Modern science began with Newton, who was a very remarkable scientist. As we all know, he discovered the law of universal gravitation and Newtonian mechanics, and was also one of the discoverers of calculus. In terms of a person's contribution to science, few can be compared to Newton. If he could do one of the above things in his lifetime, he would be called a very great scientist, but Newton did three things.

There is a well-known legend about Newton: while taking a nap, an apple fell on his head, which inspired him and led to the discovery of the law of universal gravitation, which is also the origin of the entire modern science. My alma mater, Nanjing University, once received the seeds of this apple tree from the University of Cambridge in the UK. If you want to see the descendants of this apple tree that has hit Newton, you can go to the new campus of Nanjing University.

There is a very interesting joke in this cartoon, to the effect that: I think the more difficult thing below is how to apply for research funding, and I can't get funding just because an apple falls on my head.

Perhaps everyone thinks that Newton's discovery of universal gravitation was a lucky coincidence, but in fact, it is not. The discovery of the law of universal gravitation has undergone many years of observation by predecessors.

A similar example is Johannes Kepler's discovery of the three laws of planetary motion, (Editor's note: Ellipse law: all planets' orbits around the sun are ellipses, and the sun is at one focus of the ellipse; area law: the line between the planet and the sun sweeps an equal area within an equal time interval; harmonic law: the square of the sidereal time time when all planets circle the sun is proportional to the cube of the long half axis of their orbits.) The discovery of Johannes Kepler's three laws is also not accidental, nor is it a sudden inspiration.

The first scientist suffocated by urine in history: Tycho Brahe

Before Johannes Kepler discovered the three laws of planetary motion, there was a Danish mathematician, Tycho Brahe, who spent a lot of time observing the movement of planets. At that time, the observation accuracy was relatively poor, and he used the naked eye to observe the movement of planets, so he spent a lot of energy.

The Danish emperor even supported him in building an observatory on the island, spending a lot of money to support his research. Interestingly, the paper he recorded at that time was provided by a specialized paper mill.

Tycho had a good relationship with the emperor, but after the emperor's death, the successor emperor did not like him, so he went to Prague, where the emperor also supported him in conducting scientific research, allowing Tycho to frequently visit the palace. Once he drank a lot of wine in the palace and died upon returning home. Everyone had been speculating about the cause of his death. One speculated that he had been poisoned by someone else, and another speculated that he had been suffocated by urine after drinking too much. In 2001, over 400 years after his death, someone decided to dig up his body to determine the cause of his death. It was found that he did not die from poisoning, but rather suffocated by urine, Tycho became the first scientist in history to be suffocated by urine.

Ten years later, there was another great controversy about Tycho. Tycho had a strange personality. In his twenties, he argued with his cousin about who was the greater mathematician. In the end, the two decided to duel, but Tycho's nose was cut off during the duel. It was not known for a long time whether his nose was made of gold or silver. In 2010, everyone decided to dig out his coffin again and study it, but it was found that his nose was made of copper.

Tycho's observation of astronomy laid the foundation of Johannes Kepler and the beginning of the law of universal gravitation. As his student, Johannes Kepler observed the movement of Mars. If we had not observed Mars at the beginning, people would have thought that the orbit of the planet was circular, so Newton finally discovered gravity, not just because an apple fell on his head.

Classical methods cannot solve the three body problem

When Newton discovered the law of universal gravitation, the first problem was to solve the multi-body problem. With the combination of universal gravitation, Newtonian mechanics and calculus, such astronomical problems became mathematical problems.

How to find the orbit of a planet's motion and accurately calculate its orbit based on these physical laws. The presence of the sun and a planet is a two body problem. We already know that the orbit of a two body problem is a stable orbit, while the presence of the sun and two planets together is called a three body problem. The more celestial bodies there are, the more complex the mathematical problem becomes. The three body problem took a long time, and ultimately people found it unsolvable.

The solar system far exceeds the three bodies, with the sun, planets, planets, satellites, and many other small celestial bodies. The entire solar system is a massive system, far exceeding three bodies, and is a more complex multi body problem. Since the three body problem cannot be solved, it is obviously impossible to solve the motion of the solar system using classical methods for multi body problems.

I need to mention Newton again here. He is also a "strange" person who has done great scientific work in his first half of his life, but he is a very devout Christian who believes that the solar system is unstable. People may ask how humans can survive since the solar system is unstable? Newton's explanation was that God would push the planet or ball every once in a while to return the Earth to a stable orbit without deviating too far.

