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 

Renate Mayntz
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 ferromagnetism 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 selforganization. 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 RenĂ© 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 selforganization. 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 nonequilibrium 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 selforganization 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 macrolevel as a consequence of microlevel processes.
4. The nature of social reality nevertheless seriously limits the potential applicability of natural science models of nonlinear dynamics.