It is said that the movement of a butterfly’s wings in a jungle in South America can cause a tornado in Asia.  This idea is the basis of what is now called “chaos theory”.

But what exactly is chaos theory, and what relevance does it have for anyone who is not an analytical physicist?

The mathematician Henri Poincaré first described chaos theory at the beginning of the 20th century, noting how “differences in the initial conditions produce very great ones in the final phenomena”.  Its modern form was first described by the meteorologist Edward Lorenz in 1960.  Lorenz was working on the problem of weather prediction.  He set up a computer, not to predict the weather, but to look at how a system to predict cycles and changes in weather conditions could be developed.  He noticed that even though he sometimes put in the same data, the results would come out differently.  At first he thought it was a mistake, but after trying again and again, he reached a different conclusion. This was no mistake.  He had set up his computer so accurately that it was in fact accurately replicating the complex systems of the earth’s atmosphere and its influence on weather.  Given such a system, the same input could have many different results.

Then, in the late 1960s, another mathematician, Ernst Mandelbrot, did a similar experiment.  He put 100 years of New York stock exchange cotton prices into a large, old-fashioned computer and noted that every change in price appeared to be random and unpredictable.  

Hence the so-called “butterfly effect”. The flapping movement of a butterfly's wings creates tiny changes in the atmosphere which, over the course of time, cause it to diverge from what would have happened without the flapping.  This can eventually cause something as dramatic as a tornado.  The small change in the initial condition of the system causes a chain of events which can lead to large-scale phenomena.  If the butterfly hadn’t flapped its wings, the trajectory of the system might have been very different.

But chaos theory isn’t only about butterflies and tornadoes. Aspects of chaos theory show up in all areas of our lives, from the smallest to the biggest: from the currents of the ocean to the flow of blood through our bodies, from how tree branches grow to the effects of turbulence on an aeroplane, from how the planets in the solar system move to how exactly milk mixes with your morning coffee.  Chaos models can be used to plan traffic flow and thus avoid jams, to make long-range economic forecasts and predict the effects of population growth.

It now seems that alongside relativity and quantum mechanics, chaos theory will be one of the great discoveries of 20th century science, a theory that fundamentally changes the way people think about the universe.  

Personally, if chaos theory can help to make sure my morning cappuccino is still warm by the time I get through the usual traffic jam on my way to work, I think it’s a vital addition to modern science.

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