Newton has been trying to prove the existence of God through mathematical methods, using mathematical formulas to unravel the orbits of planets. Now it seems very absurd, so some people jokingly say that after Newton was hit by an apple, his brain was actually not very good.

As for the stability of planets, every great scientist will put forward his own opinions, which are sometimes between mathematical analysis and speculation.

Why is the novel 'Three Body' very interesting?

Everyone knows that mathematicians like to write speculations, such as the classic science fiction work "Three Body". Why do you think this novel is very interesting?

I just mentioned that because the three body problem cannot be solved using classical methods. The three body system is a chaotic system, and the most important feature is unpredictability. The movement of the three bodies cannot predict how it will change in the future if the time is not long enough. The novel "Three Body" utilizes this feature to describe a world with three suns, whose movements are in a very unpredictable state. It is possible that the three suns suddenly appear, causing all life on the planet to die of heat. It is very likely that the three suns will not appear for a period of time, making the planet very cold and freezing all life to death. This is the scientific principle in the novel "Three Body".

For humans, there is no need to worry about the stability of the solar system. Scientists have calculated that there will be no problems for millions or even billions of years, and even if it is unstable, it will take billions of years for things to happen.

Why do humans care about the stability of the solar system? I want to say that the development of science is not based on practicality. Modern science comes from Newtonian mechanics, and Newtonian mechanics comes from celestial mechanics, and celestial mechanics was initially to satisfy human curiosity, but science has brought revolutionary development to human life, which is different from technology. Technology is competitive, science is revolutionary, and modern life is all due to the development of science, so it is wrong to look at scientific research with a utilitarian perspective.

Mathematicians have a very profound theory called KAM theory (Editor's note: KAM theory is a famous theory in classical mechanics that discusses the dynamic behavior of nearly integrable conservative systems: Hamiltonian systems, reversible systems, and volume preserving maps. K, A, and M respectively represent three recognized mathematicians who founded the theory in the 1950s and 1960s, namely, Russian mathematicians Kolmogorov and Arnold, and German mathematician Moser), Many mathematicians have made great contributions to this. One of the concerns people have about mechanical systems is the long-term behavior of the motion process and the state it ultimately reaches. The long-term behavior of dynamic systems may take various forms: equilibrium or fixed points, periodic vibrations, quasi periodic motion, chaos, all of which are stationary states.

The deterministic view of Newtonian mechanics has dominated for a long time because of its success in solving the problem of planetary motion in the solar system. However, the three body problem in mechanics and the problem of the motion of heavy rigid bodies around fixed points have become a problem that has puzzled people for nearly a century. KAM theorem proves the stability conditions for the motion of weakly integrable systems, which shows that chaos is common in the motion orbits of nonlinear systems above three dimensions.

The opposite of stability is chaos, and cognitive progress has made us realize that the world is becoming increasingly diverse, and we are increasingly discovering that stability is unlikely. In most cases, it is dynamic stability or chaotic systems.

Poincare: The First Scientist to Describe Chaos

The picture above shows Emperor Oscar II of Norway, the only mathematician emperor who studied mathematics with a bachelor's degree and has always enjoyed science and art. He regularly organizes science lectures in the palace. During his reign, he founded a mathematical magazine called Acta Mathematica, which is still one of the four major journals in the field of mathematics.

In 1887, a mathematician named Mitag Lefler suggested that he establish a scientific prize: whoever can solve the three body problem should be awarded this prize. Although we now know that the three body problem is unsolvable, at that time everyone did not know.

Who is Mitag Lefler? Let me tell you a story, why didn't there be a mathematician in the Nobel Prize? Legend has it that Nobel's lover was kidnapped and taken away by a mathematician named Mitag Lefler.

In 1895, the emperor invited the mathematician Pantheon from the University of Paris to give a lecture at the palace. At that time, Pantheon proposed a guess, now known as the Pantheon guess, which lasted for less than a hundred years. Finally, in my doctoral thesis, I used chaos problems to derive an understanding.

Why does it take so long? Because our understanding of science has developed step by step, Poincar é and Pandev were mathematicians of the same period. In fact, the speculation I proved was a joint exploration by Poincar é and Pandev. Poincar é wrote an article on how to solve the three body problem. Although he did not solve it, the award committee ultimately decided to give him a grand prize. But what's interesting is that his students found errors in the article, and Poincare rewrote another article in which the concept of chaos was correctly described in mathematics for the first time.

