What does the butterfly effect mean?

Edward lorenz, an American meteorologist, analyzed this influence in the paper 1963 submitted to the New York Academy of Sciences. "A meteorologist mentioned that if this theory is proved to be correct, a seagull flapping its wings is enough to change the weather forever." In his later speeches and papers, he used more poetic butterflies. The most common explanation for this effect is: "A butterfly flapping its wings in Brazil can trigger a tornado in Texas a month later." The source of this sentence is that meteorologists have made a computer program that can simulate climate change and show it with images. Finally, he found that the image was chaotic, and it looked like the wings of a butterfly, so he explained the figure vividly in the way of "butterflies flapping their wings", so he had the above statement. Butterfly effect is usually used in weather, stock market and other complex systems that are difficult to predict in a certain period of time. This effect shows that the result of the development of things is extremely sensitive to the initial conditions, and the smallest deviation of the initial conditions will cause great differences in the results. Butterfly effect is used in sociology to explain a bad micro-mechanism, which will bring great harm to society if it is not guided and adjusted in time, and is dubbed as "tornado" or "storm"; A good micro-mechanism, as long as it is guided correctly, will have a sensational effect after a period of efforts, or it will be called a "revolution." The butterfly effect, also called nonlinearity, often appears in chaos. Let's talk about the discovery of Lorenz, a meteorologist at MIT. In order to forecast the weather, he solved the 13 equations simulating the earth's atmosphere by computer, so as to improve the accuracy of long-term weather forecast by using high-speed operation of computer. In an experiment of 1963, in order to examine the results more carefully, he took out an intermediate solution of 0.506, improved the accuracy to 0.505438+027 and sent it back. But when he went to the cafe for a cup of coffee and came back, he was surprised: the difference was not big, but the result was 108 thousand Li! After checking again, I found that there was nothing wrong with the computer. Lorenz found that because the error will increase exponentially, in this case, a small error will have completely different consequences as it goes on. He later identified it as "extremely unstable to the initial value", namely "chaos", also known as "butterfly effect". Asian butterflies flapping their wings will make a tornado worse than the strong wind in the United States in a few months! This discovery is so serious that scientists don't understand it, and several scientific magazines refuse to publish his articles. They think it is "against common sense": if similar initial values are substituted into some equations, the results should be similar, how can there be a big deviation? 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 celestial motion; 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. [Edit this paragraph] The butterfly effect was put forward by meteorologist Lorenz 1963. A butterfly flapping its wings occasionally in the tropical rain forest of Amazon River basin in South America may cause a tornado in Texas within two weeks. 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. This effect shows that the result of the development of things is extremely sensitive to the initial conditions, and the smallest deviation of the initial conditions will cause great differences in the results. 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). Contrary to the butterfly effect, the fixed point is an automatic regression. Here is an example. This is a formula for finding the root: x (n+ 1) = xn+(a/x (k-1)-xn)1/k (5) (n, n+1stands for the lower angle) The formula for finding the root is: When it is assumed that Issuers have a standard formula: x (n+ 1) = xn+(a/x 2-xn)1/3 (where n, n+1is the lower corner). For example, A=5, and 5 is between the third power of 1; 2 to the third power; The initial value X0 can be 1. 1, 1.5, 1.2, 1.3, 1.4,1.5,65438. For example, we take X0 = 1.9 according to the formula: Step 1: x1=1.9+(5/1.92; - 1.9) 1/3= 1.7。 Input value is greater than output value, negative feedback. That is, 5/1.9×1.9 =1.385041.3850416-1.9 =- That is, take a 2-digit value, namely 1.7. Step 2: x2 =1.7+(5/1.72; - 1.7) 1/3= 1.7 1。 Input value is less than output value, positive feedback. That is, 5/1.7×1.7 =1.73010, 1.73- 1.7=0.03, 0.03×/kloc-. Take 3 digits, one digit more than the previous one. Step 3: x3 =1.71+(5/1.712; -1.71)1/3 =1.709. The input value is greater than the output value, which is negative feedback. Step 4: x4 =1.709+(5/1.709 2; -1.709)1/3 =1.7099, the input value is less than the output value, and the feedback is positive. This method can be adjusted automatically. The values in the first and third steps are too large, but the output value will be reduced automatically after calculation. In the second and fourth steps, the input value is small and the output value automatically increases. That is, 5 =1.7099 3; Of course, the initial value X0 can also be 1. 