The study of Chaos has become the latest fad in modern science. This in itself is of major interest, since it is obvious by their mode of dress that scientists don't often follow fads of any sort. The science of chaos is, in its simplest terms, the attempt to find mathematically unpredictable results in systems that are thought to be orderly. This idea was discovered by a group of physicists who had met one evening to attempt to figure their income taxes. The right situations, conditions, and amounts of black coffee prodded these scientists into developing the basis for what today is a booming study of things that most people have already figured out through common sense.
The quintessential example of chaos is what is known as the "Lorenz Butterfly Effect." Edward Lorenz noticed that no matter how close the initial points were, graphs of weather pattern behavior would always spiral away from each other unpredictably. The analogy states that if we were to know every single element of the weather, we still would be unable to predict it, since something as simple as the fluttering of a butterfly would irreversibly destroy those predictions. His award winning paper, Let's Shoot all the Butterflies spelled out this notion in mathematical terms, a notion which most of humanity had taken for granted since the advent of television weathermen. In an attempt to follow up on his earlier glory, Lorenz published the paper Chaos in Studio 3B, an attempt to prove that it was mathematically impossible to predict if NBC meteorologist Willard Scott would continue wearing a toupee. This second paper was poorly received. At any rate, the science of chaos seems to be here to stay, at least as long as grant money doesn't dry up.
Part 2: Fractals, or Large grants, powerful computers, and really nifty pictures.
The late 1970's witnessed the publication of an extraordinary book. This was, of course, the novilisation to Saturday Night Fever. However, a less popularized work, The Fractal Geometry of Nature also appeared. This book brought the new science of chaos and mathematics together, and gave us a large number of very stylish pictures and even some special effects for Star Trek II: The Wrath of Khan. Benoit B. Mandelbrot came up with the notion that if he could create a computerized version of an acid trip, then he would gain international fame and fortune. He was successful in designing the colorful and intricate Mandelbrot set, but because he had a very silly name, was unable to garner the fame and fortune he sought. His great achievements remain relegated to art posters and t-shirts sold by starving grad students at physics symposia. There are allegations that Mandelbrot did not invent the mandelbrot set, but rather borrowed the work of now deceased colleagues. However, it is unlikely that it would have been termed anything else, since all his colleagues were French or Belgian, and "Mandelbrot" was less silly and probably much easier to spell than any of their names.
Fractals used to be the domain of mathematicians only, as they were the only ones who had access to the computing power needed to create them.1 Now, anyone with a personal computer can create vividly-colored, beautiful fractal pictures, using software available at little or no cost.2 This has elicited violent reactions from old-garde mathematicians, many of who staged sit-ins in their computer labs and began burning their computer punch-cards in protest. Mandelbrot was probably the most vocal, openly discussing violence as a solution to the fractal-access problem. There were even rumours that at one conference, closed to all non-mathematicians, he asked to be referred to as "Benoit X" and suggested that only a violent overthrow of the U.S. government would place fractals back into the hands of their creators. A disturbed colleague disclosed to journalists that he thought Mandelbrot had become, quote "loopy as a loon." These reports are, however, JUST rumours. There is no firm evidence that a fractal-mad group of mathematical terrorists will hold the United States hostage.3
But what are fractals? Fractals are complex geometric patterns that are self-similar at every level of magnification. In layman's terms, a fractal is a constantly repeating pattern, the same no matter how closely one analyzes it. Applying this definition, examples of fractals are coastlines, clouds, and political campaigns. The Mandelbrot set is the most easily recognizable fractal, since it vaguely resembles the paisley neckties that all fashionable men wore during the late 70's (Ironically, the Set was discovered at that period as well. There may be a correlation).
Fractals and chaos are integrally related. The behavior of a chaotic function can be described on a graph as a fractal picture. Sometimes the functions produce beautiful pictures, such as the Julia and Mandelbrot sets. Often they end up looking vaguely like something that is commonly found growing beneath refrigerators in college dormitories. That falls into the realm of artists and aestheticians, and has no meaning to anyone in the scientific community except the grad student trying to make a fast buck selling a "Chaos and Fractals" T-shirt. Graduate students have played a great role in the development of fractal geometry, human mentality and its link to chaos.4 Several mathematicians organized a project in conjunction with many clinical psychologists and counterintelligence experts, an experiment involving subjecting a group of desperate starving doctoral candidates to several days in a sensory deprivation tank (they were paid at least minimum wage). Upon their release, many of them described seeing colorful patterns in front of their eyes. The mathematicians claimed that they were describing fractals, since the behavior of the released students was clearly chaotic. The psychologists called it mere hallucination, and were subsequently beaten and subdued by the mathematicians (the counterintelligence experts, who had supplied the sensory-deprivation tank, merely smiled grimly, took some notes, and returned to Washington). Whether chaos and fractals are actually related outside the twisted imaginations of scientists and mathematicians is a hotly debated topic.
Part 3: Human Interaction with Non-linear Dynamical Systems, or Deal with it.
There is conclusive evidence that all the forces of nature are ruled by chaos. Every man, woman, and child on this planet (or any other) is going to have to learn to coexists with this powerful natural phenomena. There are several ways to do so: