Butterfly effect, also known as billiards effect, is a figurative term that chaotic systems are extremely sensitive to initial values, and it is also the direct cause of chaotic phenomena in nonlinear systems under certain conditions (which can be called critical conditions or threshold conditions).
First, the origin of the butterfly effect
The butterfly effect originated from the discovery of American meteorologist Lorenz in the early 1960s. In the book "The Legend of Chaos and Fractal Theory-Exploration of Singularity", it is described as follows: "One winter day in 196 1, E. Lorenz calculated the weather forecast on the royal McBee computer. In order to investigate a long series, he gave up halfway. He typed the final output directly as the initial value of calculation, and then went downstairs through the hall to have coffee. An hour later, when he came back, something unexpected happened. He found that the weather changed quickly from the last model, and in a short time, the similarity disappeared completely. Further calculation shows that a small difference in input may soon become a huge difference in output. This phenomenon is called sensitive dependence on initial conditions. In the weather forecast, this is called the butterfly effect ... ""Lorenz first used the seagull effect. ""Lorenz's speech at the American Association for the Advancement of Science in Washington on February 29th:' Predictability: A butterfly is in Brazil. "
Second, the meaning of the butterfly effect
A small butterfly flapping its wings over a certain place disturbs the air, which may lead to a storm in the distance for a long time. This is a metaphor. Long-term large-scale weather forecast often leads to unpredictable and serious consequences because of a little tiny factor. Small deviations are inevitable, which makes long-term weather forecast unpredictable or inaccurate. This is like playing billiards, chess and other human activities, which are often "thousands of miles away" and "one careless move will lose the game"
Long-term large-scale weather forecast is the observation, calculation, analysis and judgment of the complex system of the earth's atmosphere, which is influenced and restricted by many factors that change at any time and place. It can be considered that the prediction of its comprehensive effect is difficult to be accurate and the butterfly effect is inevitable. Our human research objects also involve other complex systems (including "natural systems" and "social systems"). There are many complicated internal factors, and its corresponding butterfly effect is inevitable. "Today's butterfly effect" or "generalized butterfly effect" is not limited to the original Lorenz butterfly effect, which is only used for weather forecasting, but is synonymous with all complex systems being extremely sensitive to initial values, which means that for all complex systems, under certain "threshold conditions", their long-term and large-scale future behavior. It is extremely sensitive to small changes or deviations of initial values, that is, small changes or deviations of initial values will lead to huge differences in the future, which are often unpredictable or random.
Third, the internal mechanism of the butterfly effect
The so-called complex system refers to a nonlinear system that exhibits chaotic phenomenon or chaotic behavior under critical conditions. The dynamic equation of nonlinear system contains nonlinear terms, which is a mathematical description of the cross-coupling mechanism of multiple factors in nonlinear system. It is this "multi-factor cross-coupling mechanism" that leads to the initial sensitivity of complex systems, that is, butterfly effect, which leads to the chaotic behavior of complex systems.
At present, the research of nonlinear science and chaotic science is in the ascendant, which indicates that human understanding of natural and social phenomena is transitioning and evolving to a deeper and more complex stage.
From a derogatory point of view, the butterfly effect often gives people a sense of crisis with unpredictable future behavior, but from a positive point of view, the butterfly effect makes it possible for us to "be cautious and make a thousand miles a day" and "control the chaos" at a small cost and gain great "blessing" in the future.
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