Technology invades the modern world

Chapter 190: The professor personally hosts the event (6.2k)

"From launch to return, every step relies on mathematics. Orbital mechanics, numerical integration, and optimal control are all extremely important in the lunar landing process. Let's start with the basics,"

Lin Ran walked to the blackboard, picked up the chalk, and drew an ellipse: "Let's start with Kepler's laws. Planets and spacecraft move along elliptical orbits, following the area law and the period law."

He wrote down the mathematical expression of Kepler's First Law: r = \frac{p}{1+e\cosheta
"r is the radial distance, p is the semi-circular diameter, and e is the eccentricity, which provides us with an analytical solution to the two-body problem."

Lin Ran then added a circle, symbolizing the three-body system of Earth, Moon, and spacecraft: "But in reality, we are facing the restricted three-body problem."

The gravitational pull of the Earth and the Moon acts on the spacecraft simultaneously, and an analytical solution does not exist.

We need numerical methods to approximate the trajectory.

He wrote down the equations of motion.

I know you might be wondering: "The numerical solution to the three-body problem is a computationally intensive task."

In reality, it would be extremely difficult for us to calculate a suitable result during the moon landing process.

This involves optimizing numerical calculation methods.

To solve these equations, we used the fourth-order Runge-Kutta method, which strikes a balance between accuracy and efficiency.

"We rely on IBM's 7094 computer, which has limited performance."

Calculating a complete trajectory often takes hours, forcing us to optimize the code and reduce floating-point operations.

“Once, our simulation ran for three days, and I found that the step size was set too small, wasting time. After adjusting it, the calculation time was reduced by half.”

Lin Ran erased the blackboard and rewrote: "Next is trajectory optimization. We need to minimize fuel consumption while ensuring the spacecraft arrives at the moon at the right time."

"What we will be using now is optimal control theory. In recent years, there have been many outstanding achievements in the field of optimal control theory."

I'll talk about something related to aerospace. We've defined a cost function, which is the integral of fuel consumption, in the form:

J =\int_0^T|u(t)|dt
"Where u(t) is the thrust control vector. We use the variational method to solve for the Euler-Lagrange equations."

Lin Ran drew a simple example: "Similar to the Blasis-Stokes problem, we are looking for the optimal path."

Lin Ran continued, "But in actual tasks, the equations are nonlinear. We use numerical methods, such as the direct shooting method, to discretize the trajectory and transform it into a nonlinear programming problem."

From Kepler and the three-body problem, to numerical integration methods, to optimal control theory for fuel optimization, and finally to error analysis and mid-course correction.

Lin Ran explained almost all the mathematical applications used in the entire moon landing process.

"I'm sorry, due to confidentiality requirements, I can only explain a lot of the content in a very basic and superficial way."

To put it simply, it's about giving people a general idea of ​​what role applied mathematics played in the moon landing process.

Most of you here are engaged in pure mathematical theory research, so you can treat the applied mathematics problems used in the moon landing as a pastime in your spare time.

In Chinese parlance, I was merely throwing out a brick to get the jade.

In my view, mathematics is the cornerstone of all applications; it drives breakthroughs in human science. I thank everyone for their contributions to the advancement of human technology.

Lin Ran bowed in thanks, and the audience erupted in the loudest applause of the day.

Lin Ran returned to his seat and sat down. Harvey Cohen, who was sitting next to him, turned to him and said, "Professor, you spoke very well."

In New York, at the New York Mathematicians' Congress, which is held on its own home turf, everyone else is addressed by their first name followed by "Professor," but Lin Ran is only addressed as "Professor."

Lin Ran asked, "What I've said is too simplistic. Like I said at the beginning, this is just an appetizer."

Harvey Cohen shook his head: "No, no, no, it gave everyone here a lot of inspiration."

"You were just talking on stage, and I was discussing with Fox that in the future, students in our math department who lack talent should be encouraged to pursue applied mathematics."

Fox is the chair of the mathematics department at Columbia University, while Harvey Cohen is the chair of the mathematics department at the City University of New York.

