When meeting Ramsey for the first time, Chen Muwu once raised an interesting question in front of the apostles of the Cambridge Apostolic Society.
Pick six random people from around the world, at least three of whom may or may not know each other.
This is actually a corollary of Ramsey's theorem. Some people call it the friends and strangers theorem.
In addition, there is another thing that is also very interesting: in a group of no less than three people, if you choose any two people, and they both have exactly one person they know in common, then there will always be one person in the group. Everyone knows him.
As for the Ramsey theorem itself, according to the statement just now about knowing or not knowing, it can be expressed as:
For any positive integers k and l, if the number of people in a party n is large enough, then regardless of the acquaintance relationship, there must be k people who know each other, or l people who do not know each other.
If two positive integers k and l are given, the minimum value of n that guarantees the above conclusion is called the Ramsey number R(k, l).
Of course, we can also turn the relationship between the people at the party who know each other and those who don't know each other into a coloring problem in graph theory, and then express Ramsey's theorem in the terms discussed.
From Ramsey's theorem, a Ramsey theory can be derived, which is used to find the inevitable substructures with iterative order in large structures without iterative order.
Ge Liheng said that Ramsey theory is a branch of combinatorial mathematics.
It was also on the basis of this theory that he proposed the "Gehrig's Number", which was once regarded as the largest number ever seen in formal mathematical proofs. In 1980, it was included in the Guinness Book of World Records.
Of course, the Gregorian number was later surpassed by TREE (3), thus losing its status as the largest number in the world.
Although Ge Liheng is an authentic Chinese name, Ge Liheng is not Chinese, but a native American.
As for his surname Graham, the literal translation should be Graham, but the reason why it was translated as Ge Liheng was because he later married a Chinese wife who was also a mathematician.
Ramsey, born in 1903, is only 23 years old this year.
In the original history, he would propose Ramsey's theorem named after his surname four years later.
At that time, he was just a 27-year-old young man. It stands to reason that Ramsey would have a bright future in the field of mathematics.
But unfortunately, he also died young due to illness in the same year.
The cause of his death was not an accident or any serious illness.
Instead, Ramsey had chronic liver disease. After an operation, he developed jaundice and died.
Now, in a conversation with Chen Muwu, Ramsey worked out the Chen-Ramsey theorem four years earlier than the original time and space. Maybe he can go further in the research on this issue.
Seeing that Chen Muwu agreed to his request, Ramsey was in a good mood.
He and Chen Muwu agreed on a time and place to meet every week to discuss the paper. He picked up the wine glass on the table and drank it all in one gulp, then put the glass back and stood up.
Before leaving, Ramsey talked to Chen Muwu about another thing.
"Brother Chen, summer is coming soon. If you have a chance, let's go swimming in the Kang River together? I've long wanted to compete with you, the Olympic champion!
"By the way, I also asked someone to help me make a pair of those swimming trunks you invented. Although it is a bit revealing when worn on the body, it does have much less resistance when swimming in the water than that one-piece swimsuit."
There is also an unconfirmed theory about the cause of Ramsey's death.
It was said that he was an avid swimmer and died of undiagnosed leptospirosis while swimming in the Cam River.
Although this statement is most likely a rumor, Chen Muwu still feels a little scared.
Although it is far away from the industrial area, the water quality of the Cam River seems to be very clear, but there may still be a lot of invisible dirty things in it.
He felt that if he wanted to swim again in the future, it would be better to go to a special swimming pool. He must not make fun of his body again.
"I'm so sorry, Brother Ramsey, although I really want to swim with you, my schedule is very full this summer and I may not be able to make time.
"And I feel that the water in the Cam River is not as clean as it looks. If you want to swim, you'd better go to a more professional swimming pool."
Ramsey said goodbye to Chen Muwu with a smile, but turned a deaf ear to the latter's words.
His father swam in the Cam River when he was in school, and he had never had any problems since he was a child.
This Dr. Chen, he is really a bit rare and strange.
