David Peat

From Clockwork to Chaos 125theory explains the ways in which natural and social systems organizethemselves into stable entities that have the ability to resist small disturbancesand perturbations. It also shows that when you push such asystem too far it becomes balanced on a metaphoric knife-edge. Stepback and it remains stable; give it the slightest nudge and it will moveinto a radically new form of behavior such as chaos.All these systems exhibit what is called nonlinear behavior. Nonlinearsystems behave in rich and varied ways. In a linear system a tinypush produces a small effect, so that cause and effect are always proportionalto each other. If one plotted on a graph the cause against theeffect, the result would be a straight line. In nonlinear systems, however,a small push may produce a small effect, a slightly larger pushproduces a proportionately larger effect, but increase that push by ahair’s breadth and suddenly the system does something radically different.Put gentle pressure on the accelerator pedal of your car and thespeed increases. The greater the pressure, the faster the car goes. This islinear behavior. But when the accelerator pedal is pressed to its limit,the passing gear kicks in and the car jumps forward in a nonlinear way.In the case of three astronomical bodies all those tiny pushes and pullson the orbits can feed back into each other and, when resonance occurs,accumulate into a much larger overall effect.Over a limited and fixed range of behavior, external influences canhave a predictable effect on a nonlinear system. But when the systemreaches a critical point, a knife-edge called a “bifurcation point,” it willjump in one of several different directions, often in an unpredictableway. Put a ball bearing at the bottom of a bowl and a small push willsend it a little way up the side until it falls back again. But balance it onthe lip of the bowl and a single breath of wind will cause it to fall backinto the bowl or alternatively fall onto the floor and roll away into thecorner of the room.A system at a bifurcation point, when pushed slightly, may beginto oscillate. Or the system may flutter around for a time and then revertto its normal, stable behavior. Or, alternatively it may move intochaos. Knowing a system within one range of circumstances may offerno clue as to how it will react in others. Nonlinear systems always holdsurprises.