From Newton, Three Bodies to Chaos: How Scientific Cognition Simply to Complex
modern science began with Newton, who was a remarkable scientist. As we all know, he discovered the law of gravity and Newtonian magic, and was one of the discoverers of calculus. From a person's contribution to science, few people can be compared with Newton, a lifetime can do one of the above, can be called a very great scientist, Newton did three things.
About Newton, there is a well-known legend: When Newton was taking a nap, an apple fell on his head, which inspired him to discover the law of gravity, which is also the origin of modern science. My alma mater, Nanjing University, has received the seeds of this apple tree from the University of Cambridge in the United Kingdom, if you want to see the descendants of this apple tree that hit Newton, you can go to the new campus of Nanjing University.
there's an interesting joke in this cartoon, to the big part: I think it's harder to apply for research funding, you can't get funding just because Apple fell on my head.
may think Newton was lucky to find gravity, but it wasn't, and the discovery of the law of gravity has been observed for many years.
Similar examples include The three laws of planetary motion discovered by Kaipler (editor's note: The elliptical law: all planets orbit the sun as ellipses, the sun is at a focal point of the ellipse; the law of area: the connections between planets and the sun sweep the same area at equal intervals; and the law of reconcile: the square of the star time of all planets orbiting the sun for a week is proportional to the cubicity of their orbits.) The discovery of The three laws of CapeLer was no accident, nor was it a flash in the pan.
the first scientist in the history of the United States to be urinate to death:
Before Kepler discovered the three laws of planetary motion, a Danish mathematician, Tygu Brach, spent a lot of time observing the motion of planets.
the Danish emperor even funded him to build an observatory on the island, spending a lot of money to support his research, and interestingly, the paper he recorded at the time was supplied by a special paper mill.
had a good relationship with the emperor, but after the emperor died, the succeeding emperor did not like him, and he went to Prague, where the emperor was very supportive of his scientific research, and the valley was able to frequent the palace. Once he drank a lot of wine in the palace, went home and died, people have been guessing what causes him to die, there is speculation is poisoned by others, another guess is to drink too much to be urine to death, more than four hundred years after his death, that is, in 2001, someone decided to exhumate his body to determine his cause of death, it turned out that it was not poisoned, but by urine, the first scientist in history to be killed by urine.
another decade, there is another great controversy about The Valley. Teigu's character is strange, in his twenties with his cousin who is the greater mathematician, and finally the two decided to duel, the result of The Valley's nose in the duel was cut off, we have not known for a long time whether his nose is made of gold or silver. In 2010, it was decided to dig out his coffin again and study it, only to find that his nose was made of copper.
observation of astronomy in the Valley laid the foundation for Capeler and laid the beginning of the law of gravity. As a student of his, Capeler observed the movement of Mars. If Mars hadn't been observed, people would have thought the planet's orbit was circular, so Newton finally discovered gravity, not just because an apple fell on his head.
can't solve the problem of three bodies by
When Newton discovered the law of gravity, the first problem was to solve the multi-body problem, which included gravity and Newtonian mathematics, plus calculus, and the astronomical problem became a mathematical problem.
how to find the orbit of the planet's motion based on these laws, and precisely calculate the orbit. The sun and a planet together is a two-body problem, we already know that the orbit of the two-body problem is a stable orbit, and the sun with the two planets together is called a three-body problem, the more objects become more complex mathematical problems. It took a long time for the three-body problem, and it turned out that the three-body problem was inso solveable.
solar system far exceeds the three bodies, with the sun, planets, planets and moons, and many other small objects. The entire solar system is a huge system, far beyond the three bodies, is a more complex multi-body problem. Since there is no solution to the three-body problem, it is obviously unlikely that the movement of the solar system will be solved in a classical way for the multi-body problem.
needs to mention Newton, who was also a "weird" man who did great scientific work in the first half of his life, but who was a very devout Christian and believed that the solar system was unstable. People will ask how it is possible for humans to survive because the solar system is unstable. Newton's explanation was that God would push the planet or ball every once in a while so that the Earth would not deviate too far back into a stable orbit.
Newton has been trying mathematically to prove the existence of God, mathematical formulas to unlock the orbit of the planet, now seems very absurd, so some people joked that Newton was hit by an apple, the brain is not really very good.
great scientists come up with their own insights about the stability of planets, sometimes between mathematical analysis and sometimes guesswork.
is it so interesting to write a three-body novel?
we all know that mathematicians like to write guesses, such as the classic sci-fi "three bodies", why do you think this novel is very interesting?
I mentioned earlier, because the three-body problem can't be deconsoced in the classic way. The three bodies are a chaotic system, the most important characteristics are unpredictable. The movement of the three bodies, if not long enough, is impossible to predict how the future will change. The "three bodies" novel is to use this feature, described a world has three suns, three suns in a very unpredictable state, perhaps three suns suddenly appear, so that all life on the planet hot death, it is likely that three suns do not appear for a period of time, so that the planet is very cold, all life frozen to death, this is the "three bodies" novel in the scientific principles.
To humans, we don't have to worry about the stability of the solar system, scientists have calculated, millions of years, or even hundreds of millions of years, even if unstable, it will be hundreds of millions of years before things happen.
why do humans care about the stability of the solar system? I would like to say that the development of science is not from the point of view of practicality. Modern science comes from Newtonian mechanics, Newtonian mechanics comes from tiandynamics, and tiandynamics is initially to satisfy human curiosity, but science to human life to bring revolutionary development and technology is not the same, technology is competitive, science is revolutionary, modern life, all because of the development of science, so it is wrong to look at scientific research with utilitarian eyes.
