## Chaos Theory

Summary: Chaos theory is a mathematical theory that can be used to explain complex systems such as weather, astronomy, politics, and economics. Although many complex systems appear to behave in a random manner, chaos theory shows that, in reality, there is an underlying order that is difficult to see.
Originators: Henri Poincaré (1854-1912), Edward Lorenz (1917-2008)
Keywords: order, chaos, complex systems, determinism, butterfly effect, sensitive dependence on initial conditions, nonlinear dynamics, chaos dynamics
Many complex systems can be better understood through the lens of Chaos Theory. Henri Poincaré, a mathematician, laid the groundwork for Chaos Theory.[i] He was the first to point out that many deterministic systems display a “sensitive dependence on initial conditions.” Poincaré described this concept in the following way: “It may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible.”
For example, Poincaré pointed out that the apparent lack of order seen in many astronomical systems was actually not random or chaotic. Instead, astronomers were just not seeing the small changes in initial conditions that were leading to humongous differences in the final phenomena that were being observed.
Later, in the 1900s, Edward Lorenz officially coined the term Chaos Theory. Lorenz studied Chaos Theory in the context of weather systems. When making weather predictions, he noticed that his calculations were significantly impacted by the extent to which he rounded his numbers.  The end result of the calculation was significantly different when he used a number rounded to three digits as compared to a number rounded to six digits.
His observations on Chaos Theory in weather systems led to his famous talk, which he entitled, “Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas?” In reference to this talk, Chaos Theory has also been described as the “butterfly effect.”
Application of Chaos Theory
Chaos theory has a lot to teach people about decision making in complex environments. The mathematical concepts used to understand physical systems are now being applied to social environments such as politics, economics, business, and other social sciences.[ii]
Although applying Chaos Theory to business settings is still in its infancy, social scientists describe the following applications as useful when making business decisions.[iii]

Thursday January 01, 1970

Chaos theory suggests that spending a lot of time trying to predict the future of complex, non-linear systems may be better spent elsewhere. Instead of trying to predict long-term future outcomes, businesses should consider and plan for multiple possible outcomes.
Chaos theory reminds business owners that small changes in business practice can lead to huge changes in future outcomes based on the concept of sensitive dependence on initial conditions. Some business managers underestimate the possibility for large unexpected changes, and should reconsider their mindset on this matter.
Chaos theory assumes that there is order behind seemingly random events. Even though businesses may not be helped by making long-term future predictions, they can make short-term forecasts to help with business decisions.
Because of the complexity and unpredictability inherent in complex systems, businesses need clear guidelines for employees to follow. However, since sudden and drastic changes are bound to occur, business owners should be ready to adapt these guidelines as necessary.

Thursday January 01, 1970

References
[i] Oestreicher, C. (2007). A history of chaos theory. Dialogues in Clinical Neurosciene, 9(3), 279-289.
[ii] Richards, D. (1990). Is strategic decision making chaotic? Systems Research and Behavioral Science, 35(3), 219-232.
[iii] Chaos theory and strategy: Theory, application, and managerial implications. Strategic Management Journal, 15, 167-178.

Thursday January 01, 1970

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