Chaos theory is that branch of mathematics that looks at how the behaviour of complex, dynamic systems are influenced by their initial conditions. It seeks to find underlying patterns in apparently chaotic systems.
The analogy of the butterfly effect is often invoked to explain how a small change in one discrete aspect of a system can significantly impact the system in a later state. The theory goes that an action as minor as a butterfly flapping its wings at a certain point in time and space precipitates the precise conditions for, say, a subsequent hurricane in a distant part of the world.
A Model of Chaos
Chaos theory is thus a concept with wide-ranging applications – anything unpredictable, such as the weather, stock markets and the human psyche, may all be interpreted under its terms. The mathematical modelling of transitions from order to turbulence includes key concepts such as feedback (think of a stock-market crash driven by the desire of people to sell their stocks at knockdown prices in order to escape the crashing market), loops, repetition and fractals (never-ending patterns).
Computers and chaos theory
The advent of the modern computer was instrumental in the development of chaos theory. One of its earliest pioneers was Edward Lorenz, who in 1961 discovered certain anomalies while running weather reports through a computer. He noticed that the weather predictions differed wildly on the basis of tiny variations in input (for example, by using numbers rounded to three decimal places rather than six). Such small differences in precision ought, experts believed, to have caused little variation in results, but Lorenz had stumbled on proof that their impact was much bigger. He came to summarize it thus: ‘Chaos: when the present determines the future, but the approximate present does not approximately determine the future.’
Chaos in a mathematical sense turns up in the most unexpected places – in the trajectory of space rockets, the ocean currents, the flow of blood through our bodies and even in music and art. Chaos theory thus gives us some chance of better predicting the unpredictable, and so to impose order where disorder might otherwise reign.