After the meeting of the Apostolic Society, others went to church for worship on Sunday, and Chen Muwu also took a day off.
On Monday, after breakfast, as soon as he left the gate of Trinity College, he was blocked by someone just like the time when Oppenheimer returned from the United States.
This time it was Dirac who stopped him.
In the eyes of those who are not familiar with him, compared with the countryman from Bristol who first entered Cambridge two years ago, Dirac is even shyer than before.
It is reasonable to suspect that although he learned a lot of knowledge at Cambridge University, more than knowledge, he may have learned how to be autistic.
But the truth of the matter is that Dirac suffered a major blow in his life at the turn of spring and summer last year.
At that time, his brother, who was left behind by his parents, first disappeared in Bristol. Then a few days later, the police who came to the door told the old Dirac couple the bad news that their eldest son's body had been found, and basically It can be determined to be suicide.
Dirac's reticence was largely due to the influence of his family of origin.
His father has a very typical paternalistic style. He often abuses his wife and scolds his children. He is the majestic head of the family.
The care Dirac received from his parents basically came from his mother, and because his younger brother was smarter than his older brother, Mrs. Dirac was very partial to her younger son.
However, Dirac's withdrawn character and excessive maternal love were also a burden to him.
On the contrary, he felt a little envious of his enthusiastic and cheerful brother, and he got closer to him.
His brother's suicide was a heavy blow to Dirac. After dealing with the funeral, he returned to Cambridge from Bristol and was confused every day. In the end, he finally found a way to relieve himself, which was to forget everything and put everything aside. Devote yourself wholeheartedly to your studies.
It was at that time that Dirac's skills in mathematical physics advanced by leaps and bounds.
During the time when Dirac was depressed, Chen Muwu happened to be doing his low-temperature physics experiments in London and was unable to stay with his good friend to comfort him.
Fortunately, there is a Kapitsa at Cambridge University.
As the funniest Russian in Cambridgeshire, Kapitsa has also experienced the pain of losing loved ones, so he knows how to comfort people.
It was precisely because of Kapitsa that Dirac did not sink deeper into grief.
"Paul, long time no see!"
"List."
"What happened to you today? Why did you come to me so early?"
"I went to the Cavendish Laboratory to look for you last week, but was told you were not there.
"That's why I wanted to try my luck at Trinity College today, but I didn't expect that I just met you."
"Sorry, Paul, I've been busy lately, so I haven't been to the laboratory."
Some time ago, Chen Muwu had been writing a paper on the Imperfection Theorem at Trinity College.
After finishing writing, he went to the particle accelerator being developed every day. Indeed, he had not been to the Cavendish Laboratory for a long time.
"That's right, Chen, I will graduate with my Ph.D. this summer. St. John's has sent me an invitation to stay in the college as a researcher after graduation."
"This is a good thing, congratulations!"
"Thank you. I also want to congratulate you for publishing such a great mathematics paper. Have you always done research on mathematics before?"
"No, it was at the beginning of this year that I suddenly became interested in this matter."
"I really envy you. You can do good experiments and come up with so many new theories, and it's not limited to physics, astronomy and mathematics. But for me, just mathematics is the most difficult to learn. It was very difficult. Take the graduation thesis as an example, it tortured me for almost a year."
"Have you finished writing? You should have finished writing, right?"
Dirac nodded: "The paper has been written, but Professor Fowler has arranged another thing for me.
"This fall, or next year, he plans to teach a course on "Quantum Mechanics" at Cambridge University, so he hopes that I can write a handout for this course.
"After receiving this task, I thought of you immediately. Are you busy recently? Do you want to study mathematics or physics? If you are not busy, can you write this book with me? After all, you are the quantum The founder of mechanics.”
Okay, okay, everyone knows that they have nothing to do recently, so they all came to visit, right?
Chen Muwu was not surprised at all that Fowler was going to give a lecture on quantum mechanics at Cambridge University.
In the original time and space, after the birth of the new quantum theory, Bohr of Copenhagen, Denmark, and Born of the University of Göttingen in Germany were competing against each other.
