Calculate

Chapter 5

"Impossible, how would you know what other people dreamed about?"

"But everyone I've asked has done it..."

Only Xavier remained unusually calm, completely focused on the man in blue's every move, paying no attention to their argument.

She gestured for the two to be quiet: "This isn't a ghost." She thought for a moment and said, "Have you heard of the Josephus Ring?" Saviel, a top student in the intelligence department, regained her logical reasoning ability.

"I've heard of it. It's about several monkeys forming a circle, counting to a certain number, and then leaving the last one standing to become the king! It's an ancient mathematical problem, and also a game." Chu Xunfeng looked at Saviel with a bit of confusion.

“Another common interpretation is that several prisoners line up in a circle and then count off, and the last one to be drawn survives.” Xavier watched the video intently. “In ancient times, there was a military rule that when defeated soldiers returned, they would form a circle, and the last one drawn would survive. There was once a soldier who was well-versed in mathematics who was defeated 10 times, but he survived each time because he knew the principle of this theorem.”

“The key lies in calculation. Standing in a specific position can avert death; that’s the ingenious use of the Josephus Ring.” Saviel seemed to have grasped something; her lips tightened, a hint of resolve appearing in the beautiful curve of her mouth. “Of course, the Roman warriors’ ability to avoid death is only the most basic application of the Josephus Ring.”

"What does that have to do with this video?" Chu Xunfeng was completely confused.

"Have you ever heard of the Lingbo Weibu (凌波微步) martial art in the novels of Jin Yong, the master of Eastern martial arts novels?" Xavier continued to ask, studying the other person's form as she spoke.

"That's just nonsense from martial arts novels; there's no such skill in real life."

"No, according to the Josephus theorem, if someone stands in a specific position, no one can touch them. In other words, this skill exists, but every position must be calculated precisely. In recent years, the development of probability theory and mathematical statistics has revealed that the random distribution of static matter can be illusory. This is a deeper application of the Josephus theorem, and my father has explored this area."

"you mean?"

"The man in blue chose a location on the Josephus Ring. He was clearly standing there, but the video couldn't capture his real image. That illusory shadow wasn't a ghost, but rather a random distribution of static matter."

Chu Xunfeng looked completely bewildered, while the hotel manager gaped open, revealing two large, yellowed teeth that looked like bamboo nails.

Note:

① Similar to birch, it is cold-resistant and drought-resistant, and is a pioneer tree species for preventing desertification.

②C Programming Problem: n people, numbered 1, 2, 3, ..., n, sit in a circle clockwise. Choose one...

Let m be a positive integer representing the upper limit of the counting. Starting from the first person, people count sequentially clockwise from 1 until they reach m. The person who counted m is eliminated, and the counting restarts from 1 with the next person in the clockwise direction, continuing in this manner until everyone is eliminated. Design a program to output the order in which people are eliminated.

③ A profound martial art described in Jin Yong's wuxia novel "Demi-Gods and Semi-Devils" is related to Zhuangzi's "Free and Easy Wandering".

Level 4 Civilization (Part 1)

When Jin Dun, deputy director of the Global Investigation Bureau, arrived in Xianyang, it was already 11:00 p.m.

This highly talented senior detective from the Global Bureau of Investigation is known in the industry as the new-era "Sherlock Holmes." The major cases he has solved include the "corpse-driving case" of the Paijiao sect in western Hunan, China; the curse case of the Great Pharaoh of the Pyramid of Giza in Egypt; the alien invasion case caused by the misplacement of the Easter Island megaliths; and the "Turing" genocide case orchestrated by "Elvis Technology" in Salt Lake City. Despite his numerous outstanding achievements, his distinctive personality has led to suppression from Director Harbis.

Jin Dun was inherently aloof and principled, making him unpopular among the Earth Federation's upper echelons. At the global federation meeting in 306, he nearly had a falling out with Professor Park Soo-seok, a leading scientific figure. Recalling the unpleasant scene from the 306 global emergency room meeting last night, he sighed and habitually rubbed his earlobe.

The incident unfolded as follows: NASA received an SOS distress signal from SpaceX, but the signal was interfered with by an unknown magnetic field. Amidst the noise and commotion, terrifying screams and the astronauts' urgent cries for help could be faintly heard.

