Today Sweden and Norway are still the United Kingdom, so Oscar II is the king of both Sweden and Norway.
His mother is a descendant of the famous Gustav.
As a king, Oscar II was very keen on science. When he attended Uppsala University, the oldest university in Northern Europe, he studied mathematics.
That's why the king had the leisure to set up a reward for mathematical problems, and also had a dedicated royal mathematical consultant.
He took over the letter that Levler submitted. Although the specific calculation process was not particularly understandable, he generally knew that it should be correct. Although the whole text was devoted to discussing why there is no exact solution to the three-body problem, in the end it was
Several special solutions are given.
Oscar II is quite satisfied with this, because in this era of mathematics, what he likes most is to determine the beauty. If you come up and tell him that there is no solution, the other party may think that you are a liar who does not understand.
Li Yu's answer also used the method of model simplification. It is well known that three points constitute a surface, so the three-body problem can be simplified to a plane problem for analysis.
As a dynamic system, each of the three points has two degrees of freedom for position and two degrees of freedom for velocity, for a total of 4 degrees of freedom. Three sky points equal 12 degrees of freedom.
In fact, one of the main conclusions of Poincaré's paper that year was to prove through invariant integrals that there are only three conserved quantities in the three-body problem: conservation of energy, conservation of momentum, and conservation of angular momentum.
These three conserved quantities can only be reduced to six degrees of freedom, and the remaining six are still unsolvable, so he said that the three-body problem has no solution.
Or to put it in a more understandable way, the system of equations of the three-body problem can be listed after all. It is a system of equations composed of three differential equations.
Since the system of equations is deterministic, in theory, as long as the initial conditions are given, the position, speed, direction, or simply the position vector at the next moment can indeed be calculated.
However, the problem lies in the "but". The time and position vectors in the system of equations are dt and dr. Anyone who has studied calculus knows that this is an infinitesimal quantity.
Even a supercomputer cannot actually calculate an infinitesimal amount, so as time goes by, the error will become larger and larger, so large that it is impossible for you to predict it.
This is actually chaos.
Li Yu went one step further to explore chaos through the three-body problem. Of course, since it was a mathematical bounty, he only brought up this problem in a relatively superficial way.
It was precisely with the emergence of chaos that he dared to say that the solar system would also be in chaos in the future, but due to chaos, time could not be predicted.
——After all, it is mathematics, it is a purely theoretical deduction.
Leaders like to see conclusions, and the more eye-catching they are, the better.
However, the conclusion given by Li Yu was still a bit too unexpected. Oscar II asked the mathematics consultant Levler: "Is there any problem with this answer? Why does it say that there is no solution and then say that there is a solution?"
Levler said excitedly: "Your Majesty, what you asked about is the most wonderful thing. This Chinese named Li Yu has really rigorous thinking. According to the differential equations he gave, it is indeed impossible to solve. But he can
Finding special solutions to complex unsolvable equations is where you excel."
Oscar II somewhat understood, "Then he mentioned that the solar system will be in chaos, is it true?"
Levler said: "This is relatively advanced knowledge, but the answer he gave is too short, and I can't see much of the reason at the moment. But regarding chaos, he mentioned that it can be simulated with a double pendulum. He said that ten can be done
If the double pendulum is lowered at the same position at the same time, it will be completely chaotic if it does not swing more than eight or nine times."
In order to prove his conclusion, Li Yu just took out the simplest chaotic system, the double pendulum.
Oscar II was puzzled: "Double pendulum? I only know single pendulum."
"I've never done anything like this," Levler said.
Oscar II said: "I know the simple pendulum, isn't it the one in the clock? I learned the period formula of the simple pendulum when I was studying. How could it be impossible to predict when adding an extra pendulum? And it seems that the double pendulum system is simpler than the three-body problem.
ten times."
"Your Majesty, I also have this question. The author Li Yu seems to have predicted our doubts, so he said that he can make a double pendulum by himself for comparative experiments." Levler said.
Oscar II asked: "Is it complicated to make a double pendulum?"
"No," Levler said, "the production of double pendulums is very simple. I can arrange for people to make ten double pendulums today."
