What is Chaos Theory

Chaos theory is a mathematical concept that explains that it is possible to get random results from normal equations. The main precept behind this theory is the underlying notion of small occurrences significantly affecting the outcomes of seemingly unrelated events. Chaos theory is also referred to as "non-linear dynamics."

BREAKING DOWN Chaos Theory

Chaos theory has been applied to many different things, from predicting weather patterns to the stock market. Simply put, chaos theory is an attempt to see and understand the underlying order of complex systems that may appear to be without order at first glance.

The first real experiment in chaos theory was done in 1960 by a meteorologist, Edward Lorenz. He was working with a system of equations to predict what the weather would likely be. In 1961, he wanted to recreate a past weather sequence, but he began the sequence midway and printed out only the first three decimal places instead of the full six. This radically changed the sequence, which could reasonably be assumed to closely mirror the original sequence with only the slight change of three decimal places. However, Lorenz proved that seemingly insignificant factors can have a huge effect on the overall outcome. Chaos theory explores the effects of small occurrences dramatically affecting the outcomes of seemingly unrelated events.

Chaos theory is highly controversial and extremely complicated. Related to financial markets, proponents of chaos theory believe that price is the very last thing to change for a stock, bond or some other security. Price changes can be determined through stringent mathematical equations predicting the following factors:

1. A trader's own personal motives, needs, desires, hopes, fears and beliefs
2. Volume changes
3. Acceleration of the changes
4. Momentum behind the changes

Core Factors Behind Chaos Theory

  • The Butterfly Effect: According to the Butterfly Effect, a butterfly in California can cause a hurricane in China if the butterfly flaps its wings at just the right point in space and time. While the result isn't immediate, the causal connection is real. The hurricane would not have happened if not for the butterfly. Expressed more generically, small changes in initial conditions can lead to drastic changes in final results. Human civilization is an ongoing demonstration of this principle in action. Who knows, for instance, what the long-term effects of teaching millions of people about chaos theory will be?
  • Unpredictability: Because all the initial conditions of a complex system are not fully knowable, it is impossible to predict the fate of a complex system. Even if all the conditions can be measured, slight errors in measurements will be amplified dramatically, rendering any prediction useless. This is why accurate long-range weather prediction will always remain impossible.
  • Order/Disorder: Chaos is not simply disorder. Chaos comprises the transitions between order and disorder, which often occur in surprising ways.
  • Mixing: Turbulence ensures that, in time, two adjacent points in a complex system will eventually end up in very different positions. For example, two neighboring water molecules may end up in different parts of the ocean or even in different oceans. A group of helium balloons that launch together will eventually land in drastically different places. Mixing is thorough because turbulence is non-linear and happens at all scales.