Calculate

Chapter 16

They are all doing well.

"You did this crazy guy? Shit!"

"Is there anything we can do about his disobedience to our world?"

"Have the peddler converted to your faith?" Chu Xunfeng asked.

“If you see your own brother turn into a madman, you won’t be obedient!” The man in blue seemed to be laughing.

"What's the story behind the repeated dream in Xianyang?"

"It's just a test of our control over the magnetic field of consciousness!"

“You’re not even human.” Herman thought of the madman bleeding from all seven orifices; he didn’t even spare someone like that.

The man in blue said gently, "Young lady, please calm down. Getting angry is one of the biggest flaws in your Newtonian world. I will slowly explain to you everything that has happened in recent years."

He turned to the golden shield and said, "You have a general understanding of our world."

The golden shield stood firm and unmoved, like a rock.

The man in blue twitched his lips again, as if he were smiling: "Then I'll tell you where I come from."

He took out a device that resembled a PDA and started calculating something. He was silent for a while, then did some more calculations, trying to organize his thoughts.

Will he reveal the secrets of that world? Where did he come from?

Chu Xunfeng felt a surge of excitement; the mystery was finally about to be revealed!

All things are numbers (Part 1)

Indeed, I come from another world. The "possible world" you've speculated about.

More than 300 years ago, we were all of the same human lineage, but 300 years later, we are developing in parallel on two different parts of the Earth.

The story dates back to the time of Newton. After the publication of his groundbreaking work, *Principia Mathematica*, the entire human race was captivated by Newton's theories. The worldview shaped by "universal gravitation" was established, and Newton was hailed as the creator of the universe.

We adhere to Leibniz's theory, having separated from the human world due to dissatisfaction with Newton's theory occupying too many people's minds and weariness with human sycophancy and lack of judgment.

If we call the world you live in the "Newtonian world," then the world we live in can be called the "Leibnizian world."

Our world is based on computation; computation is existence itself. We entrust everything, whether tangible or abstract, to mathematics for processing.

Circular reasoning① and mathematical logic are the biggest differences between the "Newtonian world" and the "Leibnizian world." The Newtonian world ultimately attributes unexplained causes to God, the so-called "first cause②," while we simply rely on calculation. If we cannot calculate the result, we seek more powerful computational tools. As your reasoning abilities improve, even producing giants like Einstein who can deduce four-dimensional space through logic, our world's computational tools are also developing rapidly.

In his book *History of Western Philosophy*, Bertrand Russell, a philosopher from the Newtonian world, wrote about Leibniz in the chapter on Leibniz: Leibniz publicly promoted a system that was optimistic, orthodox, absurd, and superficial; another system, which was gradually discovered by editors in his manuscripts much later, was profound, coherent, Spinoza-esque, and had astonishing logic.

Russell was only half right. The Leibniz World is indeed profound, coherent, and has an astonishing logic, but it is also orthodox and the best choice for mankind to seek the truth of the universe. It is just that foolish mortals cannot understand it.

To the "Newtonian world," Leibniz's birth in 1646 was perhaps as ordinary as that of Descartes and Gauss—just a star in the galaxy of history. Many ordinary people were completely unaware of this encyclopedic genius. In your eyes, Newton and Einstein are your absolute coordinates. But Leibniz's birth was the day of creation for us; he is our God, and we revere him as our ancestor.

"On the Art of Combinatorial Analysis" is the origin of the founding thought of the Great Ancestor (Leibniz), and also the paper most admired by Nie Longping, the great scientist of the Earth Federation WAR. In the "Newtonian World," apart from a few exceptional geniuses who clearly understood its significance, most simply compared it to Euler's "Introduction to Infinitesimal Analysis." It is the spark in the hall of thought of the Great Ancestor's "mathematical logic," shining with unparalleled wisdom and a piercing brilliance. The "Newtonian World" ultimately had to admit that the Great Ancestor was the founder of their mathematical logic, and they had to use mathematical logic as the foundation of computer technology, and had to work along the lines of Leibniz's ideas.

