According to mathematics our world is steeped in unpredictability, popularly referred to as chaos. The very course of our lives from the crib to the grave meanders through a wilderness of unpredictability, passing through random events and circumstances, and sometimes spontaneously changing course on an unexpected dime. Weather patterns, geological formations, and stock market fluctuations are all examples of chaotic systems, impossible to predict.
And yet, arbitrary lines can paint a picture. Patterns can emerge from chaos and incredibly complex structures begin to hint at an order underneath it all. A grand design, if you will. And just when we think we know what is going to happen next, a new variable changes everything and the order is disrupted. This chaos-to-order-to-chaos dynamic is all around us but what does it mean? How does one live confidently and comfortably in an unpredictable world?
In 1961 an MIT meteorologist named Edward Lorenz, while attempting to model weather patterns, observed that slight deviations (to one-millionth of a decimal point) in the initial variables of a very simple system could result in highly erratic and unpredictable behavior. He explains in the resulting paper “Deterministic Nonperiodic Flow” that:
“Two states differing by imperceptible amounts may eventually evolve into two considerably different states.”
A popular analogy, termed the “butterfly effect,” was coined by Lorenz in his 1972 paper, “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” The idea was to illustrate how seemingly innocuous and insignificant events (the flap of a butterfly’s wings) can have drastic consequences over time (a tornado in Texas). Minute details, over time, can become exaggerated. Moreover, as it is impossible to account for all conceivable variables at any one moment, even in the most controlled environments, unpredictability—or chaos—is unavoidable.
Take an experiment as simple as flipping a coin. There are perceptively only three variables affecting the outcome: the force imparted to the coin, the height at which it is tossed, and the air resistance. Theoretically, it should be possible to control these variables entirely and to predict how the coin will land. It turns out, however, that in practice it is impossible to control exactly how fast and how high a coin flips. Any slight variance to the degree of a hundred decimal points caused by a random fluctuation in air pressure can dramatically alter the sequence and disrupt its predictability.
According to Andreas Albrecht and Daniel Phillips of the University of California at Davis, random quantum fluctuations such as those caused by one molecule colliding with another, can be amplified sufficiently by known physical processes to account for nearly all probabilities in the macroscopic world. 
In other words, chaos, or unpredictability, is deeply woven into the fabric of the cosmos.
Discovering a Pattern
A few years later, Benoit Mandelbrot, an employee at IBM, noticed something rather peculiar while analyzing historical fluctuations in the prices of cotton. Looked at day-to-day the prices seemed to fluctuate at random, yet when scaled over time a pattern began to emerge: fluctuations from one day to the next mirrored those from one month to the next. This pattern remained constant over sixty years and two world wars.
A distinct peculiarity of this pattern was that it was self-similar, meaning the picture of the whole was replicated within its parts. The animation shown below demonstrates how a self-similar shape replicates within itself.
These types of patterns, known as fractals, are all over the natural world. The weather works in fractal patterns, coastlines form in fractals, the way trees and lakes meander are fractals. The universe replicates fractal patterns; compare a diagram of an atom to that of the solar system:
Order and chaos go hand in hand, oscillating with the same ebb and flow as the tides. They are the yin and the yang of physics.
Confident Amidst the Chaos
All of these patterns, remarkable as they are, are still entirely unpredictable. Although the leaves on a tree share a pattern, we cannot use that pattern to build a replica of the tree. The order must grow organically on its own. In other words, we may be able to understand the laws of nature but that does not bring us any closer to forecasting what actions nature will take.
And perhaps the patterns are in the eye of the beholder. A recent study suggests the human brain might invent patterns to offer up a sense of self-control. To some degree all people seek to gain the upper hand in the game of life. A sense of control makes the world feel safer, not so threatening. Yet, at some point it is essential to realize that the world is not in our control. No matter how perfect our models are, no matter how much knowledge we have attained, there is simply no way to account for all the infinite variables that may or may not play in to our lives. Total control is impossible.
And that’s okay. Order comes on its own. The Earth and everyone on it emerged from a chaotic soup of atoms, molecules, and star-dust and yet we are not all flying off into the ether.
This natural fluctuation between order and chaos is the rhythm of the cosmos. It is the beat to which we all must dance, like it or not.
Really, who would have it any other way?
Posted by Zimmerman
1. Lorenz, E.N. (1972) Predictability; Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas? Available from The American Association for the Advancement of Science (http://eaps4.mit.edu/research/Lorenz/Butterfly_1972.pdf) (Back to Post)
3. Mandelbrot, B. The Variation of Certain Speculative Prices. The Journal of Business, Vol. 36. No. 4 (Oct., 1963) (The University of Chicago Press) (Back to Post)