Enter the Immortal Cultivation

【1200 plus】

According to the history of the earth, the discovery of chaos theory consists of several stages.

The first stage is that scientists in different fields discovered chaotic phenomena. ,

In this stage, only one meteorologist realized the significance of his formula and the mathematical significance of chaos before all mathematicians.

However, the paper named "Butterfly Effect" by meteorologist Edward Lorenz was not taken seriously after it was completed. In fact, many people, including many meteorologists, thought that his paper was wrong.

The second stage is the cross-industry communication that emerged with the dawn of the information age. Those individual scientists who had discovered the chaos phenomenon gradually connected in series.

The third stage is the birth of chaos theory.

However, chaos theory has deeper roots in mathematics. Henri Poincare launched an attack on the three-body problem and completed the initial work. Almost at the same time as him, Russian mathematician Alexander Lyapunov completed the Lyapunov index, a measure of the trend of the divergence measure of the near orbit. Later, American mathematician Steven Smale described the universal topological conditions that ensure that dynamical systems approach complex limit sets. And finally, French mathematician Benoit Mandelbrot's fractals truly depicted strange attractors.

The Lorenz attractor, with a dimension of about 2.07, became the shape of chaos remembered by the world.

This is the history of the Earth.

However, the history of Shenzhou is somewhat special.

In the history of the Earth, the discoverers of chaos phenomena, including Edward Lorenz, the discoverer of the Lorenz formula, were not at the top of the mathematical level, and they did not know the great achievements of Henri Poincaré. The chaotic attractor was waving at them in the pile of computer printouts in their office, but they could not understand it.

However, in this world, due to the existence of "Xiandao", the development history of this discipline is completely different from the original.

Suanjun Poincaré completed chaos theory alone.

Well, it is not impossible to think about it carefully. In Shenzhou Xiandao, topology is the private reserve of Li Zong. Suanjun is even the leader of Li Zong and the first person in contemporary topology. He traveled across the sea of ​​stars, so naturally he had the opportunity to see the movement of various stars. If he could carefully deduce the gravitational system between celestial bodies, he could easily find a dynamic system with "chaos". With his attainments in topology, it is not difficult to describe the universal topological conditions that ensure that the dynamic system is close to the limit set of complexity.

For Suanjun, realizing this level is probably a matter of concept. As long as he breaks through his own knowledge barrier, the last step is within reach.

Therefore, Wang Qi was eager to know what step Suanjun had reached.

Mi frowned: "Now my speed of transmitting spiritual resonance is very limited, you'd better not..."

After all, the Holy Emperor should not be underestimated. Now the clusters outside Linghuang Island, Mi, dare not make big moves, for fear that the Holy Emperor will find out something and cause the failure of this experiment.

"It's okay, it's okay!" Wang Qi said, "It's okay to be slow, the key lies in the series of papers by Suan Jun. It's best to get them. It doesn't matter if they are exposed."

Mi's illusion kicked Wang Qi angrily: "That's enough! You don't plan to cherish it if it's not your body, right?"

"Sister, just think of it as losing weight, those papers are really important!"

"I can't do anything to you." Mi sighed: "Wait, one hour later."

After Mi disappeared, Ru Tianqi dared to show up and asked: "Mr. Wang, you haven't moved for a long time..."

It has been nearly a month since he fell into Wang Qi's hands. Originally, he thought Wang Qi would wipe out Luochen Sword Palace with thunder. But he didn't expect that Wang Qi had been staying here since he took over this quiet room, never leaving the house, and didn't even order him to do anything. He just let him study and ponder the Nine Chapters of Mathematical Classics, and told him directly if he had any insights. Apart from occasionally speaking to him and the mysterious demon, the little thief spent most of his time meditating in this quiet room, as if in seclusion.

At first, Ru Tianqi felt more comfortable this way. He didn't have to personally wipe out the Sword Palace, so he naturally didn't have any mental pressure.

But soon, he couldn't handle it.

The pressure was too great

The thousands of years of accumulated power of the Holy Emperor could not be eliminated overnight. For thousands of years, the image of the "Holy Emperor" that could not be violated had penetrated into everyone's bones bit by bit. This was not something that could be changed by the power displayed by Wang Qi.

The state of mind of the Spiritual Division ensured that Ru Tianqi would not lose his mind because of this "power" and would not dare to resist the Holy Emperor. However, he was not so thick-skinned that he could walk around under the eyes of the Holy Emperor.

Even if Wang Qi had assured him that this place was safe and even if Wang Qi was a strong man who could "hard-hit" the Holy Emperor, this emotion always existed.

