Exploring Immortality Cultivation

What should mathematics look like?

Precise? Mechanical?

Not at all.

Mathematics can also be random, arbitrary, chaotic, and fuzzy.

From precision to fuzziness, from certainty to chaos, this marks yet another major breakthrough in mathematics.

And Wang Qi's exposition of fuzzy theory indicates that his understanding of mathematics has penetrated its essence, even faintly presenting the possibility of pioneering a new branch of mathematics, one that could stand alongside the Carefree at this age!

That's right, just unveiling a possibility. Wang Qi had no intention of completely revealing this new mathematics yet. After all, such an achievement was definitely on the Carefree level in this world, and without a certain immersion in cybernetics and systems theory, it would be impossible to find the inspiration. The detailed proofs of numerous concepts and theorems are a pitfall, something that cannot be completed without the decade-long commitment of a mathematics master. Most importantly, without the contributions of Gödel and Turing in mathematical logic, this fuzzy theory is nothing more than a tower built on shaky foundations, unable to withstand scrutiny.

Was he tossing out such a theory, which he likely wouldn't have time to study and whose foundations bore little resemblance to the theories of Shenzhou, because he wanted to deepen the suspicion that he was a Banished Immortal? In comparison, whether cultivators from the Wanfa Sect and other mathematically accomplished sects could accept it now seemed like a minor problem.

What Wang Qi was doing now was to elucidate the concepts and part of the thought process of fuzzy theory, verbally outmaneuvering the Bo Family disciple before him, and then all the high-order cultivators watching this match.

"Senior Brother Wang." Bao Xiaoya had been deeply captivated by Wang Qi's content and spoke much more politely, "I still have a few questions."

Wang Qi was almost flattered. The Bo Family was known for its audacious members, or to put it less charitably, it produced many rudely direct men. When he first met Bao Xiaoya, she was incredibly haughty, but who would've thought that in just a few days, she would be calling herself 'little sister'!

Hahaha, Shenzhou, truly the paradise of science men!

"Ask anything you like."

With an open mind, Bao Xiaoya sought guidance: "The Wanfa Sect, through the Mathematics Dao, calculates the myriad things of heaven and earth, aiming to calculate all there is under heaven and earth. Dare I ask, what does this fuzzy mathematical reasoning calculate?"

Wang Qi smiled and shook his head, holding up a finger: "Firstly, your question is somewhat inappropriate—does mathematics necessarily have to concern itself with 'calculating something'? Before Taiyi Heavenly Venerable, how many knew that surface geometry was about calculating space-time? Before the Wave Motion Lord, did anyone know that Xiangyu could calculate the Quantum Cloud?"

"The act of calculating is a tool to penetrate mysteries and dispel confusion. We mathematicians should not agonize over 'what to calculate', because others will naturally take up the tools that we forge, and dispel the mists of mystery that veil the Great Dao. We arithmeticians should simply focus on crafting good tools."

On Earth, the reason mathematics is known as the queen of sciences is that it has always been ahead of science. Euler's Euler β function, researched in the 18th century, was only found two hundred years later to be able to describe superstrings; Robachevsky's Non-Euclidean Geometry, discovered one hundred and fifty years earlier, was later used by Einstein to describe the curvature of space-time.

Then, Wang Qi raised a second finger: "Secondly, you've realized it, haven't you? 'These seem to be things defined by humans.' This was your exact quote earlier. You should have also realized that within the human heart, many concepts are fuzzy and without clear boundaries, making them difficult to express with traditional mathematical reasoning. This calculation, calculating the human heart to the fullest."

"And if we can calculate the human heart to the fullest, then how far off could creating human hearts be?"

The moment Wang Qi said this, the crowd was astounded. It was fine for the new disciples and small sect Grandmasters in the square. But how could high-order cultivators like Chen Jingyun and Deng Jiaxuan, who paid close attention to the very forefront of the Modern Immortal Path, and core disciples of the Immortal Alliance like Su Junyu, Bao Xiaofeng, and Ai Qinglan not be alarmed? How could they not be?