The "Newtonian world" loves to cite the fact that Leibniz and Newton simultaneously created calculus as the reason for Leibniz's greatness. However, the creation of calculus was merely a secondary event in Leibniz's life. Unlike Newton, Leibniz didn't care much about the creation of calculus; it didn't cause him any great harm. Calculus, however great, is just a mathematical tool. The most tragic thing is that Leibniz spent his life finding the key to unlocking the truth of the universe—the theory of logical operations using binary code. This theory was only suppressed by the Priory of Sion, and few ordinary people believed it. All of Europe was shrouded in the light of "universal gravitation" and seduced by the edifice of mechanics built by Newton.

In his contest with Newton, due to the limitations of the production tools at the time, Emperor Shizu, who had mastered the greatest theory, was mistakenly believed by ignorant people to have been defeated by Newton, and died with his eyes wide open in disbelief.

Fortunately, Emperor Shizu had the foresight to know that his theories would be difficult for the world to accept. In order to ensure that his theories could be passed down, he established a "possible world" that was different from the secular society.

Emperor Shizu served the Brunswick family for a long time, and was also employed by the royal families of Vienna, Berlin, and St. Petersburg. He also had connections with Peter the Great, Frederick I, the Emperor of Vienna, and even the Kangxi Emperor of China. Many people believe that he did this to gain the protection of imperial power or to establish an academy of sciences, but the more important reason was that he wanted to obtain more financial support.

The choice of Loulan as the birthplace was purely accidental. Emperor Shizu was deeply interested in Eastern culture and spent considerable time corresponding with European missionaries in China. He learned much about China from the Jesuit missionary Joachim Bouvet, including information on metallurgy, mining, astronomy, geography, mathematics, and writing. He also consulted numerous Western-translated Eastern texts. While reading the *Record of Buddhist Kingdoms*, written by the eminent monk Faxian in 400 AD during his pilgrimage to the West, he wrote: "Passing through Loulan, there were no birds flying above, no beasts running below; as far as the eye could see, only the withered bones of the dead served as landmarks." Loulan, a vital town on the Silk Road, flourished for nearly 500 years before suddenly becoming deserted and disappearing silently from the stage of history. As an archaeologist, Emperor Shizu was very interested in the lost ancient kingdom of Loulan. After many investigations, he finally established the ruins of the ancient city of Loulan and calculated that Loulan, which was at the time of the war between the Han Dynasty and the Xiongnu, had a highly secret underground palace. At that time, Emperor Shizu was investigating the location of the "possible world" and thus came up with the idea of establishing the "possible world" there.

Emperor Shizu also learned from Han Dynasty texts that "the Lop Nur region, southeast of the ancient city of Loulan, is three hundred li in size, and its water level remains constant, neither increasing nor decreasing in winter or summer, and is always abundant." Even in the Qing Dynasty, when Lop Nur flooded, there were still "small lakes that were eighty or ninety li long from east to west and two or three li or one or two li wide from north to south." Emperor Shizu speculated that "an underground river flows underground, and to the south, Jishi, is the Chinese River."

Water is the source of all things; where there is water, life can exist. Although Loulan was eroded by wind and sand at that time, underground rivers flowed beneath the ancient city of Loulan, teeming with life. Not far from Loulan, the groundwater of the northern Tianshan Mountains continuously flowed into the underground Tarim River.

Emperor Shizu established his "possible world" at the Loulan ruins in China. This was also because Shizu was quite famous in Europe at the time, and his every move attracted attention. He also faced persecution from the Priory of Sion, led by Newton, making it difficult for many followers of Leibniz's theories to gain a foothold in Europe. At the same time, he was extremely interested in Eastern culture and was a promoter of Sino-Western exchange. Practicing his theories in the vast and ancient Eastern countries was certainly a gratifying experience.

To expedite the construction of the "Possible World" and align it with his own theories, Emperor Shizu maintained close ties with Joachim Bouvet, a highly respected missionary in China at the time, and with the Jesuit order. Due to Shizu's acceptance of Eastern culture and his siding with the Eastern Jesuits in the "Rites Controversy," coupled with his influence over figures in Europe, the "Possible World" received strong support from the Chinese Jesuit order. All of this was conducted in secret. Later, many European missionaries came to China, including some from the "Possible World," and many believers also traveled from the Russian continent to the "Possible World."