The distress call threw NASA into chaos. Human space exploration has been remarkably smooth in recent years; the Turing six-winged satellite, launched 10 years ago, has already reached Proxima Centauri. Last month, space transport ship 4409 successfully landed at the X-planet spaceport, sending back the Alexander's captain's exaggerated longing for Mother Earth.

Besides this SOS distress signal, news of "aliens invading Earth from Planet X" has flooded various media outlets. The famous British tabloid, The Moon, even quoted the Bible to speculate that aliens will launch a full-scale attack on Earth on X month X year, and that the Nostradamus prophecy will soon be fulfilled.

Director Alden Pyle was shocked upon receiving the distress signal. Not because he believed in supernatural tales or prophecies, but because the strong magnetic field interfering with the signal matched perfectly in the spectrum of the three magnetic fields that had disrupted the Earth's magnetic field the previous month. Three magnetic field disturbances in a single month without solar flares is unprecedented in human history. It seems the theory of the "Alpha Centauri G invasion" is being validated: advanced life forms from the mysterious Alpha Centauri G are using magnetic fields as weapons to invade Earth.

Upon receiving the SOS distress message, the Federation's Supreme Leader, Mr. Mister, urgently convened a meeting in the early morning with the heads of major federal agencies, including the AEC (Atomic Energy Commission), NASA (Space Agency), WAR (World Research Association), GSB (Global Bureau of Investigation), and SIA (Space Intelligence Agency), to discuss countermeasures. To avoid causing panic, in addition to keeping the meeting closed to the media, all attendees were leading figures from the Earth Federation agencies.

Mr. Mister, with his blood-red hair, briefly described the predicament of the Earth Federation: "On September 11th, a nuclear explosion occurred in Loulan, western China. The Chinese Federation representative stated that no nuclear tests have been conducted in recent years, and the Atomic Energy Commission Chairman Hussein's report on western China also indicated that the explosion originated from Planet X, not underground. On October 5th, 15th, and 25th, every ten days, the Earth's magnetic field was interfered with by an unknown strong magnetic field, causing seven civilian aircraft crashes and the deaths of 668 passengers. On November 15th, an SOS distress signal was received from Planet X's base, but the signal was also interfered with by the same magnetic field. Simultaneously, three leading scientists in the field of WAR have gone missing. I request that the Federation's elite discuss countermeasures and reach a consensus." After speaking, Mr. Mister gave the Intelligence Director Roosevelt a sharp look and said, "Mr. Roosevelt, please provide a detailed report on the events of the past two months."

Faced with a series of unprecedented strange phenomena recently observed on Earth, the federal leadership is clearly divided into two camps. One camp, led by Professor Park Suk-seok, believes in an "Alpha Centauri G invasion." They argue that the mastermind behind these phenomena is Alpha Centauri G lifeforms and advocate for their destruction before they establish a firm foothold and fully understand Earth's technological capabilities. The other camp, led by Kim Duan, Deputy Director of the Investigation Bureau, is the "306 Investigation Faction." They do not believe that Alpha Centauri G lifeforms have necessarily invaded Earth and advocate for investigating the truth of the events before discussing countermeasures.

Mister was torn between the two factions, pinning his hopes on the analysis that Director Roosevelt had conducted over the past two months.

Mr. Roosevelt, known for his meticulous and unsmiling nature, wore a long face, as if everyone owed him a gambling debt. He was renowned in the intelligence community for his empirical evidence, and his conclusions were always rigorous and convincing. Today, however, he seemed somewhat hesitant and uneasy. He opened his mobile terminal and said, "Damn it, according to information from NASA, the intelligence agency has deciphered an extremely chaotic noise; to be precise, they haven't completely deciphered the message. The information was interfered with by a strong external magnetic field." Roosevelt still used the same vulgar expression. Mr. Mister frowned. Fortunately, this time Roosevelt wasn't as arrogant as usual for failing to decipher the message; he looked embarrassed. In truth, no one would blame this 21-year-old genius who derived the concept of "information negative entropy" from "Maxwell's Demon"④. Everyone present was simply stunned: information that even the intelligence agency couldn't decipher was unheard of.

