Chaos is the science of surprises, of the nonlinear & the unpredictable.

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It teaches us lớn expect the unexpected. While most traditional science đơn hàng with supposedly predictable phenomemãng cầu like gravity, electricity, or chemical reactions, Chaos Theory giao dịch with nonlinear things that are effectively impossible to lớn predict or control, lượt thích turbulence, weather, the stoông chồng market, our brain states, & so on. These phenomemãng cầu are often described by fractal mathematics, which captures the infinite complexity of nature. Many natural objects exhibit fractal properties, including landscapes, clouds, trees, organs, rivers etc, and many of the systems in which we live exhibit complex, chaotic behavior. Recognizing the chaotic, fractal nature of our world can give us new insight, power, and wisdom. For example, by understanding the complex, chaotic dynamics of the atmosphere, a balloon pilot can “steer” a balloon to lớn a desired location. By understanding that our ecosystems, our social systems, và our economic systems are interconnected, we can hope to lớn avoid actions which may over up being detrimental lớn our long-term well-being.

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Principles of ChaosThe Butterfly Effect: This effect grants the power lớn cause a hurricane in Đài Loan Trung Quốc lớn a butterfly flapping its wings in New Mexico. It may take a very long time, but the connection is real. If the butterfly had not flapped its wings at just the right point in space/time, the hurricane would not have sầu happened. A more rigorous way to express this is that small changes in the initial conditions lead to drastic changes in the results. Our lives are an ongoing demonstration of this principle.

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Who knows what the long-term effects of teaching millions of kids about chaos và fractals will be?Unpredictability: Because we can never know all the initial conditions of a complex system in sufficient (i.e. perfect) detail, we cannot hope lớn predict the ultimate fate of a complex system. Even slight errors in measuring the state of a system will be amplified dramatically, rendering any prediction useless. Since it is impossible lớn measure the effects of all the butterflies (etc) in the World, accurate long-range weather prediction will always remain impossible.Order / Disorder Chaos is not simply disorder. Chaos explores the transitions between order & disorder, which often occur in surprising ways.Mixing: Turbulence ensures that two adjacent points in a complex system will eventually kết thúc up in very different positions after some time has elapsed. Examples: Two neighboring water molecules may end up in different parts of the ocean or even in different oceans. A group of helium balloons that launch together will eventually lvà in drastically different places. Mixing is thorough because turbulence occurs at all scales. It is also nonlinear: fluids cannot be unmixed.Feedback: Systems often become chaotic when there is feedbaông xã present. A good example is the behavior of the stoông chồng market. As the value of a stoông xã rises or falls, people are inclined to lớn buy or sell that stoông xã. This in turn further affects the price of the stoông chồng, causing it khổng lồ rise or fall chaotically.
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“As far as the laws of mathematics refer lớn reality, they are not certain, and as far as they are certain, they bởi vì not refer to lớn reality.”

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