What do chaos theory and butterfly effect mean?
Butterfly effect is a concept in chaos theory. It refers to the dependence on the sensitivity of initial conditions. Small differences at the input end will quickly amplify to the output end. Butterfly effect is everywhere in economic life: China announced the launch of missiles, and US$ 654.38+0 billion from Hong Kong and Taiwan flowed to the United States. 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 Legend of Chaos and Fractal Theory-Exploration of Singularity and other books, it is described as follows: "One winter day in 196 1, Lorenz calculated the weather forecast on the Royal McBee computer. In order to forecast the weather, he solved the 13 equation simulating the earth's atmosphere by computer. In order to study a long sequence, he took a shortcut, not to let the computer run from the beginning, but to start 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 rapidly from the previous pattern, and in a short time, the similarity disappeared completely. Further calculations show that subtle differences in input may soon become huge differences in output. There was nothing wrong with the computer, so Lorenz decided that he had discovered a new phenomenon: "extreme instability to the initial value", namely "chaos", also known as "butterfly effect". The flapping of Asian butterflies will make a tornado worse than strong winds appear in the United States in a few months! This discovery is so serious that scientists don't understand it, and several scientific journals also refuse to publish his articles, thinking that it is "against common sense": if similar initial values are substituted into some equations, the results should be similar, how can they be far apart! The reason is that the movement of butterfly wings leads to the change of the surrounding air system, producing weak airflow, which in turn will cause the corresponding change of the surrounding air or other systems, causing a chain reaction, which will eventually lead to great changes in other systems. Linearity refers to the proportion and linear relationship between quantity and quantity, representing regular smooth motion in space and time; Nonlinear refers to the non-proportional and nonlinear relationship, which is characterized by irregular movement and mutation. For example, how many times is the eyesight of two eyes more than that of one eye? It's easy to think it's twice, but it's actually 6- 10! This is nonlinearity: 1+ 1 is not equal to 2. The generation of laser is nonlinear! When the applied voltage is small, the laser is like an ordinary electric lamp, and the light scatters in all directions; When the applied voltage reaches a certain value, a new phenomenon will suddenly appear: the excited atoms seem to hear the command of "align to the right" and emit monochromatic light in the same phase and direction, that is, laser. The characteristic of nonlinearity is that it spans all professions and permeates all fields, which can be said to be "everywhere". "For example, there is chaos in the movement of celestial bodies; The oscillation of electricity, light and sound waves will suddenly fall into chaos; The geomagnetic field changed direction 16 times in 4 million years, also because of chaos. Even human beings are inherently nonlinear: contrary to traditional thinking, the EEG and heartbeat of healthy people are not regular, but chaotic, and chaos is the expression of vitality. Chaotic systems respond faster to external stimuli than non-chaotic systems. It can be seen that nonlinearity is around us and can't be hidden. 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. Lorenz1979 65438+Speech at the American Association for the Advancement of Science in Washington on February 29th: Predictability: Will a butterfly flapping its wings in Brazil cause a tornado in Texas? "
Second, the significance 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 for long-term large-scale weather forecast, which often has 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 "a thousand miles away, a tiny difference" 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"), and their internal constraints are also complex, and their "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 behaviors are extremely sensitive to small changes or deviations of initial conditions, that is, small changes or deviations of initial values will lead to huge future prospects.
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 precisely because of this "multi-factor cross-coupling mechanism" that the initial sensitivity of complex systems, that is, butterfly effect, 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 that the future behavior is unpredictable, 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. The butterfly effect is a metaphor, not a hurricane caused by butterflies.
In February 65438, Lorenz pointed out in a speech of the American Association for the Advancement of Science in Washington that a butterfly flapping its wings in Brazil might cause a tornado in Texas. His speech and conclusion left a deep impression on people. Since then, the so-called "butterfly effect" has spread like wildfire, and its reputation has spread far and wide.
The reason why the butterfly effect is fascinating, gripping and thought-provoking lies not only in its bold imagination and charming aesthetic color, but also in its profound scientific connotation and inherent philosophical charm. Chaos theory holds that in a chaotic system, very small changes in initial conditions, after constant amplification, will cause great differences in its future state. We can use a folk song circulating in the west to illustrate this image.