Chapter 97: The Style of the History of Aura Universe Technology [Second Update]

Wang Qi said in despair: "I can't believe it, I can't believe it... I would have such a serious intellectual disability in normal life... It's true, I can't relax for a moment..."

Wang Qi said so.

how to say……

In the history of mathematics on earth, the war between formalism and intuitionism has indeed been fierce.

However, the story after the fight is not so popular.

In the following period, the history of mathematics was dominated by the Bourbaki school, Pope Grothendieck, who mastered half of mathematics, and the Langlands Program.

As for formalism and intuitionism... to be precise, they are new formalism and intuitionism, but some people are also practicing them.

But after all, it is on the fringes, and it is not so dazzling in history.

Well, how to describe it...

There are more people studying the history of the Qing Dynasty in the history department than those studying the history of the Southern Ming Dynasty, right?

In the Ming Dynasty, "the emperor guarded the country, and the king died in the country", Nanming was just a salted fish that had lost the inheritance of its ancestors, and was not even qualified to compete.

History buffs will forget it when they see Chongzhen. How many people will study this salted fish of Nanming?

That's about it.

To be honest, the disciples of intuitionism and formalism were not without achievements in the follow-up.

For example, the later theory of recursion can be regarded as a typical "achievement of leaving the sect".

But whether it is recursion theory with obvious deviant characteristics or type theory with obvious continuous characteristics, they all have a common feature - that is, they are part of computer science.

In other words, we simply live dependent on computer science.

In other words, they are all wage earners under the command of computer science.

This can indeed be called miserable.

In Henri Poincaré's later years, the intuitionism that first appeared was like the Western Zhou Dynasty, which was the common master of the world.

The intuitionism of David Hilbert's era was like the Eastern Zhou Dynasty. It only had the title of "orthodoxy" but no one cared about it.

——If we take into account the three-party melee between formalism, intuitionism and logicism, perhaps it is more appropriate to use "Shu Han" and "Eastern Han" as metaphors?

Later on, intuitionism becomes even weaker, almost like a younger brother. This is like being a descendant of the Zhou royal family in the Warring States Period. Let's talk about it, it can be regarded as an identity.

But the Bourbaki school over there are all trying to play the game of "The King of Qin sweeps Liuhe, how powerful is the tiger's eye". Who cares about you being a mere "descendant of the Zhou royal family"?

At that time, formalism and intuitionism can only be applied.

They can't get involved in the orthodox dispute over the "Foundation of Mathematics" involving Jiuding.

This is also the reason why Wang Qi withdrew from the Geting Sect. The inheritance of the Gotin School was orderly. Even if Hovel was really willing to give him a certain amount of authority, he would not be able to reverse the ethos of the Gotin School and replicate the achievements of the Bourbaki School.

Even if the calculator is no longer there, He Weier and Ai Ruoche are both very powerful calculators.

He couldn't establish his influence all at once.

However, no matter how you say it, the Bourbaki school can be regarded as a deviant school according to the world's classification.

He never expected that "type theory", a typical achievement of the sect, would be born in the hands of a member of the fundamental sect.

Especially since this member is his wife.

"The world view is about to be challenged..." Wang Qi covered his head: "Oh my god, my god..."

Zhao Qingtan also froze: "How is this possible..."

"Yeah...how is this possible?"

Zhao Qingtan was stunned for a moment and was shocked: "Could it be said that a manuscript written by Suanjun can turn a disciple who left the sect into a disciple of the sect? Is it so dangerous?"

"Well...well, Yujia actually preferred to apply the direction when she was young...Maybe she is the one among us who least cares about the separation between sects and sects." Wang Qi said.

Zhao Qingtan did not dare to read Suanjun's manuscript. He asked Wang Qi directly: "What did junior sister come up with?"

Wang Qi was stunned.

…………………………………………………………………………

In the Heavenly Palace, Ke Lanyin released his arm holding the Heavenly Sword.

He found that his back was covered in cold sweat.

"It's really scary..."

It was difficult for him to describe what kind of changes had occurred to Wang Qi as a whole at that moment. He felt that Wang Qi's aura suddenly became like a bomb, as if it would collapse at any time.

At that time, he almost thought that the Dragon King's prophecy had occurred. Wang Qi is about to die.

And the mana of his celestial demon spirit series will also leave an indelible impact on this realm of the sun.

But luckily, this feeling lasted only a moment.

