Complexity: The Emerging Science at the Edge of Order and Chaos

by M. Mitchell Waldrop

In part because of their computer simulations, and in part because of new mathematical insights, physicists had begun to realize by the early 1980s that a lot of messy, complicated systems could be described by a powerful theory known as “nonlinear dynamics.” And in the process, they had been forced to face up to a disconcerting fact: the whole really can be greater than the sum of its parts. Now, for most people that fact sounds pretty obvious. It was disconcerting for the physicists only because they had spent the past 300 years having a love affair with linear systems—in which the whole is precisely equal to the sum of its parts. In fairness, they had had plenty of reason to feel this way. If a system is precisely equal to the sum of its parts, then each component is free to do its own thing regardless of what’s happening elsewhere. And that tends to make the mathematics relatively easy to analyze. (The name “linear” refers to the fact that if you plot such an equation on graph paper, the plot is a straight line.) Besides, an awful lot of nature does seem to work that way. Sound is a linear system, which is why we can hear an oboe playing over its string accompaniment and recognize them both. The sound waves intermingle and yet retain their separate identities. Light is also a linear system, which is why you can still see the Walk/Don’t Walk sign across the street even on a sunny day: the light rays bouncing from the sign to your eyes are not smashed to the ground by su...