Chapter Seven: The Double Paradox

"The story of the tortoise and the hare," Li Fengyin said. "I am not a real researcher, but I spent some time pondering this paradox when I first heard it."

"If we set the tortoise's speed at 0.1 meters per second and the hare's at 1 meter per second, with the tortoise starting one meter ahead, after one second, the hare has covered one meter and the tortoise 0.1 meters. The hare is still 0.1 meters behind. In the next 0.1 seconds, the hare covers a total of 1.1 meters, the tortoise covers 0.11, leaving a gap of 0.01 meters. The hare still hasn't caught up. Then another 0.01 seconds pass... theoretically, if you continue this way, the hare can never catch the tortoise."

"Go on."

Shen Liangxin rarely heard such introductions from others. While these were theories accessible to the average person, they contained profoundly deep implications.

"But in reality, the hare absolutely catches the tortoise," Li Fengyin mused. "That is to say, this method of calculation is correct, yet it does not exist in reality."

"It's like the concept of cutting a rod in half every day. It sounds reasonable that you could never finish, much like Zeno's tortoise. One involves addition, the other subtraction; both are mathematically correct but contradict reality. Even if you take half every day, there will eventually be an end."

Li Fengyin had made his point clear: both were inverse facts and inferences—one increasing, one decreasing—yet both could be disproven.

"An interesting thought," Shen Liangxin said. "It seems you are a person who enjoys thinking. In fact, the explanation scientists give for Zeno's paradox is that even the sum of an infinite number of values is not necessarily infinity."

"Actually, I have another thought."

Just as Shen Liangxin was about to say "You pass," Li Fengyin blurted this out. Shen Liangxin’s eyes brightened slightly, signaling him to continue.

"If we compare the two paradoxes, and we use the theory that an infinite sum is not necessarily infinite, doesn't that imply that the rod being cut in half can truly never be finished?"

Li Fengyin seized the chance to pose his question. Now, it was Shen Liangxin’s turn to ponder. She habitually lowered her head slightly, her fair index finger pressing against her chin. "I hadn't thought about that..."

*The subject before me seems even more precious than I imagined...*

Seeing the quantum computer running outside the glass wall, Shen Liangxin’s brow relaxed, and she said, "Quantum!"

"Yes!" Li Fengyin nodded. "My thought is that between 0 and 1, and 1 and 0, there must be a boundary, and that boundary lies at the quantum level."

"This is indeed related to my research," Shen Liangxin said with a smile. "You’ve given me a new perspective."

"However, this is only my conjecture," Li Fengyin sighed. "I don't have any real theory to prove it."

Looking at the young man, Shen Liangxin felt as if she had discovered a treasure. "Now you have the opportunity. Would you like to join my research team?"

Li Fengyin's cognitive ability truly surprised her; this was not a level an ordinary person should reach!

"Oh, right," Shen Liangxin immediately remembered. "You are the legendary schizophrenic with an outrageous brain."

"..."

Li Fengyin fell into a brief silence, then gradually began to brighten. "This is the first time someone has spoken of my illness so equitably..."

Tears welled up in his eyes. Li Fengyin turned away to secretly wipe them; he was still the same easily moved child.

"You're a bit like a child, aren't you?"

Shen Liangxin stood silently, waiting for the man who had saved her just yesterday to turn back around. Everyone has their fragile side; she would let him vent for a moment.

"In fact, I need to use quantum entanglement to break the shackle that everything is governed by rules." Shen Liangxin's expression became serious. "If everything is governed by rules, then everything is predetermined. This is a difficult problem to solve."

Li Fengyin had never pondered such things. He listened quietly, as Shen Liangxin had not finished.

"Initial motion is a straight line," Shen Liangxin explained her logic as concisely as possible. "Curves appear due to the interference of two or more forces. But if a perfect curve exists that can persist eternally, then it is a circle—the end of pi."

"Actually, I prefer to call the sum of the quantities in Zeno's paradox 'infinite'," Shen continued, organizing her thoughts. "Everything is eternally existent—an endless past, an endless future. That is the answer. But it is precisely this answer that gives me the possibility that everything is repeating; otherwise, eternity could not be reached. True eternity is a circle."

"A perfectly repeating circle," Shen Liangxin said softly. "I choose to call it infinity."

"Only that which repeats infinitely is truly infinite..."

Li Fengyin pondered silently. In reality, the symbol for infinity is the Möbius strip, which never ends and always repeats; the two concepts represented the same thing.

However, only a perfect existence could ensure that no errors would ever occur, which naturally meant a circle.

"Recently, my experiments have hit a bottleneck," Shen Liangxin sighed. "All I can rely on is this quantum computer and my own theories."

"And I have discovered something truly terrifying."

Li Fengyin’s interest was piqued. "What is it?"

"I'm not sure I want to tell you; I'm afraid you won't be able to handle it." Shen Liangxin raised the corner of her mouth slightly. "Of course, if you really want to know, I can tell you."

Li Fengyin realized immediately that she was playing hard to get—she would definitely tell him, but she was warning him of the horror of the matter.

"The most terrifying thing I know, the one that makes me shudder the most, is the question of where the world we live in, the Earth we stand on, and the universe we understand actually are. Perhaps they are all just a dream-like place."

After saying this, Li Fengyin smiled as well. "Please, tell me!"

"Good, that's the spirit!" Shen Liangxin joked, a rare occurrence. "What I know is that, at the very least, since 1993, everything on Earth has become incredibly precise. To be exact, everything became easy to deduce and certain. But before 1993, even a quantum computer could not deduce things quickly."

"Would you like to use your high-powered brain to think about the reason for this?"

As the chapter came to a close, Shen Liangxin posed this lethal question to the boy before her.