Today Sweden and Norway are still the United Kingdom, so Oscar II is the king of Sweden and Norway.
His mother was a descendant of the famous Gustav.
As 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 mathematics problems, and also had a dedicated royal mathematics 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 a large part of the entire 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 mathematics in this era, what he likes most is to determine the beauty. If you come up and tell him that there is no solution, the other person may think that you are a liar who does not understand.
Li Yu's answer also used the method of model simplification. As everyone knows, 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 in position and two degrees of freedom in velocity, for a total of 4 degrees of freedom. Three heaven points are 12 degrees of freedom.
In fact, one of the main conclusions of Poincare'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, and direction at the next moment can indeed be calculated, or simply put, the position loss can be calculated.
However, the problem lies in the "but". The time and position variables in the 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 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 what excels.”
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 don't see much reason for it 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 in the same position at the same time, it will be completely chaotic if it does not exceed eight or nine swings."
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 haven't 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 by 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, "making 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 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, Drottningholm, 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, carefully correcting everyone's gestures and positions to ensure that the swings were exactly the same when released.
It wasn't until he felt that there was no problem that he said to King Oscar II: "Your Majesty, you can 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: "In theory, it is true."
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 swing of the ball seems to be exactly the same.
Oscar II raised the corners of his mouth 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 were completely different and had almost nothing to do with 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, why did it become 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 seven or eight beats.
Oscar II did it more than ten times in a row, with exactly the same effect.
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: "Amazing! I can't explain it with my current knowledge at all. He has opened our eyes again."
Oscar II picked up Li Yu's article. It 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 tell anything.
"Is my mathematical knowledge so backward?" Oscar II showed Li Yu's letter to Levler, "Leffler, please explain to me."
Levler spread his hands: "Your Majesty the King, I have read this article several times, and indeed I do not fully understand its profound meaning."
"What should we do?" Oscar II thought hard.
Levler thought 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 put it bluntly.
"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 establishment of the Nobel Prize is entirely in compliance 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 no 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."
"That's it!" Li Yu's news from a while ago was still vivid in his mind. The experiments mentioned in just a few sentences in his paper today were so mysterious that they were indeed worthy of being commissioned! Oscar II agreed: "Send a telegram directly and ask Li Yu to explain in detail the problem of the double pendulum and why the solar system is chaotic. After receiving the paper, you will personally find several top mathematicians to review it. If it passes, I will also personally Award him."
Levler asked: "Bonus setting?"
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 mathematical 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! 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 kroner back then is about 6.4 million RB today. Taking into account the relatively expensive and scarce materials back then, the actual purchasing power is far more than 6.4 million. After all, there were far fewer places to spend money at that time. The eleventh century is so rich.
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 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 person is known as "one of the greatest investors of the 20th century." Before he sold the Brandy Fund he founded to AG in 2001, he 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 RB 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 has long exceeded 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. Cultivating a Nobel Prize-level discovery is simply not something you can do with 7 million.
Even if we can spend 70 billion 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"!
