Exploring Immortality Cultivation-Chapter 902 - 231: Before the Curtain Falls

The oracle machine is something that cannot be constructed. Its nature is more akin to "thought experiments" and "ideal conditions" in physics—things that cannot be reproduced in reality.

An oracle machine concerning undecidable problems, from the very start, cannot be constructed.

This is merely using an imaginary concept to ponder a possible concept to achieve a real and genuine result.

However, this result, upon hearing, naturally sparks despair.

"Not even the Great Dao Sacred Sound in fantasies can complete this proof?" Feng Luoyi smiled wryly, his eyes revealing an unhidden disappointment.

Even with the strongest powers from human imagination, one cannot bypass the boundary drawn by "self-reference."

Master Turing sipped his tea and whispered, "I think, perhaps we need not pursue this direction any further..."

"Concepts that cannot be explained even by listening to 'Great Dao Sacred Sound'…" Feng Luoyi seemed troubled, repeating the phrase.

"Teacher, perhaps it is our imagination that limits our means," Wang Qi said. "Master Turing's idea indeed pushed imagination to its limits. However, Master Turing's 'imagination' is still derived from his 'experience'—from reasoning based on 'finite' experience. Maybe, there really is a method in the world that can bypass self-reference, only our minds are completely unaware of it at present."

Feng Luoyi's tone carried a hint of desolation: "Infinite and finite... Once we touch 'arbitrary' and 'infinite,' we become utterly stuck... Is finite to infinite the limit of our understanding? Or, perhaps, was the Mathematics Lord right all along? Does infinity not exist in the world at all?"

In the cosmic domain, the mass of matter is finite—otherwise, according to gravity's property of infinite extension, in an infinite universe, the gravity at every point within would be infinite.

With total mass being finite, the number of basic particles in the universe is also finite.

The entire universe seemingly has no need for anything to be measured with infinity.

Humans have never comprehended "infinity;" all concepts about "infinity" are actually deduced from the finite that humans understand.

Therefore, there is a group of mathematicians who strongly advocate for removing the concept of "infinity" from the annals. Infinity is merely a "metaphor," a "description," not something that truly exists in the world.

As for people who research "infinite" problems, they are all purely foolish.

Wang Qi shook his head and countered: "Is there a finite boundary line in the real world?" He extracted a tea leaf from the cup: "What is the actual perimeter of this leaf?" He then conjured up a map of the sea: "And how long is the coastline of Shenzhou's Western Border?"

This is the reality of infinity.

The edges of any plant leaf have serrations. On those serrations, there are even finer serrations. Of course, this "fineness" does not persist indefinitely. But in reality, everything is always constituted by more fundamental structures.

The length of the coastline is similar.

Like the leaf, the coastline is ultimately composed of a line folding in an infinite manner.

Strict one-dimensional line segments or standard two-dimensional figures as per geometry do not exist in the domain of nature.

This kind of fractional dimension between one-dimensional and two-dimensional is more prevalent.

This is the genuine existence of "infinite."

The Mathematics Lord's approach is too extreme. To discard infinity, is akin to severing a finger from mathematics.

Feng Luoyi's demeanor remained somewhat downcast: "Even if, as you say, our cognition limits us, and the possibility of bypassing this limitation lies beyond our cognition... what can we do?"

"Our life has limits but knowledge has none. Using the limited to pursue the unlimited is perilous."

Human cognition is ultimately finite. Yet, mysteries seem infinite. Chasing infinite cognition with finite life is inherently tragic.

Especially when what you pursue lies beyond your cognition from the start, when it cannot be known from the beginning.

It's as if destined.

For a Seeking Dao Seeker, nothing is more sorrowful than this.

Yet Wang Qi's expression remained unshaken. On Earth, he experienced the baptism of related logic and philosophy, with a heart steeled beyond measure: "No, teacher, in this world there's no 'unknowable,' only 'currently unconfirmable.'"

This world has no "unknown," only "not yet known."

It seems like merely a worldview direction, but for Wang Qi, this direction is the foundation of his aspirations.

"Yet unknown" signifies that eventually it may become "known" or even "already known."

"The appearance of such a situation only illustrates that our mathematics is still primitive, still at the starting point. Even the inherent logic of natural laws, we haven't fully grasped. We have a long way to go."

Master Turing's eyes revealed a hint of curiosity: "To open the door, one must obtain the key, yet the key is on the other side of the door. To get the key, the door must be opened... even so, do you believe we can break the impasse?"

"The door may not be the only one; the key may not be unique. But it's just that we haven't finished exploring 'this side of the door,' hence naturally we can't find the 'key.'

"Sounds more like faith."

Wang Qi laughed and said, "I believe in this."

Feng Luoyi's wavering persisted only for a brief moment. Soon he cleared away all trace of decadence from his eyes and regained his usual calm and poise: "Yes, I understand... It's just unfortunate. I originally intended to find a way out of the impasse and then show Ximen Master, to keep him from losing hope..."

