changing values, or technical development, macro events are explained by macro variables, and there is no need to go back to the micro level of individual action. Only when attempts are made to explain macro events by micro action, to paraphrase the title of a famous book by Thomas Schelling (1978), are we confronted by the challenge of linking micro and macro levels.
About 40 years ago, Talcott Parsons (1951) made the attempt to link the micro level of social action and the macro level of societal change in one theory, but his conception of a hierarchy of system levels and of the interpenetration between social and personal systems is better suited to explain the macro determination of micro events than the generation of emergent macro phenomena from micro interactions. More relevant is the concept of unintended consequences, which have often been identified as the proper object of sociological enquiry. A generation ago, Hayek formulated this view as follows: "If social phenomena showed no order except in so far as they were consciously designed, there would be... only problems of psychology. It is only in so far as some sort of order arises as a result of individual action, but without being designed by any individual, that a problem is raised which demands theoretical exploration" (Hayek 1955: 39).
Where sociologists are interested to explain emergent macro phenomena by reference to the actions and interactions of individuals, they adopt a perspective that has a long tradition in economics. Not surprisingly, therefore, the most explicit contributions to the formulation, if not to the theoretical solution of the micro - macro problem in sociology, have not been made by systems theorists, but by authors who do not only use an actor's perspective, but are at the same time methodological individualists using a rational choice approach (Lindenberg 1977; Boudon 1977). The adoption of such a perspective is also motivated by a particular extra-scientific cognitive interest - they query whether man by his own actions will unintentionally bring about the annihilation of society.
There exists, however, a limit for the fruitful transfer of natural science models of nonlinear dynamics in general and of chaos theory in particular. This limit is drawn where the basic premises of physical and chemical theories no longer hold in the social world. These are in particular the premise of the spatial and temporal invariance of the system's elements, and the premise that we are dealing with multi-component systems, systems with very large numbers of similar elements. There are surely types of social situations where these basic premises for the occurrence of discontinuities - both transitions from order to chaos and from chaos to order - are approximated, if not fully met. Such situations can be found where we deal with collective behaviour in spatio-temporally circumscribed but large populations or quasi-groups. The behaviour of their elements - individuals, households, or firms - may be culturally or normatively regulated and subject to mutual influence, but their actions are not organized and purposefully coordinated, and no basic innovation takes place. Examples of such social situations cannot only be found where we deal with typical mass behaviour, but also in processes of public opinion formation and political mobilization, in the cyclical change of all kinds of fashions, in the emergence of settlement structures and generally in all social processes that are governed by the logic of ideal - typical markets. In such cases it may well be feasible to describe the behaviour of the elements by a few relatively simple rules that remain stable for the period under consideration.
Even in situations of collective social behaviour, however, learning can take place that changes the behavioural predispositions that, had they remained unchecked, would over time have led to a specific macro event, e.g. chaos. At this point, the original model is no longer applicable. True, in nonlinear models the elements affect each other's behaviour and are affected by the aggregate state that the system has reached in the previous time period, to which they themselves may have contributed. But it is not assumed in such models that the elements involved in a process that is for instance beginning to escalate or to become irregular, will react by deliberately controlling the relevant system parameters so as to avoid this happening. This, however, is exactly what human actors will often do. They are able to anticipate future system states, evaluate them, analyse their presumable causes, and set about changing the antecedent conditions of future states held to be undesirable. As von Weizsäcker (1990: 46) has argued explicitly, it is unlikely that under these circumstances discontinuities as described by the mathematical theory of deterministic chaos will be found in society.8 When market processes, demonstrations, or mass movements appear to get out of hand or when emergent structures of settlement or inequality are considered undesirable, powerful corporate actors such as central banks, police departments, and government intervene to check the spontaneous processes. The same holds in the case of violent external disturbances (e.g. natural catastrophes) and of the consequences of complex interdependencies. Social systems are complex, nonlinear systems, but they are partially organized rather than disorganized complex systems, i.e. the type giving rise to both processes of self-organization and deterministic chaos.9
It is conceivable that those situations, to which models of the spontaneous (unintended) generation of order and disorder can be applied, are becoming more frequent in modern societies. The dissolution of traditional forms of group solidarity and the erosion of hierarchies might well mean that situations that are governed by the logic of markets rather than by the logics of hierarchy or solidarity are increasing. But even if this were so, it is in any case only a limited part of social reality that is amenable to an analysis in terms of natural science models of nonlinear dynamics. This is basically so because human beings are capable of learning and of purposefully organizing for the pursuit of collective goals. For better or for worse, it is not only Adam Smith's invisible hand that governs society. The capability to organize and to formulate collective goals is closely linked to the ability of learning consciously from experience and using such knowledge strategically (instead of being restricted to learn as biological populations learn, i.e. through selective survival). Thus both individuals, and, more importantly, powerful corporate actors who have come to dominate in our highly organized modern societies intervene and try to control spontaneous processes if their anticipated outcome appears undesirable. Spontaneous processes of collective behaviour are therefore permanently being checked and redirected. In consequence, only a few social macro events are therefore really emergent phenomena of the kind analysed in natural science models of nonlinear dynamics. Nor can it be said that the unintended and potentially destructive macro effects are mainly caused by processes that follow the natural science paradigm of the breakdown of order. Such destructive events are just as much the result of planned intervention, i.e. of planning mistakes or the result of situations of strategic interdependence that have the character of social traps.