After a long silence, Roosevelt's face grew even longer: "Damn it, one thing is certain: according to the spectral information separation field, the external strong magnetic field is the same as the strong magnetic field that interfered with the Earth's magnetic field on October 5th, 15th, and 25th of last month."

The strong magnetic field suggests that the "manipulators" behind this are of the same lineage. If what was previously just a glimpse into the nature of things was now further confirmed by Park Seok-seok's claim that "Alpha G life forms" attacked Earth using magnetic fields. It seems that the media reports are not just sensationalist rumors. Considering the mysterious disappearances of three top scientists from WAR this month, it appears that Alpha G's massacre of Earth has already begun.

Roosevelt activated the static energy decoder in his hand, and the terrifying screams and desperate cries for help from the X-planet astronauts came through. The sounds seemed to come from hell, desperate cries before destruction, sending chills down one's spine!

He pulled out two spectral analysis charts and said, "One is the average analysis chart of the strong magnetic field that interfered with the Earth's magnetic field last month, and the other is the analysis chart of the interference encountered by the X-star base. Ignoring the interference of the audio magnetic field, we can assume that they are consistent."

Mr. Hussein, the chairman of the Atomic Energy Commission, was bald with a shiny bald head. He blinked and said, "Damn it, besides this image, the analysis chart of the nuclear explosion in the ancient city of Loulan in western China also matches these two spectra." This Pakistani physicist had made significant contributions to promoting reconciliation on the Indian subcontinent and won the Nobel Peace Prize that year. He had inadvertently picked up Roosevelt's catchphrase. Hussein blushed and scolded himself for his bad breath: "Now the Federation is focused on news of alien invasions, but has ignored the nuclear explosion in western China on 9/11. The Atomic Energy Commission investigated the Loulan area in western China and found that it was just a strong magnetic field, or rather, a burst of strong energy, similar to the energy produced by a nuclear explosion. The final investigation found that the energy source came from Planet X. I have another question: why does the spectra of the 9/11 nuclear explosion in western China match these two images? The source target is also Planet X. What exactly happened on Planet X in the past two months?"

The conclusion is chilling: this series of events was certainly not accidental; was it a planned act by extraterrestrial life?

Secretary General Mister's face was grave, his blood-red hair seemed to turn crimson, and he was completely devoid of his usual wit and humor when dealing with major events. "Is the nuclear explosion in western China also related to this? Or is it just a coincidence?"

Roosevelt stated unequivocally, "Damn it, the separation of spectral information is never a coincidence. It can be accurate to the power of 10⁻³⁶, which is equal to the error of the critical rate of expansion of the universe?"

"What does the professor mean?" Mister glanced at Professor Park Seok-seok, whose face was pale—a staunch supporter of the Alpha G invasion. He was coughing repeatedly, seemingly weak. "...cough, cough...deterrence, or rather, a test!" The world-renowned Nobel Prize chairman's hair was disheveled, and his deep, unfathomable eyes were obscured by something. He coughed twice and stood up, his sickly appearance unchanged, but his words carried an indescribable authority.

"For the past decade, the astronomical community has been concerned about an invasion from advanced life forms on Alpha Centauri G. Ten years ago, when humanity explored Proxima Centauri, I strongly opposed it, fearing that humanity might disturb Alpha Centauri G under immature conditions. But humanity listened to Professor Nie Longping's advice, saying that the Triple Star System ⑤ was the most logical, so they targeted Proxima Centauri with the greatest space program in human history. It's as if the Federation is discussing logic, not studying science!"

When Park Seo-seok heard Professor Nie Longping being "tried in absentia," Jin Dun, a supporter of Professor Nie Longping's theory, disagreed. This staunch supporter of the "306 Investigation Faction" moved his mustache slightly: "Professor, the key is that we need to figure out the reasons, and then discuss countermeasures."