Emperor Shizu (King Yongle) once asked a friend to apply to Emperor Kangxi for Chinese citizenship, but the Qing emperor, confident in his national strength, refused to condescend to accept this "barbarian" from a foreign land. After several attempts, Shizu had no choice but to give up. It is a great regret of the "Leibnizian world" that he could not witness the miracles he created before his death. However, when our theories once again govern humanity, we will surely place Shizu's monument at the center of any possible world.

In the first 100 years of establishing the "Possible World," like all closed worlds, we encountered difficulties. Like a small fish swimming in a long river, we seemed to be kept in a goldfish bowl. To avoid the extinction of our small world, we established new laws of nature. We try to maintain contact with the outside world, but we are not completely closed off, and we often absorb new members, bringing new blood to the "Leibnizian" world.

The essence of the new natural law is to adjust the ability to recognize and adapt to the evolutionary environment, increasing the proportion of intelligent systems in evolution while reducing the natural evolutionary capacity. Furthermore, it categorizes natural behaviors such as sleep, eating, and photography as computable forms of intelligence, minimizing the use of natural behaviors. As a result, our language functions have gradually deteriorated, and our blood has begun to cool.

After nearly 100 years of arduous exploration by our predecessors, we are finally able to rely on intelligent evolution to move forward smoothly in a "closed hypothetical world" and improve the surrounding environment.

In the following 100 years, we frantically improved our computing skills, developing computing capabilities that were unattainable in the era of Emperor Taizong. During these 100 years, Napoleon's conquest of Europe did not distract us, and Emperor Qianlong's conquest of the Dzungar Khanate in China did not hinder the progress of Leibniz's world. We evolved from mechanical calculations under Emperor Taizong to more powerful electronic calculations, creating and inventing the electronic calculator, and acquiring more powerful computing tools.

For the second century, the ancient city of Loulan remained relatively quiet, with only occasional passing desert warlords and lost caravans. Choosing Loulan proved fortunate; for centuries after the Qianlong Emperor, China was plagued by internal and external troubles, repeatedly ravaged by war, leaving neither the time nor the resources to investigate the ancient kingdom of Loulan. Furthermore, Loulan was surrounded by bandits, and no one dared to venture into the area; Leibniz's world remained undiscovered.

Just as we were enjoying a period of technological brilliance, Danish explorers arrived at the Lop Nur desert from the left bank of the Peacock River in 1900 and discovered the ruins of Loulan. Subsequently, they discovered the ancient city of Loulan, buried by sandstorms, in the southeastern part of the ruins. From then on, the Loulan site became a focus of global attention, attracting a large number of archaeologists, geographers, and geologists in the early 20th century. These included the American Huntington Expedition in 1905; the British Stein Expedition in 1906; the Japanese Otani Kōzui Chō Expedition in 1908-1909; and the second Japanese expedition led by Otani Kōzui and Kōzui Chō in 1910-1911. During their explorations, they acted recklessly, drilling holes, looting artifacts, and severely disrupting the "Leibnizian world."

Meanwhile, the ancient city of Luntai, the Qiemo ruins, ancient tombs, ancient beacon towers, mummies, ancient rock paintings, and more have all become world-class tourist attractions. The interest and enthusiasm shown by people towards the Loulan culture became unbearable for us. After concealing the underground palaces of Loulan, we migrated eastward along the underground river, eventually reaching the Qin Chuan area in recent years.

During our eastward migration, we continuously improved our computing technology, expanding from electronic calculators to quantum calculators. In terms of computation, we have far surpassed human capabilities, and our theories have become increasingly perfect. Twelve years ago, thanks to this leap forward in computing, centuries of hard work finally paid off, and the "Leibniz World" discovered the ultimate force in the universe—black holes.