Oscar II was obviously very interested in this simple and incredible mathematical problem, "Hurry up, I want to see it with my own eyes!"
The double pendulum is the most common chaotic system in life, and it is very simple to make.
The Royal Swedish Academy of Sciences has its own laboratory, and there are a lot of experimental facilities for pendulums. All it takes is to simply change the length of the pendulum and add another pendulum, so it didn't take long to make ten identical pendulums.
Naturally, the appearance cannot be exactly the same, but the pendulum length is exactly the same.
Drottningholm Palace, Royal Palace of Sweden, Stockholm.
Levler placed ten pendulums in front of the throne, and then ten attendants lifted them upright in the same position.
Levler was very attentive and carefully corrected everyone's gestures and positions to ensure that the swings were exactly the same when they were released.
It wasn't until he felt there was no problem that he said to King Oscar II: "Your Majesty, it's time to start. Please give the order."
Oscar II felt very strange: "Even if the swing is really different, at most it is just a slight error in the time when several waiters let go. How can you say the word 'chaos'? Levler, what do you think?"
Levler also agreed with Oscar II: "This is true in theory."
Oscar II cleared his throat, "You ten must act in unison and listen to my command, three, two, one, release!"
Ten waiters released their pendulum balls at the same time.
Once, twice, three times, the swinging pace of the swing ball seems to be exactly the same.
The corner of Oscar II's mouth raised slightly, "I'll just say it!"
Four times, five times, six times, still no difference can be seen.
Even Levler was a little confused, but with such a big halo, Li Yu shouldn't talk nonsense, right?
Seven times, eight times...
etc!
The seventh swing was at a similar pace, but when it jumped to the eighth swing, the ten swing balls went in completely different directions, with almost no relationship to each other!
The subsequent swings were even more chaotic. The ten double pendulums were completely different from each other, and it was impossible to tell that they were swinging at the same time.
Oscar II rubbed his eyes: "What did I just see? Isn't it wrong?"
Levler was also stunned, "It's a mess, it's really a mess!"
"If I counted correctly, it only took seven or eight strokes, how could it be like this?" Oscar II was greatly surprised.
Levler immediately stopped: "Do it again!"
The second time, Levler was more serious. In order to eliminate the problem of inconsistent movements of the waiters, he even asked the king to select ten guards. They were regularly trained and their movements were uniform.
But even so, under the command of King Oscar II, if both pendulums are lowered at the same time, it will still lead to complete chaos after beating seven or eight times.
Oscar II conducted more than ten experiments in a row, and the results were exactly the same.
In fact, not to mention human operation, later generations of computers simulated 50 double pendulums whose initial speeds differed by only one millionth, and after about ten swings, they all became chaotic.
Now Oscar II and Levler are really convinced!
"Why is this happening?" Oscar II also graduated with a bachelor's degree in mathematics, and was completely unable to understand everything in front of him.
As the Royal Mathematics Advisor, Levler was also unable to answer the king's question. He was just shocked and said: "It's amazing! I can't explain it with the existing knowledge at all. He has opened our eyes again."
Oscar II picked up Li Yu's article, which was only a dozen pages long, and the following discussion about "the solar system will be chaotic" was only a few pages long. He read it several times but couldn't find anything.
"Is my mathematical knowledge so backward?" Oscar II showed Li Yu's letter to Levler, "Leffler, please explain it to me."
Levler spread his hands: "Your Majesty the King, I have read this article several times, and I really do not fully understand its meaning."
"What should we do?" Oscar II thought hard.
Levler's mind turned quickly: "Your Majesty, we can ask him for a manuscript, and we can even award him a mathematics medal."
"Math Medal?"
"Yes, Your Majesty! We have established the Nobel Prize in Physics, Chemistry, Physiology, Literature and Peace, but there is no Mathematics Prize yet." Levler said clearly.
"Well, that makes sense." Oscar II nodded. As a mathematician himself, it is indeed difficult to understand that the Nobel Prize dominated by his country does not have a mathematics award.
Of course, the award setting of the Nobel Prize is completely in accordance with Nobel's will.
Although many people suspect that the Nobel Prize does not include a mathematics prize is due to his personal emotions, in fact it is not, and it is really entirely due to Nobel's scientific concepts.
