Butterflies and Bifurcations: Can Chaos Theory Contribute to Our Understanding of Family Systems?

Abstract

To the novice, chaos theory appears at once exotic--with terminology like strange attractor and butterfly effect--and mathematically abstruse. Yet the concepts are finding their way into the social sciences. For example, they have been used in lifespan development (e.g., Thelen, 1989), psychology (e.g., Barton, 1994), and family therapy and research (e.g., Chubb, 1990; Elkaim, 1990; Gottman, 1991, 1993,a, 1993b). Because these ideas are gaining currency, some assessment of their relevance to family systems is appropriate. Does chaos theory offer fresh insights or is it merely a case of new jargon, old problems? COMPLEX DYNAMICAL SYSTEMS A system is a complex of interacting elements that includes not only the-members but also the relationship among them (Bertalanffy, 1968). Some systems are linear in their operation. That is, their action can be predicted by information about their starting point and their rules of operation. Many apparently deterministic systems, however, have two possible forms: regulated and wildly unpredictable (Nicolis & Prigogine, 1989). Relatively recently, a theory of complex dynamical systems (more popularly known as chaos theory), which explores processes in such systems, has emerged. There are two general thrusts to the theory. One branch emphasizes the hidden order that exists within so-called chaotic systems. The other looks at the spontaneous self-organization of systems out of apparent disorder. In this theory, chaos is not used in the popular sense of total randomness. Instead it refers to systems like the weather or the stock market that are complex and unpredictable, but do have some kind of form and structure that is imposed by the nature of the environment (Field & Golubitsky, 1992). In spite of their diversity, these systems share a number of qualities. They operate far from a state of equilibrium. They do not show simple linear cause and effect sequences; rather, they are nonlinear and small causes may produce disproportionately large effects, or none at all. Such systems are sensitive to initial conditions. That is, unless these conditions can be determined with infinite precision, an impossible standard to achieve, the small inaccuracies will multiply so that two apparently similar events will produce widely varying consequences. They are characterized by discontinuous shifts between phases. Once these shifts occur, the system's behavior tends to settle into a particular delimited range. Often these consistencies in behavior appear to come from the system itself; that is, it shows self-organization (Nicolis & Prigogine, 1989). Much of the argument of chaos theory has been developed through complex formulae that may initially overwhelm social scientists who do not have a grounding in mathematics. Some theorists, such as Gottman (1991), have already used key formulae to analyze sequences in family interaction. Yet the mathematical basis need not be a deterrent. Historically, general system theory also had a mathematical basis (Fivaz, 1991); yet most family systems thinkers are quite comfortable using the concepts nonmathematically. If chaos concepts, in their turn, are to be widely adopted, they must be applicable to families either directly or metaphorically. In fact, the process is underway in Elkaim's (1990) use of chaos principles in family therapy and Gottman's (1993b) exploration of the process of marital dissolution. SYSTEMS FAR FROM EQUILIBRIUM One of the key characteristics of complex dynamical systems is that they operate far from equilibrium. In traditional Newtonian physics, when a mechanical system is relatively closed to the environment and does not import additional energy, it eventually runs down and stops. That is, it is entropic; it turns energy into a form that cannot be used for work. Equilibrial systems are exemplified by a pendulum that gradually reduces its swing as it loses energy from the initial push that started it (Bertalanffy, 1968). …