Exploring Immortality Cultivation-Chapter 884 - 123: Exchange [Update 2]

Wang Qi understood that for two scientists, a paper might sometimes be an even better way of communication than face-to-face talks.

Papers have formats and paradigms. Even every sentence in them has its own rules. Simply put, papers are akin to the old eight-part essay, strictly regulated in language.

For those who understand, reading such material is satisfying and easy to comprehend.

When someone introduces a poetic metaphor while explaining their theory, that's truly unbearable.

Moreover, an advantage of paper communication is that it effectively prevents intellectual exchanges from turning into physical conflicts.

Right now, Wang Qi was in Langde, while Lu Xiaoqian was at the Mysterious Palace. Even if the paper she wrote was completely at odds with Wang Qi's ideas, he couldn't possibly strike her across the distance.

While reading the paper, Wang Qi incidentally did a search in the Immortal Alliance's archives. To his surprise, this paper seemed not to have been published at all.

"Unpublished? This world actually has this concept of a 'preprint'?"

A preprint refers to research results by scientists that are not yet officially published, but voluntarily released for academic exchange purpose either at conferences or through the internet.

With advances in communication, scientists on Earth have long been dissatisfied with the speed of academic journals, believing they slow down their exchanges. However, the most authoritative "peer review system" on Earth is still mostly based on journals. Without going through journals, the credibility of a paper is not necessarily high.

But the publication speed of physical journals is still too slow.

Therefore, Earth's scholars came up with so-called preprints. Preprints are not considered formal publications, and they are generally not protected. The credibility of preprints, not having undergone peer review, is not as high as that of journal articles.

The greatest advantage of preprints is "speed."

But this advantage should only manifest on Earth. Shenzhou's academic system is entirely different from Earth's. Due to the Technology Black Box being easier to form, the Ten Thousand Immortals Illusion Realm has already taken on the responsibility of exchange before physical journals. 𝘧𝓇ℯ𝑒𝓌𝑒𝑏𝓃𝘰𝘷𝘦𝘭.𝒸ℴ𝓂

In the Ten Thousand Immortals Illusion Realm, any paper that passes a simple review and has no logical errors can be uploaded. Once uploaded, anyone can read it by paying a fee.

The Immortal Alliance's archives themselves also have characteristics similar to arXiv—a digital preprint archive established by the Los Alamos National Laboratory in the United States.

"How strange, why insist on private exchange?"

Wang Qi finished reading Lu Xiaoqian's letter and paper in one go, then shook his head: "I see. The many-worlds decoherence... So, this Senior Sister Lu actually believes this? No wonder she didn't publish it; she wanted to discuss it with others first."

The discussion on "why the wave function collapses" seems to hold little significance at present. To a large extent, this debate has already become a kind of abstract argument devoid of objective reality—even though this argument is logically rigorous and mathematically grounded. However, no matter the debate, it cannot deny the absence of factual support and experimental verification.

Additionally, regardless of which interpretation you support, it does not affect scientists' understanding of subsequent, deeper theories. This is most important.

For someone at Lu Xiaoqian's level, this kind of debate might only be considered a kind of "leisure."

No, what she said about being "busy" probably isn't just modesty. She's genuinely busy now. Her master, Master Po Li, is said to be the most stringent cultivator. Stealing a moment of leisure amidst her busyness must be quite difficult.

Especially since this paper contradicts the mainstream thoughts of the Mysterious Palace.

"It seems like no one has it easy." Wang Qi shook his head, then picked up a pen to reply.

He certainly wouldn't refuse to communicate with a colleague.

Furthermore, sometimes certain "marginal" discussions can spark "intellectual sparks" and ignite some "great inspiration"!

.................................................................................

While Wang Qi was communicating with his new pen pal, at the Wanfa Sect thousands of miles away, a more intense collision of thoughts was brewing.

The new and the old, two kinds of ideology.

In the secret training ground of the Wanfa Sect, a group of cultivators was engaged in intense exchanges. The number of participants had multiplied compared to before. Unlike a month ago, the training now involved not only those below the Golden Core Stage.

Currently, most of the disciples participating in the training belonged to the Primordial Spirit Stage.

Xiang Qi no longer dared to secretly sneak in. At this point, Su Junyu was almost forsaking sleep and food, pondering over the issues of "incompleteness" and "incompleteness."

Bao Xiaofeng always felt that this old friend of his was almost about to deviate. He tapped his sister's shoulder: "Sister, I feel like... this guy has been acting strangely lately."

"Strange... I don't think so…" Bao Xiaoya's expression was somewhat unnatural: "Isn't everyone saying that the Master of Calculation's ideas are problematic..."

