THE JULIA SET - Image
THE MANDELBROT SET - Image
In the East, it was theorised thousands of years ago that everything that happens anywhere, anytime around the world will have an effect somewhere, somehow on the other side of the globe.
There are no known human laws to describe this consequential series of events. No scientific laws have been established to substantiate such a claim. Now in this age, and in our time, inexplicable events are beginning to cause a vortex of coincidences that are beginning to stir man's imagination.
It is a zone of no time and no space. It is in effect called the Black Hole of human reasoning because no of us has been able to venture there.
But the ancient ones in the East had been able to comprehend this effect to a limited extent. Lao Tze called it The Tao and it has remained as such over eons. The unnamed, enlightened ones who walked unidentified among us know the everything is linked.
For want of a better description, this is called the Butterfly Effect. The basic premise is that the fluttering of a butterfly's wings can affec the climatic conditions in the city of New York, half-way across the world.
Here is where the Mathematics of Chaos comes in. According to my limited knowledge, Chaos Theory was born one day when some scientists and mathematicians thought it would be fun to punch in numbers into the computer and watch the sequential numbers being generated and the patterns of its random behaviour.
Apparently, only computers can tolerate such a boring chain of events or the game as it is called. From the theory of chaos was born chaos systems. Again here, it was determined that chaos systems are not really that random. However, they are very sensitive to factors found at its birth. Thus, minuscule shifts at its fledging state can trigger enormous changes at its conclusion. Hence, the Butterfly Effect.
Scientists found out that Chaos Systems only appear to be disorderly. In reality, they are not. In fact, they have a sense of order. If you sometimes call the state of your workplace, an organised mess, you are in effect referring to the chaos system.
Picture this, two chess grandmasters are pitting their mental skills against each other. Over the long, silent hours, two minds match each other move for move. In the end, one surrenders, or it could be a draw when the end is inconclusive.
Kasparov, the Azarbajian chess grandmaster, has been known to refer to this intense state of chess play as finding order in the state of chaos. Now, are you getting the idea?
In the big game of mental gymnastics, mathematicians and scientists found out that there's an indelible link between fractals and chaos. It is recorded that fractal geometry is the geometry that paints a decipherable picture of the chaotic systems man finds in nature.
There are ways to describe geometry and fractal is the language that explains it. Fractal geometry is translatable by algorithms. It is a set of rules that point the way to fractals.
Computers being the unfeeling tangible structures explain the splendid images human view as fractal visions.
Then there's also the Euclidean Geometry. This branch of geometry deals with triangles, circles, lines and others.
The man who discovered this theory of chaos was a metereologist by the name of Edward Lorenz. He was trying to solve some problems relating to the weather and had lined up 12 equations. Just for fun, he experimented with the numbers and came up with different results.
Before you can shout his name Lorenz, he stumbled onto a fascinating avenue of mathematics that boggled his mind. And thus was born the theory of chaos. All this happened back in 1960. That's actually not so long ago.
From his magnificent discovery, Edward Lorenz later published his magnus opus work called the Lorenz Attractor. His mathematical solution was butterfly-shaped. So now you know. There's an order in his chaos theory, and it links science, mathematics and computers.
If you want to know more about this utterly fascinating subject, you should also read more about two other characters by the names of Benoit Mandelbrot and Gaston Julia. Mandelbrot is an expert in fractal geometry and Julia has been acclaimed as one of the forefathers of modern dynamical systems theory.
Now what am I leading to, you may ask. It's simple. Everything good you do will have an effect that stretches longer and further than you can ever imagine. So just think of some of the most ordinary good deeds that you have done or are going to do and think of all the wonderful effects it will have on earth and its inhabitants.
Just think about it this Christmas. That's your assignment!
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