Lin Ran thought to himself, "Those who work in applied mathematics feel offended."

Fox's voice came from beside Harvey Cohen: "Professor, we thought you would stay at NASA for eight years at most, and after Kennedy left office you would leave Washington and return to academia in New York."

I can't wait to enjoy my retirement early and hand over the position of head of the mathematics department to you.

You could stay in the position of head of the mathematics department at Columbia University for at least fifty years.

This would be a perfect reinvention of the Göttingen School in New York.

As a result, year after year, Professor, you've become the director of NASA.

My question is this: will you return to teach at Columbia University?

Fox was somewhat desperate.

Year after year, you've actually become the head of NASA.

The White House Special Assistant for Affairs and the NASA Administrator are completely different concepts.

The former follows the president, while the latter has a chance to remain in their position as a technocrat.

Moreover, now that the moon landing has been successfully completed, Gagarin is undoubtedly a hero of all mankind, and Lin Ran's reputation has also reached an unprecedented high.

Let alone the Donald Party, even if President America were replaced by the Elephant Party, they wouldn't rashly replace Lin Ran.

Furthermore, Nixon and Fred, powerful figures within the Elephant Party, frequently mentioned in media interviews that they had close relationships with the professor.

It's obvious that Lin Ran's position as NASA director is secure.

“Professor, if you don’t return to Columbia University to teach full-time for the next ten years, I’ll consider finding someone else to take my place,” Fox said helplessly.

Harvey Cohen exclaimed in a low voice, "Fox, aren't you supposed to be retiring in the next couple of years?"

Fox said, "If Randolph is willing to go back to Columbia University to take over, I can grit my teeth and do it in another ten years."

In order to give Lin Ran the position of head of the mathematics department as soon as possible, Fox was willing to delay his retirement.

Harvey Cohen initially thought the sacrifice was too great, but then he realized that it wouldn't be impossible if it were a professor.

In fact, positions like the head of the mathematics department are not that important in the American University system, and many top students don't care about them.

Of course, some people do care.

The reason Fox felt it was important to sit in his position and wait for Lin Ran to leave NASA so that he could take over the position immediately was mainly because he was afraid that other universities would poach him.

If other universities poach Lin Ran by offering him similar administrative positions, then Columbia University will suffer a huge loss.

Based on Lin Ran's interactions with White House officials, he deduced that they were influenced by the traditional Chinese mindset of scholars, farmers, artisans, and merchants, and therefore cared more about these things.

This is Fox's thinking.

Lin Ran said, "Professor Fox, I don't know, and I don't know how long I will work at NASA."

Fox sensed from this that he might not return. "Well, Professor, I'll ask you every year. If you haven't given me a definite answer by the time I retire, I'll retire as planned."

Lin Ran smiled and said, "No problem, I'm not that concerned about the position of head of the mathematics department."

Rather than that, I'd rather become the president of Columbia University; I believe the board of trustees would be more than willing.

Fox was stunned for a moment, then said, "I think those old men would definitely agree."

"Yes, how could I forget that?" Fox thought to himself. Columbia University is a project directly supported by the Rockefeller Foundation.

David Rockefeller served as chairman of the Columbia University Board of Trustees.

Given his relationship with Rockefeller and Morgan, as well as his own reputation, he would have been more than qualified to be the president of Columbia University.

Fox felt that his past worries were completely unnecessary.

At the banquet that evening, mathematicians came one after another to raise a toast with Lin Ran.

The Mathematicians' Congress turned into a Randolph fan meeting.

"Mr. Lin, you truly are a source of pride for the Chinese people. The honor you've brought to the Chinese community this time far surpasses that of the Nobel Prize." As a Chinese person, Chen Xingshen chatted with Lin Ran in Chinese for a few more minutes.

Lin Ran said, "The living conditions for Chinese people in America are difficult. In addition to academics, we also want to do as much as possible for our compatriots."

All I can do is offer some reputational support. If there are any future donations specifically for the Chinese community, please let me know, and I'll do my part financially as well.

