In a nonlinear world, what kind of phenomenon does the so-called butterfly effect refer to?
You may not think that the nonlinear world was discovered by a meteorologist.
For thousands of years, people have used experience to estimate whether it will be sunny or rainy tomorrow by observing clouds. Scientists have long hoped that forecasts of weather changes could be as predictable as eclipses and tides. In the early 1960s, Professor Lorenz, a famous meteorologist at the Massachusetts Institute of Technology in the United States, was the first to try to use computers to simulate weather. This attempt is entirely based on the belief that nature has laws and the laws can be understood. Once people master this law and know the initial conditions, they can simulate the past and foresee the future through the bridge of logical and mathematical inevitability.
Lorenz confidently attempted computer weather simulations. He performed computer processing on many relationship equations such as temperature, air pressure, wind speed, air flow, and wind direction related to weather changes. In Lorenz's words, the complex and changeable weather is reduced to its bare bones - digital laws, and computer weather simulation is performed. With the gradual revision of computer weather change models, the output curves of computer weather simulations have begun to approach the curves of actual weather changes. However, one day, for the sake of convenience, Lorenz accidentally made a small change to an input value of 0.506127, changing it to 0.506. Unexpectedly, this 1‰ error caused disastrous consequences. : Two almost identical weather simulations, resulting in two diverging curves.
In classical science, a numerical error of 10‰ is often negligible. In Lorenz's view, a small change in the input value is at best a small wind in the entire weather. Why is the entire weather simulation system so sensitive?
Meteorologist Professor Lorenz is in Science , is keen on the subject. He does not look for answers to questions in classical science, but finds new ways to answer the deep-seated scientific questions behind the phenomena. He believes that weather changes are a large and complex nonlinear dynamic system, and traditional linear dynamic models cannot describe those non-periodic and sensitive dependencies on initial conditions. In complex systems, there are often phylogenetic critical points. In the words of Prigogine, the founder of the famous dissipative structure theory, there are bifurcation points and fluctuation mechanisms in the system. Any small disturbance that is not surprising from the perspective of classical science will often cause the system to shift from stability to stability. Unstable, or moving from instability to stability.
In an academic lecture in Washington in the late 1970s, Lorenz proposed a new concept, the "butterfly effect", that is, "predictability: a butterfly flapping its wings in Brazil will cause a sudden change in Texas." Cause a tornado?" Lorenz revealed a nonlinear world through the "butterfly effect", which is also a realistic world.
Lorentz decided that long-term weather forecasting was doomed to fail. Although the computing speed of today's computers has reached an astonishing level, the global weather model calculates a system of 500,000 equations, which is millions of times better than the 12 equations processed by the computer weather simulation at that time, but , faced with such a complex non-linear system of weather, forecasts for more than two or three days are just speculation, and weather forecasts for more than a week are worthless. It is impossible to use a computer to predict whether it will be sunny or rainy in Princeton, New Jersey, on a certain day a month from now. Because weather changes do not follow the route set by determinism.
Subsequently, Lorenz put his specialty, weather modeling, aside. And to study complex nonlinear problems in fluids-chaos.
A new perspective on understanding nature - Chaos
In contemporary academic trends, the word "chaos" appears very frequently. Some scholars even believe that "the science of the 20th century only Three things will be remembered: relativity, quantum mechanics and chaos. "Relativity rules out the Newtonian illusion of absolute space and time. Quantum theory rules out the Newtonian dream of controllable measurement processes. Chaos rules out Rapp." The fantasy of the predictability of Lars’s determinism.”
From an overall perspective, modern science rejects “chaos” from the door of science. Modern scientists believe that the mission of science is to discover the laws of nature, and only the laws of mechanics based on determinism are models for natural scientific research, and the orderly connections between things are the objects of scientific research. Chaos, as a disorderly phenomenon, is undoubtedly something beyond the scope of science, and it is reasonable to reject it.
However, the research on modern chaos theory reveals to people that those chaotic phenomena characterized by chance and randomness are not scientific exceptions. When we face the regularity of spatial arrangement and the periodicity of time changes, At the same time, the real world is dominated by contingency and randomness in the structure of space and time. In a sense, chaos is a very common natural phenomenon. The concept of chaos in modern chaos studies is no longer the concept of chaos in the traditional sense, and chaos is not synonymous with disorder. As Hao Bolin, an academician of the Chinese Academy of Sciences and an expert on chaos, said, "Chaos is by no means simple disorder, but more like an ordered state without periodicity and other obvious symmetry characteristics." Now people are beginning to realize that chaos is a science of process rather than state, and a science of evolution rather than existence. The "chaos" state is a state of macroscopic disorder and lawlessness, but microscopically orderly and regular state.
It is essentially different from equilibrium disorder. Chaos phenomena may have deep order hidden behind the macroscopic disorder, and there may be truly irregular random motion behind the microscopic order.
In the face of complex nonlinear systems, classical science ended here because it could not establish order and rules for it, but modern science did not stop here. It used brand-new ideas and methods to do it. Establishing a new order and rules is the charm of modern chaos theory. Just like J., one of the founders of chaos theory in the United States. Farmer said: "Here is a coin with two sides. One side is order, with randomness emerging from it: just one step away, and the other side is randomness, with order implicit in it." From this From a perspective, modern scientific theories and thinking are moving towards dialectical thinking. Modern chaos science shows that order and disorder are inherently complementary to each other. In the same background and process of evolution, the so-called order and disorder are inherently inclusive of each other: order originates from chaos, and at the same time, it breeds chaos. , Chaos comes from order, and at the same time, it produces order. Behind the surface order lies a strange chaos, and deep within the chaos lies an even more strange order.
As the famous scientist Einstein lamented: It is amazing that the world is like this, and it is even more amazing that such a world can be understood by us!