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Chaos theory, complexity theory and emergence


Karen Tesson writes:

Chaos theory came to prominence during the 1980s and deals with systems that apparently follow the normal rules and laws of physical systems, but do so in a highly unpredictable fashion (Gleick, 1987; Kauffman, 1995; Cambel, 1993). Chaotic systems can be found in many different domains; examples that have been studied include the turbulent flow of fluids, irregularities of the heartbeat, growth of certain insect populations, the dripping of a tap and the collisions of atoms in a gas (Stewart, 1990). Chaotic systems are extremely sensitive to initial conditions, and even the smallest event can trigger large consequences. A frequently quoted demonstration of this is the “butterfly effect” in weather systems, where a butterfly that flutters its wings say in Tokyo, could set off a chain of chaotic events in a weather system that result ultimately in a hurricane in Brazil a month later (Cohen and Stewart, 1995).


Kauffman explains, however, that the only reason that the behaviour of a chaotic system is unpredictable is that its extreme sensitivity to initial conditions means that one could never identify all of the factors that will play a role in its behaviour (Kauffman, 1995). To use the example I have just quoted, if one were able to precisely identify, to the minutest detail, every aspect of the butterfly’s movement, then one would be able to predict how the chaotic system would react. The problem however, is that a chaotic system is sensitive to an infinite degree, and empirical science does not, nor ever will, allow us to measure in sufficient detail or with enough precision to meet this sensitivity.


Complexity theory developed from chaos theory and represents the body of research concerning systems that have complex characteristics. Complexity theory concerns systems that exhibit complex global behaviour as a result of the local interaction of components, or “agents”, where the behaviour of the components is determined by relatively simple rules ( Cohen and Stewart, 1995). Like chaotic systems however, the outcomes of these local interactions may not be linearly related to the initial conditions of the system (Miliata, 1997), and so the global action of a complex system cannot necessarily be predicted from an understanding of the behaviour of the lower-level components alone. Complex behaviour may be found in many different kinds of system, from traffic flows, to cell differentiation, to population dynamics, and turbulence. Complexity science is relatively young, and although many are studying complex systems, a definition of complexity hasn’t really been settled upon yet. The consensus seems to be that the one thing that complex systems have in common is the fact that they are complex! (Cambel, 1993).


Some complex systems exhibit features that are referred to as “self organization” or “emergence”. These systems, which are fundamentally chaotic, or complex, have the capacity to produce patterns that are seemingly non-chaotic and predictable in behaviour. To return to an example that I used earlier, the weather is a chaotic system with emergent properties. Although the precise initial conditions that trigger individual weather patterns cannot be identified, or used to predict the detail of an outcome, the global weather system does produce some emergent patterns. These patterns, which include cold and warm fronts, recognisable cloud formations and so on, can be used to predict the overall behaviour of the system (Holland, 1998). Another example of an emergent feature in an otherwise chaotic system is the Great Red Spot on the surface of the planet Jupiter (Ball, 1999; Kauffman, 1995 ). Jupiter’s atmosphere is a chaotic system of turbulent gases, yet amongst its apparent disorder, the red spot remains constant and has done so for at least several centuries. The red spot is actually a vortex of swirling gases; basically it is a persistent storm system – it is a self-organized zone of constancy amid an otherwise chaotic system.


In the non-linear sciences, boundaries are treated quite differently from those in the classical Cartesian/Newtonian model. In the classical model, boundaries are often either ignored, or considered merely to be locations of entry and exit to the system. By contrast, in systems, chaos and complexity theories boundaries are viewed as fixed locations where important phenomena occur. It is known that emergent phenomena are more likely to occur at the boundary between a chaotic system and one that is ordered than elsewhere in the systems (Kauffman, 1995), giving rise to the term “edge of chaos”, which refers to these boundaries.


Central to all of these non-linear theories (chaos, complexity, and to a certain extent to systems theory also), are the concepts of non-linearity itself, and of non-locality. Actions or events in a chaotic or complex system may have consequences that are apparently not directly connected; and local events in a system may have global consequences. This contrasts with the classical Cartesian/Newtonian model where cause and effect are always directly and closely linked. It has also meant that, at least for non-linear systems, researchers have had to review the way that they emphasized prediction and control in a system. Chaos and complexity theories suggest that it will never be possible to control some kinds of system, as their behaviour is so unpredictable that it will never be possible to be certain how they will respond.


Despite the differences between the classical analytical model and the new whole systems models of systems theory, chaos and complexity theories, they do still have elements in common with the mechanistic view. For example, the systems theory search for general systems concepts and processes clearly reflects the classical search for cause and effect relationships, and for definable stepwise processes that lead from and to particular events or phenomena in a system. In essence, in searching for “processes”, the researcher is still seeking to identify linear relationships that are pre-eminent in classical approaches to systems.



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