Unfortunately, in this domain, the more discoveries seem to lead closer to despair. Initially, Wang Qi merely drew a faint line, telling everyone that beyond this line, everything is unfathomable. This time, Master Turing virtually killed all thoughts of "cross-border exploring."

No road ahead.

Master Turing shook his head, "Mr. Yue Han, do not blame yourself. This isn't your fault... if blame is to be assigned, it can only be that I failed the task entrusted to me."

Feng Luoyi had entrusted Master Turing, the most talented in this area, months ago, to find a way to break the impasse.

"Failed the entrusted task... I wouldn't say so," Feng Luoyi's tone was flat: "Logic is like the Dao, constant, not flourishing with saints, not perishing with demons. You merely discovered it."

Master Turing asked, "Then now..."

"We can't delay any longer." Feng Luoyi closed his eyes. "Incompleteness and undecidability have weighed down on me for nearly half a year. Half a year! Now Geting is still being dragged along the path you negated by Ximen Master... This absolutely won't do."

"Although it sounds a bit heartless, we are like this, unable to stop for one person."

"Especially... we now have new structures for calculators to promote. The more your two papers are held here, the later the new research in the Ten Thousand Immortals Illusion Realm will unfold."

"It's not just about that!" Master Turing was not intimately acquainted with Ximen Master and did not share Feng Luoyi's sentiments. He appeared somewhat enthusiastic: "I still have some vague ideas. I feel we are about to step beyond the realm of the twenty-three questions, entering a new domain."

From now on, the foundation of logic and even human cognition must change!

"I understand. I will arrange these matters; you two go back first... I still need to plan carefully, need some quiet."

Wang Qi nodded and was about to leave when Master Turing called out to him: "Young friend, I have a few ideas I'd like to discuss with you. You can come through the Ten Thousand Immortals Illusion Realm to my place later."

Wang Qi naturally wouldn't refuse to communicate with an arithmetician of such caliber. He nodded and left first, then Master Turing also left using the Xiangyu Travel method.

Feng Luoyi sat quietly for a while, suddenly speaking: "Since you're here, why not show yourself?"

Pang Jialai of the Pang Family seemed to squirm out of a small hole using some Bone Shrinking Skill, his form awkward beyond measure. After a while, his manifestation returned to normal. He snorted: "To 'step beyond the realm of the twenty-three questions'? That effeminate one really dares to say that. I've never cared for that nonsense realm of twenty-three questions." 𝗳𝚛𝗲𝕖𝕨𝕖𝗯𝚗𝚘𝕧𝕖𝗹.𝗰𝗼𝕞

At first, it was unclear if it was due to a difference in views or personal emotions, but when the Master of Calculation listed the twenty-three questions, several domains where Pang Jialai made the greatest contributions were ignored intentionally or unintentionally.

Among those domains also included a major category like "Topology."

Feng Luoyi did not engage in dialogue with the other party, merely snorted coldly: "Eavesdropping is improper, tarnishing the demeanor of a Mathematics Lord."

"Demeanor is made to show wretches. I find it unnecessary." Pang Jiailai seemed to have no intention of denying it: "Besides, I wanted to listen openly, but your illusion barrier is too robust, forcing me to intrude—this old man simply doesn't like your logic, not that I don't understand it; this barrier can't keep me out."

Feng Luoyi was not surprised at Pang Jialai's ability to "force" his way in, nor did he ask how much he heard, but asked directly: "Do you have any thoughts?"

"No special thoughts. I originally came to urge you to publicly disclose incompleteness and undecidability. Since you've already made the decision, I'll pretend I didn't speak." Pang Jialai did not conceal his stance. He didn't care about incompleteness and related matters; he was only concerned about when the likes of Xi Baiche will be removed from the mathematical world, restoring "his world" to peace: "I think you've invested too much in this matter. In the beginning, we endorsed you to handle Shenzhou's affairs, not to waste the Wanfa Sect's resources helping Xi Baiche, that fool, bypass the knowledge barrier."

"This matter does not require your instruction," Feng Luoyi responded, showing no anger in his gaze: "The reason I invited you back was merely to exert a deterrent effect. As for the specifics, they require no intervention from an elder."

"Ahahahahaha." Pang Jialai laughed out loud: "An elder... But I don't feel so. By the way, I take back my frontier; I don't find you completely useless."

"Indeed, with inspiration from you, I've made new discoveries in mathematics! Seeing Xi Baiche's miserable situation, I feel even more strongly that one must not be misled by preconceived notions, must not be bewildered by established methods. Recently, I feel I'm about to make a breakthrough again... no more talk, back to immersion in research."

After Pang Jialai left, the quiet room returned to silence. Moments later, Feng Luoyi's fingers drew through the air for a moment: "Let us begin..."

Begin the curtain call of the Master of Calculation and the Genting Sect's most flourishing era.