CHAPTER 956: CHAPTER 41: DOMAIN OF CHAOS

[Extra 1200 Monthly Ticket Update]

According to Earth’s history, the discovery of chaos theory consists of several stages.

The first stage was when scientists from different fields discovered phenomena with chaotic characteristics.

In this stage, only a meteorologist realized the significance of his formula, recognizing the mathematical meaning of chaos ahead of all the mathematicians.

However, the paper by meteorologist Edward Lorenz, which named the "butterfly effect," was not taken seriously after its completion. In fact, many people, including several meteorologists, thought his paper was wrong.

The second stage was marked by cross-industry communication that emerged with the dawn of the information age. Those individual scientists who had discovered chaotic phenomena gradually began to connect with each other.

The third stage was the birth of chaos theory.

However, chaos theory has deeper mathematical roots. Henry Poincaré launched an attack on the Three-Body Problem, completing the initial work. Almost simultaneously with him, Russian mathematician Alexander Liapunov completed the Lyapunov exponent, a measure of the tendency for nearby orbits to diverge. Subsequently, American mathematician Steven Smale described the universal topology conditions that ensure a dynamical system approaches a complex limit set. Finally, the fractals of French mathematician Benoît Mandelbrot truly depicted the strange attractor.

The Lorentz attractor, with a dimensionality of approximately 2.07, became the chaotic form remembered by the world.

This is Earth’s history.

However, Shenzhou’s history is somewhat special.

In Earth’s history, the discoverers of those chaotic phenomena, including Edward Lorenz, the discoverer of the Lorenz equation, did not have top-tier mathematical levels, and they did not understand the great achievements of Henry Poincaré. The chaotic attractors were waving at them from the stack of computer printouts in their offices, but they couldn’t understand it.

However, because of the existence of the "Immortal Dao" in this world, the development history of this discipline is completely different from the original.

Mathematics Lord Pang Jialai alone completed chaos theory.

Well, upon careful consideration, it’s not impossible. In the Shenzhou Immortal Path, topology is originally the Li Sect’s domain. Mathematics Lord is the leader of the Li Sect and the foremost topologist of the contemporary era. He traverses the Star Sea and naturally has opportunities to witness various celestial movements. If he were to carefully deduce the gravitational systems between celestial bodies, he could easily find dynamical systems with "chaos." With his achievements in topology, it wouldn’t be difficult to describe the universal topology conditions that ensure a dynamical system approaches a complex limit set.

For Mathematics Lord, grasping this weight is perhaps just a matter of concept. Breaking through his own knowledge barrier could easily make the last step attainable.

This is why Wang Qi urgently wants to know how far Mathematics Lord has progressed.

Mi furrowed his brow: "Now, the speed at which I transmit the Spirit Sense is very limited. You better not..."

The Holy Emperor Venerable is not to be underestimated after all. Now, Mi dared not make any big moves around the outer cluster of Spirit Phoenix Island, for fear that the Holy Emperor Venerable would discover something, causing the failure of this experiment.

"It’s okay, it’s okay!" Wang Qi said, "Being a bit slow is fine, the key is in that series of papers by Mathematics Lord. It would be best if they could be obtained. Exposure doesn’t matter either."

Mi’s illusion angrily kicked at Wang Qi: "Enough! Seems like you don’t plan to cherish it just because it’s not your body, huh?"

"Senior Sister, just consider it as a way to lose weight; those papers are really important!"

"I can’t do anything about you." Mi sighed, "Just wait, one cirulation later."

After Mi disappeared, Ru Tianqi dared to come out and asked: "Mr. Wang, you haven’t moved for a long time..."

Since he fell into Wang Qi’s hands, it has been nearly a month. Initially, he thought Wang Qi would sweep away Luochen Sword Palace with the momentum of thunder. But unexpectedly, ever since Wang Qi seized this quiet room, he stayed indoors and didn’t give him any commands, just let him study and ponder the Nine Chapters on the Mathematical Arts, sharing any insights with him directly. Apart from occasionally speaking with him and that mysterious Great Demon, most of this thief’s time was spent meditating in this quiet room, as if in seclusion.

At first, Ru Tianqi felt more comfortable this way. Without having to personally destroy the Sword Palace, he was naturally free from mental pressure.

But soon, he found it unbearable.

The pressure became too great.

The thousands of years of accumulated prestige of the Holy Emperor Venerable cannot be eliminated overnight. For thousands of years, the image of the "Holy Emperor Venerable" as unchallengeable has seeped into everyone’s bones. This isn’t something that can be changed by the power displayed by Wang Qi.

The mental state of the Divine Separation Stage ensured that Ru Tianqi wouldn’t lose his mind due to this "pressure" and could still resist the Holy Emperor Venerable. But he was also not thick-skinned enough to wander freely under the eyes of the Holy Emperor Venerable.

Even though Wang Qi assured him of the safety, and even though Wang Qi is capable of "confronting" the Holy Emperor Venerable, this sentiment remains.

