Butterfly effect is a metaphor of chaos, which was first applied to meteorological research. What it says is: There are many beautiful butterflies in the tropical rain forest of the Amazon River basin in South America. A butterfly flapping its wings occasionally may trigger a tornado in Texas within two weeks. It means that small changes in initial conditions will lead to unpredictable events in the future.
1. Mathematical model of early meteorology
Looking back a century, the first attempt to predict the weather by mathematical model was in the book "Predicting the weather by numerical processes" published by British mathematician Lewis Fry Richardson in 1922. He spent ten years studying the use of finite difference equations to simulate the differential equations that control meteorological conditions.
He said, instead of finding a clear function to solve the equation, we choose some points on the surface, measure their initial values at time t0, and then derive the value of T 1 with approximate values, and then gradually calculate the corresponding values at each subsequent time. The idea itself is not surprising. The weather changes with time and geographical location, but it doesn't need 5 minutes of data per square kilometer: it can be satisfied with low accuracy.
After defining the equations of atmosphere and wind pressure, Richardson simulated the weather situation on a certain day. According to the measurement results in Central Europe on that day, after complicated manual calculation, it was shown that the atmospheric pressure in a certain area would drop to 145 millibar (1 millibar = 100 pa), which was an absurd result. He must find effective solutions and design new technologies to bypass the data and avoid sudden fluctuations. A few years later, mathematicians succeeded in finding these methods. They use the same data, and the pressure drop is calculated in millibars. Therefore, the theoretical validity of Richardson's method has been recognized.
After 1950s, the United States, with the help of the first generation of electronic computers, used the new Richardson formula to carry out meteorological simulation on the map of the North American continent. The results are satisfactory and can simulate the 24-hour weather evolution.
With the upgrading of computers, meteorologists predict that it is possible to obtain very accurate forecasts within 14 days by using mathematical models in the future, and achieve sufficient accuracy within 30 ~ 180 days by increasing statistics and historical analysis of data (now it seems that the judgment at that time was obviously wrong? )。
After 10 years, Edward, a mathematician and meteorologist at MIT? Lorenz came, and he used a mathematical model to predict the weather on the computer. At that time, computers began to be miniaturized and their performance improved.
196 1 year, when Lorenz studied the equation on the computer, he chose some data and began to copy it carefully and simulate it. The result is not ideal. He finally found that the computer used six decimal places, and the data he entered only had three decimal places, so a number like 0.50 127 became 0.506. The difference between these two figures is very small. At that time, people thought that this might only lead to a small deviation, but the result was obviously not the case.
Mathematically, small changes can lead to huge differences in results. For example, a set of numbers very close to 1: 0.98, 0.99, 1.00, 1.0 1.02. There is little difference between these figures, but their index values are after 180, and 0.99 180, 1.00 180,1.65438 are at 65438. The result is quite different, completely beyond the intuitive imagination.
Secondly, the term butterfly effect is put forward.
1963, Lorenz published an article "Decisive Aperiodic Flow", in which there was a passage: two states that were slightly different at first will eventually evolve into two completely different states. Therefore, if you make any mistakes when observing the current state, which seems inevitable in any real system, it is almost impossible to produce an acceptable prediction result of the immediate state in the distant future. In view of the inevitable inaccuracy and incompleteness in weather forecast, there seems to be no long-term accurate forecast.
Then, Lorenz described the phenomenon that this result was amplified by small changes as? Seagull effect? And replaced the seagulls with poetic butterfly images. Finally, in 1972, an article entitled "Predictability: Will a butterfly flap its wings in Brazil cause a tornado in Texas?" "Speech. Lorenz explained in his speech that he picked up this title just for fun, and it is impossible to make an accurate prediction with this title. Unfortunately, no one takes this sentence seriously.
Third, is the butterfly effect terrible?
Today, the computers we use are more powerful and faster, and data can usually be shared between many cities and even many countries. For example, all European weather forecasts are based on data from the European Center for Long-range Weather Forecasting in Reading, England (central weather bureau, China is also authorized to publish weather forecasts in Reading). It is proud that the current 7-day forecast is as accurate as the 3-day forecast more than 30 years ago.
In practice, although the prediction is reasonable, meteorologists cannot predict catastrophic events with 100%. As far as weather forecast is concerned, especially in mountainous areas with complex terrain, it is not as easy as in plain areas. The ability of meteorologists to read and apply the received data is still very important. If you ignore the data, you may be extremely surprised at the changes after 6 months caused by this error.
Now, many scholars have applied the butterfly effect to sociology, financial economics, language mathematics, natural phenomena and other aspects to explain the elusive chaos phenomenon. They believe that the development of everything has a fixed number and changes, and the development of things has its own trajectory to follow. A small change can affect the development of things, indicating that the development of things is complicated. For example, the Fed's interest rate hike can lead to various violent oscillations in the global financial industry, manufacturing industry, aquaculture, stock market and futures market. People also call this phenomenon the butterfly effect.
However, the enlightenment of the butterfly effect is more important in philosophy: for some people? Tiny? Signs and symptoms should not be ignored, but should be paid attention to and adjusted in time.
Lorenz used butterflies as a metaphor in his speech, and the picture was beautiful and poetic. At the same time, he also poured cold water on everyone: the butterfly effect is just a joke, not true at all. As the title of his early speech, this word has been widely circulated for many years, sometimes misinformed and even exaggerated.
So, is the butterfly effect terrible?
There is no doubt about the answer! The evolution of nature, the change and development of human society, although there are certain laws to follow, are as difficult to predict accurately as the change of weather. Those poor butterflies have done nothing wrong.