Nobel ended his public secondary education at the age of 16 and did not continue to go to university. Instead, he received some private education from an outstanding Russian organic chemist.
In fact, it was the Russian Prize in Organic Chemistry that drew Nobel's attention to nitroglycerin in 1855.
Nobel was a typical genius inventor in the second half of the 19th century. His inventions required materials, decisiveness and intuition, but did not require any advanced mathematical knowledge.
This was indeed the case for experiments in the field of chemistry at that time, so Nobel's mathematical knowledge may not have exceeded the four arithmetic operations and proportionality, which is almost the level of modern junior high school mathematics.
However, the subsequent development of chemistry was very fast. Just a few years after Nobel's death, it was impossible for the Nobel Prize to ignore the influence of mathematics.
Levler said: "Your Majesty, the mathematics in Germany, Britain, and France is booming. We can start first and ask Li Yu to write a mathematics paper for us."
"Just do it!" Li Yu's news some time ago was still vivid in his mind. The experiments mentioned in just a few sentences in his paper today are so mysterious that they are indeed worthy of being commissioned! Oscar II made the decision: "Directly generate electricity.
If you submit the paper, let Li Yu explain in detail the problem of the double pendulum and why the solar system is in chaos. After receiving the paper, you personally find several top mathematicians to review it. If it passes, I will personally award it."
Levler asked: "What's the bonus set up?"
Oscar II proudly said: "Same as the Nobel Prize in Physics or Chemistry, it is also 150,000 kronor! But of course the money will not go to the Nobel Foundation. This is a bonus provided by our royal family."
Good guy, what a big deal!
Levler asked again: "This mathematical bounty?"
"Of course the award must also be awarded to Li Yu." Oscar II said.
The reward for the mathematics reward is 2,500 crowns, which is equivalent to about 350 taels of silver.
But 150,000 crowns is really incredible, a full 21,000 taels of silver!
This is a huge number.
Therefore, the Nobel Prize can be so dazzling from the first session, attracting the attention of all top scientists, and becoming the world's top scientific award. It is entirely because of the sincerity given from the beginning! It is so sincere!
At that time, there was no scientific award to such an extent, and it naturally attracted the attention of most scientists and scientific research organizations.
If you look at it now, the 150,000 Swiss kronor back then is about 6.4 million RMB today. Taking into account the relative scarcity of materials back then, the actual purchasing power is far more than 6.4 million. After all, there were far less places to spend money at that time.
So rich in the first century.
It must be said that Nobel is really rich. He left a total of 31 million kronor to the foundation in his will.
Since it is called a foundation, you can understand it as using the interest or income earned from investments to issue bonuses. This is also the reason why the Nobel Prize has not been spent all after being awarded for more than 100 years.
What we want is a steady flow of water!
Of course, currency inflation will occur, especially since there have been successive world wars of World War I and World War II.
Since 1901, the prize money has actually begun to decline year by year. In the following 90 years, the Nobel Prize prize money has been lower than in the first year.
The Nobel Foundation really almost ran out of money. Fortunately, in the 1950s, the foundation gave money to some international investment institutions, and things turned around.
Among them is an extremely powerful investment guru, Foster Fleiss. The Nobel Prize should indeed be thanked to him. This man is known as "one of the greatest investors of the twentieth century". In 2001, he founded his own
Before the Brandy Fund was sold to AMG, it obtained a cumulative return of more than 1,000%.
In short, taking inflation into account, it was not until 1991 that bonuses again exceeded those in the first year.
Even starting in 2020, Sweden has increased the award to 10 million kronor, which is equivalent to about 7 million RMB according to the exchange rate (the exchange rate has been changing, which is almost the same amount).
Of course, the honor of the Nobel Prize itself now far exceeds money. 7 million has become insignificant in front of the Nobel Prize. The scientific value and influence value it brings cannot be measured by money at all. Cultivate a Nobel Prize-level
I found that it is not possible to do it with 7 million.
Even if 70 billion can be spent to finally produce a Nobel Prize-level result, no country will have even a trace of heartache.
But this is all a story for another day. In short, at the beginning of its birth, the Nobel Prize was completely "the peak is at the debut"!