None of these theories hold water. Taglia's straight lines and curves are replaced by parabolas. Until today, we have no convincing theory to explain the distance between planets, although Titius of Vidim's Berg discovered the rule of thumb (but this credit is generally attributed to John? Bode), using the modified geometric series to describe the model of the planet. Kepler made amazing achievements. He found that the orbit of the planet was elliptical. But the shocking success belongs to Isaac? Newton, whose Mathematical Principles of Natural Philosophy (1687) announced that he had discovered "the system of the world", and he did it. People think Newton's success is because he thinks in the way of a physicist rather than a mathematician. His research is not based on the preconceived idea of what kind of mathematics should be used in nature, but on the observation of the actual operation law of nature, and he has obtained mathematical skills. Therefore, he avoided common mistakes and created an example of a natural mathematical model. His achievements are so convincing that few people have challenged him in three centuries.
Newton described the behavior of the physical universe with mathematical equations-in modern terms, it is modeling-which is the so-called differential equation. These equations describe the difference between the current state and the state in a short time in the future. Now people use a more memorable and vivid term: power system. The power system describes the recent situation completely according to the current state. Therefore, the dynamic system predicts the recent behavior according to the current behavior. By repeating this process several times in succession, the future state of the system can be predicted at will in principle. In a very important sense, the power system is deterministic: if the power system is used accurately twice in the same state, then from then on, the power system will continue to operate accurately in the same way in both cases.
According to Newton's paradigm, any object or particle system is certain. In principle, this paradigm applies to the whole universe. Pierre, the late expositor of mathematical model determinism philosophy? Simon Laplace (1749 ~ 1827) said: An intelligence knows the mutual position of all the forces that make nature full of vitality and the beings that make up nature at any given moment. If this intelligence is big enough to analyze the data in nature, this intelligence can compress the motion of the largest object and the lightest atom in the universe into an equation: because such intelligence cannot determine what does not exist, therefore,
This is Hitchcock's guiding view of the universe: supercomputer "deep thinking" is giving satisfactory answers to the big questions of life, the universe and everything. This is an example of the clock mechanism universe. Once the gear starts to move, it will never deviate from its original direction. Although the computer has made mistakes, it has helped mankind to understand the world around us. Its work does involve many aspects of life, such as the pattern of spots and stripes on the cheetah's tail, the increase and decrease of the number of insects and fish, and the complex folding form of DNA molecules. Computers have discovered many secrets of the structure of the universe, from Godfrey's Kenji flow, the huge and mysterious wind formation process found at Saturn's North Pole-a nearly perfect hexagon-to the rotation of galaxies until the moment of the Big Bang.
Laplace believes that mathematical models can explain all phenomena in our universe. However, science has the habit of emphasizing its own success and covering up its failures. Thousands of textbooks explain the victory of world determinism, but few textbooks talk about the defects of science. A photo taken by the space shuttle Voyager launched by NASA completely solved this embarrassing situation. The most striking thing in the photo is the red dot, which is very stable in the storm of Jupiter's rotation. The diameter of this vortex is twice that of the earth. Human understanding of this red dot has not changed for at least 300 years. It is recorded in the Journal of Philosophy of the Royal Society: "... Dr. (Robert) Hook, who is original in spirit, has observed it for several months with a very accurate telescope with a diameter of 12 feet since he told a friend about his research plan. A few days after the observation, one night (1May 9, 664) around 9: 00, he announced that he had discovered the red dot on Jupiter's largest belt ... "This red dot is the concrete embodiment of stability and determinism. However, before Voyager made its important exploration journey in 1979, several eddies behind the red dot were never discovered by humans. This is a spiral that rotates violently, just like the wake vortex formed after a whale swims past. These eddies are irregular, irregular, transient and unpredictable, which are completely different from the eddies produced by red dots.
The movement and stability of red dots are the result of mathematical principles of fluid mechanics. This is a fatalistic equation, which ruthlessly exists in the examples of Newton and Laplace. However, why is the stable and definite structure of the red dot accompanied by a vortex-like long tail, and it changes dramatically? The same equation explains the order determinism of the red dot, can it explain the disorder of the vortex that accompanies it? How did this happen?
The first theory of this phenomenon and general turbulence is that this phenomenon has not happened. Like all mathematical models in the real world, the theorem of fluid mechanics includes the approximation of fluid structure. For example, this approximation is made up of infinitely separated substances, not separated atoms. When turbulence occurs, substances are widely separated and the approximation becomes invalid. Turbulence theorem is a different theorem.
It is easy to make this theory unchallenged. The process of fluid mechanics is complex and difficult to handle. When they can be solved by some mathematical formulas, they must be active in a wonderful way. Turbulence is obviously difficult to deal with, so it is difficult for you to solve the problem of this physical process at a high speed.
But now we have a new tool-computer. The computer has proved that the theorem of controlling the orderly flow of red dots can also control turbulence. This is consistent with the second theory of turbulence, which is the Russian physicist Lev? Credit of Dao Lang (1908 ~ 1968). His theory holds that obvious irregularities are a small part of the whole order, and these irregularities are so complicated that we can't fully understand them. This theory is basically correct, although it is wrong to show a complex program in a small process-a mixture of many unique periodic movements, like a whirlpool of various specifications. The current theory is a new mathematical structure, alias is chaos, and chaos is a science to study this phenomenon.