In order to control the black hole program and find a workable theory, Leibniz, for the first time, humbled his pride and secretly sent two people to Newton's world for support. Their efforts were rewarded; they found a suitable theory. However, Leibniz also lost a great predecessor; he got lost in the sandstorms of Xianyang, and the ancient silver coin that had accompanied him throughout his life was later found by Xavier.

The Leibniz World has no other decorations. The silver coin that the patriarch presented to Augustus, which is inscribed with the patriarch's creation theory, is of commemorative significance. Each person in the Leibniz World has one; it is our totem.

For the past 12 years, we have been trying to transform black holes into computers, finding the best way to perform calculations and manipulate their inputs and outputs. Two months ago, we succeeded—we can now freely control the most powerful computer in the universe—the black hole computer—and use computation to solve one intractable problem after another. It can be said that we are now omnipotent.

After more than 300 years of darkness and perseverance, the great mathematical logic has finally been proven to be the ultimate truth: computation is indeed real!

The tool that Emperor Shizu had dreamed of was finally mastered by the "Leibnizian world," and Emperor Shizu's theories were invincible. The day of vindication had finally arrived.

Note:

① Circular reasoning: In this type of argument, the truth of the proposition is proven by the evidence. Conversely, the truth of the evidence depends on the proof of the proposition. It generally manifests as: If A, then B; if B, then C; if C, then A. Here's an example: A: Jesus is the Son of God. B: How do you know that? A: Because it's written in the Bible. B: Is what's written in the Bible reliable? A: The Bible was written by Jesus, the Son of God, so of course it's reliable.

② In his later years, Newton devoted himself to the study of theology, rejecting the guiding role of philosophy, devoutly believing in God, and immersing himself in writing works on theological subjects. When encountering inexplicable celestial movements, he proposed the theory of "God's first mover." He said, "God rules over all things, and we are his servants who fear and worship him."

③ The Priory of Sion is a religious organization. Sion, meaning Mount Zion, is located east of Jerusalem and is considered a holy mountain by Jews. Founded in Europe in 1099, the Priory of Sion was a powerful secret society whose mission was to unify Judaism and Christianity through the display of scriptures and artifacts, and to build a new "Holy European Empire." Its members are traditionally believed to include Sir Isaac Newton, Botticelli, Victor Hugo, and Leonardo da Vinci. This is detailed in *The Da Vinci Code*.

④ In the 16th century, missionaries in China clashed over Chinese customs of ancestor worship and Confucian veneration. Some missionaries (including Jesuits) believed these customs were not contrary to doctrine, while others (including Dominicans) argued they violated it. Unable to reach a consensus, they appealed to the Vatican. The "Chinese Rites Controversy" transformed from a theological dispute within the Catholic Church into a power and political struggle between the Vatican and the Chinese government. In 1704, the Vatican declared Chinese rites heretical and banned them. Emperor Kangxi was furious upon hearing this, stating that the Pope had no right to interfere in Chinese affairs, and subsequently expelled and imprisoned some missionaries. In 1715, Kangxi decided to ban Catholic activities, and Pope Clement XI issued an edict prohibiting Chinese Catholics from performing outward ceremonies of ancestor worship and Confucian veneration. This was a significant event in the conflict between Eastern and Western cultural differences.

Part 12

Newton's Black Box (Part 1)

At this point, the man in blue let out a piercing metallic cracking sound. This was probably their world's proud "maniacal laughter."

"For more than 300 years, the unwavering belief supporting the 'Leibnizian world' has been that the patriarch's theory is perfect and will inevitably rule the world, illuminating every corner of the universe. The world you live in is merely, as Professor Nie said, a new coat of Newtonian vanity and nihilism."

It turns out they wanted to rule all of humanity with their theories—what a terrifying ambition! The man in blue's cold face looked almost ferocious.

"Is your theory really that perfect?" Jin Dun interrupted the man in blue's smug laughter. "It's nothing but self-deception."

The man in blue's laughter was somewhat hysterical, and Jin Dun worried that he might attack them.

