# Chaos Theory: the Smallest things can have big consequences

One can tell by the name itself what chaos theory might mean. Chaos means something that is unpredictable, random and unstable. There are many known and predictable phenomena in science such as electricity, gravity or chemical reactions; however, chaos theory examines things that are not possible to control. For example, nature:  weather, earthquakes, clouds, trees, tsunamis, and tornadoes. Other than nature, there are human-related unpredictable things, such as the stock market and our brain states. Chaos theory is a field of mathematics that deals with complex systems whose behavior is highly sensitive to the slightest changes in initial conditions. For example, someone clapping their hands could change the weather, so even the smallest alterations can have big consequences.

Chaos theory emerged around the second half of the 20th century. This is because chaos theory has complex systems and these systems contain many elements that move. For this reason, computers are needed to calculate all the different possibilities.  How did chaos theory come to be? A man named Edward Lorenz, a meteorologist, created a weather model on his computer in 1960. This weather model consisted of an extensive array of complex equations to predict weather conditions. This model always gave different sequence of numbers that represented weather conditions. One day he became curious and ran his own tests to see what the outcome would be. After running a sequence, he started running the same sequence halfway through, re-entering the numbers the first sequence had given him at that point. The results were not what he was expecting; they were entirely different from his first outcomes. The second time, he entered numbers that were rounded to three instead of six digits (for example, .506 versus .506127). Since the difference between these numbers is not much, he expected the results to be only slightly varied. However, that small error gave completely different outcome. Form this he concluded that even the slightest differences in initial conditions makes prediction of past or future outcomes impossible.

Image: J.L.Westover.

There are many principles of Chaos. One of them is the butterfly effect, also described by Lorenz. It is said that even a small butterfly flapping its wings in America can create a hurricane in Japan; if the butterfly did not flap its wing at the “right” time in space then the hurricane would not have happened. Even the smallest behavior has a direct effect in the future. Another principle is unpredictability. Since it is not possible to know all the initial conditions of a complex system in adequate detail, we can’t possibly know the outcome of those. As explained above, even the smallest change in numbers can lead to a big errors in prediction; outcomes  can be completely different from what is expected.

We can never know for certain when we might have a storm or tsunami until few days before it’s about to happen. Similarly to the weather, chaos is present in our daily life. For example,  the bus you usually take was late and you decided to take another bus, and randomly you meet a person, and you both start talking, he makes an impression on you, you go on a date with him, fall in love, get married and grow old together. Now imagine that the person had a similar situation: he decided to take this bus rather than his usual bus and met you. What if he never got on that bus at the right time to meet you, and what if you had decided to wait for you usual bus? It is scary to think about how one small decision makes such a big difference in your life.

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