What is probably one of the most exciting potential advances in psychiatry is occurring slowly, possibly too slowly and has gone unnoticed by many. I am talking about ‘Chaos theory’, which is a mathematical concept that has influenced the study of such diverse subjects as the weather, evolution and the electroencephalogram. Is it our lack of mathematical training that makes us so fearful? This may be so, but we can still understand chaos theory without having to learn large mathematical formulae.

Chaos theory is about dynamic non-linear systems that are orderly at first, but may become completely disorganised over time. That is initial conditions that are alike in the beginning, may have markedly different outcomes over time. An analogy commonly drawn from weather studies is the butterfly effect. This draws on the premise of initial conditions which is a butterfly fluttering its wings in Tokyo can lead over time and distance to a storm for example over New York. In other words a small perturbation in a non-linear system can lead to great variations in outcome. The chaos theory is about how phenomena can vary between different kinds of states around what is called a ‘strange attractor’ and obtain from this a semblance of order out of what initially can be perceived as disorder.

In this way chaos differs from random behaviour and causal systems. Eventual outcome in a random system is not determined by initial conditions. The eventual outcome in a causal system has a linear relationship with its initial conditions. In other words a small change in initial conditions will lead to a small change in the eventual outcome. But in Chaos theory a small change in the initial conditions can lead to major changes in the eventual outcome. These changes become exponential over time.

The original example of a chaotic system was developed by Lorenz. In his early work on weather systems he found using computer simulations that started with similar, but slightly different initial data, orbits would stay close to each other for a while but would eventually diverged in a manner that turned out to be exponential over time. His model was deterministic, that is the orbits were unique in the sense that there was only one orbit passing through a given point of the space in which the orbit lay. The three variables he was measuring were convective air circulation in relation to vertical and horizontal temperature variations.