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Simple Complexity
In the case of the messenger city, the system eventually became complex because we loaded lots of complex relationships and contingencies into it. But sometimes complexity can arise quite suddenly and unexpectedly from a handful of simple elements. Here is an example that comes to us from programmer and mathematician John Casti, concerning planetary physics: It's known that the behavior of two planetary bodies orbiting each other can be written down completely in closed form. Nevertheless, it turns out to be impossible to combine the solutions of three two-body problems to determine whether a three-body system is stable. Thus, the essence of the Three-Body Problem resides somehow in the linkages between all three bodies…. So here is a case in which complicated behavior arises as a result of the interactions between relatively simple subsystems. [3]
Casti is referring to the fact that in the study of planetary motion, systems with two planetary bodies (such as a star and a single planet orbiting it) can be mathematically articulated to precisely predict the motion of the two bodies in space. But once a third element is added to the system, gravity from each planetary body affects the other two, drastically complicating the mathematical factors determining their relative motion. The addition of a third planetary body into this system changes everything: the system crosses Campbell's "complexity barrier" to become a genuinely complex system. The relationships among the elements in the system become intertwined in such a complex fashion that the resulting dynamics have yet to be mathematically resolved. What is striking about this example is the low number of elements the system contains. Two planetary bodies have a simple relationship; the addition of just one more element into the system introduces complexity of a completely different order.
There are many examples of seemingly simple systems that in reality are staggeringly complex. A conversation, for example, might only have two people interacting with each other. When all of the cognitive, social, perceptual, linguistic, and contextual factors are taken into account, however, it is clear that even a simple conversation is an exceedingly complex process. [3]John Casti, Complexification: Explaining a Paradoxical World Through the Science of Surprise (New York: HarperCollins Publishers, 1994), p. 40-41.
