Reborn and become a Great Scientist

225 Chapter 173

As we all know, people cannot set flags.

The bull that was blown out on a whim will turn into a slap and slap him in the face again in a short time.

In the history of science written in Chinese, the act of setting up a flag by scientists likes to be called "building a building".

The two most famous of these, one occurred in 1900 and the other also occurred in 1900.

The protagonist of the first time was Lord Kelvin who had just helped Chen Muwu and provided him with a sum of money to develop a particle accelerator.

It is said that in his Royal Society New Year's speech in 1900, he looked forward to the development of physics in the coming new 100 years, and then he said the famous sentence:
"The edifice of physics has been completed, and there are only some knocking and finishing work left. In the beautiful and clear sky, there are only two small dark clouds floating."

Mr. Lu Xun once said more than once: "I never said such a thing."

But this time Lord Kelvin also said: "I didn't say anything like that either."

In fact, Kelvin did mention the concept of dark clouds back then, but he never mentioned buildings.

The venue of the speech is not the Royal Society, but the Royal Institute, and the time is not the first day of the new year, but April 27.

Kelvin gave a lecture that day entitled "Nineteenth Century Dark Clouds Overlaying the Dynamic Theory of Heat and Optics".

What he said in his speech was not as calm as the Chinese expression: "The kinetic theory asserts that both heat and optics are forms of motion. Now the beauty and clarity of this theory are obscured by two dark clouds. It's getting eclipsed."

The word eclipsed reflects the seriousness of these two dark clouds, and it is not as calm and breezy as in the first expression, as if the two small dark clouds are insignificant.

Chen Muwu always feels that the use of the word "building" in Chinese is intended to describe a sense of crisis where the foundation is not solid and crumbling.

Then two fierce men, Planck and Einstein, "helped the building to collapse", opened up two new paths for the development of physics, quantum theory and relativity.

As for the second non-existent building, it happened at the Second International Congress of Mathematicians in Paris, the capital of France, in 1900.

I don’t know whether it was at the opening ceremony or the closing ceremony. The convener of the conference, the French mathematician Henri Poincaré, is said to have said something like this: “…With the help of the concept of set theory, we can build the entire mathematical building… Today we can say that absolute rigor in mathematics has been achieved!"

Poincaré said that he did not mention the above paragraph, and only appeared in the speech about the building in the history of Chinese mathematics, which is somewhat doubtful.

It's just that the mathematics building at that time was just as crumbling as the physics building.

After that, mathematicians came up with a bunch of paradoxes, among which Russell, the philosopher who recruited Chen Muwu into the Cambridge Apostolic Society, put forward the most famous "Russell's Paradox".

In some popular science books, Russell's paradox is simplified as the barber's paradox.

In a city, there is a barber.

He declared that he would shave all the people in the city who did not shave themselves, and that he would shave only these people.

One day, the barber saw in the mirror that his beard had grown, and he subconsciously grabbed the razor, but before he did it, he suddenly remembered what he had said.

If he doesn't shave himself, he's one of the "city unshavers," so he shaves himself.

But if he shaves himself, he belongs to the "person who shaves himself", so he should not shave himself.

In addition to the barber's paradox, Russell's paradox has another easy-to-understand form of popular science.

A library compiles a dictionary of book titles, which contains all the books in the library that do not list their names.

It doesn't matter whether this dictionary lists your name or not. The principle is similar to the barber paradox above.

The proposal of Russell's paradox severely slaps the mathematicians who say that "all mathematical achievements can be based on set theory".

Gottlob Frege, a German logician, wrote a book on the fundamental theory of sets.

Just as the book was about to reach the printing press, Frege received a letter from Russell about Russell's paradox.

He immediately found that his book was so messed up by Russell's paradox that he could only add a sentence at the end of the book: "The worst thing that can happen to a scientist is that when his work is about to be It was found that the foundation of the work done was crumbling."