Now, he found that Wang Qi seemed to be very anxious about something, and felt that he had to remind this guy what his main job was.

Wang Qi was quite helpless about Ru Tianqi's anxiety. He wondered if these ancient cultivators were born with the gene of fearing the dragon clan, just like the monsters in the sea of ​​Shenzhou, and had the meme of "obeying the Holy Emperor"?

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

"Mr. Wang, do you know that there are more and more rumors outside... There are already elders who have doubts about your origins!" Ru Tianqi tried his best to sound sincere and sincere: "If you and I don't go out, I'm afraid... There are villains here to spy..."

"You can do whatever you want. I don't plan to go out until the basic work is done." Wang Qi waved his hand and asked Ru Tian to do whatever he wanted: "You are also a cultivator, you should know a solid The role of the foundation in future development, right?

His main task now is to improve his virtual divine realm and completely integrate his practice with this virtual divine realm.

However, this step is still very difficult for Wang Qi at present.

In the afternoon, Wang Qi finally saw Suanjun's paper.

"Tsk, in this world, the Lyapunov exponent was also discovered by you? Tsk! Cellular automata are equal to Turing machines under some rules... What is the use of this in the process of proving this chaos theory..."

Some of Suanjun's proof process was as expected by Wang Qi, while others gave Wei Qu a lot of unexpected surprises.

For example, Suanjun's delineation of universal topological conditions that ensure that dynamical systems approach complex limit sets gave Wang Qi great development.

Wang Qi's mastery of topology is indeed far above the level, but it is far inferior to Suan Jun. This task is quite difficult for Wang Qi now.

"Tsk, this old senior is not idle in the sea of ​​stars!"

I'm afraid this is not a day's work, but the result of many piecemeal thoughts in series.

Finally, Wang Qi saw Suanjun's recently published paper - "Three Weeks of Chaos Theory"

In a single-variable discrete dynamic system that a certain mathematician once studied, after three time unit steps, that is, after one week. Even if only one point repeats its own value, chaos will inevitably arise.

This is a strict mathematical proof.

"Rather than a proof to Li Tianyan and James York, it is closer to...Shakovsky's proof." Wang Qi thought: "During the Cold War, the Soviet Union's mathematical thinking was indeed closer to this The Wanfamen Lianzong on the other side...and the power models chosen are completely different."

The model used by Suanjun to prove chaos theory is not the one used on Earth, which is similar to the "single-variable equation of group competition for scarce resources" discovered by biologist Robert May, but the motion of some special self-gravitating particle groups. Model.

"This is already a pretty mature chaos theory... Hmm, it seems like there is nothing I can interfere with at the moment."

Wang Qi shook his head gently, feeling a little regretful.

After he discovered that the idea of ​​causality was particularly deeply rooted in China, he had the idea of ​​using this field to gain a lot of reputation. However, it was obvious that gaining reputation in the logic field was faster, so he had temporarily ignored this field in the past two years.

Unexpectedly, there are people who can break through the knowledge barrier in China on their own.

Moreover, it is actually Pang Jialai who was the king of fortune a few eras ago.

Sure enough, the real level of the "peers" monks in China exceeds those of the "originals" on Earth.

——No one in this world should be underestimated.

"If a monk doesn't die, will there be unlimited possibilities..."

Wang Qi thought so, and then smiled: "This feeling of 'one day being able to see the great road is probably the motivation for the immortal Taoist to tirelessly strive for immortality..."

Speaking of which, what does the realm of chaos have the greatest impact...besides the dynamic system...Hmm, I seem to remember...it seems...to prove the principle of synergy of simple biological cells such as nerve cells? Maybe that boy Chenfeng will be happy...

Wang Qi shook his head, and then asked Mi: "Is there any other news?"

"Master tells you, take it easy. Due to this wave of impact, the Immortal Alliance's decisive battle plan has been postponed again. During this period of time, you will perfect your practice... Wait a minute, there is no ambiguity here, only the literal meaning. mean."

Wang Qi didn't seem to hear the accusation, but grasped the key point in Mi's words and asked: "This impact... How are the seniors such as Lord Bai Ze and other seniors..."

Lord Bai Ze is Su Junyu's elder, and he once saved Wang Qi's life. Wang Qi still has a certain respect for this old man.

His words were concise and concise: "Shenjun Bai Ze is still alive."

Wang Qi nodded and remained speechless.

This is one of the risks of living too long. There is a chaotic mechanism in the world, and you never know how it will develop in the future. What you believe may not be considered truth in the distant future.

Then, Wang Qi's eyes lit up when Mi's next words came out.

"In addition, there is a message from Master Turing. He hopes you can think about a few questions..." (To be continued ~^~.)