Principles of Chaos Theory

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Science is an art that depends heavily on predictability, organization, and painstaking accuracy. Since its earliest inception, scientists have worked to provide humanity with the most accurate and precise view of the world as possible. Using the one-two punch of mathematics and physics, mankind slowly progresses through every great phenomenon and mystery the world has to offer, attempting to explain it with simple, rational definitions and equations. Because of this, we are accustomed to having a linear view of the world – every question, no matter how complex, can have a one simple answer that completely addresses it. In many respects, this is a perfectly acceptable way of thinking. After all, we have a thorough understanding of many patterns found in nature. However, there are still many things left that linear mathematics is not able to explain. For example, how can we mathematically predict the shapes of clouds? Or the exact path of a lightning bolt? Or the pattern of a tree's bark? Questions like these are beyond the reach of conventional mathematics. To explain them, a different type of thinking must be used – something that can take science and mathematics to a different level and relate them to the inherent unpredictability in the world around us. This thinking is known as Chaos Theory.

Although the word "chaos" is traditionally associated with total disorder, it is misleading when describing Chaos Theory. In 1986, a group of scientists submitted a new definition for chaos: "Stochastic behavior occurring in a deterministic set." This definition was later changed to "Lawless behavior that is ruled by law." Although Chaos Theory has only been around for about 50 years, its principles have been around for much longer than that. It wasn't until recently that scientific knowledge progressed to the point where the distinction between linear and chaotic science began to become apparent. In 1898, a French mathematician named Jacques Hadamard...
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