An Introduction to Chaos Theory

Edward Lorenz was a meteorologist who was obsessed with predicting the weather. In 1960, he had a computer set up, with a set of twelve equations to model the weather. Though it failed to predict the weather it managed to theoretically predict what the weather might be. Anytime in the future if he wanted to check for the weather using his formulae he would start from the middle values, the results would drastically differ from his original findings. This is supposedly the beginning of chaos theory. The name "chaos theory" comes from the fact that the systems that the theory describes are apparently disordered, but chaos theory is really about finding the underlying order in apparently random data. Gollub and Solomon contend that a chaotic system is defined as one that shows sensitivity to initial conditions. That is, any uncertainty in the initial state of the given system, no matter how small, will lead to rapidly growing errors. The main catalyst for the development of chaos theory was the electronic computer.

It is said that the amount of difference between the two extreme points of the curve is so small that a it can be encompassed by the flapping wings of a butterfly. The flapping of a single butterfly's wing today produces a tiny change in the state of the atmosphere. Over a period of time, what the atmosphere actually does diverges from what it would have done. A fish swimming off the coast of Japan can produce tidal waves near the equator. The agglomeration of small seemingly events can lead to drastic and permanent changes. The universe is a chaotic place. It is full of uncertainty and it can be difficult to predict exactly what is going to happen at any given time be it the present or the far future. Everything that exists is constantly subjected to the chaos present in the universe. The existence of chaos has been documented over the ages. The concept can be seen in early Hindu religious philosophy to the Babylonian epics. Even the most ordinary household tasks are subject to the theory.

Chaos theory expert James Gleick provides a startling insight into chaos theory in his documentation of the experiment conducted by Mandelbrot. An employee of IBM, Benoit Mandelbrot was a mathematician studying this self-similarity. One of the areas he was studying was cotton price fluctuation. No matter how the data on cotton prices was analyzed, the results did not fit the normal distribution. Mandelbrot eventually obtained all the available data on cotton prices, dating back to 1900. When he analyzed the data with IBM's computers, he noticed an astonishing fact. The numbers that produced aberrations from the point of view of normal distribution produced symmetry from the point of view of scaling. Each particular price change was random and unpredictable. But the sequence of changes was independent on scale: curves for daily price changes and monthly price changes matched perfectly. Incredibly, analyzed Mandelbrot's way, the degree of variation had remained constant over a tumultuous sixty-year period that saw two World Wars and a depression.

Chaos theory progressed more rapidly after mid-century, when it first became evident for some scientists that linear theory, the prevailing system theory at that time, simply could not explain the observed behavior of certain experiments. It has been said that if the universe is an elephant, then linear theory can only be used to describe the last molecule in the tail of the elephant and chaos theory must be used to understand the rest. Linear systems in nature are relatively rare, and almost all interesting real world systems are described by non-linear systems. Moore's law regarding the increase in the processing speed of the processor has brought the scope of chaos theory into the common domain. The human heart too has a chaotic pattern. The time between beats does not remain constant; it depends on how much activity a person is doing, among other things. Under certain conditions, the heartbeat can speed up. Under different conditions, the heart beats erratically. It might even be called a chaotic heartbeat. The analysis of a heartbeat can help medical researchers find ways to put an abnormal heartbeat back into a steady state, instead of uncontrolled chaos.

A lot of occurrences in the world are attributed to chaos theory. But the funny part is that most of what is attributed may not have anything to do with chaos theory. Now why do we need to create more chaos?