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An Introduction to Chaos Theory

Anish Chandy May 13, 2019
According to chaos theory, giant tidal waves are formed in the equator, because of the movement of a fish is Japan.
Edward Lorenz was a meteorologist, who was obsessed with predicting the weather. In 1960, he had a computer set up with twelve equations, to model the weather. Though it failed to model 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 formula, he would start from the middle values, and the results would drastically differ from his original findings. This was supposedly the beginning of chaos theory.
Its name comes from the fact that the systems that the theory describes are apparently disordered, but it 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 this 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 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 in the future.
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 seemingly small 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, through 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, 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 this 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, amongst 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 it.