"You Newtonian world are deceiving yourselves. Look at what you've become! You've cut down so many forests, extracted so much oil, and hunted so many animals. Pollutants on Earth are multiplying, pathogens are mutating more and more, and the ecological environment is deteriorating. If you continue like this, the destruction of Earth is only a matter of time. And yet you're still there shouting about how great your achievements are, how much space you've conquered. But what's the use of that?"

When the man in blue got to this point, his usually steady voice became a little hurried, indicating that he could also get agitated. Fortunately, he calmed his anger in an instant and did not do anything too unusual.

“Human development will always encounter some problems, which is normal,” Jin Dun said. “It’s nothing serious. Your world also faces problems.”

"Look at your questions! World War II killed over 50 million of our own kind. Do you know how important population was to the Leibniz world!" The man in blue seemed to let out a long sigh. Chu Xunfeng and the other two could sense the deep compassion in his voice, as if he were mourning the deaths of humanity. "Incomprehensible! The two nuclear superpowers possess nuclear bombs with a TNT equivalent of 13,000 kilotons. Just 5 kilotons of TNT equivalent would plunge the Earth into darkness and freezing cold. Surface water would freeze, animals would die of thirst, and plants would wither. That's almost three times the amount needed to create a nuclear winter. Has the Newton world gone mad, storing enough explosives to destroy its own home under its bed? Do you know who was most worried about nuclear war back then? It was the Leibniz world."

"Are you also worried about freezing to death?" Herman asked.

"It's not that I'm worried about freezing to death. Newton's world may be extinct, but perhaps we can still survive. It's just that Emperor Shizu's theory cannot be universally accepted, and that's the most heartbreaking thing."

It seems Leibniz's world has never given up its ambition to dominate all of humanity, Jin Dun sighed inwardly. The man in blue's words weren't without merit; human development had indeed reached a dead end. On the surface, the world was at peace under the Federation's rule, but the north and south were at odds, and the east and west were in conflict. Extreme wealth and poverty were rampant, and environmental degradation seemed intractable. Desertification alone had already pushed humanity back step by step; the Earth was truly on the verge of collapse.

“But the achievements of Newton’s world over the past 300 years are also undeniable, from the internet economy to today’s life science and space economy①. From the successful moon landing to Turing’s arrival at Proxima Centauri, from laser technology to quantum technology, from large accelerators to the Hubble Space Telescope to spacetime overclocking… all are products of this era. Mathematics, physics, chemistry, astronomy, emerging life sciences, aerospace sciences, materials science, and computer science are also quite good. Are our achievements smaller than Leibniz’s world?” Jin Dun argued vehemently.

Hearing this, the man in blue twitched his face again, seemingly dismissing these achievements with disdain. "Yes, you have made considerable progress in many disciplines, but that's just adding and removing what was previously done, creating contradictions. The so-called progress you've mentioned is nothing more than a grain of rice; compared to the ultimate truth found in Leibniz's world, it's nothing more than child's play."

"I don't believe you," Hermann said, raising his head high and letting his curly blond hair cascade down like a waterfall. "Bragging is all the rage these days!"

"For example, you still can't solve a quintic equation."

The three fell silent. The quintic equation was indeed beyond human comprehension, because mathematicians specializing in number theory had reached a common conclusion: the quintic equation was not unsolvable, but it required the construction of auxiliary equations, which were far more complex than the quintic equation itself. This rendered the quintic equation practically unsolvable.

"Then can you prove that the quintic equation can be solved?" Chu Xunfeng countered.

The man in blue chuckled softly: "We don't need proof, because we can calculate the solution directly."

The three fell silent again. The man in blue was irrefutable; if the answer could be calculated directly, why bother proving it?

The man in blue said, “You can’t be blamed for this. The guiding theories of Newton’s world are flawed. The entire edifice of human truth is built on nonexistent axioms. Any natural breeze will cause this world to be riddled with flaws. When even the most fundamental things are uncertain, it’s normal to wander in the alley of false evidence. Newton’s three axioms in mechanics and Euclid’s five axioms in mathematics are self-evident in Newton’s world, which is ridiculous in Leibniz’s world. For any proposition, we will calculate carefully. There are no axioms, no authority. Only the result of calculation is immutable and absolute truth. Leibniz’s world does not need assumptions.”