However, Ke Lanyin still felt a little panic.

"You can't let me, an old man, do this kind of work... It's true, I'm so many years behind the times..." Yun Zhongjun laughed at himself helplessly.

I should make an application and ask them to send one or two more Xiaoyao over...

It had better be something stronger, otherwise you really can't beat this junior.

………………………………………………………………

In the history of the earth, "type theory" was an attempt to break through Gödel's incompleteness theorem. In fact, it was somewhat successful. Gödel's first incompleteness and second incompleteness were both broken through one after another.

However, this is only a "shallow layer".

Gödel's incompleteness theorem has not been completely broken through so far.

Intuitionism has always regarded "mathematics" as a constructive activity of human wisdom.

In the era of increasingly advanced computers, intuitionist researchers have put forward a new slogan.

"Definition is construction, construction is proof, and proof is program."

They intend to use the computing machines developed by formalists to prove their mathematical theories.

To study a mathematical entity at a type level, metamathematics equal to or higher than this type is required.

Therefore, studying mathematical entities involving infinite superfiniteness becomes metamathematics that requires infinite superfiniteness.

Intuitionism does not recognize the existence of "infinite entities".

It's like there is no "infinite entity" in the physical world.

The most stringent type system has no loops and self-reference.

Therefore, this system, even if it involves "infinite" problems, can still be shut down because it will not cause infinite logical loops.

Because strongly normalized type systems are finitely terminated, that is, all functions can be shut down and give a unique result.

There are no ghosts of self-reference and infinite loops on the two halting problems.

This is an exploit of the halting problem at the expense of Turing completeness.

In other words, "type theory" is an achievement in the field of basic mathematics.

And derived from this is an absolutely reliable computer language.

Or "a class".

That is, a "strongly typed" language.

Because it is the "most stringent" system, the degree of freedom of strongly typed languages ​​is really low. Especially the "strongly standardized type", because of the sacrifice of Turing completeness, this language is very prone to logical contradictions. A little error will cause a direct shutdown.

But the advantage is that this type of language will never go wrong.

But really, have you heard of a language that can be called "never go wrong"?

Your Windows has never had a blue screen? Your Android has never crashed?

That's because strongly standardized types are really not for everyone.

It is precisely because of this that strongly standardized type languages ​​have not spread among programmers. If you want to use strong standardized types well, you must memorize and infer a lot of pointer and parameter types. Only when they are completely matched, the program will run. If there is even a slight mismatch, it will directly shut down.

This is the vicious consequence of sacrificing "Turing completeness".

To be honest, this is also a test of your level. It can be said that Turing completeness allows some ordinary people to participate in the work of "programming". When "Turing completeness" is sacrificed, the IQ requirements for programming are increased.

But on the other hand, talents with high IQ usually prefer to create more freely and are impatient to memorize so many things.

This is also the reason why the industry abandons this type of language-this type of language cannot be mastered by cheap programmers.

However, it is precisely because of its stability and reliability that the aerospace industry also uses it.

After all, if this thing crashes, it will be hundreds of millions of yuan.

If you look at it from the perspective of type theory, then... Wang Qi's previous Wanxiang Guawen should be regarded as... untyped language.

Untyped language has a high degree of freedom, which can lead the calculation process of advanced mathematics to be implemented directly on physical machines, and is closer to human thinking habits.

Or it is closer to those high-level languages ​​before the birth of earth type theory, which belongs to the category of "type insecurity".

——It can even be said that the Wanxiang Guawen has the labels of "untyped" and "unsafe type" at the same time.

It is free, but relatively speaking, it is not very useful.

If a compilation error really occurs, the computer is likely to output unpredictable results instead of shutting down directly.

This means that programmers must know what they are coding very well, and even need to use their mental arithmetic ability to correct their own coding.

This also requires a high level of ability for programmers.

However, in this world, as long as you practice the Wanfamen skills such as Yaoding Suanjing, you can solve this problem.

In other words, everyone has not minded being a human error corrector for so many years.

This is the general situation of this theory on Earth.

In this world, the situation is a bit weird.

Chen Youjia, with the help of the current debate between clans in Shenzhou, deduced this theory from the beast mechanism cluster algorithm of Suanjun.

Moreover, it was inspired by formal linguistics.

Formal linguistics can be regarded as a parallel development of computer science.

However, this process...

is indeed...

full of the style of the technological history of this universe.