“Mr. Kim, this isn’t about settling old scores. It’s about elaborating on our points.” Park Seok-seok showed deference to the legendary detective before him. “By extending our perspective and not limiting ourselves to our current viewpoint, we can see things more clearly.” He tapped the plasma screen of the conference room, displaying the entire universe and galaxies. He pointed to a red planet with a plasma pen: “In modern astronomical research, this star in Alpha Centauri is called Alpha G. According to decades of calculations by the most powerful computer, Entropy, it harbors an advanced life form based on O and Fe elements. Information obtained from the Hubble Telescope in California indicates that this life form is extremely aggressive. The Extraterrestrial Intelligence Research Institute has received advanced coded information from Alpha G on multiple occasions.”

Park Seok-seok bent over and coughed for a long time, clearly quite ill: "The cosmic environment of Alpha Centauri G is similar to that of Earth, and they have existed for 4.85 billion years. The nearest star to it is Proxima Centauri, scientifically known as Alpha Centauri C, and the two are close relatives. Alpha Centauri G is 4.21 light-years from the Sun, equivalent to 30 trillion kilometers. The Turing spacecraft launched by Earth arrived at Proxima Centauri, and according to trajectory calculations, it just barely passed by Alpha Centauri G..."

Habis, the Arab director of the Global Investigation Bureau, yawned, revealing an impatient expression. He was a Saudi Arabian prince with a net worth of over 100 million, recommended by the Arab League to be the director of the Global Investigation Bureau, and also the direct superior of Golden Shield. However, in reality, Golden Shield handled most of the major cases, which was why two people from the Global Investigation Bureau were present.

Park Seok-seok seemed oblivious to Habis's distraction: "On August 27th last year, Turing arrived at Proxima Centauri. Alpha Centauri G was at its perihelion. If they detected human activity, they would have followed the trajectory at a speed of 951,230 kilometers per second, which is one of the standard speeds for extraterrestrial life to advance outwards. This year, on August 16th, they arrived at Proxima Centauri X, exactly three months ago. There's another ominous conclusion: according to data sent back by Turing, the state of Proxima Centauri is already undergoing subtle changes. Based on combined information from the Purple Mountain Observatory and the Columbia Observatory, its helium flash moment is imminent."

The helium flash of Proxima Centauri means that its galaxy will be completely destroyed. If there is advanced life in that galaxy, then it will have to find a similar planet as a "second home," which means intergalactic migration in the universe.

“Professor, we have no assumptions, only logic and empirical evidence. You seem to be telling us an interstellar story.” Jin Dun remained as calm as ever, his white robes giving him an icy air, and his mustache exuding the demeanor of a wise man.

"This isn't hypothetical; it's logic, it's empirical evidence, it's the result of decades of calculations integrating information from various sources. The advanced O and Fe life forms on Alpha G have repeatedly sent coded messages to Earth—an absolutely advanced life language. The date of the Proxima Centauri helium flash was also calculated, and the deaths of living beings are empirical evidence. I can cite many more horrifying space messages you don't know about; the Space Intelligence Research Institute also..."

"What about nuclear explosions in western China?" Jin Dun asked arrogantly.

"A test. Two months ago, they arrived at Planet X and used it as a base to study Earth. The 9/11 nuclear explosion in western China was their initial little trick. It's true that Atomic Energy Council Chairman Hussein said the energy came from Planet X. Planet G conducted a small test of its energy in western China." Professor Park Shu-seok was not angry in the face of Jin Dun's aggressive questioning.

"Why not just come to Earth?"

"The reason why they don't come directly to Earth is simple. Just like when humans discover their own kind, they will naturally study them gradually. When they see that there is intelligent life on Earth, they will naturally first find out about humans."

"Then why did it interfere with the Earth's magnetic field last month?"

"It was also a test, but it was a comprehensive test, unlike the nuclear explosion in western China which was just a separate test. This test caused the Earth Federation to lose 7 civilian aircraft and the lives of 668 passengers in one month."

"Were the astronauts on Planet X also their doing?"

“The desperate cries for help are proof of this.”

"Then why interfere with the Earth's magnetic field, and not something else?"

"When conducting macroscopic tests on a planet, testing its magnetic field is the best approach. For example, when astronomical institutes examine Degus in the Milky Way, the first thing they do is examine the planet's magnetic field composition. The magnetic field is a macroscopic property of a planet."