The breakdown of social systems is therefore rarely the consequence of the unchecked dynamic of a given nonlinear system, given specific initial conditions. A theory designed to explain the breakdown of social systems would have to take into account the interference between spontaneous developments and planned action, the action - reaction links between disturbances of a precarious order, and efforts to cope with them. So far, no attempt has been made to integrate available research findings into an authentic sociological theory of the breakdown of social systems. By way of concluding this paper, let me briefly sketch the outlines of such a theory.10
All social systems continously face internal and external disturbances; it is an essential feature of social systems that they react to disturbances, including endogenous growth impulses or any kind of innovation. System collapses only occur if in the face of potentially disruptive disturbances the strategies or mechanisms to cope with them fail. System breakdowns are therefore due to the incongruity between the requirements and problems facing a system on the one hand, and the system's ability to react on the other.
The collapse of a system may, first, be caused by the cessation or ineffectiveness of restraining mechanisms that previously prevented the occurrence of specific disruptive disturbances. Simple examples are measures aiming to prevent events that may trigger violent collective behaviour. Attempts to control disturbances ex ante are also present when children are taught what they are not allowed to do, when binding contracts are signed, when legal norms are established and applied, and when corporate actors concur to forestall undesirable developments - the arms race, inflation, soil erosion. If mechanisms of social control fail, the "man-made" social order collapses. System breakdowns that are caused by the failure of a restraining factor can occur quite suddenly when the preceding state of rest is based on balancing highly antagonistic forces, as is often the case between aggressive and repressive forces prior to revolutions.
Social systems are not dependent on the ability to prevent the occurrence of disturbances if instead they succeed in mastering them without jeopardizing the order of the system. The failure of such compensating mechanisms represents the second important cause of system breakdowns. Examples of compensating mechanisms include the substitution of increasingly scarce resources by new materials, energy resources, or production processes. Compensation also takes place when unions offer various benefits to attract members in spite of declining class consciousness. Compensatory strategies make use of the fact that equifinality is a frequent phenomenon in the social world, i.e. that the same goals can be reached by different paths and that the same effects can be the result of different causes.
Disturbances that can neither be avoided nor compensated require adaptive transformations. The failure to bring about such a necessary structural change is a third cause of system breakdown. If change is necessary in the interest of long-term preservation, an obstruction of learning processes that conserves the existing order may lead to the collapse of a system or a radical structural change. A good example for this is Michel Crozier's vicious bureaucratic circle, which starts when the continuous adaptation of a bureaucratic organization to changing external demands is forestalled by the organization's rigidity (Crozier 1964). Growing dissatisfaction among clients follows and finally causes responsible politicians to force reform upon the unwilling bureaucracy; this represents a structural break. Adaptive transformations may be especially difficult to achieve by systems that are equipped with well-developed and initially even well-functioning restraining and compensating mechanisms.