Jin Dun pondered for a long time, his brow furrowed with an indescribable confusion, the lines between his brows revealing a certain pain. Chu Xunfeng and Hermann guessed that Jin Dun was caught in a strong internal conflict. He wanted to find a good reason to refute the other party, but seemed powerless to do so.

Chu Xunfeng's lips twitched, as if he wanted to say something, but he didn't.

The man in blue immediately stared at him and said, "You want to ask what Newton's new clothes mean?"

Chu Xunfeng wanted to refuse, but he couldn't. The other party could calculate his thoughts.

"Actually, I've already told you. Newton's New Clothes means that the Earth Federation is built on a spacetime based on Newtonian theory, which in turn relies on truth as its foundation, but these foundations are themselves illusory and powerless. Therefore, the Newtonian world is basically a castle in the air, and everything you have is just a reflection in the water and a flower in a mirror. Russell's paradox is an obvious flaw in the Newtonian world, and the barber's problem has already shown how vulnerable your theoretical system is. Most scientists are just charlatans who edit beautiful fabrics, and everything in the world is as false as the Emperor's New Clothes! Professor Nie is just the child in the fairy tale who uttered the first cry."

The three suddenly realized that "Newton's New Clothes" meant that Newton's theory in this world was unreliable, and the world constructed under this theory was a mirage. Everything was fake and untrustworthy.

“But Newton’s theory is just one of our theories. Even if, as you say, it has its flaws, can we deny the achievements of others?” Chu Xunfeng was somewhat unwilling.

"After the edifice of classical mechanics was completed, its quantitative analysis became the cornerstone of Newton's world, capable of explaining almost the entire macroscopic universe, leaving only two minor lingering questions—the later, remarkably well-developed theories of relativity and quantum mechanics. However, relativity and quantum mechanics are ultimately just follow-ups to Newton's theory, supplements to it, and still belong to the traditional mechanistic approach. For most of their time, relativity and quantum mechanics have essentially filled in the gaps in classical mechanics. In other words, the world today is still built on the foundation of classical mechanics. For example, how many of you truly understand four-dimensional space and voids…?"

The three were speechless at the words of the man in blue, including Jin Dun, a logically rigorous and outstanding figure.

But how could it be possible that Newton's theory, which has been in operation for hundreds of years, and the three axioms of mechanics that we have known since childhood, are not rigorous? The three of them stood there dumbfounded, completely bewildered.

At that moment, they had only one thought on their minds: How could this be? How could this be?

“Actually, you don’t need to argue with me. Even Newton himself knew long ago that his theory had shortcomings.” The man in blue glanced at Jin Dun, a smug look on his face. “Mr. Jin Dun, you should know the story of Newton’s black box, right? I think Professor Nie said there were records of it on his personal computer…”

At this point, the man in blue suddenly stopped, and a slight change appeared on his face.

Something important must have happened, otherwise his expression wouldn't have changed at all.

The man in blue slowly turned his head.

Then the three of them saw a six or seven-year-old child with fair skin standing at the door.

He stared wide-eyed at Chu Xunfeng.

Chu Xunfeng stared at him for a long time, then suddenly smiled slightly and took a small step forward. The child followed suit, taking a step forward just as he had when they first met. It seemed he had come back to find him.

"Who is he?" Jin Dun asked, though he already knew the answer in his heart.

The man in blue and the child gazed at each other for a long time, his expression gradually softening. A look of affection seemed to linger in his eyes: "He is the prince of the Leibniz world." He paused, then seemed to be speaking to the child again. "He is also my son, the only child in our world." At this point, a barely perceptible smile appeared on the man in blue's face. It seemed that, like his son, that world held deep love for him.

"How did he get here?" Hermann stared wide-eyed at the almost legendary child. How adorable he was! Delicate features, serene expression. He truly resembled the Little Prince, just as Chu Xunfeng had described.

“He saw Saviel and then came looking for you!” said the man in blue.