The most basic concept of chaos: the growth rate at the geometric level is particularly fast

The following story is believed to have been heard by many people. A mathematician invented chess, and the emperor was very happy to ask him what kind of reward he wanted. The mathematician said it was very simple. You put 1 wheat in the first grid, 2 wheat in the second grid, 4 wheat in the third grid, 8 wheat in the fourth grid, and 16 wheat in the next grid on the chessboard. This is enough to fill the chessboard. The emperor believed that the requirements of mathematicians were not very high, but he only asked for a few grains of wheat, and immediately agreed. How many wheat grains are actually needed in total? The chessboard has a total of 64 squares, with the first grid being 1 and the last grid being 2 to the 63rd power. The total is 2 to the 64th power minus 1, which is approximately 140 trillion liters of wheat. From this, it can be seen that the growth rate at the geometric level is particularly fast, which is also the most basic concept in chaos.

Let's take a look at the box in the picture, where gas molecules are placed. The molecules move very quickly inside the box. If there is a small error, it doubles in the first second, doubles again in the second, doubles again in the third, and after 60 seconds, 2 to the 60th power. Any small error is doubled in the same way as before. From this, it can be seen that the consequences of molecular motion are very large, and what is the amount of chaos, It depends on how long it takes to double.

In aerodynamics, air moves relatively fast and may double in just a few seconds. The motion of the solar system is relatively slow, and the error doubling time may take decades or hundreds of years, but there is a common property that the error doubles time and time again! After a prolonged period of time, you cannot know its original state because the consequences of repeatedly doubling are unpredictable in the future, which is the principle of unpredictability in the future.

The meteorological system is the most typical chaotic system. You may have met it before. When you are going out for a weekend, when you see that the weather forecast is sunny, it begins to rain heavily at the weekend. You may accuse the Meteorological Observatory of inaccurate forecast. In fact, the weather is a very chaotic system, and there is no way to predict for a long time. Originally, Guangzhou should have clear skies for thousands of miles, but a butterfly waved its wings in Chicago, USA. Its impact on the air may double in a second, and it will affect the climate of Guangzhou in two weeks.

This is the butterfly effect, which is why the meteorological system is a typical chaotic system. To accurately predict the weather, you must know what every butterfly in Chicago did two weeks ago, but there are many larger influencing factors than butterflies, such as cars, airplanes, and people. To predict the climate of Guangzhou in two weeks, you must know all the phenomena that occur on the other side of the earth, which is almost impossible, So short-term weather forecasts are possible, but long-term forecasts can only be based on probability.

Is chaos good or bad?

Everyone knows that chaos is very bad, does that mean it's not good? Let me give a good example of a chaotic system. Nowadays, countries such as China, the United States, and India all want to conduct space exploration, such as going to the moon and Mars, so they need to launch many satellite probes.

In April 1991, Japan launched the HiTen lunar probe. It was only after reaching the sky that it was discovered that there was not enough fuel. People may think that this problem should not occur because there were many uncertain factors during the launch process. Putting too much fuel would increase the weight, and putting an extra pound of fuel would require putting an extra pound of scientific instruments. The fuel was just enough, but in special circumstances, there may be a shortage of fuel. The JPL laboratory at California Institute of Technology in the United States sent a mathematician named Belbruno to assist the Japanese in redesigning the orbit.

The solution is to use limited fuel to send the detector to a chaotic region, where the future is uncertain and may appear anywhere. When reaching a favorable location, let it pass, and when reaching an unfavorable location, spend some fuel to push it. In October 1991, scientists successfully sent the detector to lunar orbit using this method.

One day, Belbruno called me and said he had read one of my articles. He spent a month searching for chaotic regions. If he had read my article on chaos first, he might have been able to quickly find the corresponding region in less than a month. I was very happy to hear that, but I didn't expect that his published paper would have practical applications.

I thought this kind of thing happened once in Japan, but it's unlikely to happen again in the future. Unexpectedly, seven years later, in 1998, a probe from Hughe Company in the United States also encountered the same problem. After launching, they found that there was not enough fuel, and then they found Belbruno again. Soon, Belbruno helped them redesign a new orbit, allowing the probe to successfully reach its original orbit.

(Note: The author of this article is Mr. Xia Zhihong)