David Peat

From Clockwork to Chaos 129The same thing happens in a pinball machine or a roulette wheel.In both cases the ball is buffeted in a complex series of collisions. Ratherthan there being no order there is an order so complex as to be beyondprediction.Likewise, while chaos theory deals in regions of randomness andchance, its equations are entirely deterministic. Plug in the relevantnumbers and out comes the answer. In principle at least, dealing with achaotic system is no different from predicting the fall of an apple orsending a rocket to the moon. In each case deterministic laws governthe system. This is where the chance of chaos differs from the chancethat is inherent in quantum theory. When a rock rolls down amountainside it is knocked here and there by the contours of the slope.The end result, where it finally lands, is random. Yet each individualbump is totally deterministic and obeys Newton’s laws of motion. Itsextreme complexity arises out of the huge number of external perturbationsacting on the rock. Chaos and chance don’t mean the absenceof law and order, but rather the presence of order so complex that itlies beyond our abilities to grasp and describe it.Chance isn’t always caused by external perturbations. In a fastflowingriver an individual, tiny region of water is being pushed thisway and that by the river itself, like a rock rolling down a mountainside.The entire system acts as a complex series of internal perturbationspushing and pulling on each aspect of itself. Feedback and iteration actwithin the system to create ever greater complexity. The result is a turbulentriver.Now let us take another glance into the mirror of chaos and discoverthat what we take to be a random system without any visibleorder can also be seen as an order of infinite richness and complexity.Each aspect of a chaotic system is deterministic and governed by internalfeedback, constant iteration, or complex external perturbations.Similarly a computer calculation must simulate these physical effects.Working with a turbulent river or a population with a varying birthratemeans that the result of one stage of the calculation (its output)becomes the input for the next round of calculations. Like the systemitself the computer calculation iterates itself again and again, with eachoutput being the input of the next cycle.