How is the butterfly effect proved?

Butterfly effect refers to a dynamic system, and small changes in initial conditions can lead to a long-term huge chain reaction of the whole system. This is a chaotic phenomenon.

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 display it with images. Finally, he found that the image was chaotic, much like the spread wings of a butterfly. So he explained this figure vividly in the way of "butterflies flapping their wings", so there was 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 often appears in chaos. Also known as nonlinear.

Give accurate information

The butterfly effect was put forward by meteorologist Lorenz 1963. A butterfly flapping its wings occasionally in the tropical rain forest of Amazon 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).

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 is easy to think that it is twice, but it is actually 6 ~ 10 times! 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 meaning of the butterfly effect

A small butterfly flapping its wings over a certain place disturbs the air, which may cause a storm in a distant place for a long time, 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.

Third, the internal mechanism of the butterfly effect

The so-called complex system refers to a system that is nonlinear and 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.

1963 12. 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 may 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.

This ballad says:

Drop a nail and break 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.

Comments on Life and Death Book: Similarly, seemingly ordinary meat-eating habits can also lead to malignant diseases, premature death, even dereliction of duty, crime, war, disaster, moral decay, world hunger, environmental damage and forest soil erosion. Buddhist scriptures say: if you lose your life, you will never recover. The human body is hard to get. Compared with life without human body, there are so few people with human body that the Buddha compared the soil on his palm with the soil on the earth. And if you lose your life because of bad karma and unfortunately fall into three evil ways: beast, hungry ghost and hell, it will be very, very difficult to be a man again. The Buddha used the metaphor that a blind turtle meets a floating hole: in the vast sea, there is a board with a hole in the middle. A blind turtle comes out of the water once every hundred years, and its head is just inserted in the hole in the board. The chance is slim! This is also the butterfly effect. Cherish life! It's rare to get it alone now. Buddhism stinks today. This body will not spend this life, but when will it spend it?

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.

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. 』

Ji Zi, uncle Wang of Shang Dynasty, was very scared when he saw Zhou Wang using ivory chopsticks. Because of ivory chopsticks, the cup was changed into a rhinoceros jade cup. With ivory chopsticks, rhinoceros jade cup will not eat coarse bean soup, but eat beef, elephant meat, leopard meat, unborn baby 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.

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. 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. Lorenz discovered chaos for the first time. So far, 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. Because of the limited knowledge here, I only made a superficial introduction. I hope more students 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.

Butterfly effect and chaos theory

Butterfly effect is a concept in chaos theory. It refers to a dependence on the sensitivity of initial conditions: small differences at the input end will be quickly amplified to the output end, and the butterfly effect can be seen everywhere in economic life.

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).

An example of the butterfly effect

The Asian financial crisis of 65438-0998 and the American stock market storm are actually "butterfly effects" in economic operation. The "El Nino" phenomenon in the Pacific Ocean from 65438 to 0998 is the "butterfly effect" caused by atmospheric movement. The "butterfly effect" is the expression of chaotic motion. When we further study life phenomena, they are neither completely periodic nor purely random. They are all "frequency-locked" to natural periodic processes (season, day and night, etc.). ) and maintain the inherent "autonomous" nature. Butterfly effect is also a concept in chaos theory. It refers to a dependence on the sensitivity of initial conditions: the small difference at the input end will be quickly amplified to the overwhelming difference at the output end, just like a butterfly flapping its wings in Beijing today, which may trigger a series of events in the atmosphere, thus leading to a storm in new york in a month.

Management enlightenment

Nowadays, the fate of enterprises is also affected by the "butterfly effect", because consumers increasingly believe in intangible values such as feeling, brand consumption, shopping environment and service attitude ... which has become their choice factor. Therefore, as long as we pay a little attention, it is not difficult to see that some companies with standardized management and good operation have such sentences in their ideas:

"In your statistics, only one customer in 100 is dissatisfied, so you can proudly say that only 1% is unqualified, but for this customer, he got 100% dissatisfaction."

"Once it is bad for customers, the company needs 10 times or even more efforts to remedy it."

In the eyes of customers, you represent the company.

Today, the "butterfly" that can change the fate of an enterprise is far more than the "planner". With the news of China Unicom's entry into telecom competition, private enterprises contracting special trains and Nanjing foreign-funded enterprises participating in public transport competition, the monopoly position of enterprises is getting weaker and weaker, and open competition forces enterprises to consider various potential factors affecting their own development.

Measures such as streamlining institutions, laying off employees, and canceling welfare houses have kept more and more people away from traditional protection, followed by deciding their own destiny. The result of the free combination of organization and individual is that whoever can catch the "butterfly" beneficial to life will not be abandoned by society.