Kim Duan's pupils constricted: "Professor Park Seok-seok, but that's just speculation. You haven't said anything more..."

Park Seok-seok, his face flushed, forced back a cough: "This is the result of decades of observation and research. All the speculations are actually calculations, and all the calculations are the accumulation of information from the astronomical community over many years. There is no true chosen one in the Milky Way, and Earth is not God's only favored child. We can't wait until disaster strikes to believe this..."

NASA Administrator Alden wanted to stand up and say something. Like Golden Shield, he was a supporter of the "306 Investigation Faction." This principal investigator of the Turing six-winged satellite, which had landed on Planet X six times, had used chemical agents to temporarily render himself impotent in order to solve the final hurdle of space travel—sexual needs. Due to the excessive number of space explorations, his "baby" had completely lost its function; one could say he had dedicated his life to humanity's space program. Now, the thought of destroying Planet X filled him with anxiety. However, Professor Park Soo-seok's passionate and eloquent speech left him no room to interject.

"WAR has inexplicably lost three great scientists in the past two weeks. These matters have been kept secret. The investigation bureau hasn't provided a reasonable answer either, Mr. Kim Shield." Professor Park Shu-seok was no longer friendly towards Kim Shield. As the chairman of the Nobel Prize committee, he was always the one criticizing others; he had never been questioned like this before.

“If it cannot be explained by another perspective, then Professor Park Seok-seok’s speculation is a rigorous deduction.” The director of the investigation bureau, Habis, had a slightly embarrassed look on his fat face. The Federation had lost three great scientists in succession, and the investigation had made no progress. As the director, he felt ashamed.

Professor Park Woo-seok covered his mouth with his hand, trying to suppress a cough: "We cannot be confined to conventional thinking. The existence of advanced life on Alpha G has been known for over a decade. It is also a consensus formed in the scientific community. Theoretically, humanity could also reach Type IV civilization. After this series of events, we can no longer judge humanity as 'the only primate in the entire universe,' otherwise it would lead to the extinction of humanity. We must be prepared."

"Mr. Roosevelt, if you had enough time, could you explain this strong magnetic field phenomenon?" Secretary General Mister turned his gaze to the Director of Intelligence.

Roosevelt shook his head: "Damn it, for Earth, solar flares are the cause of the geomagnetic field disorder. In all the data and literature, the various changes in the Earth's magnetic field are only related to solar activity, but this year is not a sunspot year. Moreover, such a strong and uniform magnetic field spectrum is not the solar system spectrum. This magnetic field is incredibly powerful and flawless, and it is obviously a magnetic field that has been processed by advanced life."

Upon hearing this answer, Mister couldn't help but tremble.

"If it's an invasion from Alpha G, we need to think of a solution quickly." Habis's forehead was covered in cold sweat.

“Even though the other side may be a civilization more advanced than ours, there are still ways to overcome them,” Professor Park Woo-seok said calmly and confidently.

Mister's expression changed, and his blood-red hair trembled in the wind: "Professor Park Woo-seok means to use the Matrix Project to deal with the planetary invasion? This matter needs careful consideration. There are more voices against the Matrix Project on Earth than those in favor. Even Professor Nie Longping has personally written articles expressing his opposition. It should not be done unless absolutely necessary..."

Jin Dun coldly interrupted Mr. Mister: "We received information before the 306 meeting that Professor Nie Longping went missing last night!"

Everyone present paled; Professor Nie had also disappeared.

While the mysterious disappearances of the first three professors at the WAR could be concealed, the disappearance of Nie Longping is absolutely impossible to hide. This academic giant, hailed as comparable to Copernicus, Bruno, Galileo, Kepler, Newton, and Einstein, a "scientific madman" who achieved brilliant accomplishments in physics, philosophy, and mathematics, won the Fields Medal at the age of 29 for his "contradiction-free hypothesis of the I Ching and arithmetic axioms." Even Professor Park Seok-seok was once harshly criticized by him, and the entire Nobel Committee was deemed "worthless" by him. His influence is immense. Lacking the reserved and low-key nature of Eastern scholars, he has always been under media scrutiny, with all his latest research findings first published online. His disappearance will undoubtedly cause a global uproar.