After Russell's paradox was published, a series of paradoxes followed: Richard's paradox, Perry's paradox, Grayling's and Nelson's paradox...

These paradoxes are called semantic paradoxes, which shake the foundation of the mathematical edifice and trigger the third mathematical crisis.

The first two mathematical crises occurred in ancient Greece.

Pythagoras' student Hippasus discovered that the length of the diagonal of a square with a side length of one is neither an integer nor the ratio of two integers.

The ancient Greek mathematicians at that time did not know the square root of two, let alone the existence of irrational numbers in the world.

Those who could not solve this problem finally chose to solve the person who asked the question:

They threw Hippasus into the Aegean Sea and fed it to the sharks.

The second mathematical crisis originated from Zeno’s paradox in ancient Greece. Can Achilles catch up with the tortoise? Does the moving arrow move or not?

The ancient Greeks first came into contact with the problems brought about by infinitesimals, and this mathematical crisis really broke out in the era of Newton and Leibniz.

The two of them invented calculus, which is very convenient to use, but there is only one problem. Is the infinitesimal quantity in calculus zero?

Infinitesimal quantities may appear in the denominator, so it should not be zero.

However, if the infinitesimal quantity is regarded as zero, and the terms containing it are removed, the obtained formula can be proved to be correct in mechanics and geometry.

At that time, some people criticized calculus as "the devil's trick" and "used double mistakes to accidentally get scientific but incorrect results".

This crisis was not finally resolved until the nineteenth century, when mathematicians headed by Cauchy perfected the specific concept of limit.

As for the third crisis of mathematics caused by these paradoxes, it is the fastest to solve.

German mathematicians Ernst Zermelo and Abraham Frankel proposed two sets of theories in 1908 and 1922 respectively, and these two sets of theories together became Z (ermelo, Zermelo) - F (raenkel, Frankel) axiom system.

This axiom system axiomatizes the construction of sets to rule out the existence of sets like Russell's paradox, which can be regarded as a solution to this mathematical crisis.

That is, in the same year, Hilbert thought of finding a universal solution to the mathematical crisis that had broken out three times.

He came up with an idea called the Hilbert project, proposing to base all existing theories on a finite set of complete axioms and to give a proof that these axioms are consistent.

Hilbert hopes that mathematics is complete and decidable, and that mathematics is based on rigorous logic and is the most impeccable truth in the world.

There is such an item in Hilbert's plan, which is the so-called completeness. People can derive all theorems from the axioms.

If it cannot be deduced, it is not a problem with the completeness of the above item, but a problem with personal ability.

Axioms are the basic mathematical knowledge summed up by people in long-term practice, and are used as the basis for judging the truth or falsehood of other propositions. They cannot be proved and do not need to be proved.

A theorem, on the other hand, is a true proposition obtained by reasoning from axioms.

Hilbert is the greatest mathematician in the world today, and his words are eloquent and very appealing.

Since he proposed this plan, mathematicians have always believed that this plan is correct, and have been trying to prove that it is correct.

It's just that many years have passed, and none of the mathematicians has been able to obtain this proof.

In the original time and space, it was not until 1931 that Gödel proved another point. In an axiom system, there is always at least one proposition that cannot be proved to be true or false. To prove or falsify these propositions, one must use the system New axioms outside.

This is the first theorem of Gödel's incompleteness. The appearance of this theorem completely negates Hilbert's plan and shatters the dreams of Hilbert and all mathematicians.

Hilbert's original intention was to completely solve the mathematics crisis, but unexpectedly, he almost knocked down the foundation of the mathematics building.

This Gödel is exactly the one who solves Einstein’s gravitational field equation, and solves the one that supports time travel in Gödel’s universe.

Chen Muwu knew this person because of Gödel's universe, so he naturally knew the two incompleteness theorems he proposed.

Hearing the incompleteness mentioned in Bohr's words, he thought of this theorem and Hilbert, a mathematician.

