In the axiomatic system conceived by Hilbert himself, there are three fundamental foundations: completeness, consistency, and decisiveness.

Completeness and consistency have been lost by one of Chen Muwu's papers, and now only this decisive is still strong, neither confirmed nor falsified.

From Chen Muwuyun's breezy questioning, von Neumann heard something unusual.

He always felt that Dr. Chen, who was beside him, was asking for his own opinion, but more like a vague reminder to himself that this decisiveness was just as unreliable as the previous completeness and consistency.

Von Neumann did not treat Chen Muwu as Cao Pi like Empress Dowager Bian, and expressed the emotion of "You have killed me for completeness and consistency, and it is decisive to kill me again".

He felt that there was a lot to be done on the topic that Chen Muwu provoked.

"Dr. Chen, I don't know the answer to this question, but since your incompleteness theorem was proposed, I don't think there are too few mathematicians in the world who have doubted the decisively correct correctness of this third article. Could it be that you have also made any new discoveries on this issue? ”

"It's not a discovery," von Neumann really took the bait, which made Chen Muwu a little happy, "At present, I just have a little clue."

"With regard to the determinability of axiomatic systems, Professor Hilbert once made the idea of 'proving the feasibility of mathematical theories by a feasible process and by a finite number of operations'.

However, in his vision, whether it is a 'feasible process' or a '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 brain.

"You know, when we study physics, we 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 'thought experiment', and Professor Einstein in Germany likes to do some thought experiments to verify his conclusions. ”

As they spoke, the two of them had already walked to a small restaurant that Chen Muwu usually went to.

Two years after Ye Gongchao left the UK, Chen Muwu finally learned to reconcile with British cuisine.

Anyway, as long as you don't order the kind of dishes that require too much cooking skills, then the taste is basically not too bad.

He ordered a steak with mushroom sauce as usual, and von Neumann, who was sitting next to him, did the same, ordering the same thing as him.

"John, you don't have to be inhibited when you come to Cambridge University, it's not a very formal restaurant, it's just a small restaurant. I don't drink, so I never order alcohol, so I order a pint of beer for you, is that enough? ”

"Dr. Chen, no need, I won't drink if you don't drink it. Drinking is just a joke, and I don't really like it. Could you please tell us what the thought experiment you just mentioned is? ”

"It's fine."

Anyway, it would take a certain amount of time to wait for the food to be served, so Chen Muwu took out his notebook, unscrewed the cap of the pen, and drew on the blank page of the notebook.

"An infinitely long strip of paper divided into an infinite number of cells on which any letter can be recorded, the binary digits 1 and 0, and blank space.

"In addition to this, there is a read/write head that can move left and right and read the contents of the paper;

"A set of rules that control the movement of the read/write head;

"There's also a status register.

"Together, these four parts form a machine, and my thought experiment revolves around this machine."

The strange machine that Chen Muwu drew in his notebook was the famous Turing machine in the original time and space.

According to the past practice, this machine will be called "Chen Ji" in the future.

Bara la la told von Neumann in the fog a lot of things about the operation of Chen Ji, and it was not until finally that Chen Muwu began to say his conclusions.

"Isn't this read/write head moving under the control of the rule table and the input terminal, just what Professor Hilbert envisions as a 'possible process'?

"At the end of the program, the read/write head moves a finite number of times and finally stays in a blank space, isn't this process equivalent to another 'finite operation'?

"In this way, Professor Hilbert's decisive assumption translates into 'whether there is such a mechanism that allows it to determine whether any program can be finished in a limited time.'"

"Yes, that's exactly what it is."

He had just finished explaining the structure of Chen Ji, and the waiter in the restaurant happened to serve two steaks to the table.

Chen Muwu took the opportunity to tighten the cap of the pen, clamped it into the notebook and closed it, and then made a gesture to let von Neumann.

"Please, John, we'll talk about it when we're done."

