David Peat

126 From Certainty to UncertaintyWhat is of particular relevance to the argument of this book is thatsuch systems are also discovered in human organizations, the stockmarket, traffic patterns, spread of diseases, fluctuations in populationsize, and so on. In all these cases, and many more, a tension exists betweenwhat can be known and determined for sure, and what lies beyondour predictive capacity.Chaotic PopulationsPlanetary chaos was introduced through the metaphor of grit in theNewtonian clock. There are other examples where regular, cyclical behaviorconceals the seeds of chaos. Take as an example of regular behaviora reedy lake containing trout and pike. If the pike are too rapaciousthey will consume their source of food and start to die out. Butthere are always a few trout hiding in the reeds and, freed from thethreat of so many predator pike, their numbers increase. Soon the lakeis well stocked with trout and the few remaining pike discover they canhave a field day. Pretty soon the pike population increases and many ofthe trout get eaten. Now the cycle begins again. Hungry pike discoverthat their prey cannot be easily found and so they begin to die of starvation.Year after year, and generation after generation, the number oftrout and the number of pike oscillate up and down in a stable andpredictable way.Cyclical oscillations of predator and prey look very much like theticking of a clock. But in this case the origin of the pendulum swing isnot mechanical; rather the results of one cycle feed back into the nextin a repetitive way. Mathematicians call this form of repetition “iteration.”Iteration means that the output of one calculation, or of onecycle, is the input for the next. Some iterations lead to stable situations,such as the population of pike and trout, while others produce chaos.To see how chaos can emerge out of regular population cycles, letus change the example slightly. Instead of pike and trout we’ll takerabbits. Release a pair of rabbits on a virgin continent and they willbreed until they have spread over the entire land. But suppose theserabbits arrive on a small desert island. At first they breed and multiply,