Relying on the Cavendish Laboratory under the leadership of Rutherford, the University of Cambridge can still be in a leading position in the world in experiments.
But in terms of theory, Fowler was the only one left struggling to support it.
Fowler, like Eddington, also came from secondary school mathematics at Trinity College.
But he often provided some theoretical support to Rutherford, and later even became the latter's son-in-law, so he also had a good understanding of cutting-edge physics.
It was he who snatched Dirac from Eddington and led him onto the path of theoretical physics research instead of becoming an astronomer.
It is a pity that after his good student graduated, he did not stay at Cambridge University to serve as his right-hand man. Instead, he visited Göttingen and Copenhagen, the two holy places of quantum mechanics, and finally joined the Copenhagen School.
When Chen Muwu taught linear algebra last year, he asked Oppenheimer to prepare lesson plans for him.
This time, Fowler also asked Dirac to write lecture notes on quantum mechanics.
Dirac didn't know that "Quantum Mechanics" he was about to write was very famous.
But, Chen Muwu knew.
He didn't expect that he would get a piece of the pie this time after he had just harvested Ramsey's wool, so he agreed to Dirac's request without hesitation.
By the way, quantum mechanics.
He also remembered that a few months ago in Rutherford's office, he had promised Bohr that after writing a mathematics paper, he would publish a quantum mechanics paper.
If Dirac hadn't reminded him today, Chen Muwu would have definitely forgotten this matter.
On the side of Zhao Zhongyao and Cockcroft, the progress of the particle accelerator was not going well.
After experiencing various blows, the two of them also became a little less confident from the beginning.
In Cockcroft's vision, Chen Muwu has already built a model of the generator, so he only needs to enlarge it to the same proportion, and then consider various possible problems such as breakdown electric field and tip discharge. By modifying the drawings, you can easily create a physical motor that meets the requirements, and use the high potential difference created by the motor to accelerate particles.
The drawings went smoothly, but when the drawings were converted into objects, the two experienced various difficulties.
First, Chen Muwu pointed out the insulation problem of the experimental environment.
This incident forced them to stop all processes and use purchased asphalt and mica flakes to finally remove this potentially life-threatening safety hazard.
Then, there was a problem with the silk that carried the charge.
Chen Muwu's entire generator model is the size of a can, so the ribbons he used in it are short and narrow and can be seen everywhere.
However, in the generator designed by Zhao Zhongyao, the spherical electrode is more than two meters high from the ground. It is a conveyor belt that carries the charge, and it goes back and forth to form a loop. This means that at least five meters of silk are needed to Meet the requirements of this generator.
Cockcroft visited almost every Chinatown in England but could not find silk that met the requirements.
He also asked the shop owner how long it would take if he ordered it to be shipped to China.
The time given by the shop owner is not optimistic, and if it is shipped all the way from China by ship or train, there are too many variables.
But I couldn't find any better way, so I had to order one from a Chinese silk merchant through the boss's channels.
In fact, Chen Muwu has a better solution to this problem.
But Cockcroft was too embarrassed to tell Chen Muwu about this. He just said that there was a problem with some parts and the manufacturing process of the generator had to be slowed down, which might take a few months to half a year.
Chen Muwu was concentrating on writing a mathematics paper at the time and did not ask any specific questions. What he thought was that with Zhao Zhongyao and Cockcroft, things would be done correctly.
So he planned to use his free time in the past few months to write a paper with Ramsey and a book with Dirac.
But before these two things happened, we had to work on the quantum mechanics paper that had been promised to Bohr.
What he wanted at the time was to ask Russell or Ramsey for help after he finished writing his mathematical paper to strictly prove that the two calculation methods of matrix mechanics and wave mechanics were mathematically equivalent.
But now that Dirac has asked him to write a book with him, it is okay to ask Dirac for help.
After Einstein and Hilbert, another invisible competition started between Chen Muwu and von Neumann.
It's just that they don't know each other that there is another opponent.
(End of chapter)