1, 1.2, 1.3. . . Any one of 1.8 and 1.9 is x1=1.7 >; . Of course, we'd better use the intermediate value as the initial value in actual operation, that is, 1.5. 1.5+(5/ 1.5^2; - 1.5) 1/3= 1.7。 If you square with this formula, you can change 3 into 2, and 2 into 1. That is x (n+1) = xn+(a/xn-xn)1/2. For example, a = 5: 5 is between the square of 2 and the square of 3; We can take the initial value 2. 1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, and it is better to take the middle value 2.5. Step 1: 2.5+(5/2.5-2.5)1/2 = 2.2; Input value is greater than output value, negative feedback. That is, 5/2.5=2, 2-2.5=-0.5, -0.5× 1/2=-0.25, 2.5+(-0.25)=2.25. Take two digits, 2.2. Step 2: 2.2+(5/2.2-2.2)1/2 = 2.23; The input value is less than the output value, and the positive feedback is 5/2.2=2.272, 2.272-2.2=-0.072, -0.072× 1/2=-0.036, 2.2+0.036=2.23. Take three digits. Step 3: 2.23+(5/2.23-2.23)1/2 = 2.236. The input value is less than the output value, and the positive feedback is 5/2.23 = 2.242, 2.242-2.23 = 0.0 12, 0.012 = 0.006, 2.23+0.006 = 2.23. Every one of them. This method is also called feedback root. It doesn't matter even if you enter an incorrect value. The output value will automatically adjust, close to the exact value. The stability of initial value under specific conditions is explained. For details, please refer to the prescription formula of Baidu Library and the prescription from binomial theorem to tangent method (Wang Xiaoming Wang Ruike). [Edit this paragraph] The meaning of the butterfly effect A small butterfly flaps its wings over a certain place to disturb the air. After a long time, it may cause a storm in a distant place, which is a metaphor for the unpredictable and serious consequences caused by a small factor in long-term large-scale weather forecast. 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. Butterfly effect refers to a very small change in initial conditions, which will have a great impact on its future state after continuous amplification. Some small things can be confused, and some small things are very important to an organization and a country if they are amplified by the system, so we can't confuse them. [Edit this paragraph] The concept of "butterfly effect" originated from Lorenz curve-knowledge was put forward by meteorologist Lorenz 1963. In order to forecast the weather, he used a computer to solve the 13 equations that simulated the earth's atmosphere, in order to improve the accuracy of long-term weather forecast by using the high-speed operation of the computer. Lorenz Curve-Knowledge The origin of it is this: In an experiment in 1963, the meteorologist Lorenz of Massachusetts Institute of Technology solved the equations of 13 which simulated the earth's atmosphere with a computer. In order to check the results more carefully, Lorenz rounded off the fourth decimal place of the initial input data in a scientific calculation. He took out an intermediate solution of 0.506, improved the accuracy to 0.506 127 and sent it back. He drank a cup of coffee, and when he came back, he was surprised: there was not much difference, but the calculation results before and after deviated from 108 thousand miles! Results the similarity between the two curves disappeared completely. After checking again, I found that there was nothing wrong with the computer. Lorenz found that because the error will increase exponentially, in this case, a small error has caused great consequences as it goes on. Later, Lorenz raised this question in a speech. He believes that in the process of atmospheric movement, even if all kinds of errors and uncertainties are small, it is possible to accumulate the results in the process and gradually enlarge them to form a huge atmospheric movement. So Lorenz decided that he had discovered a new phenomenon: the result of the development of things was extremely sensitive to the initial conditions. He later identified this as "extreme instability to the initial value", namely "chaos", also known as "butterfly effect". Since then, the so-called "butterfly effect" has spread like wildfire. [Edit this paragraph] The internal mechanism of butterfly effect The so-called complex system refers to a nonlinear system that exhibits chaotic phenomena or behaviors 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. 