"The flapping of a single butterfly's wing today produces a tiny change in the state of the atmosphere. Over a period of time, what the atmosphere actually does diverges from what it would have done. So, in a month's time, a tornado that would have devastated the Indonesian coast doesn't happen. Or maybe one that wasn't going to happen, does." (Ian Stewart, Does God Play Dice? The Mathematics of Chaos, pg. 141)
Chaos theory has been widely studied to describe how small changes can have tremendous effects within complex non-linear systems. Gleick's article introduces the story of the earliest pioneer in chaos theory, Edward Lorenz, who was working on the problem of weather predication using a simple digital computer.In an attempt to repeat a sequence of data and save time he started the simulation in the middle of its course, he found that the machine began to predict was completely different from the weather calculated before. This phenomenon, common to chaos theory, is also known as sensitive dependence on initial conditions. Just a small change in the initial conditions can drastically change the long-term behavior of a system. Lorenz's discovery proved that meteorology could not reasonably predict long-term weather conditions. Currently, the chaos theory has become a ubiquitous part of science to explain phenomena in complex systems. Some interesting examples include Jupiter’s red spot, fractal geometry, and economic forecasting.
Chaos theory has also been considered as the skepticism towards the human ability to understand the nature. However, in my opinion, chaos theory is more than just to admit the apparent disorder in complex systems. Chaos is not random, and the aim of chaos theory is really about finding the underlying order in apparently random data. As shown in many studies, chaotic systems actually reveal stable statistical patterns which might help us to understand how they work.
Reference Article: Chaos Theory: A Brief Introduction. http://www.imho.com/grae/chaos/chaos.html