Now, seeing that Wang Qi seemed very concerned about something, he felt it necessary to remind this guy about his main business.

Regarding Ru Tianqi’s anxiety, Wang Qi was rather helpless. He was very suspicious, wondering if these Ancient Method Practitioners, like the demon beasts of Shenzhou’s sea, had a genetic predisposition to fear the Dragon Clan, came with a meme of "obedience to the Holy Emperor Venerable"?

He waved his hand and said, "I have my own plans for this matter."

"Mr. Wang, do you know, outside, there are more and more rumors... some elders are already questioning your origins!" Ru Tianqi tried to sound earnest: "If we don’t go out soon, I’m afraid someone might come to spy..."

"Do as you please. Before completing foundational work, I have no plans to go out." Wang Qi waved his hand, telling Ru Tianqi to go on with his work: "You are a cultivator as well; you should know the importance of a solid foundation for future development, right? Sharpening the axe does not delay the cutting of firewood!"

His main task now is to perfect his virtual domain and fully integrate his cultivation method with this virtual domain.

However, this step remains quite challenging for Wang Qi at present.

By the afternoon, Wang Qi finally saw the Mathematics Lord’s paper.

"Tsk, in this world, the Lyapunov exponent was also discovered by the Mathematics Lord? Tsk tsk! Cellular automata under certain rules are equivalent to Turing machines... What is the use of this in proving this chaos theory..."

Some of the Mathematics Lord’s proof process was as Wang Qi expected, while others gave him quite a few surprising delights.

For instance, the Mathematics Lord outlining the universal topological conditions for ensuring a dynamical system approaches a complex limit set provided Wang Qi with significant inspiration.

Wang Qi’s grasp of topology is indeed above the baseline but far inferior to the Mathematics Lord. This task remains quite challenging for the current Wang Qi.

"Tsk, this old senior wasn’t idle in the Star Sea!"

It’s probably not an effort that can be achieved in a day but rather the result of piecing together numerous fragmented thoughts.

Finally, Wang Qi saw the Mathematics Lord’s recently published paper—"Three Circulations Chaos Theory."

In a discrete dynamical system of a single variable once researched by the Mathematics Lord, after three units of time or one circulation, even if only one point repeats its value, chaos will inevitably emerge.

This is a strict mathematical proof.

"Rather than resembling the proofs of Li Tianyan and James York, it’s closer to... Shakowsky’s proof." Wang Qi thought: "During the Cold War, the mathematical thoughts from the Soviet Union were indeed more akin to those of the Wanfa Sect here... Moreover, the chosen dynamical model was distinctly different."

The model used by the Mathematics Lord to prove chaos theory wasn’t akin to the single-variable equation of competition for scarce resources discovered by biologist Robert May on Earth but rather a model of the motion of some special self-gravitating point group.

"This is already quite a mature chaos theory... Hmm, it seems there’s nothing at present I can contribute to."

Wang Qi lightly shook his head, feeling somewhat regretful.

He had initially thought of exploiting this domain to gain considerable reputation after discovering the deep-rooted causal theory in Shenzhou. However, clearly, gaining reputation in the logical domain was faster, so he temporarily ignored this domain for the past two years.

Unexpectedly, someone was able to break through the knowledge barrier of all Shenzhou on their own.

Moreover, it was the Mathematics Lord Pang Jialai, from several eras ago.

Indeed, the real level of "equivalent" cultivators in Shenzhou surpasses those of their "original bodies" on Earth.

—No one in this world should be underestimated.

"As long as cultivators are undying, there are infinite possibilities..."

Wang Qi thought this, then smiled: "This feeling of ’someday being able to see the Great Dao’ must be the driving force behind the Modern Immortal Path’s relentless pursuit of longevity..."

Speaking of which, the chaos field influences what the most... apart from dynamical systems... Hmm, I think I remember... something akin to proving the principles of simple biological cell coordination like nerve cells? Chen Feng might be pleased...

Wang Qi shook his head and then asked Mi, "Any other news?"

"Master advises you to take it easy. Due to this recent impact, the Immortal Alliance’s decisive battle plan has been postponed again. During this period, focus on perfecting your cultivation method... wait, there’s no ambiguity here, just the literal meaning."

Wang Qi seemed not to hear the reprimand but grasped a key point in Mi’s words and asked, "This impact... How are the older generation like the Bai Ze God Monarch doing..."

The Bai Ze God Monarch is Su Junyu’s elder and once saved Wang Qi’s life. Wang Qi maintains a certain respect for this elder.

Mi succinctly said, "The Bai Ze God Monarch is still alive."

Wang Qi nodded, silent.

This is also one of the risks faced by living too long. The world has a chaotic mechanism, and you will never know how the future will develop. What you believe in might not be considered truth in the distant future.

Then, Mi’s next words made Wang Qi’s eyes light up.

"Additionally, there’s a message from Master Turing. He hopes you can ponder a few questions..."