Mathematicians have a very profound theory called KAM Theory (Editor's Note: KAM Theory is a well-known theory in classical mathematics that discusses near-accumulation conservative systems: Hamilton systems, reversible systems, dynamic states that maintain volume mapping. K, A, and M represent the recognized three-digit scientists who founded the theory in the 1950s and 1960s: the Russian mathematicians Kolmogorov and Arnold, and the German mathematician Moser, for which many mathematicians have contributed greatly. One of the concerns people have about the system of aesthetics is the long-term behavior of the motor process and the state it will eventually reach. The long-term behavior of power systems can take many forms: equilibrium or immobility, periodic vibration, quasi-periodic motion, chaos, all of which are the norm.
The determinism of Newtonian dynamics has dominated for a long time because of the success of solving the problem of planetary operation in the solar system, but the problem of three bodies in dynamics and the motion of heavy rigid bodies around fixed points have become difficult problems that have plagued people for nearly a century, and kam theory shows that the chaotic phenomenon of motion orbits of nonlinear systems above three-dimensional is universal by proving the stability conditions of motion of weak non-accumulation systems.
the opposite of stability is chaos, cognitive progress makes us realize that the world more and more meta, more and more discovery of stability is unlikely, most cases are dynamic stability, or chaotic systems.
: The first scientist to describe chaos is
above is Norway's Emperor Oscar II, the only mathematician emperor who has read mathematics, has always loved science and art, and regularly organizes science lecture halls at the palace. When he was in his time, he founded Acta Mathematica, one of the four major journals in mathematics.
1887, Mitag Lefler, a numberologist, suggested that he set up a science prize: who could solve the three-body problem, and award it to him. Although we now know that the three-body problem is inexplicable, we did not know at that time.
Mitag Lefler, too? I tell you a story, why is there no mathematician in the Nobel Prize? Legend has it that Nobel's lover was abducted by a mathematician named Mitag Lefler.
In 1895, the emperor invited The Mathematician of the University of Paris, Pam Levy, to give a lecture at the palace, when Panlevi made a guess, now called Panlevi Guess, which lasted less than a hundred years, and finally came to terms with the question of chaos in my doctoral thesis.
you might ask why it took so long? Because our understanding of science is developing step by step, Pongale and Panlevi are mathematicians of the same time, in fact, I proved that the guess is that Pongale and Panlevi jointly discussed the speculation, Pongaleh wrote an article on how to disintegrate the three, although not solved, but the award committee finally decided to give him a prize. But it was interesting to see that his students found errors in the article, and Pongale rewrote an article in which the concept of chaos was correctly described in mathematics for the first time.
the most basic concept of chaos: geometric levels are growing particularly
The following story believes that many people have heard, a mathematician invented chess, the emperor was very happy to ask him what kind of reward he wants, mathematicians say very simple, you put 1 wheat in the first grid in the chessboard, 2 wheat in the second grid, 4 wheat in the third grid, 8 wheat in the fourth grid, and then 16 wheat in the next grid, in this way to fill the board is enough. The emperor thought that the mathematician's request was not very high, but asked for a few wheat, and immediately agreed. How many wheat do you actually need? The board is a total of 64 squares, the first grid is 1, the last grid is 2 of 63 squares, a total of 2 of 64 squares minus 1, about 140 trillion liters of wheat. Thus, the geometric level is growing particularly fast, which is also the most basic concept in chaos.
We look at the picture above this box, a box into the gas molecules, molecules in the box moving very fast, if there is a small error, the first second doubled, the second second doubled, the third second doubled, 60 seconds later, 2 of the 60 squares, the original small error is just this way doubled, so it can be seen that the consequences of molecular movement is very large, and how much chaos, depending on how much.
aerodynamics, the air moves faster and may double in a matter of seconds. Solar system movement is relatively slow, the error double time may take decades, hundreds of years, but there is a common nature, the error in one time double! After a long time, you can't know its original state, because the consequence of double-doubleing is that the future is unpredictable, and that's how the future is unpredictable.
meteorological system is the most typical chaotic system. Everyone may have encountered, ready to go out for the weekend to play, a look at the weather forecast is sunny, to the weekend but began to rain heavily, we may blame the weather station forecast is not allowed, in fact, the weather is a very chaotic system, basically no way to predict for a long time. Guangzhou should have cleared the sky, but a butterfly waved its wings in Chicago, USA, and its impact on the air could double in a second and affect the climate in Guangzhou in two weeks.
That's the butterfly effect, and why the weather system is a typical chaotic system, if you want to accurately predict the weather, you have to know what every butterfly in Chicago did two weeks ago, but there are many factors that are bigger than butterflies, such as cars, planes, people, want to predict the climate in Guangzhou two weeks later, you have to know that all the phenomena that happen on the other side of the globe, it's almost impossible, so short-term weather forecasts can be predicted, but long-term can only be predicted from the probability.
chaos is good or bad?
we all know that chaos is very bad, does that mean bad? Let me tell you a good example of a chaotic system. Now China, the United States, India and other countries, we all want to carry out space exploration, on the moon, on Mars, so to launch a lot of satellite probes.
In April 1991, Japan launched HiTen's lunar probe, only to find that there was not enough fuel, we may feel that this problem should not occur, because the launch process has many uncertainties, put too much fuel, weight will increase, put more than a pound of fuel will be put less than a pound of scientific instruments, and fuel is just enough, but in special circumstances may be insufficient fuel situation. JPL Labs at California Institute of Technology sent a numberologist named Berbruno to help the Japanese redesign the track.
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