David Peat

128 From Certainty to Uncertaintydata from many years to work out the complex pattern of oscillationsand so be able to predict the population for the following years.While the cycles within cycles are complex, the underlying mathematicalequation is quite simple, and with the help of a computer,scientists can watch the way cycles increase in complexity each timethe birthrate is increased very slightly. It would be natural to assumethat the end result would be an infinite number of cycles, a vast machineof incredible proportions containing a limitless number of cogswithin cogs. But, infinitely complex as this may be, this is still a regularform of behavior, since if one were willing to wait for an infinitely longperiod of time the same behavior would cycle round again.This, in fact, is not what happens. The system reaches a criticalpoint at which the very slightest increase in birthrate no longer generatesan additional cycle but, rather, chaotic behavior. The populationnow jumps at random from moment to moment. No amount of datacollection can be used to predict the population at the next instant. Itappears to be entirely without order. It is truly random and chaotic.With the aid of this example we encounter one of the paradoxesthat lies within the heart of chaos theory: What does it mean to saythat something is random or that it has no order? Toss a quarter in theair and you can’t predict if it will come down heads or tails. Throw aball into a roulette wheel and you don’t know if it will end on black orred. The result is random. Knowing the results of a long sequence ofcoin tosses is no help in predicting the next result. If someone hastossed six heads in a row the chance of the next throw coming downheads remains exactly 50:50. The sequence of heads and tails is random.But this does not mean that the process by which the coin landshead or tails is itself without any order. Each time you flick a coin youuse a slightly different amount of force and so the coin spins in the airfor a slightly different amount of time. During this same period it isbuffeted by chance air currents and when it lands on a table it bouncesand spins before settling down heads or tails. In coin tossing the coin issubject to a large number of perturbations and disturbances that arebeyond our control. Moreover these contingencies are so complex asto be beyond any normal sort of calculation. Nevertheless, at everyinstant of the coin’s flight everything is completely deterministic.