Chaos in all directions

It wasn’t like that always however. Mathematics was one of the less glamorous of the sciences and mathematicians, in the public eye, were no more exciting than accountants.

This all changed one wintry afternoon in 1975 when an IBM mathematician by the name of Benoit Mandelbrot, preparing his first major book-length work for publication, thumbed through a Latin dictionary looking for a word that would describe some peculiar-looking shapes his calculations had come up with.

He came across the adjective fractus from the verb frangere - to break. And, with a little playing around, the word fractals, was born.

Fractals, as the name suggests, are a family of jugged, tangled, twisted, splintered and fractured shapes which seem to underlie the very fabric of nature. They are present not only in static shapes like serrated edges and coastlines but also in the shapes formed by charting the scaling of motion (in the way a butterfly beats its wings or a pendulum swings, for example) or the rise and fall of cotton prices in the Stock Exchange and the way molecular cells transmit data.

Many of us will have probably seen the twisted, colourful designs which fractals today make, but what is truly beautiful about them is that their forms, as complicated as the mind of God according to those who study them, require but the most basic of instructions to recreate.

Using powerful IBM computers to analyse the formation of these structures, Mandelbrot discovered that they are but a variation of a single fractal shape which has since become known as the Mandelbrot set.

The essense of the discovery illustrates the sensitivity of any event to initial conditions and became the foundation of the inter-disciplinary science of Chaos.

Like new magicians, the Chaoticians that sprang up in the wake of Mandelbrot’s discovery, did not look upon the world in the reductionist, analytical manner of their predecessors but sought to gain an understanding of the underlying simplicity governing the behaviour of complex systems.

What Chaos teaches is that nothing can ever be predicted with accuracy because even the tiniest change in initial conditions can be responsible for tremendously large effects.In a statement of almost metaphysical quality chaoticians say that “the gentle beating of the wings of a butterfly in China is responsible for the tornadoes in Texas”!

If you think that’s overstating matters a little, or even edging away from the cold, precise logic of science, more shocks are in store, for the language used by today’s Chaoticians to describe the nature of fractals and the physical events they affect parallels that used by the historian and theoritician of magic, Eliphas Levi, and subsequently the controversial, self-styled ‘Great Beast’ Alistair Crowley.