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

Chapter 90 Chaos
However, the dignified gods Euler and Lagrange only solved the restrictive three-body problem after all.

For the three-body problem in ordinary situations, it was Poincaré who first gave results.

It's just that the three-body problem was not paid as much attention to as the conventional sun-earth-moon system, because at that time people didn't think that the three-body system would really exist.

Poincaré's greatest contribution to this is actually a bit like Galois who solved the root of the quintic equation mentioned above.

Galois used a complete set of complex and advanced group theory to prove one thing: the root of the quintic equation cannot be found by conventional methods.

Poincaré also used a set of complex differential equation theory to prove one thing: the three-body problem has no solution.

Strictly expressed in mathematics, there should be no definite analytical solution, but there can be a specific solution, which is a common feature of differential equations.

It seems that the result is a bit ridiculous. After a long time, two problems that have plagued human beings for hundreds of years, in the end, there is no result!
In fact, this kind of thing is very common in the history of mathematics. The key is that people have discovered many amazing new mathematical theories in the process of proving that it has no solution.

The later Fermat's last theorem is also the same. Although Fermat hated to write down the phrase "the space here is too small, I can't write the proof process", but in the next 300 years, many new ones were born to prove this theorem. mathematical method.

Some people even say that after Fermat's last theorem was proved, a hen that could lay golden eggs died.

In short, the current three-body problem is much simpler to offer a reward for soliciting papers. Li Yu only needs to use Poincaré's differential equation to solve it.

This is very similar to my homework when I was in college.

He is very familiar with differential equations, and he is also very familiar with the three-body problem because of the subsequent fire.

In fact, in the world he once lived in, Poincaré tried to calculate the solution of the three-body problem purely by hand, but it was really difficult.

He also said: "These solutions are so messy that I can't draw what they look like."

Indeed, calculation is a very labor-intensive task. Generally, the masters of mathematics only give ideas, and do not actually do the calculations.

But since this is a question offering a bounty, it would be best if a few solutions could be solved.

Li Yu can do it!
Because the calculation is complicated, but he has a calculator!

Moreover, people in later generations have indeed calculated many specific solutions, and he also knows it.

But even so, writing this reply letter was not an easy task.

It is still very difficult to solve differential equations. Many people may not have any concept of "differential equations", because everyone usually learns mathematics and feels that solving equations is not difficult at all, and even equations are not an important difficulty in mathematics for the college entrance examination.

In fact, it is because the real differential equation is too difficult!
Let's just say that two of the seven math problems of the millennium are partial differential equations.

Wei Shen Wei Dongyi, his research is the Navier-Stokes equation in the differential equation, which is about fluid mechanics.Powerful bosses can take a look at it, but I can't understand a single word.

Anyway, you only need to know two points about partial differential equations. The first is very difficult, and the second is that there is no general solution and can only be solved violently.

It's just that it is difficult to solve it violently in Poincaré's era, because hand calculation is too non-violent.

Li Yu could use the limited conditions and then use a calculator to calculate several solutions, which in fact perfectly answered the reward question.

It's just that it's not sensational at all.

Fortunately, after the question of the reward offered by the King of Sweden and Norway, he mentioned the sun-earth-moon system.What was supposed to be just an add-on problem turned out to be horrific.

Because he knew the answer: the solar system will definitely be chaotic in the future!
After all, the result of the three-body problem itself will be very, very messy.

cough cough!Don't worry, everyone!
It's hard to say the time of this chaos, ranging from hundreds of millions of years to billions of years, and it may not be chaotic when the sun explodes.There is no need to worry that the money in the bank card will not be spent when the earth perishes.

Li Yu can also make a general calculation after giving the initial conditions, and it is impossible to be too precise, but the conclusion that the solar system will be chaotic is enough to shock the world.

But it will take him a long time to write something later.

After all, all of the above involve a relatively large and well-known mathematical theory: chaos.

It was Poincaré who knocked on the door of chaos theory, but Poincaré was really unwilling to calculate too many solutions, so although he had peeked into the corner of chaos, it was a pity that he did not step in.

Fortunately, Li Yu's calculator has a certain degree of violence, at least it can save a lot of time.

Chaos theory is an amazing thing.Li Yu suddenly felt that he had something to do during this period of time, but he still needed to get a few special solutions to the three-body problem first, and then consider other things, and it was impossible to achieve much results in a short time.

Li Yu returned to the house, planning to buy more manuscript paper tomorrow. It would be even better if he could buy pencils and pens.

The next day, Li Yu searched all the four treasures of the study shops in Liulichang, but he couldn't find any Western stationery. He just bought some white paper in Rongbaozhai.

It seems that I have to give advice to Martin Martin in the future. In any case, we should ask the Imperial University to buy more stationery!