Chen Xingshen smiled and said, "Okay, I certainly won't be polite. I plan to develop scholarships specifically for Chinese people. I plan to ask Li Zhengdao and Yang Zhenning for their opinions."

If they are willing, the four of us can establish a "Pride of the Chinese" scholarship, hoping that the Chinese recipients will become future role models for the Chinese community.

Chen Xingshen was very enthusiastic about it, after all, doing this would be a way to elevate his own status.

Mathematicians are no different from ordinary people when it comes to seeking fame and fortune.

After the mathematicians' dinner, news about Lin Ran, who was the focus of attention, was quickly reported by the media.

On December 24, 1964, Professor Randolph Lin delivered a lecture at Columbia University’s Havemeyer Lecture Hall, detailing to mathematics professors and doctoral students the advanced mathematical methods used in the joint US-Soviet lunar landing mission.

The professor is considered a key figure in the lunar landing because his precise calculations helped Soviet cosmonaut Yuri Gagarin return to Earth.

The lecture, with its insightful yet accessible explanations and cutting-edge technology demonstrations, left the hundreds of attendees in awe.

This lunar mission marked the first collaboration between the United States and the Soviet Union during the Cold War, signifying a milestone in human space exploration. The professor's calculations ensured that the landing point error between the fuel tank and the lunar module was within 1200 meters, a true engineering marvel.

In a lecture lasting an hour and a half, the professor used clear logic and vivid examples to illustrate the core roles of orbital mechanics, numerical integration, and optimal control theory in missions. His remarks frequently drew applause from the audience, highlighting the decisive power of mathematics in space exploration.

Columbia University's Department of Mathematics Chair, Professor Fox, praised the lecture, saying: "The professor's lecture not only revealed the mathematical mysteries behind the moon landing mission, but also demonstrated the infinite potential of applied mathematics. His explanation was inspiring and opened up new horizons for us."

Professor Fox stated that he plans to nurture more promising students to pursue careers in applied mathematics.

The mathematics doctoral students exclaimed excitedly: "I never imagined that mathematics could so directly change history. This lecture has inspired me to dedicate myself to applied mathematics research." "The professor's concepts of numerical analysis are awe-inspiring; the computational precision that NASA can achieve is unimaginable."

In an interview, the professor claimed that the most arduous task was signing autographs for the attendees, which was even more demanding than the moon landing mission itself.

At the end of his lecture, the professor appealed: 'Mathematics is the cornerstone of space exploration. It is through rigorous models and precise calculations that we sent humans to the moon and brought them back safely. I hope young mathematicians can draw inspiration from this to meet the challenges of the future.'

This remark drew prolonged applause, and the audience rose to their feet in respect.

Inside the University of Göttingen, Siegel was reading the news that Doilin had handed him:

"Well done! You truly deserve to be an outstanding graduate of the University of Göttingen!"

Siegel was gratified that his students were renowned worldwide, and he felt equally proud.

To be a mathematical master of the first half of the 20th century, and for one's students to be not only mathematical masters but also high-ranking White House officials and top aerospace engineers—what a perfect experience it is to have students surpass their teachers!

Aside from a slight regret that he wasn't in Göttingen, the more Lin Ran achieved, the more Siegel felt he had gotten a good deal.

No matter where Lin Ran was, his connection with Göttingen was shallow, but his relationship with Lin Ran was very close.

In the modern academic system, the relationship between mentors and students is one that cannot be ignored.

Although only in name.

But both he and Lin Ran admit it, so who dares to deny it?

Not to mention academia, if he were to go to West Berlin now, which high-ranking official in the Berlin Senate would dare not give him face?

When I went to London, 10 Downing Street personally arranged for someone to receive me.

Which other mathematical master would receive this treatment?
Does Pierre of the École Normale Supérieure in Paris have one? Does Grothendieck of Princeton have one?
Only I, Siegel, have it. Why? Isn't it because of my students?

Therefore, Siegel has fully accepted the fact that he is Lin Ran's mentor and is completely enjoying it.

Doyle naturally saw through Siegel's passive attitude; what difference would it make if I let him go?

He said with a hint of helplessness, "Professor Siegel, could you take another look?"

