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 published a study describing the chaotic motion of free particles gliding on a negative curvature. Hadamard was able to show that their trajectories were unstable and unpredictable, diverging exponentially from one another. In the early 1900s, Henri Poincare, the great French mathematician/philosopher/physicist, declared the existence of non-periodic orbits. Both of these discoveries would play a major role in the formation of Chaos Theory 60 years later. As scientific and technological knowledge began to expand dramatically in the mid-1900s, it became more and more apparent that linear science could not explain certain observations. However, it wasn't until the invention of the computer that the stage was set for Chaos Theory to emerge. Early computers, such as ENIAC, were often used to run simple weather forecasts. One early user of these systems was Edward Lorenz, an American meteorologist. In 1961, Lorenz was using a basic computer to run a weather simulation. His goal was to use a sequence of data to simulate weather conditions at a future point in time. To do this, he composed a list of data variables corresponding to the different factors required to predict weather. As was a relatively common mathematical practice at the time, he decided to enter his numbers with three decimal places of accuracy. To his surprise, he got completely different results every time he ran the simulation. When he looked into it, he found that the simulation required at least 6 decimal places of accuracy to get any sort of consistency in simulation results. He was highly intrigued How could a 0.000001 variation in any one of his factors be the difference between sunshine and rainstorm? It was a crucial realization that heralded the unofficial birth of modern Chaos Theory: Tremendously small changes in initial conditions produce large changes in the long-term. In 1963, Lorenz published his findings in a meteorological journal. Because he was not a mathematician or...

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 published a study describing the chaotic motion of free particles gliding on a negative curvature. Hadamard was able to show that their trajectories were unstable and unpredictable, diverging exponentially from one another. In the early 1900s, Henri Poincare, the great French mathematician/philosopher/physicist, declared the existence of non-periodic orbits. Both of these discoveries would play a major role in the formation of Chaos Theory 60 years later. As scientific and technological knowledge began to expand dramatically in the mid-1900s, it became more and more apparent that linear science could not explain certain observations. However, it wasn't until the invention of the computer that the stage was set for Chaos Theory to emerge. Early computers, such as ENIAC, were often used to run simple weather forecasts. One early user of these systems was Edward Lorenz, an American meteorologist. In 1961, Lorenz was using a basic computer to run a weather simulation. His goal was to use a sequence of data to simulate weather conditions at a future point in time. To do this, he composed a list of data variables corresponding to the different factors required to predict weather. As was a relatively common mathematical practice at the time, he decided to enter his numbers with three decimal places of accuracy. To his surprise, he got completely different results every time he ran the simulation. When he looked into it, he found that the simulation required at least 6 decimal places of accuracy to get any sort of consistency in simulation results. He was highly intrigued How could a 0.000001 variation in any one of his factors be the difference between sunshine and rainstorm? It was a crucial realization that heralded the unofficial birth of modern Chaos Theory: Tremendously small changes in initial conditions produce large changes in the long-term. In 1963, Lorenz published his findings in a meteorological journal. Because he was not a mathematician or...

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