Chaos Theory: Definition, History & Examples

Instructor: Emily Cummins
This lesson discusses the branch of science called chaos theory, which helps us to understand non-linear and difficult to predict phenomenon. Test your knowledge with a quiz following the lesson.

Definition of Chaos Theory

Have you ever thought that the world is a chaotic place! When we think of chaos, we might think of a disorderly crowd or a riot. But there's another use of the word 'chaos' and, in fact, there's a branch of science and mathematics devoted specifically to study chaos. It's called chaos theory, and it's the science of dealing with non-linear, hard to control phenomena in our world.

Chaos theory helps us understand complicated behavior or natural occurrences and studies large and complex systems. For our purposes here, think of a complex system as scenarios or events that have many, many components which make them quite difficult to understand.

In a way, chaos theory is meant to help us study surprises! Now, this may seem funny because how can you study something you are not expecting? Let's try and figure out what chaos theorists are talking about.

Principles of Chaos Theory

Chaos theory has a few important principles, starting with one you've probably heard of - the butterfly effect. This principle suggests that the cause of a typhoon off the coast of Japan can be traced to a butterfly flapping its wings in Mexico. According to the butterfly effect, if the butterfly had never flapped its wings, the typhoon would not have happened. Another way to put this is that initial conditions are extremely important, and they have a major impact on the outcome of things. Something small at the beginning (a butterfly flapping its wings) leads to something major (a typhoon) in the end.

Another important principle of chaos theory is unpredictability. Basically, we can never possibly know every single initial event of a complex system. This means that the ultimate outcome of an event is never truly known. We can't possibly accurately predict most things because even very small errors or oversights could change the outcome.

History of Chaos Theory

Chaos theory is a large and complicated body of work and its history, fittingly, is not exactly linear. But, let's talk about some of the earliest work that was most important to the development of chaos theory.

In the early 1900s, a french mathematician by the name of Henri Poincare began studying orbits in the solar system.

Henri Poincare
Henri Poincare, Chaos Theory

Early work on the solar system, such as that done by the physicist Newton, had developed nice, neat equations that showed the ways in which orbits worked. Curious, Poincare decided to see what might happen if he added more elements into these equations.

When Poincare changed the initial starting point of some of the orbits in the solar system, he found very different results! Poincare found that even very small changes to the initial equations made it almost impossible to predict how orbits might work. This discovery by Poincare led people to refer to him as the father of chaos theory.

Then, the invention of the computer really propelled chaos theory forward. In the 1960s, a scientist by the name of Ed Lorenz, working at the Massachusetts Institute of Technology (MIT), developed a computer program based on complex mathematical formulas that generated weather patterns. Lorenz generated a number of variables he thought could predict weather patterns. After a few months, Lorenz decided he wanted to see the weather patterns again. So, he re-entered all of the data but got very different results! What had happened?

He had made a decimal error when reentering the values! He found that this dramatically impacted the patterns the computer generated. Both of these different examples support what we mentioned in the beginning of the lesson about initial conditions: indeed, changing something at the beginning, even if very small, leads to very different outcomes!

Because scientists had focused on linear ways of thinking about problems, complex systems had been understudied. Non-linear systems, like weather patterns, are much more complicated and required new ways of thinking. So, thanks to Poincare's early work on orbits and Lorenz's work on the computer, mathematicians, physicists, and philosophers alike began working more in the field of chaos theory.

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