Chen Muwu didn't have much prejudice against Hilbert, but he clearly remembered Hilbert once said, "Physics is really too difficult for physicists."

His original intention was to say that although modern physics is highly dependent on advanced mathematics, it has always been used less rigorously.

But this sentence is said from the mouth of a mathematician, and it is still very uncomfortable for a person who studies physics to hear it.

Anyway, the particle accelerator is now being manufactured step by step, and Chen Muwu has nothing else to do besides supervising the work.

Well, now that this has been thought of, why not figure out this incompleteness theorem, which can be regarded as a little shock from physicists to Mr. Hilbert.

After "slamming" the Germans, Chen Muwu once again fell into a long distraction.

Rutherford had long been used to his lover coming out of his body from time to time, so he simply took his other lover, Bohr, to discuss and teach the management experience of laboratories and research institutes.

After a long time, Chen Muwu woke up from the samadhi, opened his mouth and blinked his eyes.

"You finally came back to life, did you think of any good ideas just now?"

Knowing the apprentice is more like a teacher, Rutherford asked with a smile.

Chen Muwu patted his head embarrassingly: "I did have some immature thoughts just now."

"Which aspect, particle...experiment?"

Bohr followed Rutherford: "Or Quantum Mechanics?"

"Uh, none of them. It's just that after Professor Bohr reminded me, I seemed to suddenly have some ideas about mathematics."

He scratched his head faster again.

Although Rutherford was used to Chen Muwu changing his research direction at any time, he still didn't expect that a good student would study mathematics.

Subconsciously, he reached for the pipe on the desk, and then remembered that Chen Muwu didn't like the smell of tobacco.

Some disappointed expressions appeared on Bohr's face.

"However, Professor Bohr, I also have a few new ideas on quantum mechanics. I may write one or two papers in the near future. I will ask for your advice then."

"It's easy to talk, easy to talk, I can't talk about giving advice, it's just a discussion between each other."

The cheerful air began to fill the office again.

After the small talk of the day, the host and guest had a good time.

Rutherford acquiesced in the purpose of Chen Muwu's trip, and did not recruit this student to the Cavendish Laboratory.

Bohr also obtained a fairly satisfactory result from Chen Muwu. Since he wanted to study theoretical knowledge, he also said that he wanted to ask himself for advice, so letters and telegrams were inevitable.

Maybe once they come and go, the relationship between the two people will become closer, so that they can gradually figure it out. We must dig him out, oh no, please go to Copenhagen.

Bohr stayed at Cambridge University for a few more days, then went north to Manchester, continued to visit relatives, friends, and old friends, and finally boarded a ship from Norwich and returned to Copenhagen, Denmark.

Chen Muwu came out of the leisurely state he had maintained for more than a year, and started the liver paper mode again.

Interlacing is like a mountain. Although I know the law of incompleteness and how Gödel proved it, it is not easy to reproduce that paper.

Fortunately, in addition to his own cheating, Chen Muwu also has a humanoid cheating at Cambridge University.

Many of the Cambridge Apostles are mathematicians and logicians. They are all students of Russell, and even Russell himself.

There is an essential connection between the incompleteness theorem and Russell's paradox, both of which involve negative self-reference and the diagonal method.

It would be a fool to have such a ready-made thigh instead of holding it, but to study it by yourself, so I took advantage of the opportunity of the Apostolic Society meeting every Saturday night.

The other princes and buddies were all chatting with wine glasses, while Chen Muwu ate the precious ingredients prepared on the dining table, and lowered his posture to ask others about mathematics and logic.

He also found an opportunity to go to Russell's office to ask for advice several times, just to be able to write this paper on the incompleteness theorem and get the recognition of the mathematics community.

There are rumors in the University of Cambridge that Dr. Chen of Trinity College became hopeless in physics after winning the Nobel Prize in Physics.

He has been very close to Russell recently, and he may be developing in the direction of philosophy.

(End of this chapter)