Creating the human heart from nothingness! Birthing will from the void! Wasn't this... one of the big questions under calculator research?

This was absolutely at the forefront of Modern Mathematics!

Wang Qi then put up a third finger: "The third point, you must have experienced it by now—in calculations where a high tolerance for error is allowed, fuzzy computing can ignore some variables and algorithms, saving a vast amount of computational power!"

In Carefree Sect, the one inclined toward empirical evidence, Deng Jiaxuan, nodded. For the Modern Immortal Path, for the Immortal Alliance, for individual cultivators, computational power is a very important resource. Cultivation requires computational power, seeking the Dao requires computational power, experiments, and processing results—everything requires computational power. If the "Fuzzy Algorithm" that Wang Qi spoke of really holds true, then once it's mature enough to be widely promoted...

At this moment, Wang Qi raised his fourth finger, "The most important point—what is the Dao we are seeking?"

Bao Xiaoya hesitated, "I don't know... My realm is too low, I dare not speak assertively about the Dao."

"No matter, just find a description from the ancients. Whichever resonates with you, just speak that one."

"'There was something chaotic yet complete, born before Heaven and Earth. Quiet! Vast! It stands alone, unchanging, it moves everywhere without danger, and can be considered the mother of Heaven and Earth. I do not know its name. Calling it forcefully, it is the Dao.'—Ah!" Bao Xiaoya suddenly enlightened, "You mean, this is about calculating the 'Dao'?"

Wang Qi replied with a smiling face, "We are far from mastering the laws of Heaven and Earth. What we cultivators can understand now is all defined by the 'Dao' determined by humans. Since it's defined by humans, it cannot possibly be clear and explicit in every respect."

Boom!

The calm words of Wang Qi dropped like a huge stone into the hearts of all the cultivators present.

Wang Qi's words seemed... maybe... sort of... to make a little bit of sense!

This algorithm, once published, could completely rewrite the foundation of Modern Mathematics, opening a new chapter in the study of mathematics!

"But..." Chen Jingyun pondered. At this moment, he was not the Great Grandmaster who disliked Wang Qi because of his Banished Immortal status, nor was he the duty-bound Sect Leader of Wanfa. Instead, he was purely an Arithmetician, "This is just an idea, an inspiration..."

Deng Jiaxuan also spoke up, "This needs proof!"

"It must be proven!" "Proof, where is it?" Su Junyu and Bao Xiaofeng said simultaneously.

All the cultivators who understood turned their gazes toward Wang Qi in unison. Those who were proficient in or fond of mathematics felt as if they were stretching out little hands from their eyes, wanting to grab Wang Qi by the neck and force him to reveal the rest of the content.

Proof is needed! The process is needed! Definitions are needed!

Bao Xiaoya, her expression still somewhat dreamy, bowed to Wang Qi, "I've learned a lot, Senior Brother Wang, do you have any... any thoughts that are somewhat similar?"

The words Wang Qi had just spoken were like pointing to a gate leading to a new world, yet the key to the gate was still missing.

The young man smiled slightly and drew a few simple geometric figures on the ground with his sword, "Let's use these figures to explain. Miss, do you know the law of excluded middle?"

Coming from a learned family, Bao Xiaoya immediately answered, "Either 'A is B' or 'A is not B', there's no third possibility. One of the pillars of classical logic."

"Then let's remove the law of excluded middle and see what happens to the logical system," Wang Qi suggested.

The girl was shocked, "How can that be... That... That would be violating logic, wouldn't it?"

Wang Qi shook his head, "Surface Geometry denies the last postulate of the Geometric God, Euclid, thus it is also called 'Non-Euclidean'. But has 'Non-Euclidean Geometry' really denied Euclidean Geometry?"