Threshold values play an important part in these processes in two respects, especially if the first two, rather "defensive" ways of warding off disturbances fail. On the one hand, previously effective mechanisms to restrain and to compensate for disturbances may fail when a "disturbing factor" suddenly rises rapidly; that is to say that the speed with which developments take place is critical. Growing rates of unemployment or of car accidents may serve to illustrate the point. A slow and continuous increase leaves room not only for a gradual revision of our expectations concerning the acceptable level of unemployment or traffic deaths; it also permits to develop and extend measures to compensate for and limit damages, for example by establishing re-education programmes, emergency hospitals, and rescue helicopters. But if we are suddenly confronted with precipitous increases in the figures for unemployment or accidents we are shocked and the public reacts with mass protests, while politicians intervene with radical political measures and the atmosphere in the economy turns sour. Gradual increases of "disturbing factors" may, on the other hand, also lead into critical zones where neither restraint nor compensation remain possible. In the area of natural processes, the existence of such critical zones is part of our everyday experience. But the proverbial straw that broke the camel's back can also be found in social situations. This is true for individual behaviour (for example when with increasing pressure for compliance, conformity turns into resistance ("reactance")), as well as for social order. Social norms usually maintain their capacity to guide the behaviour of the majority in spite of a certain number of violations; should however those violations reach a critical level, social norms will suddenly lose their social (if not necessarily their juridical) validity. Similar observations can be made for solitary behaviour in groups; differing interests and latent conflicts can be tolerated to a certain degree, but if the strain reaches a certain intensity group integration may suddenly collapse.11
Disturbances that rapidly increase or reach critical levels and thus render existing restraining or compensatory mechanisms useless call for structural adaptations. Some disturbances, however, preclude or render the chances of coping with them by gradual adaptation practically unrealistic, and thus cause the system to collapse. Three types of disturbances in particular seem prone to cause breakdowns by more or less fundamentally overstraining the ability of social systems to react.
In the first case, one element of a widely ramified set of interdependent institutions fails (for whatever reasons) and causes the whole complex to collapse. Max Weber's analysis of the social reasons for the downfall of the classical culture may serve as an example. Weber claims that this collapse was caused by the abolition of a - seemingly rather insignificant - institution, namely the slave barracks, which resulted in the abolition of several other structural elements for which they had actually served as an indispensable foundation. As no more slaves were introduced into the system, the existing slaves became unfree socagers. As a consequence, landed property gained importance, the barter economy grew at the expense of the urban commodity economy, and this impeded the formation of monetary assets. This not only caused the marble splendour of ancient cities to vanish and poetry and historiography to dwarf but also the standing army and salaried civil service to disappear.12 Certainly this decline of a culture represents a collapse of a system only when observed by a historian in a quick-motion effect. Nevertheless, the example very well illustrates how a stable context of interdependent elements may collapse because of the abolition of one element.
A second type of disturbance that easily exceeds a system's ability to react can be seen in the appearance of changes in parts of the system's environment that endanger the system but are unnoticed until they develop into an acute threat that then, however, cannot be mastered any more because it is too late for any attempt to restrain, compensate, or gradually adapt. Destructive external interventions that an existing social system was neither able to prevent nor is able to master, as for example the invasion of settlements of peaceful farmers by roving tribes, are less interesting than those threats that are brought about endogenously and could be mastered or even avoided if noticed in time. The political intervention in the previously mentioned bureaucratic vicious circle represents one of many possible illustrations. The history of bankruptcies also provides numerous examples, and even Karl Marx's hypothetical "gravedigger model," according to which capitalists by their own actions produce the powerful class enemy that destroys them, follows the same logic.
The last type of disturbance to be mentioned here is caused by an accidental - and as far as the participants are concerned unforeseeable - concurrence of events that together lead to a system breakdown. This is typical of catastrophies in large socio-technical systems for which (in contrast to natural disasters) human actions are responsible.13 At the bottom of such man-made disasters that lead to the collapse of socio-technical systems lies typically the unexpected concurrence of several "mistakes." Although safeguards exist, they fail in the case of an unexpected combination of circumstances following from separate cause-and-effect chains that only accidentally intersect at a certain point. Precautions can only be taken against the expectable. Once the calamitous constellation of factors happens, the accident - the explosion, the crash, etc. - occurs at such a speed that it cannot be prevented by external interventions, i.e. there is no time for either compensation or gradual adaptation.
