Overview

The musical notes are only five in number but their melodies are so numerous that one cannot hear them all.

The primary colors are only five in number but their combinations are so infinite that one cannot visualize them all.

The flavors are only five in number but their blends are so various that one cannot taste them all.

In battle there are only the normal and extraordinary forces, but their combinations are limitless; none can comprehend them all.

For these two forces are mutually reproductive; their mutual ineraction as endless as that of interlocked rings. Who can determine where one ends and the other begins?

Sun Tzu, The Art of War

Sun Tzu s poetic metaphors about how the complexity of warfare arises from the ineffably infinite combinations of otherwise simple elements offer a remarkably precise and prescient view of one of the central tenets of modern complex adaptive systems theory. Namely, that surface complexity can emerge out of a deep simplicity. Complex systems theory teaches us that what at first appears to be complicated behavior-particularly when viewed from a birds-eye perspective, from which the behavior of the whole system may be observed all at once in fact may actually stem from a much simpler set of underlying dynamic rules. The reverse is also often true, of course. Surface simplicity can emerge out of a deep complexity: enormously complicated systems that a priori have very many degrees-of-freedom and therefore are expected to display complicated behavior, can, either...