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What is Complexity?

The discovery that complex properties may emerge from simple rules is one of the most important discoveries of modern science (e.g., Holland, 1995; Johnson, 2001; Kaufman, 1995;Waldrop, 1992;Wolfram, 2002). Many discoveries across diverse disciplines of science show that extremely simple rules can produce complex phenomena. This is especially characteristic of systems consisting of elements that interact in a nonlinear fashion. Even if the system’s elements are relatively simple, nonlinearity in their interactions may lead to highly complex dynamic behavior, such as self-organization and pattern formation (cf. Camazine, 2002; Haken, 1978; Johnson, 2001; Kelso, 1995; Prigogene & Stengers, 1984; Wolfram, 2002). The emergence of both order and chaos, for example, has been documented in neural networks (Amit, 1989) and cellular automata (Wolfram, 1986, 2002), in which the basic elements are essentially binary.

In the dynamical systems approach, it has been shown that even systems composed of a few variables may display very complex patterns of temporal changes (Shuster, 1984). The temporal trajectory of such a system may be chaotic and unpredictable over longer time periods. Such a dynamic is characteristic of weather patterns modeled in meteorology (Lorenz, 1963) or in hydrodynamics (Ruelle & Takens, 1971). Complexity may also be produced in a spatial pattern Very simple rules of interaction of nearby cells, for example, can reproduce the patterns of pigmentations observed in living organisms or shapes of plants and shells (e.g., Meinhart, 1995; Wolfram, 2002) or in the arrangement of columns in visual cortex (Miller, Keller, & Stryler, 1989). Within psychology, the appearance of complexity from simple rules has been demonstrated in both cognitive (Port & van Gelder, 1995)  and social psychology (Nowak & Vallacher, 1998; Read & Miller, 1998; Vallacher, Read, & Nowak, 2002).

The realization that complexity may be the flip side of simplicity, rather than its opposition, has profound consequences for theory construction in the social sciences. If simple rules can produce complex phenomena, then complex processes and structures can be explained by simple models. This provides a way to follow the principle of parsimony without sacrificing the depths of our understanding or trivializing what we are trying to explain. It follows that a simple model can be built that will exhibit the complex properties of a psychological or social phenomenon. Complexity may appear in systems governed by simple rules only if these rules interact with each other or with the environment (Goldstein, 1999; Weisbuch, 1992). The minimalist model thus needs to be dynamic.