In the hearts of Hungarians, it is as uncomfortable as reading the wonderful points of an online article, but the author breaks off.

Even though there was a not-so-tempting English steak in front of him, he was not in the mood to swing his knife and fork like Chen Muwu beside him.

He didn't care about any etiquette or impropriety, and directly opened the notebook he had just closed and pushed it in front of Chen Muwu again.

"Please wait a minute, Dr. Chen. The downtime question that you raised really describes Professor Hilbert's decisive problem more vividly. However, this does not mean that this is decisive, whether it is right or wrong...... Wait a minute! ”

Von Neumann even more rudely unscrewed Chen Muwu's fountain pen and wrote and drew quickly on Chen Muwu's notebook, while at the same time reciting words in his mouth.

"Suppose there is such a machine that can make a judgment on whether to end the operation in any situation......

"If the run is judged to be over, it will output yes, and if it is not over, it will output no.

"Then you just need to improve this machine, when it outputs 'yes', connect it to an endless loop that can never end the operation, and when it outputs 'no', it will simply stop running.

"In this way, Chen Ji judged that the operation of 'yes' should have stopped but would not stop, and judged 'no' in the opposite situation.

"This contradicts the previous assumption that it is possible to make a judgment on whether or not to end the operation in any situation.

The concept of Chen Ji is equivalent to the decisive assumption put forward by Professor Hilbert.

"Since Chen Ji can't make a judgment on whether to end the operation, then in other words, it is also not feasible to decide this matter!"

Von Neumann wrote in his notebook that he overturned the last of his teacher Hilbert's three assumptions.

But at this time, he didn't have the kind of remorse in his heart for "deceiving the teacher and destroying the ancestors, rebelling against human ethics", and he was not afraid that Hilbert would take away the word "Feng" in his name.

Von Neumann just got up from the chair very excitedly, and accidentally touched Chen Muwu's bare pen to the ground, making a crisp sound of "Ding Lingdang".

Chen Muwu didn't feel sorry for this at all, anyway, the old Feng family had money, and they could spend money to buy nobles, so they couldn't even afford a pen.

However, the waiter at the restaurant, seeing that von Neumann was 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 ground.

The Hungarian stared at the waiter with a look of incredulity: "Do you know what a significant academic discovery Dr. Chen has made just now?" If you don't care about the impact of this on the development of mathematics, why should you care about a broken plate that is not worth a few dollars? ”

"Rare and strange," the waiter, who spoke in a serious English accent, glanced at von Neumann, a gringo with a European accent in English, "Sir, do you know how many important discoveries Dr. Chen has made in this restaurant?" Maybe it's just the least of his discoveries that excite you.

And Dr. Chan is so young that he will only make more and more discoveries in the future.

"But the plates here are different, they've been handed down from my grandfather's generation. If everyone is as rash as you are, then the number of plates will only get smaller and smaller. ”

With that, the waiter pouted, and motioned to von Neumann with a slight expression on his face, asking him to see what Dr. Chen, who was sitting next to him and had just made a major discovery, was doing at this time.

Chen Muwu had already cut the steak into small pieces with a knife and fork, then forked one of them, dipped it in the sauce and put it in his mouth gracefully, chewing it carefully to taste this not very delicious delicacy.

Von Neumann, who had been deflated by the waiter, could only sit down in his seat again.

He bent down to pick up the fountain pen on the ground, looked at the tip of the pen, and said sorry to Chen Muwu guiltily, and said that he would definitely compensate him for a new one in the future.

"Little things, it's all small things, eat John, or the food will be cold."

Von Neumann felt that he couldn't let the waiter in this Cambridge tavern look down on, so he resisted the excitement in his heart and ate steak like Chen Muwu.

Although everything had just happened, he still felt the right amount of warmth in his mouth when he took the first bite of steak.

After 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 Cavendis's lab, he was thinking about how to propose it to Dr. Chen, and the two of them would write a paper together, but he suddenly thought of another point.