Charles Perrow, who analysed numerous accidents in large technical systems, emphasizes two features of these systems that increase the likelihood of catastrophies to develop according to the pattern just described: the close coupling of parts of the system and processes, and the interactiveness caused by the high degree of complexity; the unforeseen influence of separate processes upon each other. These features cannot only be found in large technical systems but also in social systems, and indeed above all in the kind that our highly developed industrial societies represent, in which the growing functional differentiation is accompanied by an increase of de facto interdependencies.
To conclude this outline of a possible sociological theory of system breakdown it should be underlined that the fundamental condition of such breakdowns is not the same as in models of deterministic chaos. The fundamental condition of social system breakdown is an imbalance between disturbances and coping, and not simply the irregular fluctuation of a given state variable. Moreover, the disturbances concerned may be of different kinds: not only endogenous but also exogenous, and not only the result of autonomous processes but also of purposive interventions. An understanding of chaos phenomena in the narrower sense may form a part of such a sociological theory, but in and of itself "chaos" in the sense used in physical and mathematical theories plays only a minor role when social systems break down.
1. This last point bears emphasis. In economic theory, for instance, the existence of nonlinear relationships has been recognized for long, but a selective interest in equilibrium conditions together with the prohibitive mathematical complexity of nonlinear systems have discouraged modelling attempts. Instead, de facto nonlinear economic relationships have mostly been linearized for mathematical treatment. A growing interest in non-equilibrium dynamics together with the greatly improved technical ability of dealing with more complex mathematical models have now led to changes in this situation (see Intriligator 1988).
2. Baumol points out that the economic literature is replete with models generating some sort of cyclical behaviour. "However, for the sake of analytic tractability the relationships were generally assumed... to be linear... the assumption of linearity introduced to make cyclical models tractable analytically effectively blinded us to the possibility that chaotic behavior patterns would emerge" (Baumol 1987: 105). Only nonlinearity is capable of producing chaotic behaviour. In the past few years, economic literature has already produced quite a crop of models capable of displaying chaotic properties.
3. Druwe (1988) calls the generalized version of a field-specific theory "model."
4. Of course, societies might be called systems remote from thermodynamic equilibrium, if we include in the concept society the organisms of its members, processes of resource utilization and the production of artefacts, but the fact of being remote from thermodynamic equilibrium is not very informative with respect to what interests us about a society. Again, social systems consume energy, but it is not this fact per se but rather its technological and social consequences that interest us.
5. An exception is Stichweh (1987: 447).
6. A similar claim has earlier been made for general systems theory, which is a good example of the generalization process referred to here.
7. De Greene 1981: 105; De Greene emphasizes this point strongly: mere growth corresponds to deterministic factors, nonlinear processes of self-organization lead to the emergence of new properties in a transition to higher levels of organization.
8. "Unterstellt man, daß zwischen dem Geschehen im Gesamtsystem und den Erwartungen der Individuen über dieses System eine Zusammenhang besteht, so gibt es sozusagen eine Rückwirkung vom künftigen Zustand des Gesamtsystems auf das heutige Verhalten seiner Elemente. Es ist unwahrscheinlich, daß sich unter diesen Bedingungen vergleichbare Chaosphänomene finden lassen" (Weizsäcker 1990: 46).
9. "In the physical realm, relatively simple systems and disorganized complex systems predominate. In the living and the human realms partially organized complex systems predominate" (West and Salk 1987: 320).
10. See for this especially Mayntz (1988).
11. The "breaking point," where the mechanisms of restraining and compensating for disturbances turn ineffective, can only be determined in relation to the concrete institution that serves that purpose and is thus not tied to a specific absolute intensity of the respective disturbance - a fact that renders social scientific analyses of such phenomena very difficult.
12. See Weber's study on "Die sozialen Gründe des Untergangs der antiken Kultur," in Weber (1956).
13. Although research on catastrophies is conducted by social scientists, they have so far mainly been concerned with the mastering of consequences of disasters and thus, so to speak, with the period in which stability is re-established rather than with the causes of catastrophies. Two important exceptions were the works of Barry A. Turner (1978) and Charles Perrow (1984), on which the following is primarily based.
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