The Chaos Theory

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Unpredictable actions.

Some things in life just don’t fit into neat predictable categories that science loves to discover and investigate.

Because of this we have the Chaos Theory that attempts to accommodate apparently disordered actions.

In the beginning there was chaos..!!

One of the main unifying themes linking the traditions of ancient cultures is the belief that in the beginning there existed nothing but Chaos. In considerably more modern times Chaos has again assumed a prominent place. This time not as a chief Cosmological explanation but as a scientific and mathematical idea that endeavours to come to terms with some of sciences more imponderable mysteries.

Disordered circumstances.

For years scientists struggled to come up with a mechanism for dealing with apparently disordered circumstances. Classical physics deals entirely with ordered states and it seemed to some that within the natural world there was a definite tendency towards disorder or even Chaos. Several of the more quoted examples include the interaction of weather systems that appear to develop entirely random patterns; the changing shape of water droplets; the swirls and eddies within a column of rising smoke, or perhaps the most famous example of them all – a butterfly beating its wings in an Amazonian rain forest causing a tornado in the Philippines.

To the theorists examples like this were certain evidence that not everything in the world could be explained by the mechanism of exact proof as science had always demanded. What was needed was the medium of an entirely new type of logic that would accommodate this thinking.

Feigenbaum Numbers.

It was not until the 1970’s – with the advent of the number crunching capabilities of computers – that the required framework for the Chaos Theory really took root. One of the principal proponents was the American physicist Mitchell Feigenbaum. His principal discovery was a consistent pattern of rate doubling as circumstances tended towards chaos. This led to the introduction of what became known as Feigenbaum numbers, which amongst other things were also found in the period doubling that occurs before heart attacks.

The Mandelbrot Set

The Chaos Theory was evolving and it was evolving in a very exciting way. It was also known to be linked with fractal geometry. Fractals involve complex shapes that are smaller variations of themselves repeated to a very fine level.

There is no greater visual representation of this than Benoit Mandelbrots which are mathematically created fractal images produced on a home computer, that later became known as the Mandelbrot Set. For those interested in creating their own variations the latest version of this programme is available for free download from the following site.

http://spanky.triumf.ca/www/fractint/getting.html

The Catastrophe Theory.

The idea of Chaos as a mathematical concept also has close links with the so called Catastrophe Theory. This was first advanced by the French mathematician Rene Thom in 1968. It attempts to deal with sharply discontinuous events that progress from one state to another in very abrupt stages. According to the theory events reach a critical point where they either fall into chaos or reorganise themselves in a new order of complexity. An example of this would be the cracking of a plank of wood when placed under strain. However for all its complexity Catastrophe Theory has attracted much criticism and often been described as impractical.

Dissipative systems.

Illya Progogine was awarded the Nobel Prize for his investigation into so called dissipative systems, which also have a close connection with the Chaos Theory. Dissipative systems like the human body maintain their identity by means of energy flow from a variety of separate sources. Progogine was able to demonstrate that dissipative systems operate far from the realms of equilibrium and therefore could exhibit strange and unexpected behaviour patterns. In specific examples chemicals in a mixture would change colour in unison at the same moment almost as if by some conscious effort.

Criticisms.

Chaos Theory, the Complexity Theory or however you choose to call it has always had its critics. One of the most obvious arguments is whether we are trying to account for true chaos or merely a more complex form of order requiring millions of tetrabytes of computing power to resolve. For instance Chaos Theory shows that even minute actions can have ultimately major consequences.

In the example quoted earlier of the butterfly in the Amazonian jungle there is a definite action of the butterfly wings creating currents of air. These currents are measurable, and so too are their direction. In turn these currents interact with surrounding vegetation creating eddies and swirling of energy – but still very much measurable. In turn these effects cause yet more effects, combining along with millions of other separate interactions, to produce a mind boggling number of unique events that are constantly changing and evolving and influencing their immediate environment.

In this analysis the butterfly in the Amazon that causes the tornado in the Philippines simply demonstrates a series of events that combine in the only way possible at that moment – a complex chain reaction that some explain as Chaos and others as a more complex form of order.

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