Why did Chen Muwu compare Professor Hilbert's decisive assumption to something as new as Chen Ji?

Chen Ji seems to be born naturally to falsify and be decisive, and since Dr. Chen has already thought of this, then hasn't he gone any further?

"Dr. Chen, have you already seen today's proof?"

Chen Muwu will definitely not deny this matter: "I just have a general idea, but I have been very busy recently, so I haven't had time to think about it." It just so happens that you are a student of Professor Hilbert and a master of mathematics, so I plan to take advantage of today's dinner time to have a brief chat with you. John, you've really surprised me. ”

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 are the first author. ”

"That's the best thing, it's still the same sentence, I don't have time lately, and this paper will trouble you a lot."

"Of course there's nothing to say!"

Von Neumann was delighted that he had picked up a paper from Chen Muwu on his second day in Cambridge.

Chen Muwu was also very happy, he was originally afraid that von Neumann had been sent by Hilbert to argue with him, but the latter's performance dispelled his concerns.

Soon after, Oppenheimer returned to Chen's office, and Dirac and von Neumann moved in.

For a time, Chen Muwu's office became the place with the highest level of mathematics among the world's physicists.

Oppenheimer and Dirac were busy writing textbooks on quantum mechanics, von Neumann was busy writing papers, and everyone's energy was devoted to academic research, so Chen Muwu, the shopkeeper, occasionally disappeared intermittently, and no one cared.

After another day's work, Chen Muwu had just walked to the door of Trinity College when he was stopped by the supervisor at the door.

He informed Chen Muwu that a guest was waiting in the reception room.

When asked who the guest of the hospital was, he put on a mysterious and unspeakable expression.

When they met, Chen Muwu recognized that the person who came should be the personal servant next to the Duke of York, and the one who was waiting outside the venue when he participated in the Olympic Games in Paris was him.

"Dr. Chen, the King's Birthday holiday is coming soon, and the Duke of York would like to invite you to London to meet you."

After the politeness, the royal servant went straight to the point and made the purpose of the trip clear.

In order to show his respect for Chen Muwu, he also specially presented a cardboard invitation with the coat of arms of the Duke of York.

"Thank you for the invitation, and please make such a trip to Cambridge University. Please tell Your Highness that I will be there on time. ”

Because of the car, Kapitsa also looked for himself several times later.

This time, the Duke of York wanted to make a model of a seat belt, and at the same time go to London, he would "cheat" some money and then come back with a car.

Taking advantage of the fact that there were still a few days left, Chen Muwu found Cockcroft, who was waiting for the charge conveyor belt to be shipped, and asked him, who was an engineer, to help make a model of a seat belt ratchet, ready to demonstrate it in public like plexiglass.

In terms of dressing, Chen Muwu did not dare to slack off in the slightest.

After arriving at the Duke's Palace, he also verified his conjecture, although it was said to be a meeting, but it was not said to be a meeting alone.

The invitation was scheduled for early evening, indicating that it was a dinner hosted by the Duke of York at his home.

At the dinner, Chen Muwu saw a lot of people who were somewhat familiar, if nothing else, these people should be the second elder brother's party.

Seeing the Duke of York, the host of the banquet, Chen Muwu naturally stepped forward to say hello.

Unexpectedly, Prince Albert seemed to be a little unhappy this time, and when he shook hands, he whispered in Chen Muwu's ear: "Dr. Chen, the article you published before, whether it was His Majesty the King, or No. 10 and No. 11 Downing Street, was not very happy about it. ”

10 Downing Street is the Prime Minister's official residence, and 11 is home to the Chancellor of the Exchequer.

Because of the revival of the glory of David Faraday's laboratory, Baldwin, who had personally visited the laboratory, had a good impression of Chen Muwu, and the elder Prague explained this to him.

Chen Muwu felt that most of the unhappiness in the Duke of York's words came from the little fat man.

(End of chapter)