In Touch - Inserts

Fractals/Chaos Theory
"Things fall apart, the centre cannot hold". So said the Irish poet, William Yeats. Nature, as we all know, is chaotic and unpredictable, constantly changing, dynamic.
Scientists have traditionally studied nature by simplifying - reducing nature's complexities to simple linear equations. Ever since Plato, the myth of an order beneath nature's careless appearance has drawn science forward like a holy grail.
But all that is changing. In the 1960's and 70's a group of researchers and mathematicians uncovered a new way of looking at nature. They called it chaos theory.
Drop two leaves into a river and see what happens. Although they start out together, their fates are quite different. The current quickly separates them. One is caught on a rock, while the other makes it's way gently downstream. They end up miles apart. This happens because the river is dynamic. The path taken by each leaf is affected by thousands of tiny factors - river currents, rocks, gusts of wind.
Traditional Euclidian geometry never took these factors into account. But Chaos Theory can. It pictures nature as an ever-changing flow where no single variable exists in isolation. How does it do it? By feeding back each tiny change in an endless loop, we can calculate how that change will accumulate, like straws on a camel's back, until the system itself is transformed.
When you feed this kind of looping equation into a graphics programme, the computer creates these images, called fractals. Each point on the screen is a complex number. By subjecting that number to feedback, and allocating a colour to the changing value you end up with a pattern that reflects a balance of order and chaos. Dark areas are stable. Coloured areas are chaotic to varying degrees.
It's the patterns that fascinate scientists. No matter how deep you look, similar shapes keep emerging.
But if a fractal image captures the essence of chaos, and chaos captures the essence of nature, then what does that say about the world in which we live?
In Touch talks to Ronald Becker at the Department of Mathematics & Applied Mathematics, UCT: " From this point of view chaos is an ordered disorder in nature, of order and disorder. Now it turns out when we look at the patterns that weather can go through and if we plot these, say, in three dimension space or maybe higher dimensional, the sets of points we get, strangely enough, are fractal in nature and that is the relationship between chaos and fractals."
Fractal patterns show that although nature is chaotic, within the belly of chaos, lies a fragile order.
And if you look close enough you can see it - in leaves, rock, bark, moss, the intricacy of snowflakes. Like wrinkles on the world's skin. It appears that nature is a kind of super-fractal - an infinitely complex algorithm tracing patterns of order and chaos in multiple dimensions.
"The ordered chaos that we do get is an ordered principle in nature that which we did not know about before perhaps forty years ago," says Ronald. "It has been clear that many phenomena like the stock exchange, like the weather - a wide variety of objects of that sort - embody this dual principle of order and disorder which makes it difficult to predict what's going to happen in any particular incidence but tells us the rough global properties of what we are looking at."
But why? What is the cause of these strange patterns of order in chaos?
Some scientists speak of "strange attractors" - powerful phenomena that keep dynamic systems in check - like gravity, magnetism or electrical energy.
But to grasp these relationships we need to understand nature in it's entirety - as a holistic system, within which everything influences everything else.
As far as science is concerned, that's putting the cart before the horse. But all is not lost - what science fails to illuminate, perhaps religion and poetry can.
Christianity speaks of the Spirit of God hovering over the face of the waters. The ancient Greeks tell of rational Apollo and mad Dionysus. The bushmen understand nature as a spiritual life force intimately entwined with their own.
But where does all this leave the scientist? Has the holy grail of "prediction" drifted out of sight? Chaos Theory shows that there are no pure forms beneath nature's veil, just ceaseless change. Fractal patterns might disillusion a few weathermen, but they enrich our self-understanding.
The study of anatomy shows that our bodies are fractal - from the patterns on our fingertips to the branching blood vessels that lie beneath. Moreover, a certain amount of physiological chaos is healthy for us - allowing our bodies to adjust easily to environmental change.
If everything is fractal, including our bodies, then perhaps our minds are too. Our daily thought life is a constant interaction between the organising, rational left brain and the creative, intuitive right brain. But if the mind conforms to fractal patterns, then so must its creations. Human civilization can be seen as an attempt to impose order upon the chaos of existence. And on an even larger scale, even history can be seen as a fractal. The fits and starts of human accomplishment over the millennia end up conforming to an overall pattern.
Chaos theory takes scientists beyond science. It's an invitation to embrace the exceptions that confound our neat cause and effect theories about life. Things still have causes, but the causes are infinite. And underlying those causes and effects is a pattern. The fractal patterns of chaos theory point to an underlying symmetry that reflects another dimension we don't fully understand. A ghost in the machine of nature.
CONTACTS
Ronald Beker