In the axiom system conceived by Hilbert himself, there are three most fundamental foundations, namely completeness, consistency and determinability.
The completeness and consistency have been destroyed by a paper by Chen Muwu, and now only this decisiveness is still strong, which has neither been confirmed nor falsified.
From Chen Muwuyun's calm questioning, von Neumann heard something unusual.
He always felt that Dr. Chen beside him asked this question, not as if he was asking for his opinion, but more like a subtle reminder to himself that this determinability, just like the previous completeness and consistency, was also not very reliable. .
Von Neumann did not regard Chen Muwu as Cao Pi like Empress Dowager Bian, and lamented, "You have killed my completeness and consistency, and you must not kill me again to determine my certainty."
He felt that there was much to be done on the topic raised by Chen Muwu.
"Dr. Chen, I don't know the answer to this question, but since your incompleteness theorem was proposed, I think the mathematicians in the world who have doubted the correctness of the third determinability theorem will not be too Less. Is it possible that you have discovered anything new about this issue?"
"It's not really a discovery." Von Neumann took the bait, which made Chen Muwu a little happy. "At the moment, we just have some clues.
"Regarding the determinability of the axiom system, Professor Hilbert once made such an idea, 'through a feasible process and a finite number of operations, to prove the feasibility of a mathematical theory.'
"But in his idea, whether it is 'feasible process' or 'finite number of operations,' these two concepts are very vague and abstract, and there is no complete definition in mathematics.
“So in order to define these two concepts, I had a very vague idea in my mind.
"You also know that we who study physics like to do experiments. Even if the experiment cannot be done in the laboratory due to various factors, we will simulate it in the brain and call this process 'thinking' Experiment', the German Professor Einstein likes to do some thought experiments to verify his conclusions."
While talking, the two of them had already walked to a small restaurant where Chen Muwu usually went.
Two years after Ye Gongchao left the UK, Chen Muwu finally learned to reconcile with British food.
Anyway, as long as you don't order dishes that require too much cooking skills, the taste won't be that bad.
He ordered a steak with mushroom sauce as usual, and von Neumann, who sat next to him, followed suit and ordered the same thing.
"John, you don't have to be formal when you come to Cambridge University. This is not a very formal restaurant, it's just a small restaurant. I don't drink, so I never order wine. I can order you a pint of beer. Is that enough?"
"Dr. Chen, no need. If you don't want to drink, I won't drink. Drinking is just for fun, and I don't actually like it. Please tell me quickly what the thought experiment you just mentioned is!"
"That's fine."
Anyway, it would take some time to wait for the food to be served, so Chen Muwu took out his notebook, unscrewed the cap of the pen, and started drawing on the blank page of the notebook.
"An infinitely long paper tape is divided into infinite grids. Any letters, binary digits 1 and 0, and blanks can be recorded on the grid.
“In addition to this, there is a read-write head that can move left and right and read the content on the paper;
“A set of rules that control the movement of the read/write head;
"There is also a status register.
"These four parts together form a machine, and my thought experiment revolves around this machine."
This strange machine that Chen Muwu drew in his notebook is the famous Turing machine in the original time and space.
According to past practice, this machine will be called "Chen Machine" from now on.
Bara, bala, told the confused von Neumann a lot about the operation of the Chen machine, and finally Chen Muwu began to express his conclusion.
"The read-write head is controlled by the rule table and the input terminal to move. Isn't it exactly the 'feasible process' envisioned by Professor Hilbert?
"At the end of the program, the read-write head moves a finite number of times and finally stays in the blank space. Isn't this process equivalent to another 'finite-time operation'?
"In this way, Professor Hilbert's idea of determinability is transformed into 'whether there is such a mechanism that can determine whether any program can end its operation within a limited time.'"
"Yes, that is indeed the case."
As soon as he finished explaining the structure of the Chenji, the waiter in the restaurant just brought two steaks to the table.
Chen Muwu tightened the cap of his pen, clamped it into his notebook, closed it, and then made a gesture to give way to von Neumann.
"Please, John, let's talk after we finish eating."
Hungarian people feel as uncomfortable as reading an online article and reading something exciting, but the author stopped reading.
