Chaos: From celestial mechanics to climate

Chaos is unpredictable behaviour arising in systems governed by deterministic laws. Since its ‘discovery’ in the 1960s by Edward Lorenz in his studies of meteorological systems, chaos has become an important way of understanding seemingly random behaviour in many other areas. These include the double pendulum, the climate, El Niño and electrical oscillators. Understanding chaos allows the limits of the predictability of a system to be determined. However, despite this recent activity this paper will show that the theory of chaos has a rich history and chaotic behaviour was originally identified in the 1890s by Henri Poincaré in his investigations of the three-body problem in celestial mechanics. But remarkably this paper will also show that chaotic behaviour can be found in such a simple problem as multiplication by 10 and it is closely linked to the question (studied by the ancient Greeks) of whether a number is rational or irrational.