"The ability of Mao Xiong's system integration is quite strong," Wang Yinan said.

"Back then, the MiG-25 developed by Mao Xiong used a simple and crude engine, as well as stainless steel that should not be used in aircraft at all, to fly at a speed of more than Mach 3, which frightened the rice country."

"Later, Lieutenant Belenko defected to the Sun Country, and after the rice country got a real MiG-25, they were really taught to be human in minutes as soon as they dismantled it, and they couldn't believe that with such a level of technology, they could actually build such a great aircraft, which is the power of systems engineering", Wang Yinan said,

"But when the complexity of the problem exceeds a certain limit, this top-down approach runs into its own bottlenecks, especially in areas that humans don't fully understand, such as hurricanes."

"The New Three Theories are also known as chaos theory, and there is a famous saying that a butterfly flapping its wings on the edge of the Atlantic Ocean will cause a hurricane in the Pacific Ocean, which is the phenomenon of chaos."

Zhou Hui stopped, "After talking for a long time, you haven't told me who G is?" She grabbed Wang Yinan's waist, and then spun it hard.

"Oh, don't worry", Wang Yinan shouted,

"G is certainly one of the greatest mathematicians and logicians of the 20th century, Godel," Wang said.

"This real big cow was born in Jerco, and spent most of his time in Princeton, the country of rice",

"By the way, he also talked to Albert Einstein. You're a good friend everywhere."

"Gödel's greatest contribution is Gödel's incompleteness theorem, which simply means that he proved that any sufficiently strong formal system must have propositions that can neither be proven true nor false," Wang Yinan said.

"Can you explain it simply", said the French commentator next to him curiously, "I know Gödel and his theorems, but it is too abstract to understand very vividly".

Wang Yinan thought for a while, "Let me give you an example",

"Do you know the liar's paradox",

"I know", this time it was Zhou Hui who answered, "The simplest liar's paradox is this sentence, "This proposition is false",

"Yes", Wang Yinan nodded, "If this sentence is true, but it means that it is false, if this sentence is false, then you will find that its statement is correct again."

"In simple terms, Gödel's work is to develop a method, much like the search for infinity diagonal sieves, in which he constructs a series of steps to prove that in any formal system that is strong enough (strong enough here to be simply considered strong enough to define natural numbers) that a proposition resembling the liar's paradox can be constructed through this series of steps."

"As we have just seen, in this sufficiently strong formal system, what is constructed, meaning that propositions such as "this proposition is false", can neither be considered true nor false."

"Okay", Zhou Hui nodded as if he didn't understand, "Is it possible to think that as long as the system is complex enough, there must be internal contradictions",

"It can be understood in this way", Wang Yinan said,

"And this contradiction does not arise from the limits of our human understanding, but by the logical limits of nature itself, and that nothing perfect can exist mathematically."

"I understand", Zhou Hui pondered for a long time, and suddenly shouted, startling the few visitors in the exhibition hall,

"I can see why GEB is put together," Zhou said.

"Because Gödel from mathematics, Escher from painting, Bach from music, with his essays and works, tell us that complexity and contradiction are the essence of nature, simplicity and structure are not",

It's really amazing, Wang Yinan thinks that Zhou Hui should be the best scientific literacy among the actors, such a summary is simply incisive.

"This understanding of the complexity and contradictory nature of the natural world is, in my opinion, the dividing line between modern science and modern science," said Wang Yinan.

"So people have gradually accepted the concept of microscopic particles in quantum physics, which is both here and there",

"So people replace the old three theories with new theories based on chaos theory",

"So the top-down approach to analysis is gradually giving way to a bottom-up approach."

Wang Yinan said and spoke, feeling as if he had grasped something, and some vague things appeared in his mind, but he still couldn't see it really.

After watching the GEB exhibition, by the way, signing his name on the clothes of the latest French admirers, Wang Yinan felt that he had been resurrected with full blood, of course, after accompanying Zhou Hui to eat a beautiful French meal in a Michelin-starred restaurant, Wang Yinan was really completely resurrected.

That night, the video discussion continued, and this time Zhou Hui listened with great interest for a while, although she basically couldn't understand a word, but it was quite interesting to watch these top scientists have a heated discussion, and even blushing and thickening their necks in a row.

"The connection between these two formulas is obviously problematic and needs to rely on an unproven hypothesis", Mr. Qiu has always been more rigorous.

"I think this hypothesis is reasonable, because if this hypothesis is not true, a series of unbelievable conclusions will be drawn", Professor Tao's point of view is also very clear, existence is reasonable,

"We can't congenitally reject conclusions just because they are incredible, you know, non-Euclidean geometry has come to a series of bizarre conclusions after denying the parallel postulate," Li Wenjing said.