When did my previous self worry about stationery? Thinking about it makes me really drunk.

He had no choice but to find Pu Lande again.

Pu Lande has already returned to Beijing, and he also wants to meet Li Yu, who has made a lot of big news in Europe.

"I said Mr. Li! You are so amazing, I don't even know how to describe it! Did you read the report I wrote in The Times?"

Li Yu smiled and said, "So you wrote it."

Pu Rand immediately shook his head and said, "It's not all about me. The Shiliang of "Shenbao" pays special attention to your news. He has a lot of reports and writes more manuscripts. I refer to some of his press releases."

Forehead!If you don't read newspapers, you really can't do it.

Li Yu said, "In the future, I should also subscribe to several newspapers."

"Of course no problem, I can directly order you a free copy of the Beijing-Tianjin Times and Zilinxi Daily for a whole year!" Pu Lande said, "As long as you can write a manuscript for us."

Li Yu asked, "Manuscript? What manuscript?"

Pu Lande said: "Our newspaper office wants to ask you for a manuscript. As for the content and theme of the manuscript, there are not too many restrictions. You can write whatever you want. It is best about the trip to Europe. I have already thought of the name, 'Scientific Journey of Pilgrimage', what do you think?"

Li Yu didn't like the title of this article, so he said: "I can write it, but I will also draw up the title myself."

"No problem! As long as you can contribute. And we will pay you a high fee. As long as you can write it yourself, we can pay you at least 100 yuan for an article." Pu Lande added fire.

"Just write casually?" Li Yu asked.

Pu Lande nodded, "Of course, the readers are the general public after all, and it's not that you are asked to write some scientific research masterpieces, otherwise everyone will not be able to understand them."

"That's easy to do!"

Li Yu is now a big celebrity. Anyone who has read the newspapers must remember his name by now. He is a big celebrity with a lot of traffic.

Maybe I can still accept advertisements in the future!Although in the era when Li Yu lived, it seemed that it was difficult for a scientific researcher to have a large amount of traffic to receive advertisements, but Li Yu seems to be doing it slowly now, which is quite amazing!

"One more thing," Li Yu asked, "Do you have a way to buy pencils or pens, I want to buy some."

"Pencils and pens?" Pu Lande was taken aback, "Of course, I'll get you some from the embassy directly, wait for me."

Pu Lande left the office and came back within a few minutes. He put down a dozen pencils and two pens on the table: "The pencils are brought from the mainland of England. There is a big box. I brought you a dozen of them, which is enough for you." used."

Then he picked up the pen again: "This is the new Parker pen, which uses a lucky curve technology called Lucky Curve, which is currently the most advanced."

Li Yu picked up the Parker pen and looked at it. Pens are not cheap now.

This Parker fountain pen can also be regarded as a representative work of the pen industry in the early [-]th century. Parker was able to break out of the pen market where the competition began to be very fierce, largely because of this patent.

Do not underestimate pens and pencils. At that time, the Qing Dynasty could not even manufacture them. It took 30 to [-] years to produce them independently during the Republic of China. Moreover, the process of starting from scratch was very difficult.

Moreover, the ordinary production process of pencils and pens is not as easy as imagined, let alone advanced technology.

Take this Parker fountain pen as an example. At that time, the feed of ordinary fountain pens had no ink buffer capacity, or could not absorb and retain excess ink, so it was difficult to ensure that the water was evenly injected during writing, and the ink either broke or suddenly dripped a large drop.

Parker's patented Lucky Curve not only solves this problem, but incidentally also solves the problem of ink spilling when the cap is closed and put in a pocket.

When an ordinary fountain pen is taken out for use again, the air inside the pen expands, causing the ink to squeeze out, drip and stain paper or the user's hand.

Parker's improvement is very ingenious. The feed is designed to go deep into the pen barrel, and then the rear part of the feed is bent to touch the inner wall of the pen barrel or the wall of the ink sac, creating a capillary action that allows excess ink on the feed to flow back into the pen.

Although this technology is very old-fashioned in later generations, it is indeed the most advanced fountain pen in the late Qing Dynasty.

Li Yu was very satisfied with this Parker pen, and then said greedily, "Is there any ink left?"

Pu Lande immediately took out two bottles from the drawer, "Take it and use it!"

"Thank you, Mr. Reporter, you will deduct the money from the subsequent manuscript fee."

"Look at what you said! It's all for you!" Pu Lande said, "As long as the manuscript can be delivered quickly."

Li Yu said: "That's not good. There is an old saying in China that you are short-handed."

Pu Lande smiled and said: "I know, at worst, I will increase the manuscript fee for you, and after deducting the fee, I will still give you no less than 100 silver dollars."

There was no need for Li Yu to refuse, so he said, "Okay, I'll write when I get back."

(End of this chapter)