What kind of phenomenon does the so-called butterfly effect mean in the nonlinear world?

Maybe you wouldn't think that the nonlinear world was discovered by meteorologists.

For thousands of years, people have estimated whether it will be sunny or rainy tomorrow by observing clouds and relying on experience. Scientists have always hoped that the prediction of weather changes can be as predictable as solar eclipses and tides. In the early 1960s, Professor Lorenz, a famous meteorologist at MIT, made the first attempt to simulate the weather by computer. This attempt is entirely based on a belief that nature has laws and laws can be recognized. Once people master this law and know the initial conditions, they can simulate the past and foresee the future through the bridge of logic and mathematical inevitability.

Lorenz's confident attempt at computer weather simulation. He used a computer to deal with many relational equations related to weather changes, such as temperature, air pressure, wind speed, airflow and wind direction. In Lorenz's words, it is to simplify the complex and changeable weather into a skeleton-digital law and carry out computer weather simulation. With the gradual revision of the computer weather change model, the output curve of computer weather simulation has begun to approach the curve of actual weather change. One day, however, for convenience, Lorenz inadvertently changed an input value of 0.506 127 to 0.506. Unexpectedly, this error of 1‰ caused disastrous consequences: two almost identical weather simulations led to two curves that parted ways.

In classical science, the numerical error of 10‰ is often negligible. In Lorenz's view, the small change of input value is just a breeze in the whole weather. Why is the whole weather simulation system so sensitive?

Professor Lorenz, a meteorologist, is keen on science and physics. Instead of looking for the answer to the question in classical science, he found another way to answer the deep-seated scientific questions behind the phenomenon. He believes that the weather change is a huge and complex nonlinear dynamic system, and the traditional linear dynamic model can not describe those non-periodicity and sensitive dependence on initial conditions. In complex systems, there is often a critical point where the system occurs. In the words of I.llyaPrigogine, the famous founder of dissipative structure theory, there are bifurcation points and fluctuation mechanisms in the system. Any small disturbance that is not surprising from the point of view of classical science will often lead to the system turning from stable to unstable, or from unstable to stable.

In the late 1970s, Lorenz put forward a brand-new concept "Butterfly Effect" in an academic lecture in Washington, namely "Predictability: Will a butterfly flapping its wings in Brazil cause a tornado in Texas?" Lorenz revealed a nonlinear world and a realistic world through the "butterfly effect".

Lorenz decided that the long-term weather forecast was doomed to failure. Although the current computer calculation speed has reached an alarming level, the global weather model has calculated 500,000 equations, which is several million times higher than the 12 equations he handled in computer weather simulation at that time. However, in the face of such a complex nonlinear system as weather, the forecast for more than two or three days is only a guess, and the weather forecast for more than one week is worthless. It is impossible for people to predict whether a day in Princeton, New Jersey will be sunny or rainy by computer. Because the weather changes do not follow the route set by determinism.

Later, Lorenz put his line-weather simulation aside. The complex nonlinear problems in fluid chaos are studied.

A New Perspective of Understanding Nature —— Chaos

In contemporary academic thoughts, the word "chaos" appears frequently, and some scholars even think that "only three things will be remembered in the 20th century: relativity, quantum mechanics and chaos." They think: "Relativity excludes Newton's fantasy of absolute space-time, quantum theory excludes Newton's dream of controllable measurement process, and chaos excludes Laplacian determinism's fantasy of predictability."

On the whole, modern science refuses to be "chaotic" outside science. Modern scientists believe that the mission of science is to discover the laws of nature, and only the mechanical laws based on determinism are the models of natural science research, and the orderly relationship between things is the object of scientific research. Chaos, as a random and disorderly phenomenon, is undoubtedly something outside the scientific field of vision, and it is reasonable to reject it.

However, the study of modern chaos theory reveals to people that those chaotic phenomena characterized by contingency and randomness are not scientific exceptions. What we are facing is the regularity of spatial arrangement and the periodicity of time change, and the real world is more accidental and random in space-time structure. In a sense, chaos is a very common natural phenomenon. The concept of chaos studied by modern chaos science is no longer the traditional concept of chaos, and chaos is not synonymous with disorder. As Hao Bailin, an academician of China Academy of Sciences and an expert on chaos, said, "Chaos is by no means a simple disorder, but more like an orderly state without periodicity and other obvious symmetry features". Now people are beginning to realize that chaos is a science of process rather than state, and it is a science of evolution rather than existence. The state of "chaos" is a state of disorder and lawlessness on the macro level and a state of order and law on the micro level. It is essentially different from the disorder of equilibrium state. Chaos may hide deep and strict order behind macro disorder, while there may be real irregular random motion behind micro order.

In the face of complex nonlinear systems, classical science ended here, because it was impossible to establish order and rules for it, but modern science did not stop there. It establishes brand-new order and rules with brand-new ideas and methods, which is the charm of modern chaos theory. As J Farmer, one of the founders of American chaos theory, said, "Here is a coin with two sides. On the one hand, it is orderly, in which randomness comes out: only one step away, on the other hand, it is random, which implies order. " From this perspective, modern scientific theory and thinking are moving towards dialectical thinking. Modern chaos theory shows that order and disorder complement each other. In the same evolutionary background and process, the so-called order and disorder are mutually contained: order comes from chaos and breeds chaos at the same time, and chaos comes from order and produces order at the same time. There is a strange chaos behind the surface order, and there is a more strange order in the depths of the chaos. As the famous scientist Einstein lamented: the world is so magical, and it is even more amazing that such a world can be understood by us!