A Man of Science and Engineering in Troubled Times Wandering in the Late Qing Dynasty

Chapter 99 Kings and Mathematics

Now Sweden and Norway are still the United Kingdom, so Oscar II is the king of both Sweden and Norway.

His mother was a descendant of the famous Gustav.

As a king, Oscar II was very keen on science. When he was studying at 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, as well as a special royal mathematics consultant.

He brought over the letter submitted by Leeffler. Although the specific calculation process was not particularly understandable, he generally knew that it should be correct. Several special solutions are given.

Oscar II is quite satisfied with this, because mathematics in this era likes to determine the beauty the most. If you come up and tell him that there is no solution, the other party may think you are a liar who doesn't understand.

Li Yu's answer also used the method of model simplification. It is well known that three points form a plane, so the three-body problem can be completely simplified into a plane problem for analysis.

As a dynamical 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 sky points are 12 degrees of freedom.

In fact, one of the main conclusions of Poincaré’s paper back then was to prove that there are only three conserved quantities in the three-body problem through the invariant integral: energy conservation, momentum conservation, and angular momentum conservation.

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 in another easy-to-understand expression, the equation system of the three-body problem can be listed after all, it is an equation system composed of three differential equations.

Since the equations are 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 equation system are dt and dr. Anyone who has studied calculus knows that this is an infinitesimal quantity.

Even if it is a supercomputer, it is impossible to take an infinitesimal amount for calculation, so as time goes by, the error will become larger and larger, so large that it is impossible for you to predict.

This is actually chaos.

Through the three-body problem, Li Yu continued to explore chaos one step further. Of course, since it was a mathematical reward, he only brought up this problem in a relatively superficial way.

It is also because of the emergence of chaos that he dared to say that the solar system will also be chaotic in the future, but because of the chaos, the time cannot be predicted.

——Is it mathematics after all? It is a purely theoretical deduction.

Leaders like to read conclusions, and the more attention-grabbing the better.

However, the conclusion given by Li Yu was a bit unexpected. Oscar II asked the mathematics consultant Leeffler: "Is there any problem with this answer? Why do you say that there is no solution for a while, and then say that there is a solution?"

Leeffler said excitedly: "Your Majesty, what you asked is the most exciting thing. This Chinese man named Li Yu is really meticulous in his thinking. According to the differential equations he gave, it is indeed impossible to solve them. But he can in the Finding a special solution in a complex equation with no solution, this is the excellence."

Oscar II understood a little bit, "Then he mentioned that the solar system will be chaotic, is it true?"

Leeffler said: "This is relatively advanced knowledge, but the answer he gave is too short, and I can't see much why. But about chaos, he mentioned that it can be simulated with a double pendulum. He said that he can do ten If two pendulums are lowered at the same position at the same time, they will be completely confused if they do not exceed eight or nine swings."

In order to prove his conclusion, Li Yu happened to come up with the simplest chaotic system, the double pendulum.

Oscar II was puzzled: "Double pendulum? I only know single pendulum."

"I haven't done anything like that either," Leeffler said.

Oscar II said: "I know the simple pendulum, it's not just in the clock. I learned the periodic formula of the simple pendulum when I was studying. How can it be impossible to predict it with one more 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." Leeffler said.

Oscar II asked: "Is it complicated to make a double pendulum?"

"No," Leeffler said, "the manufacture of double pendulums is very simple. I can arrange personnel to make ten double pendulums today."

Oscar II was clearly interested in this simple and incredible math 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. There are a lot of experimental facilities for simple pendulums. It only needs to simply change the length of the pendulum and add another pendulum. Therefore, ten identical simple pendulums were made in a short time.

Naturally, the shapes cannot be exactly the same, but the pendulum lengths are exactly the same.

Drottningholm Palace, Royal Palace of Sweden, Stockholm Queen's Island.

Leeffler placed ten double pendulums in front of the throne, and ten attendants pulled them up vertically in the same position.

Leeffler was attentive, carefully correcting everyone's gestures and positions, making sure the swings were exactly the same when they were released for a moment.

It was not until he felt that there was no problem that he said to King Oscar II: "Your Majesty, you can start now, give your order."

Oscar II felt very novel: "Even if the swing is really different, at most it is just a slight error in the time when a few waiters let go. How can you say the word 'chaos'? Levler, what do you think?"

Leeffler also agrees with Oscar II: "In theory it is true."

Oscar II cleared his throat, "You ten must move in unison, listen to my password, three, two, one, let go!"

The ten waiters released the swing balls in their hands at the same time.

Once, twice, three times, the swinging pace of the swing ball seems to be exactly the same.

The corners of Oscar II's mouth raised slightly, "I'll just say it!"

Four, five, six, still can't see any difference.

Even Levler didn't know why, but with such a big halo, Li Yu shouldn't just talk about it, right?

Seven, eight...

and many more!

The seventh swing was about the same pace, but when they jumped into the eighth swing, the ten swing balls went in completely different directions, and they 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 no matter what, it was impossible to tell that they were swinging at the same time.

Oscar II rubbed his eyes: "What did I see just now? Can't I see it wrong?"

Levler was also stunned, "It's messed up, it's really messed up!"

"If I counted correctly, how could it be like this after only seven or eight counts?" Oscar II was greatly surprised.

Leeffler stopped immediately: "Do it again!"

The second time Leeffler was more serious. In order to rule out the inconsistency in the waiter's hands-off movements just now, he even asked the king to choose ten guards. They were often trained and their movements were uniform.

But even so, under the command of King Oscar II, if the pendulums were lowered at the same time, they would still go into complete chaos after beating seven or eight times.

Oscar II made more than a dozen experiments in a row, and the results were exactly the same.