Siegel then noticed a detail in the New York Times article that he had missed: "You mean the twin prime conjecture?"

Doylein nodded and said, "That's right."

This is the 8th of Hilbert's 23 questions.

The people of Göttingen raised the question of the century, and the people of Göttingen solved the question of the century—what a wonderful legacy!

As a result, we can only watch helplessly as this honor ends up in Colombia.

Or it was due to the decline of the Göttingen school after World War II.

Of the 23 questions in Hilbert's Century Questions, questions 3 and 18a were solved by scholars from the University of Göttingen, and question 2 also received significant contributions from scholars at the University of Göttingen.

But all of this happened in the first half of the 20th century.

After World War II, no Göttingen scholars were ever found to solve Hilbert's century-old question.

That's why Doilyn felt particularly regretful.

Finally, one emerged, a veritable reincarnation of Gauss from the Göttingen school, but he ended up living in exile.

Doilin's idea was no different from China's feeling that the Imperial Seal of the State was out of reach.

Doilyn sighed, his face full of regret, which made Siegel embarrassed and change the subject:
"I have some tickets here. Could you ask if any professors want to go and distribute them to everyone?"

Doyle asked in confusion, "Tickets? What tickets?"

Siegel said: "On December 31, the BBC Face to Face special in London will feature an interview with Randolph Lin and Korolev."

Dubbed the "interview of the century."

Siegel took out five tickets from the drawer, which were carefully printed with the trajectories of the moon and the earth, as well as the outlines of Lin Ran and Korolev's faces.

The ticket itself has an artistic feel to it.

Doilyn was about to swear: "Was zum Teufel!"

(Was zum Teufel means something like "damn it" in German)
He took the ticket and examined it carefully.

Siegel continued, "Randolph had the BBC send it to me, inviting me and my family to watch the interview live."

I was thinking of sharing it with everyone.

Doylein nodded and said, "Okay, but it's too few. There are only four. There are more than four professors in our mathematics department."

Siegel nodded and said, "So let's draw lots."

Watching Doilin walk away, Siegel finally realized: "No, the four people you mentioned, did you include yourself?"

"And what about me?"

Five tickets, four to be divided among, Siegel thought he was a must-go.

Doyle said, "Professor Siegel, you certainly won't have trouble getting a ticket. Just ask Randolph for another one."

If the two of us each take one vote, then there will only be three votes left for the professors to distribute, which is far too few.

"Every extra copy is valuable; Randolph can't just watch you not go to the event."

Siegel was momentarily speechless. "This works?"

Catch a sheep and plunder it!

The meeting room on the third floor of the London Broadcasting Building.

Outside the window, a thin winter mist enveloped Portland Square.

On the long table in the conference room, the headline of The Times read: "Gagalin returns from the moon, US-Soviet cooperation shocks the world."

The clock on the wall ticked, reminding everyone that there were only three days left until the "interview of the century" on December 31st.

In the center of the conference room, program producer Edward Thompson stood before the whiteboard, sleeves rolled up. His gaze swept over the team seated around him: host John Freeman, assistant producer Sarah Jenkins, technician Tom Harris, and news editor Mary Brown. Each person wore a mixture of excitement and nervousness on their face.

Everyone knows that this is a once-in-a-lifetime opportunity for the BBC.

The Kremlin dared not send Korolev to New York, and the White House dared not send Lin Ran to Moscow.

Thompson cleared his throat and said in a loud voice, "Ladies and gentlemen, we have just received confirmation that Dr. Randolph Lin from NASA and Sergei Korolev from the Soviet Union will participate in a special interview on New Year's Eve. Their schedules have been finalized."

This is a milestone for the BBC and a moment that has garnered global attention.

The entire event will be broadcast on television, simultaneously worldwide, and we must ensure that nothing goes wrong.

Sarah Jenkins pushed up her glasses, her voice brimming with barely suppressed excitement: "Edward, you mean Korolev? Is it really true?! Is this interview of the century really being handled by the BBC?"

Thompson nodded, a smile playing on his lips: "That's right, Sarah."