Even though the unappealing British steak was in front of him, he was not in the mood to wave the knife and fork like Chen Muwu next to him.
Regardless of any etiquette or impoliteness, he opened the notebook he had just closed and pushed it in front of Chen Muwu again.
"Please wait a moment, Dr. Chen. The halting problem you raised can indeed describe Professor Hilbert's determinability problem more vividly. However, this does not explain this determinability. Is it correct or not? Wrong…wait a minute!”
Von Neumann even more rudely unscrewed Chen Muwu's pen and quickly wrote and drew in Chen Muwu's notebook, while mumbling something.
“Suppose there is such a machine that can judge whether to terminate the operation in any situation...
"If it is judged that the operation is completed, output yes, if it is not completed, output no.
"Then we just need to improve this old machine. When it outputs 'yes', connect it to an infinite loop that can never end. When it outputs 'no', it will directly stop running. .
"In this way, if Chen Ji judges 'yes', the operation should stop but will not stop, and if he judges 'no', the situation will be exactly the opposite.
“This is contradictory to the previous assumption of being able to judge whether to end the operation in any situation.
“And the concept of Chen Ji is equivalent to the decisive assumption put forward by Professor Hilbert.
"Since Chen Ji cannot make a judgment on whether to end the operation, it means that it is also unfeasible to decide!"
In his notebook, Von Neumann personally overturned the last of the three assumptions of his teacher Hilbert.
But at this time, he had no regrets at all about "deceiving his master and destroying his ancestors, violating human ethics", and he was not afraid that Hilbert would take away the word "Feng" from his name.
Von Neumann just stood up from his chair in excitement, and accidentally touched Chen Muwu's pen with its exposed tip to the ground, making a crisp sound like "ding, ding, ding, ding, rang, ding, ding, ding, ding, ding, ding, ding, ding, ding, ding, ding, ding, ding, ding, ding, ding, ding, ding, ding."
Chen Muwu didn't feel sad about this at all. Anyway, the old Feng family had a lot of money and could spend money to buy nobles, so they wouldn't be unable to afford even a pen.
On the contrary, the waiter in the restaurant, seeing von Neumann so excited, quickly put down his work and ran over, reminding him not to touch the tableware on the table, mainly the plates, to the floor.
The Hungarian looked at the waiter with a look of disbelief on his face: "Do you know what a major academic discovery Dr. Chen just made? Just don't care about the impact this has on the development of mathematics. , why do you still care about a broken plate that is not worth a lot of money?"
"It's so strange." The waiter, who spoke with a serious English accent, rolled his eyes at von Neumann, a foreigner with a European accent in English. "Sir, do you know how many important achievements Dr. Chen has made in this restaurant?" Did he make a discovery? Maybe what excites you is just the least significant of his discoveries.
“And since Dr. Chen is so young now, he will only make more discoveries in the future.
"But the plates I have here are different. They are passed down from my grandfather's generation. If everyone is as reckless as you, the number of plates will only become less and less."
After saying that, the waiter pursed his lips and signaled von Neumann with a slight expression on his face, asking him to look at what Dr. Chen, who was sitting next to him and who he said had just made a major discovery, was doing at this time.
Chen Muwu had already cut the steak into small pieces with his knife and fork, then forked one of them, dipped it in the dipping sauce and put it into his mouth leisurely, chewing carefully to taste the not-so-delicious delicacy.
Von Neumann, who was exhausted by the waiter, could only sit down again.
He bent down and picked up the pen on the ground. After looking at the pen tip, he apologized guiltily to Chen Muwu and said that he would definitely compensate him for a new one in the future.
"Little things, they are all small things. Eat quickly, John, otherwise the food will get cold while waiting."
Von Neumann felt that he could not let the waiter in this small Cambridge restaurant look down upon him, so he suppressed the excitement in his heart and ate the steak like Chen Muwu.
Despite all the things that had just happened, he still felt the right amount of warmth in his mouth when he put the first bite of steak into his mouth.
In just one meal, von Neumann got a paper from Chen Muwu for nothing, and it was in line with his research direction.