The Master of Calculation's ideas are problematic. Possibly, the notions of completeness and decidability are mistaken.

The many newly arrived Primordial Spirit Cultivators were mostly young cultivators in their rising phase, highly talented, having undergone longer periods of study compared to those Golden Core Stage junior brothers and sisters, and possessing a deeper understanding of mathematics.

Many among them began to harbor doubts about the Master of Calculation's ideology.

However, the notion that "mathematics is incomplete and undecidable" is still too shocking.

If the Li Sect proves mathematics to be an incomplete system and identifies its incompleteness, then mathematics as understood in sectarian beliefs is probably also incomplete. Li Sect and Lian Sect are merely in ideological conflict, a conflict of approaches. Their concept of mathematics is essentially the same.

After all, mathematics is essentially the inherent logic of Heaven and Earth, an objective reality. There is only one mathematics under Heaven.

Even the Li Sect is unlikely to accept the notion of "incompleteness."

However, the seed of doubt had been planted.

"How is it possible... Could mathematics really be incomplete?"

Bao Xiaofeng forced a smile, his tone already carrying anxiety. Mathematics to him, from the Bo family tradition, was something deeply ingrained, almost like a belief.

This is why there was such unrest among the people here.

Many had vaguely guessed something, yet hesitated to think further.

Bao Xiaoya shook her head: "Brother, you... This isn't good. Really. Mathematics is the manifestation of the Great Dao; it won't reverse for you…"

Bao Xiaofeng rudely interrupted Bao Xiaoya: "That's not… That's not the issue here. If mathematics is indeed incomplete, then what am I supposed to do? What is the path we seek?"

"Junior Brother Bao, don't you think this could also be considered a good thing?" Perhaps it was because of Bao Xiaofeng's raised voice, a pale-faced young cultivator suddenly interjected into the siblings' conversation.

Bao Xiaofeng hurriedly saluted: "Senior Brother Gao... is your health all right?"

This was Gao Jiyang, the chief disciple from the previous generation of Wanfa Sect. He had just entered the Primordial Spirit Realm this year and was among the first batch of Primordial Spirit Stage disciples selected for "training."

However, this person perhaps had too high an understanding. Just a few days ago, he seemed to have inadvertently realized something, a flash of inspiration in his mind. But at that moment, his thoughts clashed with his own mana, causing him to vomit blood on the spot.

"It wasn't anything serious." Gao Jiyang laughed: "I've adjusted myself. That blood, I spat out my obsessions from my chest. I figured it out. Why isn't mathematics allowed to be incomplete? Why isn't it undecidable? Besides, if the Master of Calculation's ideas come true, that might not even be a good thing for mathematics."

Bao Xiaofeng was at a loss for words. In fact, no one had been able to prove the completeness and decidability of mathematics. Even if the Master of Calculation "believes" it, he can only say "that's my opinion," and honestly apply his resources and connections to propel the proof of this proposition.

"Good for mathematics..." Bao Xiaoya widened her eyes, utterly confused.

This kind of thorough negation of the foundation of mathematics is beneficial for mathematics?

Gao Jiyang smiled, asking: "Do you know about the infinity of prime numbers?"

The infinity of prime numbers, one of the oldest propositions in number theory of mathematics. Prime numbers, also known as primes, are numbers that have no other divisors besides one and themselves. Two is the smallest prime number. The distribution of prime numbers becomes sparser as numbers increase. The bigger the number, the lesser the likelihood of it being a prime. So, when numbers become large enough, does that possibility become zero? Is it possible that beyond a certain limit, prime numbers no longer exist?

Most of today's arithmeticians know that prime numbers are indeed infinite. They can easily understand this issue. Middle Ages' arithmeticians had proven this issue. The count of prime numbers and natural numbers is infinite, both are an "Aleph Zero."

"If, for the sake of argument, prime numbers were not infinite, then the majority of today's 'number theory' would not exist. Additionally, many other ideas, thoughts, and tools derived from researching this 'number' would not have emerged either." Gao Jiyang stated: "If completeness and decidability were proven, our Wanfa Sect would have no reason to exist."

"This precisely indicates we are about to reach the ultimate theorem within mathematics." Bao Xiaofeng argued: "Senior Brother Gao, your statement is problematic. To preserve Wanfa Sect's existence, abandoning the quest for Dao is putting the cart before the horse."

The Wanfa Sect, and indeed the entire Modern Immortal Path, exists for the purpose of reaching that ultimate "Dao."

Gao Jiyang retorted: "Junior Brother Bao, do you think we now appear to have already touched the 'ultimate'?"

Bao Xiaofeng still wanted to retort. But just then, a loud, bright laughter resounded throughout the entire secret land.

"I know it! I know it! Hahaha! I know it!"