Technology invades the modern world

Chapter 34 A true message
A true word is passed on, and a thousand volumes of books are falsely passed on.

If Lin Ran had not pointed it out directly, Chen Jingrun might not have realized until many years later that Professor Lin had crammed a lot of mathematical knowledge related to intercontinental missile trajectory optimization into this mathematics seminar.

He finally understood why only young students were accepted to attend the seminar, but not professors from Hong Kong University.

On the surface, it was because he liked dealing with young people and wanted to cultivate the next generation of Hong Kong mathematics.

In fact, it was because it was difficult for students to keep up, unless they were top geniuses. But when Shing-Tung Yau was still in elementary school, there were no such mathematical geniuses in Hong Kong.

The possibility that students can understand the true meaning of Lin Ran’s course from such complicated content is not very small, it is impossible, but professors may be able to understand it, especially professors recruited from England.

Who knows the other party’s past background? Did he help the Allied forces with logistics and missile design during the war?
As long as the other party has a similar background, this possibility will begin to rise rapidly.

"If we consider this multivariate differential equation as the flight trajectory of a ballistic missile, it will be affected by factors such as the Earth's gravity and air resistance, and the constant is undoubtedly the Earth's gravity.

This is air resistance, but what do the subsequent terms mean?"

"I understand that it has been simplified to a linear recursive least squares filter, but what are its application scenarios?"

"Here, by expanding the formula with small parameters, we simplify the complex high-dimensional formula into a low-order equation to reduce the amount of calculation.

These should be factors such as changes in air density and the curvature of the earth, which answers the first-order air resistance approximate equation solution provided by Dean Qian! "

Chen Jingrun understood that the cases mentioned in Lin Ran’s class were like ores, some of which contained real gold.

After analyzing dozens of cases one by one, he found that one of them contained the solution to the mathematical problem raised by Qian Xuesen.

What’s more important is that what the other party gives is not a value, but a universal model.

Using this model, the originally complex equation can be simplified into a linear recursive least squares filter. Combined with the piecewise constant error model taught by the other party, an approximate solution can be obtained for this type of problem by manual calculation.

Even in his understanding, the approximate solution obtained in this way will be at least two decimal points better than the original accuracy.

Previously, it would have taken a lot of manpower to calculate, and even if it could be calculated, it could only be approximated to one decimal place at best. Now, it can be approximated to three decimal places with conventional manpower.

Although he was not engaged in missile design and was not clear about the significance of this formula, he knew that this equation given to him by Qian Xuesen was the top priority among many problems.

Then it will be of great significance to China today.

Even if there is only this one equation, it is not excessive for him to activate channel 3.

Because in his opinion, such a sophisticated method was something he had never seen in the most cutting-edge mathematics journals at the Institute of Mathematics of the Chinese Academy of Sciences.

Although what has been able to spread to China has little to do with the cutting-edge, it is at least two years behind.

But after he came to Hong Kong, because he was admitted to Lin Ran's seminar, Hong Kong University gave them various privileges according to student treatment. He was able to go to the library of the Department of Mathematics of Hong Kong University to read the most cutting-edge journals.

He also did not find similar methods in these journals.

However, what Chen Jingrun is worried about now is which of the 37 cases are valuable.

In short, I didn't sleep all night.

The next day I went to class with dark circles under my eyes, and then at ten o'clock in the evening I stood in front of No. 3, Area 08, Kowloon Tong, ate a bowl of ramen, and waited until eleven o'clock in the evening.

All the shops on the street were closed. A Rover P4 whizzed past, slowed down in front of Chen Jingrun, and drove away.

In those three short seconds, Chen Jingrun had practiced this technique exactly three hundred times in Guangzhou. When the prepared document bag was accurately dropped through the glass window, Chen Jingrun finally felt relieved. His mission was accomplished.

But he didn't know that the trajectory of his life was about to change drastically, and his mission was not completed, but had just begun.

"Old Qian, the Science and Technology Commission needs you to attend an urgent meeting.

The car is ready downstairs!"

Qian Xuesen, who had already fallen asleep, heard a quick and short knock on the door, and then his wife got up, opened the door, and called him awake in his ear.

He stood up and glanced at his May Day watch on the bedside table. It was 2:30 in the morning.

He wondered what important thing could happen at this time. Could it be related to Professor Lin Ran on the other side of the river?
Qian Xuesen packed up his things with questions in his mind and walked into the night.

When he arrived at the Science and Technology Commission building, he found that the blackboard was already densely covered with formulas.

"Come, Dean Qian, please take a seat. Take a look at this document first."

Qian Xuesen took the materials from the other party and after reading only two lines of words, he could no longer suppress his excitement and walked to the blackboard.

"Yes, that's right."

"What's used here is a Monte Carlo simulation."

"Here we use manual sampling, and we can simulate randomness using only a mechanical computer and manual sampling."

"Just what is here?"

"No, there must be some meaning here. Since Lin Ran chose to package the entire algorithm together and talk about it, then this definitely cannot be meaningless."

"No, it could also be noise, noise that exists to cover up the real purpose."

"No, Xiao Zhang! Hurry up and help me find the second notebook in the lower right drawer of my office!"

"This reminds us that we can use Monte Carlo simulation. Yes, this should be Monte Carlo simulation!"

Qian Xuesen stood in front of the blackboard, apparently having a conversation with Lin Ran from Hong Kong. The middle-aged man next to him saw that Qian Xuesen was immersed in his own world and did not interrupt him.

After waiting for a long time and seeing Zhang Kewen still not bring his notebook, Qian Xuesen couldn't help but walk over and light a cigarette.

At this time, the middle-aged man stepped forward and asked, "Dean Qian, what is the Monte Carlo simulation you just mentioned?"

Qian Xuesen explained: "This was the numerical simulation method that scientists in the Manhattan Project during World War II came up with when they needed to solve complex physical problems such as neutron diffusion, but analytical solutions were difficult to obtain.

Von Neumann and Stanislav Ulam developed a systematic Monte Carlo method for numerical simulations using random sampling. Nicolaas Metropolis first used the term Monte Carlo in 1947.

I had heard of this method, which used manual sampling combined with a mechanical computer to simulate nuclear reactions, but they never let me know the specific details of the algorithm.

"So it can be used to make nuclear bombs?" The middle-aged man's eyes lit up.

　Don't rush me, for the new book, I'll write two chapters a day without fail, okay!

　　
　
(End of this chapter)