Like Park Seok-seok, Nie Longping was also originally scheduled to be invited to the meeting, but he was eccentric and behaved strangely, and had always been at odds with Park Seok-seok. At the last meeting of the 306th Division, upon hearing that Park Seok-seok would be present, he immediately refused Mr. Nie's request.

Park Seok-seok frowned: "Nie Longping is missing? Is it confirmed that he is missing?"

“We’ve searched using GPS global positioning, Galileo 3, and super iris sensor. Like the previous three, they didn’t leave any information,” Jin Dun said.

A barely perceptible sneer appeared on Park Seok-seok's face, a slight blush creeping onto his pale cheeks, but he quickly regained his usual pitying expression: "Four top scientists vanished from the earth without a trace. How do you explain that? Has the investigation bureau found absolutely no clues? Are they just letting this situation continue..."

Jin Dun observed all of this and slowly replied, "Based on my speculation, there exists a mysterious organization on Earth that has close ties to the mathematician Leibniz, who lived more than 300 years ago..."

“It’s speculated? A mysterious organization, Leibniz from over 300 years ago… Mr. Golden Shield. We have no assumptions. Only logic and evidence.” Park Seok-seok mimicked Golden Shield’s tone. “You’re far more outrageous than I am. If such an organization truly existed, capable of confronting the federal government, causing scientists to mysteriously disappear one by one, and leaving astronauts from Planet X’s base without a trace, the Federation is now on the verge of collapse. We don’t want to hear these excuses. Just say there’s a cult using sorcery to shirk the Bureau of Investigation’s responsibility.”

Kim Duan gave Professor Park Sook-seok a cold look and said nothing more. His lean and refined face became even more stern, and his neat mustache lost its usual elegance.

"Not a single clue was left behind," said Federal Secretary-General Mister, who was quite shocked by Professor Nie's disappearance.

“Leave behind these five words: Newton’s New Clothes.”

Everyone was stunned. Newton's New Clothes—what did this mean?

"Any other clues?" asked Federal Secretary General Mister.

"A 17th-century German silver coin."

"Who was the last person Professor Nie Longping came into contact with?" Habis asked.

“His daughter, Saviel.”

Where are you now?

"With my boyfriend in Xianyang, China, at the Mausoleum of King Wen."

...

Note:

①The "corpse-driving technique in western Hunan" has always been a mystery. This technique is said to have appeared in the mid-Qing Dynasty and was used to transport the bodies of Hunan immigrants who died in Sichuan back to their hometowns.

②A Christian who once wrote the poem "In July 1999, the King of Terror fell from the sky," now used to refer to the end of humanity.

③ It is mainly composed of the aerospace academy, the life sciences research school, and several Nobel laureates, and has a strong voice in the scientific community.

④ The "Maxwell's Demon" scenario describes a box filled with gas, divided into two parts by a partition. A small window in the partition allows one gas molecule to pass through at a time, and this window has a frictionless latch that can open or close it. Next to the window is a tiny demon who can open and close the window. When the demon sees a high-speed molecule flying towards the window on the left, it opens the window to let the molecule pass to the right; conversely, if a low-speed molecule flies towards the window on the right, it also opens the window to let the molecule pass to the left. In this way, the temperature of the gas on the right increases, while the temperature of the gas on the left decreases. Because the window is frictionless, the demon reduces the entropy of the system without doing any extra work, which contradicts the second law of thermodynamics.

⑤ Proxima Centauri is a triple star system. They orbit each other, so the title of "closest in the world" has actually been held by these three stars in turn at different historical periods.

⑥ Helium flash: An explosive phenomenon that occurs when the core temperature of a helium-flash giant star rises to a level that allows helium to fuse.

⑦ The Fields Medal (full name: The International Medals for Outstanding Discoveries in Mathematics) is an award presented at the International Congress of Mathematicians of the International Mathematical Union. It is awarded every four years to mathematicians under the age of forty who have made outstanding contributions, with a maximum of four recipients each time. Its aim is to reward young mathematicians. It was established at the request of Canadian mathematician John Charles Fields. The Fields Medal is considered the Nobel Prize of mathematics.