What are the domino and butterfly effects?

The butterfly effect was put forward by meteorologist Lorenz 1963.

In the tropical rain forest of Amazon River basin in South America, a butterfly occasionally flaps its wings, which may trigger 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.

Sociology uses "butterfly effect" to explain a bad tiny mechanism, which will bring great harm to society if it is not guided and adjusted in time, and is dubbed "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."

Explain in detail:

Nonlinear, commonly known as "butterfly effect".

What is the butterfly effect? Let's talk about the discovery of Lorenz, a meteorologist at MIT. 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. 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. He went to the cafe for a cup of coffee, and when he came back, he was surprised: there was not much difference, but the result was a hundred thousand miles away! 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. He then decided that it was "extremely unstable to the initial value", that is, "chaos", that is, the so-called "butterfly effect". The flapping of Asian butterflies would make a tornado worse than strong winds appear in America 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!

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.

1979 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.

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.

In a word, the law of chaos can only be observed, pondered, intuited and speculated, but not revealed, deduced and accurately described. 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.

domino effect

domino effect

Xinhua News Agency reported on June 5438+February 3, 2000 1 CCTV reported on June 6, 2006/KLOC-0: In the last few minutes of the 20th century, a new Guinness World Record for dominoes was born in the gymnasium and tennis hall of Beijing Summer Palace Sports Health City. 62 young students from China, Japan and South Korea successfully knocked down more than 3.4 million dominoes, breaking the previous world record of 2.97 million created by the Dutch. As can be seen from the TV screen, the scene of dominoes falling down in turn in an instant is very spectacular, during which the patterns displayed are rich and amazing, which contains certain scientific truth.

This is the domino effect. The energy generated by this effect is enormous.

The physical reason for this effect is that when the domino stands upright, its center of gravity is higher, but when it falls down, its gravitational potential energy is converted into kinetic energy. When it falls on the second card, the kinetic energy is transferred to the second card, and the second card transfers the sum of the kinetic energy transferred from the first card and the kinetic energy converted from its own gravitational potential energy in the falling process to the third card. ...

A Whitehead, a physicist at the University of British Columbia, once made a set of dominoes, *** 13, and the first one was the smallest. It is 9.53mm long, 7.6mm wide and 1. 19mm thick, which is not as big as a small nail. In the future, each block will be expanded by 1.5 times. This data is based on the fact that a domino can knock down a domino whose volume is 1.5 times when it falls. The largest is 13, which is 665444. The size of the deck is close to that of playing cards, and its thickness is 20 times that of playing cards. If you arrange this set of dominoes at an appropriate interval and gently press the first card, it will inevitably affect 13. 13 The energy released when dominoes fall is more than 2 billion times larger than that when the first card falls, because the energy of domino effect increases exponentially. If you knock down the first domino, you need 0.024 microjoules. It can be seen that the energy generated by the domino effect is really eye-catching.

However, A. Whitehead didn't make the 32nd domino after all, because it would be as high as 4 15m, twice as high as the Empire State Building in New York. If someone really made such a set of dominoes, skyscrapers could be knocked down with one finger!