For the first time ever, the Soviet Union agreed.

After Lin Ran found out, he spoke with 10 Downing Street by phone. It was a high-ranking official from 10 Downing Street who personally notified him.

Lin Ran didn't quite understand what the English were so excited about. Would the Soviets agree? Wasn't that a blatant mockery of them? To think that London was much safer than New York for the Soviet Union and Korolev—was that a good assessment?
Lin Ran really couldn't understand the English people's thought process.

John Freeman leaned back in his chair, tapping his fingers lightly on the table, weighing the weight of the program in his mind.

He had interviewed Carl Jung and Edith Sitwell before, but this time was different. The two space giants from the US and the USSR were on the same stage, and a slight misstep could cause an unnecessary controversy.

He said in a low voice, "This will be one of our most challenging programs. The questions must be designed precisely, digging into technical details while avoiding political minefields."

Mary Brown opened her notebook and said calmly, "The public wants to know how they worked together, how Cold War adversaries could team up to land on the moon. But we have to be careful not to let the show get out of control."

Tom Harris scratched his head, his pragmatic nature as a technician making him more concerned with practical matters: "What about the sound system and translation? Does Korolev speak English? If real-time translation is needed, we have to make sure the microphones and headsets don't malfunction."

Thompson responded: "The professor speaks Russian, oh my god, what a bizarre turn of events, a Chinese man and a Slavic man broadcasting live in Russian to the world on the BBC in London."

Therefore, we will definitely need to prepare for real-time translation and communicate with the professor in advance to see whether he speaks English or Russian.

The microphone absolutely cannot malfunction!

It wasn't until this point that Thompson realized something was wrong.

A BBC interview featuring Russian dialogue unfolded in a bizarre way – did London become Moscow?

Freeman opened the outline and said calmly, "I want to start with the technology and ask the professor how to control the error. Korolev can talk about the design of the lunar module, such as how to deal with the low gravity on the moon."

Sarah interjected, her eyes sparkling with curiosity: "Could you ask some more personal questions? Like, what was the most intense moment of the mission? What were their impressions of each other?"

The audience isn't interested in these technical issues you're talking about!

Mary frowned: "Being humane is fine, but we have to be careful. Asking about how it goes might lead to political topics. We have to remain neutral."

Thompson nodded: “Mary is right. The BBC’s position is science and human achievement, not Cold War power struggles. I suggest asking them for their views on future space exploration, such as whether there will be more joint missions.”

Freeman added, "I could ask, 'Does this collaboration pave the way for peace?' But I would use an open-ended question and let them answer it themselves to avoid being accused of bias."

Sarah said in a low voice, "The public certainly wants to know about the possibility of peace. I've even heard people in coffee shops say that this could be a turning point in the Cold War."

Mary sneered: "Turning point? Don't be naive. Nikita and Johnson are still locked in a nuclear war; this cooperation is just a stopgap measure."

Thompson slammed his hand on the table: "Alright, let's get back on track. We need to show the audience the allure of science without turning the show into a diplomatic battleground. John, you set the tone for the questions. Sarah, gather the background information."

Three days later, Lin Ran arrived at the BBC building a day early. The conference room was filled with questions prepared for face-to-face interview programs.

Lin Ran can still enjoy home advantage in England.

Despite these questions being held in Korolev's hands on the special plane.

Home advantage is what the English believe to be a home advantage.

Lin Ran said to the program producer:

“I admire Major Freeman, but I hope this interview will be without a host.”

Edward was shocked: "No host?"

Lin Ran nodded and said, "That's right, there's no host."

Or to be more precise, I am the host.

Doesn't "face-to-face" mean one-on-one?
Major Freeman interviewed both me and Korolev at the same time; what do you call face-to-face?

Edward was caught in a dilemma; more accurately, he was contemplating how to refuse the White House official in front of him.

Before he could answer, Lin Ran said directly, "It's settled then. Don't worry, my one-on-one with Korolev will definitely be much more exciting than your hosting."

　I'm offering 10,000 words, please vote with a monthly pass!

　　
　
(End of this chapter)