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. This ballad says: I lost a nail and broke a shoe; Broke a shoe and a horse; Fold a horse and hurt a knight; Wounded a knight and lost a battle; Lost a battle and lost an empire. Whether a nail on the horseshoe will be lost is a very small change in the initial conditions, but its "long-term" effect is the fundamental difference between the life and death of an empire. This is the so-called "butterfly effect" in the field of military politics. It's a little incredible, but it can really cause such bad consequences. A wise leader must prevent procrastination, but seemingly trivial things may lead to disintegration within the collective. Is it too late to regret at that time? A suspension bridge across a deep valley usually begins with a small stone tied to a thin line. The theory of "butterfly effect" proves China's explanation of The Book of Rites more than 300 years ago: "The Book of Changes says:' A gentleman is cautious at the beginning, and the difference is a fraction. "Shu Wei Le Zhi": "Only the spirit is completely empty, and the millet is big and small, and the difference is thousands of miles." This shows that perception is more direct than cognition, its so-called attractor is the role of meta-external field in mixed-element field theory, and its chaotic nonlinear theory is the absolute counting time system of matter-element independence in mixed-element field theory. Research significance of butterfly effect: the choice between chaos and non-chaos, logical deduction system and fault is the significance of our concern about butterfly effect. In ancient China, there was also a school that paid attention to the problem of good beginning and good ending, that is, it was good at developing a system and ending it, and studied methodology for this purpose. Furthermore, it can be said that the essence of butterfly effect is a methodology, which recognizes the boundary of the system and is a method to explore the finiteness of the universe based on the infinity theory of the universe. China's "Everything is wrong, I am old" used to be like a hairpin bend, which frightened Ji Zi. I think that elephant chopsticks will not be added to the earth, but will be rhinoceros jade cups. Like a jade cup, it must be like a leopard tire. Like a leopard's fetus, it must be eaten under a hut without short clothes and brown clothes, so it will be decorated with nine heavy clothes and a wide room platform. I am afraid of his death, so I am afraid of his beginning. After living for five years, I became a meat garden, set up a barbecued pot, climbed to a bad place, and died near the wine pool. Therefore, Ji Zi knew the disaster of the world when he saw the elephant chopsticks, so he said, "Seeing small is light. Wang Shuji of Shang and Zhou Dynasties was very scared when he saw Zhou Wang using ivory chopsticks, because with ivory chopsticks, the cup became a rhinoceros jade cup. With ivory chopsticks, rhinoceros jade cup will not eat coarse bean soup, but will eat beef, elephant meat, leopard meat, fetal meat and other exquisite foods. Eating meat such as beef, leopard meat and fetal meat won't be eaten in a hut in short coarse cloth, but in a gorgeous palace in a lot of fine cloth. Ji Zi is afraid of her national subjugation. It's a little incredible, but it can really cause such bad consequences. A wise leader must prevent procrastination, but seemingly trivial things may lead to disintegration within the collective. Is it too late to regret at that time? A suspension bridge across a deep valley usually begins with a small stone tied to a thin line. This effect shows that the result of the development of things is extremely sensitive to the initial conditions, and the smallest deviation of the initial conditions will cause great differences in the results. For example, there is chaos in celestial motion; 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. Scientists' definition of chaos is that chaos refers to the seemingly random irregular motion that occurs in a deterministic system, but the behavior of the system described by deterministic theory has the characteristics of uncertainty-unrepeatable and unpredictable, which is the chaotic phenomenon. Further research shows that chaos is an inherent characteristic of nonlinear dynamic systems and a common phenomenon in nonlinear systems. Newton's deterministic theory can handle most linear systems perfectly, and most linear systems are simplified from nonlinear systems. Therefore, chaos is ubiquitous in real life and practical engineering and technical problems. Since Lorenz first discovered chaos, the research on chaos has been concerned by scientists, sociologists and humanists. Studying chaos is actually looking for order in disorder, but there are still too many unpredictable and chaotic things in today's world, and this topic will definitely become a human problem. Here, due to the limited knowledge, we only made a very superficial introduction, hoping that more people can walk into the door of chaos and see the world with deeper eyes. Maybe we can devote ourselves to this research in the future.