Reborn and become a Great Scientist

Chapter 242 190 The Duke of York's Invitation

In the axiom system conceived by Hilbert himself, there are three most fundamental foundations, which are completeness, consistency and decidability.

Completeness and consistency have been lost by a paper by Chen Muwu, and now only this determinability remains strong, neither proven nor falsified.

From Chen Muwu's calm questioning, von Neumann heard something unusual.

He always felt that Dr. Chen next to him asked this question, not as if he was asking for his own opinion, but more as if he was vaguely reminding himself that this determinability, just like the previous completeness and consistency, is also not very reliable. .

Von Neumann did not treat Chen Muwu as Cao Pi like the Queen Mother Bian did, expressing the emotion of "You have killed me for completeness and consistency, and you must not kill me again for decisiveness".

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

"Dr. Chen, I don't know the answer to this question, but since your incompleteness theorem was proposed, I think mathematicians in the world who doubt the deterministic correctness of the third rule will not be too Not much. Is it possible that you have discovered anything new about this problem?"

"It's not really a discovery." Von Neumann was hooked, which made Chen Muwu a little happy, "It's just a little clue now.

"Regarding the decidability of the axiom system, Professor Hilbert once made such an idea, 'Prove the feasibility of mathematical theories through a feasible process and a finite number of operations'.

"However, in his idea, whether it is 'feasible process' or 'limited 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 have a very vague idea in my brain.

"As you know, 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 'thought' Experiment', Professor Einstein in Germany, likes to do some thought experiments to verify his conclusions."

While talking, the two of them had already walked to a small restaurant that Chen Muwu usually went to.

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

Anyway, as long as you don't order dishes that require too much cooking skills, the taste will basically not be 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 as him.

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

"Dr. Chen, there's no need. I won't drink if you don't drink. Drinking is just a joke, and I don't really like it. Please tell me what the thought experiment just mentioned is!"

"Alright."

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 began to draw on the blank pages of the notebook.

"An infinitely long paper tape is divided into infinite grids, and any letters, binary numbers 1 and 0, and blank spaces can be recorded on the grids.

"In addition, there is a read-write head that can move left and right and can read the content of the paper;

"a set of rules tables 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."

The 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" in the future.

He told von Neumann a lot of things about the operation of Chen Ji, and it was only at the end that Chen Muwu began to say his conclusion.

"The read-write head is controlled by the rule table and the input terminal to move, isn't it just the 'feasible process' envisaged by Professor Hilbert?

"At the end of the program, the read-write head moves for a limited number of times and finally stays in the blank space. Isn't this process equivalent to another 'limited calculation'?
"In this way, Professor Hilbert's decidability assumption has been transformed into 'whether there is such an old machine that can determine whether any program can end running within a finite time'."

"That's right, that's exactly what it is."

He just finished explaining the structure of Chen Ji, when the waiter in the restaurant just brought two steaks to the table.

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

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

At this time, the Hungarians feel as uncomfortable as when they read the wonderful part of the online article, but the author is interrupted.

Even though the unattractive British steak was in front of him, he was not in the mood to wave a knife and fork like Chen Muwu beside him.

Regardless of the etiquette and impoliteness, he directly opened the notebook that had just been 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 decidability problem more vividly. However, this does not explain whether this determinability is correct or not. Wrong...wait a minute!"

Von Neumann unscrewed Chen Muwu's pen more impolitely, and quickly wrote and drew in Chen Muwu's notebook, while still chanting words.

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

"If it is judged that the operation is completed, output yes, and if it is not completed, output no.

"Then you only need to improve this old machine. When it outputs 'yes', connect it to an endless loop that can never end, and when it outputs 'no', it stops running directly. .

"In this way, Chen Ji judged 'yes' that the operation should stop but would not stop, and judged 'no' the situation was just the opposite.

"This is contradictory to the previous assumption that 'it can be judged whether to end the operation for any situation'.

"And the concept of Chen Ji is equivalent to the deterministic assumption proposed by Professor Hilbert.

"Since Chen Ji can't make a judgment on whether to end the operation, in other words, the matter of determinism is also unfeasible!"

In his notebook, von Neumann personally overturned the last of his teacher Hilbert's three assumptions.

But at this time, he didn't have the regret of "deceiving teachers and destroying ancestors, rebelling against human relations", and he was not afraid that Hilbert would take away the "Feng" in his name.

