Manifestations of Chaos [1/20] |
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From the first four lessons, you have learned that in a chaotic system, using the laws of physics to make precise long-term predictions is impossible, even in theory. Making long-term predictions to any degree of precision at all would require giving the initial conditions to infinite precision. | ||

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Manifestations of Chaos [2/20] |
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At the time of its discovery, the phenomenon of chaotic motion was considered a mathematical oddity. In the decades since then, physicists have come to discover that chaotic behavior is much more widespread, and may even be the norm in the universe. | ||

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Manifestations of Chaos [3/20] |
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One of the most important discoveries was made in 1963, by the meteorologist Edward Lorenz, who wrote a basic mathematical software program to study a simplified model of the weather. | ||

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Manifestations of Chaos [4/20] |
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Specifically Lorenz studied a primitive model of how an air current would rise and fall while being heated by the sun. | ||

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Manifestations of Chaos [5/20] |
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Lorenz's computer code contained the mathematical equations which governed the flow the air currents. Since computer code is truly deterministic, Lorentz expected that by inputing the same initial values, he would get exactly the same result when he ran the program. | ||

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Manifestations of Chaos [6/20] |
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Lorenz was surprised to find, however, that when he input what he believed were the same initial values, he got a drastically different result each time. | ||

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Manifestations of Chaos [7/20] |
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By examining more closely, he realized that he was not actually inputing the same initial values each time, but ones which were slightly different from each other. | ||

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Manifestations of Chaos [8/20] |
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He did not notice the initial values for each run were different because the difference was incredibly small, so small as to be considered microscopic and insignificant by usual standards. | ||

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Manifestations of Chaos [9/20] |
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The mathematics inside Lorenz's model of atmospheric currents was widely studied in the 1970's. Gradually it came to be known that even the smallest imaginable discrepancy between two sets of initial conditions would always result in a huge discrepancy at later or earlier times, the hallmark of a chaotic system, of course. | ||

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Manifestations of Chaos [10/20] |
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Scientists now believe that like Lorenz's simple computer model of air currents, the weather as a whole is a chaotic system. This means that in order to make long-term weather forecasts with any degree of accuracy at all, it would be necessary to take an infinite number of measurements. | ||

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Manifestations of Chaos [11/20] |
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Even if it were possible to fill the entire atmosphere of the earth with an enormous array of measuring instruments---in this case thermometers, wind gauges, and barometers---uncertainty in the initial conditions would arise from the minute variations in measured values between each set of instruments in the array. | ||

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Manifestations of Chaos [12/20] |
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Because the atmosphere is chaotic, these uncertainties, no matter how small, would eventually overwhelm any calculations and defeat the accuracy of the forecast. | ||

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Manifestations of Chaos [13/20] |
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This principle is sometimes called the "Butterfly Effect." In terms of weather forecasts, the "Butterfly Effect" refers to the idea that whether or not a butterfly flaps its wings in a certain part of the world can make the difference in whether or not a storm arises one year later on the other side of the world. | ||

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Manifestations of Chaos [14/20] |
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Because of the "Butterfly Effect," it is now accepted that weather forecasts can be accurate only in the short-term, and that long-term forecasts, even made with the most sophisticated computer methods imaginable, will always be no better than guesses. | ||

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Manifestations of Chaos [15/20] |
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Thus the presence of chaotic systems in nature seems to place a limit on our ability to apply deterministic physical laws to predict motions with any degree of certainty. The discovery of chaos seems to imply that randomness lurks at the core of any deterministic model of the universe. | ||

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Manifestations of Chaos [16/20] |
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Because of this fact, some scientists have begun to question whether or not it is meaningful at all to say that the universe is deterministic in its behavior. This is an open question which may be partially answered as science learns more about how chaotic systems operate. | ||

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Manifestations of Chaos [17/20] |
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One of the most interesting issues in the study of chaotic systems is whether or not the presence of chaos may actually produce ordered structures and patterns on a larger scale. | ||

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Manifestations of Chaos [18/20] |
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Some scientists have speculated that the presence of chaos---that is, randomness operating through the deterministic laws of physics on a microscopic level---may actually be necessary for larger scale physical patterns to arise. | ||

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Manifestations of Chaos [19/20] |
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Recently, some scientists have come to believe that the presence of chaos in physics is what gives the universe its "arrow of time," the irreversible flow from the past to the future. | ||

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Manifestations of Chaos [20/20] |
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As the study of chaos in physics enters its second century, the issue of whether the universe is truly deterministic is still an open question, and it will undoubtedly remain so, even as we come to understand more and more about the dynamics of chaotic systems. | ||

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