A brief introduction to chaos theory

In science there is a complex and well-developed theory that explains phenomena that are nonlinear and unpredictable. Known as chaos theory, there are principles that can be applied to the understanding of natural phenomena that are effectively impossible to control: turbulence, the weather, the stock market, brain states, and so on. In chaos theory, complex and specialized mathematics are employed to provided understanding of how things are connected and how multiple factors can have long-reaching effects.

Chaos theory is not the study of disorder. It is rather the search for order in systems that are so complex that they cannot be predicted. Recognizing, studying and beginning to understand the chaotic, fractal nature of our world can yield new insight, power and wisdom. One example is the ability of the pilot of a hot air balloon to take off from one location and land at a predicted spot. There are many factors affecting the direction and speed of flight. The atmosphere is complex and displays chaotic dynamics. The wind doesn’t blow in the same direction or at the same speed at all altitudes. Variations in temperature and relative humidity affect the rate of rise or descent of the balloon. Balloon pilots don’t land in the same field every time and they can’t predict with complete accuracy the duration of their trip, but the more they understand, the more precise their flights become. In some locations balloon tour operators have honed the experience into a marketable adventure. That is just one example of chaos theory in application.

Another area of study that has yielded increased understanding from the application of chaos theory is the study of ecology. A seemingly small cause in one location can have a dramatic effect in another. When wolves were reintroduced to Yellowstone National Park, certain fish species began to increase in population. The wolves practiced predation on the elk herds, decreasing their size. The elk then ate less of the waterside plants which allowed the beaver population to increase. The increase in beaver activity produced more pools and ponds as fish habitat. This brief summary is a very elementary overview. The actual process was much more complex, but you can see how in an ecosystem, there can be distant and seemingly unpredictable results. The more we understand chaos theory, the more responsible we can become in the decisions we make.

Once again, chaos theory posits that the world isn’t merely random. It is not based on total disorder, but rather on the study of the complexity of systems.

One principle of chaos theory is known as the butterfly effect. The theory is that a butterfly flapping its wings in New Mexico, causes a small disturbance in the air surrounding it. This disturbance affects other factors, such as the density of water molecules that can be suspended in the tiny space around the wings. That effect in turn increases the water density in other ares of the atmosphere. It might even contribute to precipitation. Effect piles upon effect throughout the entire atmosphere of the planet. If we could fully understand all of the effects, there would be a traceable relationship between that butterfly and a hurricane in China. This is not to say that the butterfly caused the hurricane, but rather that small changes in initial conditions can lead to drastic changes in the results.

Another important principle of chaos theory is unpredictability. It is simply impossible to know all of the initial conditions of a complex system in perfect detail. There will always be factors that we failed to observe. Therefore we cannot predict outcome with complete accuracy. Even a slight error in measuring one factor can be amplified dramatically rendering the prediction useless. To return to the butterfly example, since we don’t know about all of the butterflies in the world, we can’t predict the weather with 100% accuracy.

In chaos theory, systems become chaotic when there is feedback present. This is directly observable in the behavior of the stock market. As the value of a stock rises or falls, people are inclined to buy or sell that stock. Their decision, in turn, affects the price of the stock. The effect results in chaotic behavior that makes the market impossible to predict with complete accuracy.

The science of chaos isn’t based in unpredictability, however, it is the search for patterns within complex systems. Chaos theory leans heavily on the search for fractals. A fractal is a never-ending pattern. The pattern is most commonly very complex, but appears to operate in a similar pattern over different scales. The process of repeating the same simple process over and over in an ongoing feedback loop in which the simple process affects the next step in the process. We can understand the simple process, and observe the repetition, but lack complete information to fully diagram the fractal. The pattern of a seashell, the distribution of trees in a dense forest, the spread of a river delta, and the shape of a mountain are examples of fractals in nature.

Albert Einstein wrote, “As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.” He wasn’t dismissing mathematics as a tool to study reality, but rather acknowledging the complexity of living systems.

People are more comfortable with chaos than you might expect.

A winning combination of Americans, not a majority, decided that they were so fed up with the status quo that they took a gamble on someone who had no government experience and had never held elected office. It was a metaphorical, “let’s throw everything up in the air and see how it lands - it can’t be worse than it is.”

The result of the decision is an increase in the unpredictability of government. The dictionary defines “rogue state” as one “that conducts its policy in a dangerously unpredictable way.” So far it appears that our country is heading in that direction under the new administration.

Chaos theory leads us to believe that there are patterns. They are complex and dynamic and very difficult to observe. A “tweet” could be the flapping of a butterfly wing that results in a diplomatic superstorm in another country.

The problem with the incoming administration is that its chaos doesn’t seem to be signaling new policies as much as the improvisation of an ill-prepared and unqualified leader. So far the unpredictability of the administration is not a theory. It’s the absence of one.

I’m no more qualified to predict the future of politics than I am to predict the weather. I guess we have to take a “wait and see” attitude. Still, I think it would be prudent to be prepared for a storm.

Copyright (c) 2016 by Ted E. Huffman. I wrote this. If you would like to share it, please direct your friends to my web site. If you'd like permission to copy, please send me an email. Thanks!