Von Neumann just stood up from the chair very excitedly, and accidentally touched Chen Muwu's pen with the exposed nib on the ground, making a crisp sound like "jingle bells clang".

Chen Muwu didn't feel bad about this at all. Anyway, the old Feng family had plenty of money, so they could spend money to buy nobles, so they couldn't even afford to pay for a pen.

On the contrary, the waiter of 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 ground.

The Hungarian stared at the calm waiter in disbelief: "Do you know what an important academic discovery Dr. Chen made just now? You don't care about the impact of this on the development of mathematics. , why do you still care about a broken plate that is not worth a lot of money?"

"It's rare and strange," the waiter speaking with a serious British 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 you discover it? Perhaps it was the least significant of his discoveries that excited you.

"Besides, Dr. Chen is so young now, he will only make more and more discoveries in the future.

"But mine is different, it's from my grandfather's generation. If everyone is as reckless as you are, there will only be fewer and fewer plates."

After all, the waiter pursed his lips and signaled von Neumann with a slight expression on his face to let him see what Dr. Chen, who he said had just made a major discovery sitting beside him, was doing at this moment.

Chen Muwu had already used a knife and fork to cut the steak into small pieces, then forked one of them, dipped it in the dipping sauce, and put it in his mouth leisurely, chewing and savoring this not-so-delicious delicacy.

Von Neumann, who ate a deflated at the waiter, could only sit down again in his seat.

He bent down to pick up the pen on the ground, looked at the nib and apologized to Chen Muwu guiltily, and said that he would definitely compensate him with a new one in the future.

"Small things are all small things. Eat quickly, John, or the food will be cold."

Von Neumann felt that he could not be looked down upon by the waiters in this small restaurant in Cambridge, so he suppressed the excitement in his heart and ate steak like Chen Muwu.

Although all kinds of things happened just now, when he put the first mouthful of steak into his mouth, he still felt a just right warmth in his mouth.

In just one meal, von Neumann obtained a paper from Chen Muwu for free, 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 would write a paper together, 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 seems to have been born for the determinism of falsification. Now that Dr. Chen has already thought of this, didn't he go further?

"Dr. Chen, have you seen the proof of today?"

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

Von Neumann was even more convinced of this in his heart, and he continued to ask tentatively: "Dr. Chen, how about the two of us writing this paper together? You will be the first author."

"That could not be better. It's the same sentence. I don't have time recently. This paper will bother you."

"Of course there is nothing to say!"

Von Neumann was very happy. He picked up a paper from Chen Muwu only the second day after he came to Cambridge.

Chen Muwu was also very happy. He was afraid that von Neumann would be sent by Hilbert to argue with him, but the latter's performance dispelled his worries.

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

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

Oppenheimer and Dirac were busy writing quantum mechanics textbooks, von Neumann was busy writing papers, and everyone's energies were devoted to academic research, so Chen Muwu, the hands-off shopkeeper, occasionally disappeared several times intermittently, and there was nothing wrong with it. People will care.

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

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

When asked who the dean's guest was, he put on a mysterious and indescribable expression.

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

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

After the politeness, the royal servant got straight to the point and stated the purpose of the trip.

In order to show his respect to Chen Muwu, he specially sent a cardboard invitation letter with the badge of the Duke of York printed on it.

"Thank you, Duke, for your invitation, and I would trouble you to make such a trip to Cambridge University. Please tell Your Highness that I will be there on time."

Because of the car, Kapitsa later found himself several times.

This time, the Duke of York wanted to make a model of a seat belt, and at the same time "cheat" some money on a trip to London, and then cheat the car back.

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

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

After arriving at the Duke's mansion, he also verified his conjecture. Although it was said that they met, they did not say that they met alone.

The invitation was booked until the evening, which made it clear that it was a dinner party hosted by the Duke of York at his home.

At the dinner, Chen Muwu met a lot of familiar people, and if nothing else happened, these people should be the second elder brother party.

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

Unexpectedly, this time Prince Albert seemed a little unhappy. When shaking hands, he whispered in Chen Muwu's ear: "Dr. NO.11 is not too happy about it."

No. 11 Downing Street is the official residence of the Prime Minister, and NO.[-] is the Chancellor of the Exchequer.

Baldwin, who had personally visited the laboratory, had a good impression of Chen Muwu because of the revival of the glory of the David Faraday Laboratory. The old Prague explained this to him.

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

(End of this chapter)