"I think there is something wrong with the direction of our thinking, can we not dwell on the rights and wrongs of the article first, and try to understand what the author of the article wants to tell us", Wang Yinan said his thoughts,

"Interesting, let's listen to it", Professor Tao first expressed his support for Wang Yinan's idea,

"I mean, can we first make an assumption that the main body of this article is correct?" , Wang Yinan said,

"You continue", this time Mr. Qiu and Li Wenjing both nodded, it seems that this idea is not bad,

"My intuition tells me that a lot of things in the article are correct, so, on this premise, let's look at what the author wants to say, or where does the author's entire chain of reasoning and logic ultimately lead?" , Wang Yinan talked eloquently.

"If the article is wrong, aren't we wasting our time?" , Li Wenjing said,

"No, even if the article is wrong, we can see from the logical chain where the final conclusion is wrong, and such counterexamples are also of great value in science," Professor Tao retorted.

"It's like you say non-Euclidean geometry".

Indeed, after removing the public assumption of parallel lines, geometry opened up a whole new field for scientists, and what is even more terrifying is that this field was developed by Einstein a few years later. You found it from the corner and predicted the existence of gravitational waves.

After determining the new direction, the discussion immediately proceeded much faster, and once the author's conclusions were not questioned, it was easier to see the grand picture that the author had sketched in his mind.

Faintly, a brand new, dazzling thing appeared in the sky.

Of course, when the third symposium was full of people again, it was already the fourth night, Wang Yinan arrived in Oxford, and Professor Tao also went to Princeton, this time the lineup was even more terrifying, Professor Wiles, who solved Fermat's conjecture, heard Professor Tao mention this matter, and he must participate, so an unprecedented five-person temporary seminar was formed, and it is not an exaggeration to call this temporary seminar the strongest combination of blue stars.

The next day, Wang Yinan also had a lecture at Oxford University, so the symposium did not go too late, and in the end, Professor Wiles, like Mr. Qiu, had a strange doubt, "How do you feel that the style of this article is so familiar, is it really the guy who has retired from mathematics?" ”，

"Are you talking about a person", Wang Yinan and Li Wenjing, who are small characters, are only curious about the baby.

"It should be a person", Mr. Qiu and Wiles glanced at each other,

"It can't be the Perelman of the hairy bear", in front of the two, Professor Tao is also a junior character, he asked,

"Of course not, Perelman is just unsociable, but he has not quit the world of mathematics."

Wang Yinan's speech in Oxford was also a great success, unexpectedly, the conservative British academic community was very generous this time, Oxford awarded Wang Yinan the title of visiting professor, and sincerely invited him to come to the lecture every year, Wang Yinan happily agreed, because Zhou Hui especially likes the streets and alleys of the city, maybe because of speaking English?

When Wang Yinan returned to the continent of Europa again, almost a week passed, and for the first time he came to the capital of this permanently neutral country, Wang Yinan was deeply moved by the beauty of the city, and sure enough, it had not been baptized by war for hundreds of years, and every building seemed to have a story, beautiful and full of historical vicissitudes.

Wang Yinan and Zhou Hui wandered in the streets and alleys of Zurich, overclocking for many days in a row, and their brains were a little overheated, and they seemed to feel the peace they hadn't seen for a long time, but Wang Yinan's heart was not as calm as it seemed on the surface.

In fact, the night before they left Britain, the Blue Star's strongest five had largely deciphered the stack of cryptic manuscripts.

The final conclusion came as a surprise to all who participated in the discussion.

Through a series of algebraic geometry and the assumptions of axiomatic logic, the article seems to go further in the direction of Gödel's theorem.

This article develops Gödel's theorem from a more basic level, and if the arguments of the article are fully valid, then the latest paper by Wang Yinan, Li Wenjing and Professor Qiu Tao, is one of the few counterexamples.

That said, the article attempts to illustrate that finding a formal explanation for complex systems that are inherently disordered is fundamentally impossible and requires a series of demanding conditions to be met.

In other words, it is not always feasible to convert the disordered neural network of the Gödel system into a mathematical theory that humans can understand, and even furthermore, it is impossible in most cases.

If this article turns out to be correct in the end, then, the final conclusion is,

In the vast majority of cases, humans cannot explain the results of neural networks with a logical system that humans can understand.

To put it another way, machines will eventually be smarter than people!

(Actually, Alpha Zero has proven this, but people don't want to admit it). 8)