On the way back to the Cavendish Laboratory, he was thinking about how to propose to Dr. Chen that the two of them co-write a paper, but he suddenly thought of another point.
Why did Chen Muwu compare Professor Hilbert’s idea of determinability to something new like Chen Ji?
Chen Ji seemed to be born to prove the determinability of falsification. Since Dr. Chen has already thought of this, didn't he go one step further?
"Dr. Chen, have you already seen today's proof?"
Chen Muwu will definitely not deny this: "I just have a general idea, but I have been very busy recently and haven't had time to think about it in detail. You happen to be a student of Professor Hilbert and a master in mathematics, so I plan to take advantage of today's I’ll have a brief chat with you during the meal. John, you really gave me a surprise.”
Von Neumann was even more convinced of this, and he continued to ask tentatively: "Dr. Chen, how about the two of us co-write this paper? You will be the first author."
"That's the best thing. As I said before, I don't have time recently, so this paper will trouble you a lot."
"Of course there's nothing to say!"
Von Neumann was very happy. He picked up a paper from Chen Muwu on the second day after arriving in Cambridge.
Chen Muwu was also very happy. He was originally afraid that von Neumann was sent by Hilbert to debate Taoism and scripture with him, but the latter's performance dispelled his worries.
Soon after, Oppenheimer returned to Chen Muwu's office, and Dirac and von Neumann also moved in.
For a time, Chen Muwu's office became the place with the highest level of mathematics among the gathering of physicists in the world.
Oppenheimer and Dirac were busy writing textbooks on quantum mechanics, and von Neumann was busy writing papers. Everyone was devoted to academic research, so the hands-off shopkeeper Chen Muwu occasionally disappeared intermittently several times, and there was no trace of it. People will care.
After another day's work, Chen Muwu had just walked to the door of Trinity College when he was stopped by the warden at the door.
He informed Chen Muwu that a guest was waiting in the reception room.
When asked who the prisoner's guest was, he put on a mysterious and unspeakable expression.
When they met, Chen Muwu recognized that the person who came was probably the personal servant next to the Duke of York. He was the one waiting outside the venue when he participated in the Olympic Games in Paris.
"Dr. Chen, the King's birthday holiday is coming soon, and the Duke of York would like to invite you to London to meet with you."
After being polite, the royal servant got straight to the point and stated the purpose of his visit.
In order to show respect for Chen Muwu, he also specially presented a cardboard invitation printed with the Duke of York's coat of arms.
"Thank you very much for the invitation, Duke. I would also like to trouble you to make this trip to Cambridge University. Please tell His Highness that I will be there on time."
Because of the car incident, Kapitsa later came to see him several times.
This time the Duke of York wanted to make a model of a seat belt, and while taking a trip to London, he could "cheat" some money and get a car back.
With a few days left, Chen Muwu found Cockcroft, who was waiting for the charge conveyor belt to arrive, and asked him, an engineer, to help him make a model of a seat belt ratchet, ready to be demonstrated in public like plexiglass.
In terms of dressing up, Chen Muwu did not dare to neglect at all.
After arriving at the Duke's residence, his suspicion was verified. Although it was said that they met, they did not say that they met alone.
The invitation was set for the evening, making it clear that this was a dinner party hosted by the Duke of York at his home.
At the dinner, Chen Muwu met a lot of familiar people. If nothing else, these people should be the second elder brother's party.
Seeing the host of the banquet, the Duke of York, Chen Muwu naturally walked up and said hello.
Unexpectedly, Prince Albert seemed a little unhappy this time. When shaking hands, he whispered in Chen Muwu's ear: "Dr. Chen, the article you published before, whether it was from His Majesty the King, No. 10 Downing Street and No one over at Eleven was too happy about it.”
No. 10 Downing Street is the official residence of the Prime Minister, and No. 11 houses the Chancellor of the Exchequer.
Because of the restoration of the glory of David Faraday Laboratory, Baldwin, who had personally visited the laboratory, had a good impression of Chen Muwu. Old Bragg explained this to him.
Chen Muwu felt that the unhappiness in the Duke of York's words probably came from the little fat man.
(End of chapter)
