Chapter 90 Strange Phenomenon [3rd Update]

The undecidability of the semi-group word problem is the first undecidable problem discovered by humans that is not created by mathematicians but exists naturally.

It also means another truth.

"Undecidability is not just limited to pure arithmetic."

It is like emphasizing the objectivity of the concept of "undecidability".

Countless Lianzong monks were like bereaved. They really couldn't believe that the language that constituted their thinking actually contained the danger of "undecidability".

However, for a moment, they couldn't even find a reason to refute.

Because, in the field of "linguistics", Wang Qi occupies a monopoly position. He uses arithmetic and logic to deal with text problems.

This is undoubtedly a field of Lizong.

Lianzong couldn't even find a point to exert his fists and feet, and he had no way to exert his strength.

"This... Feng Luoyi, Wang Qi, this pair of master and apprentice, are they going to join forces to destroy the family?"

A Lianzong monk shouted in horror.

However, compared with Lianzong, Lizong was equally uncomfortable.

This paper once again emphasized the status of "undecidability".

"This guy, in order to promote himself, is he going to attack us?"

Some Li Zong monks were also gritting their teeth.

Wang Qi's paper was undoubtedly a heavy punch, hitting the spine of Li Zong monks hard.

This time, neither Li Zong nor Lian Zong got any benefit.

However, soon, Lian Zong Xiaoyao responded.

Many Lian Zong Xiaoyao have finished their current tasks in Zhengtian Division and are concentrating on preparing for this debate.

Now, a new direction has gradually emerged within Lian Zong.

They actually tried to learn the "logic" of Li Zong, absorb the knowledge of Li Zong, and use the theory of Li Zong to fight back against Li Zong.

This should be regarded as a counterattack against Feng Luoyi's use of Lian Zong's research results of "cutting off self-reference" and then starting to study the practice of excluding self-reference sets.

Unexpectedly, the Snow Country School, which has always been at peace with the world, actually revealed its intention to end at this moment.

The current leader of the Snow Country School, "Snow Country Master" Komogo [Andrei Kolmogorov] also published a new paper.

He gave a completely new account of the theory called "realizability".

The Snow Country School is also a model of Lian Zong, and also belongs to the "Intuition School", and will also pay homage to the Master of Calculation.

However, there are subtle differences between the "intuition" of the Snow Country School and the "intuition" of the Master of Calculation.

In fact, different Lian Zong monks have different ideas about the construction of "intuition".

The Snow Country Master's paper points out a strange fact. For any proposition, there is a corresponding non-proposition, and the validity of the non-proposition means the absurdity of the proposition. The proof of a non-proposition is a function that transforms the proof of the proposition into an absurd proof.

Standard examples of absurdity can be found in arithmetic. Assume 0=1, and perform mathematical induction: 0=0 is obtained by the equality axiom; (inductive hypothesis) if 0 is equal to a specific natural number n, then 1 will be equal to n+1, but because 0=1, 0 is also equal to n+1; by induction, 0 is equal to any number, so any two natural numbers are equal.

This is obviously absurd.

Perhaps it is a low-level joke to describe it in natural language? But in arithmetic, it does have an important position.

Almost at the same time, another Lianzong Xiaoyao monk also independently completed similar results.

He rewrote the important achievement of Lizong-arithmetic axioms in a form that seemed a bit weird to the Lizong monks.

All of a sudden, the entire Wanfamen began to become chaotic.

All the monks who studied mathematical theory fell into thinking about three questions.

——Which side am I on? Lianzong or Lizong?

——What am I studying? Which direction?

——Who are my teammates? Ge Ting faction? Feng Luoyi? Ji faction? Xueguo faction? Or the Shaoli Sect?

This is an unprecedented chaos.

Although in history, the Lian Sect would absorb the achievements of the Li Sect, and the Li Sect would absorb the achievements of the Lian Sect, that was all done based on "transformation to a mathematical foundation".

Use geometry to fuse arithmetic, and use analysis to accommodate geometry, and so on.

But now, everything is in chaos. The Li Sect and the Lian Sect have never competed for a field like this. They are almost conducting research in the form of a relay race.

After you study for a period, I continue to study for a period based on yours, and then you continue to study on my achievements.

After the split of the Li Sect and the Lian Sect in the Middle Ages, this is the first time in 40,000 years that such a chaotic scene has appeared.

The division between the Li Sect and the Lian Sect is still extremely obvious, but they are in a mess in research.

It can be said that they are purely fighting.

Especially the Snow Country Sect, which has always been aloof from fighting, and the Ji Sect, which has been newly established but has always been aggressive, are forces that cannot be ignored.

As Lian Sect, there are also differences between the Snow Country Sect and the Shaoli Sect.

As both are Li Sects, the relationship between the Ji Sect and the Ge Ting Sect is not harmonious.

Everyone is killing each other.