In fact, not to mention human manipulation, later generations of computers simulated 50 double pendulums whose initial velocities differ by only one millionth of a millionth.

Now Oscar II and Leeffler are really convinced!
"Why is this happening?" Oscar II was also considered a graduate of mathematics, so he couldn't understand everything in front of him at all.

As the royal mathematics advisor, Levler was also unable to answer the king's question, but said in shock: "It's amazing! I can't explain it with the existing knowledge, and he opened our eyes again."

Oscar II picked up Li Yu's article, it was only a dozen pages long, and there were only a few pages later on about "the solar system will be chaotic", and he couldn't see anything after reading it several times.

"Could it be that my mathematics knowledge is so backward?" Oscar II showed Li Yu's letter to Leeffler, "Leeffler, please explain to me."

Leeffler spread his hands: "Your Majesty, I have also read this article several times, and I really don't fully understand the meaning of it."

"Then what should I do?" Oscar II thought hard.

Leeffler's mind turned quickly: "Your Majesty, we can ask him for a manuscript, and even award him a mathematics medal."

"Math Medal?"

"That's right, Your Majesty! We have established the Nobel Prizes in Physics, Chemistry, Physiology, Literature and Peace, but we don't have a Prize for Mathematics." Leeffler said straight away.

"Well, that makes sense." Oscar II nodded. As a mathematician himself, but the Nobel Prize dominated by his country does not have a mathematics award, it is really hard for people to understand.

Of course, the award setting of the Nobel Prize is completely in accordance with the Nobel will.

Although many people suspect that the Nobel Prize does not have a mathematics award because of his personal emotional reasons, in fact it is not, it is really entirely due to Nobel's scientific concepts.

Nobel ended his public secondary education at the age of 16 and did not go on to university, but received some private education from an outstanding Russian organic chemist.

In fact, it was the Russian Prize in Organic Chemistry that brought Nobel's attention to nitroglycerin in 1855.

As a typical genius inventor in the second half of the 19th century, Nobel required materials, decisiveness and intuition for his inventions, but did not require any knowledge of advanced mathematics.

The experiments in the field of chemistry at that time were indeed like this, so Nobel's mathematical knowledge may not exceed four arithmetic operations and proportional ratios, which is almost the level of modern junior high school mathematics.

However, the follow-up development of chemistry was very fast. Within a few years after Nobel's death, it was impossible for the Nobel Prize to ignore the influence of mathematics.

Leeffler said: "Your Majesty, mathematics is booming in Germany, Britain, and France. We can definitely start with Li Yu and ask Li Yu to write a mathematics paper for us."

"Just do it like this!" Li Yu's news from a while ago is still vivid in his memory, and the experiments mentioned in just a few sentences in his paper today are so mysterious, it is indeed worth asking for a paper!Oscar II made the decision: "Send the telegram directly, and ask Li Yu to explain in detail why the double pendulum and the solar system are in chaos. After the paper is received, you will personally find several top mathematicians to review the manuscript. If it passes, I will also personally review it." Award him."

Leeffler asked: "The setting of the bonus?"

Oscar II proudly said: "Like the Nobel Prize in Physics or Chemistry, it is 15 kroner! But of course the money will not go to the Nobel Foundation. This is a bonus provided by our royal family itself."

Man, what a great deal!
Leeffler asked again: "This time there is a reward for mathematics?"

"Of course the award should also be awarded to Li Yu." Oscar II said.

The reward for the mathematics reward is 2500 crowns, which is about 350 taels in silver.

But 15 crowns is really incredible, a full 2.1 taels of silver!

This is a huge number.

Therefore, the Nobel Prize has been able to be so dazzling from the very first session, attracting the attention of all top scientists, and becoming the world's top scientific award, it is entirely due to the sincerity given from the very beginning!Sincerity is too much!
At that time, there were no scientific awards to such an extent, which naturally attracted the attention of most scientists and scientific research organizations.

If you look at it now, the 15 Swiss kroner back then is about 640 million RMB today, and considering the relatively scarce materials back then, the actual purchasing power was far more than 640 million. After all, the places where money could be spent at that time were far from the 21st century. so rich.

I have to say that Nobel is really rich, and he left a total of 3100 million crowns to the foundation in his will.

Since it is called a foundation, you can understand that the interest or income earned from investment is used to distribute bonuses, which is why the Nobel Prize has not been spent for more than 100 years.

What you want is a long flow of water!

Of course, currency inflation will occur, especially after 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 prize money of the Nobel Prize has been lower than that of the first year.

The Nobel Foundation really almost had no money at one time. Fortunately, in the 50s, the foundation gave money to some international investment institutions, and a turning point appeared.

Among them is an extremely powerful investment guru, Foster Fleiss.The Nobel Prize should indeed thank him, who is known as "one of the greatest investors of the twentieth century."Before he resold the brandy fund he founded to AMG in 2001, he obtained a cumulative return of more than 1000%.

All in all, taking inflation into account, it wasn't until 1991 that the bonus again surpassed that of the first year.

Even starting from 2020, Sweden increases the award to 1000 million kroner, which is equivalent to about 700 million RMB according to the exchange rate (the exchange rate keeps changing, it is almost this amount).

Of course, the honor of the Nobel Prize itself has long surpassed money, and 700 million has become insignificant in front of the Nobel Prize. The scientific value and influence value it brings cannot be measured by money.Cultivating a Nobel Prize-level discovery is simply not something that can be done with 700 million people.

Even if it can spend 700 billion yuan to finally produce a Nobel Prize-level achievement, no country will feel even the slightest heartache.

But this is something for later, in short, at the beginning of its birth, the Nobel Prize is completely "the peak is the debut"!
(End of this chapter)