On the Emergence of Complex Systems on the Basis of the Coordination of Complex Behaviors of Their Elements
Synchronization and Complexity T he purpose of this article is to challenge the view, often expressed and perhaps prevalent in most discussions, that the essence of complex systems lies in the emergence of complex structures from the nonlinear interaction of many simple elements that obey simple rules. Typically, these rules consist only of 0 -1 alternatives selected in response to the input received, as in many prototypes like cellular automata, Boolean networks, spin systems, etc. We do not intend to deny that quite intricate patterns and structures can occur in such systems. However, these are toy systems, and the systems occurring in reality rather consist of elements that individually are quite complex themselves. 1 This brings in a new aspect that seems essential and indispensable to the emergence and functioning of complex systems, namely the coordination of individual agents or elements that themselves are complex at their own scale of operation. This coordination dramatically reduces the degrees of freedom of those participating agents. Understanding the mechanisms responsible for achieving and maintaining this coordination seems the key to understanding, for example, the major transitions in evolution [1]. Even the constituents of molecules, the atoms, are rather complicated conglomerations of subatomic particles, perhaps ultimately excitation patterns of superstrings. Genes, the elementary biochemical coding units, are complicated macromolecular strings, as are the metabolic units, the proteins. Neurons, the basic elements of cognitive networks, themselves are cells. While their activity follows an apparently simple pattern of firing vs. resting, this depends on a slower learning dynamics tuning the strengths of the synaptic connections between them according to the history of temporal correlations between pre-and postsynaptic activities. At an even higher level of aggrega