Some extreme disciples finally stopped distinguishing between Li Sect and Lian Sect.

All Wanfa Sect disciples who are different from us can be considered "enemies"!

With the chaos on the theoretical level, the Wanfa Sect finally gradually lost its stability.

Even the law enforcers who maintain the sect rules can't maintain pure gravity.

The sect master Chen Jingyun had to urgently transfer a group of law enforcers from other sects to maintain the basic stability within the Wanfa Sect.

Seeing this, Zhao Qingtan was a little confused: "I just came to buy flour... I just want to have a good New Year!"

"What a shitty New Year!" Su Junyu gritted his teeth: "This is bullying our Ji sect... bullying our Li sect!"

"... No, I don't think the supporters of the Ge Ting sect like the Ji sect very much."

"It's not important!" Su Junyu waved his hand: "Now, the most noteworthy person should be the Lian Zong Xiaoyao named Hai Ting [Alande Hai Ting]."

Although Hai Ting is also Xiaoyao, he is probably an unknown individual. He achieved Xiaoyao more than ten years ago. At that time, the master of calculation was in his heyday, and after promoting the calculation of Yuan Suan in the entire Wanfa Sect. The glory of Hai Ting's generation of Lian Zong cultivators was almost overshadowed by the master of calculation.

No, even if there was no master of calculation, he would not be too dazzling. As long as Suanjun is still there, all other intuitive Lianzong monks can only be counted as stars - and Suanjun is like the bright moon.

However, now, this unknown Xiaoyao has actually completed similar content independently with the Snow Country Lord, and even rewritten the arithmetic axioms.

Although the arithmetic axioms also have hidden dangers based on incompleteness and undecidability, and are not as certain and complete as the Huatian axioms [Euclidean geometry axioms], this was the glory of the Lizong in the past.

As a Lianzong, he absorbed the logic of the Lizong so successfully that he almost opened up a new path.

"Then what are you going to do? Are you going to end it too?" Zhao Qingtan asked back: "Wang Qi should have lost interest in this level of debate, and publishing that paper is just a coincidence. The basic school will not go deep into this debate."

He knew Wang Qi's research ideas too well. The basic school only focuses on the "foundation". That paper is a larger part of the puzzle, not thrown out for the debate.

"Well, I understand this very well." Su Junyu nodded and looked at his hands.

Although they only communicated through letters and papers, he gradually realized some things over the years.

Wang Qi has set his sights on a higher area. For him, "incomplete calculations" are a thing of the past. He wants to transcend these things, go to a higher realm, and see the broader beauty of mathematics.

Not only basic mathematics, but also the material world.

The picture that Wang Qi completed underground ultimately needs an extremely amazing and beautiful mathematical theory to support it.

Although it's a bit strange to say this... In this regard, he is somewhat similar to Suanjun.

"It can be regarded as fulfilling a little of my obsession, right?" Su Junyu smiled: "I have read the papers of the Ge Ting School and Senior Feng recently, and I do have some new ideas... I have been improving the basic school's mathematical theory over the years, and my level has also improved, right?"

"Hey, what do you want to do?" Zhao Qingtan frowned slightly: "Even if Master Hai Ting is a bit marginal, he is also a free and easy master! Do you want to fight with a free and easy cultivator?"

Su Junyu's mouth twitched: "Why should I specifically fight with a free and easy cultivator?"

Zhao Qingtan was about to breathe a sigh of relief, and Su Junyu continued: "Of course it's Lian Zong!"

"You..."

"Although I am not as good as Wang Qi, when I was a child, I was indeed considered to have the talent of the free and easy level, right?" Su Junyu smiled and said: "Moreover, the source of this melee was several years ago. What about our leader's carelessness? As a member of the basic school, I am here to end it. It can be regarded as a legitimate reason, right?"

Zhao Qingtan stopped talking.

So, before the end of the year, Su Junyu started his research.

However, he followed the idea of ​​"relative consistency" given by the master of calculation, looking for a different direction from the Ge Ting School, and continued to climb.

In the blink of an eye, it was time for the new starship to set sail for a foreign land.

Zhao Qingtan brought a disciple to Shenjing.

Looking at the hometown city that had become familiar again behind him, Zhao Qingtan was a little dazed.

This time, Su Junyu did not come out to see him off.

Before leaving, he just asked Zhao Qingtan to bring some drafts. This was the result of his recent days.

Zhao Qingtan felt that the manuscripts were unusually heavy.

——I don’t know what kind of future is waiting for Junior Brother Su.

He took the Wanfamen disciples who had just joined the Ji Sect and boarded the starship.

He returned to his hometown.

After holding a welcome banquet for the newly joined monks, Zhao Qingtan found Wang Qi alone and reported his achievements in the past six months.

And presented Su Junyu’s manuscripts.

Wang Qi took a quick look and was shocked: "Tsk tsk, it's actually... this?"