Alchemy Principles of Type-Moon World

Xing Qingfu is in this state now. He is completely immersed in this feeling of nothingness and cannot perceive anything except his own thoughts.

The five senses completely lost their functions, but were replaced by sharper thinking.

He felt as if he were trapped in an endless black hole, the world around him completely drained away, leaving only a bottomless void. He could feel his thoughts racing through his mind, each one incredibly clear, yet this clarity couldn't extend to any external perception.

He tried to raise his hand, but couldn't feel any muscles move. He tried to blink, but couldn't tell if his eyelids were there. Worse still, he couldn't even tell if he was in a freezing cold cellar or surrounded by warm sunlight. Every inch of his skin seemed to have lost its existence.

Xing Qingqiu inexplicably relished this feeling. After discarding all external things, only thought itself remained. In this environment, his mind became exceptionally pure, free of impurities and distractions. Every thought shone with crystal clarity. His consciousness drifted in this endless nothingness, like a solitary star twinkling in the boundless universe.

But now, his top priority is to find a way to get out of here.

Newton had once described imaginary space to him. Even now, as Xing Qingfeng submerged within it, imaginary space itself remained nonexistent to him. There was no up, no down, no light, no darkness. All sensory information was stripped away, leaving only pure consciousness and thought wandering in the invisible.

He inexplicably recalled what his former calculus teacher had said.

“Although many people study advanced mathematics,” the old man once said in class, “there are very few people who can truly understand mathematics.”

"Even though you've learned advanced mathematics, understand how formulas are used, and even understand how they're proven—"

“—But you don’t have the mathematical mindset.”

The old man looked nothing like a math teacher, more like a Chinese language teacher, his hallmark being his tendency to wander off topic mid-lecture. He would casually lean on the edge of the podium, eyes slightly squinting, as if he'd been mentally pondering every word countless times.

"Your understanding of mathematics is still too intuitive, and you think that mathematics must reflect the truth of the world."

"You've learned this far, but you still hold on to such naive ideas. That's why you can't understand mathematics."

"Abandon your idea that mathematics must correspond to reality. When you realize that mathematics does not reflect the world, that mathematics is abstract, a building built on axioms and self-consistent theorems—"

"—You have finally touched the threshold of mathematics."

"I finally understand what that old man said back then, even though I was forced to do so." Xing Qingfeng thought, "Yes, the five senses themselves are unnecessary here."

Abandon the intuitive understanding of mathematics, abandon the dependence on the five senses, and rely on pure logic and reasoning to understand this "unknowable" world.

"Calculating constantly, maintaining a mapping relationship with the real world..." Xing Qingfeng felt a headache as he recalled Newton's words. He had simply used a conversion formula to transform his coordinates from the real coordinate system to the complex plane. Ignoring the mapping relationship left him feeling quite lost in imaginary space.

“In this state,” he continued to ponder, “how can I reconnect with the real world?”

He tried to reconstruct the coordinate system of the real world in his mind, trying to find a way to find the projection of reality in the imaginary space.

If we talk about mapping relationships, the relationship between real numbers and imaginary numbers, the relationship between exponential functions, trigonometric functions and complex numbers, then Liu Leng? 児栮山? 肆把爸爸(四#) 凌.梦——

——I guess it’s only that beautiful overpass.

e^πi+1=0

The entire formula consists of only five elements: the natural constant e, pi, the imaginary number i, the smallest positive integer 1, and the most special real number 0. This formula perfectly incorporates these five special mathematical elements, as concise and beautiful as poetry.

It extends the exponential function to the complex number domain, like a bridge built between real numbers and imaginary numbers, becoming a bridge to communicate between the two.

Now, it will become a bridge between the imaginary space and the real world.

Xing Qingfeng diligently reconstructed these relationships in his mind. He first tried to recall the coordinates when he entered the imaginary space, then began a meticulous and complex calculation: "First, obtain the modulus of the current coordinate vector and its projection on the real axis..."

Xing Qingyu's mind raced through various mathematical operations and geometric transformations, attempting to determine his position, but none of these methods seemed sufficient to provide a definitive answer. He could only vaguely remember the coordinates of his entry into imaginary space, so he decided to calculate a target location first, so that he would at least have a direction to move in.

"...Do we need to use quaternions?" Quaternions are the extension of complex numbers in three-dimensional Euclidean space and one of the simplest hypercomplex numbers. They have important applications in rotation and three-dimensional space transformation.

"...No, this fucking imaginary space might have more than three dimensions. We need to use other hypercomplex numbers," he thought. "Calculate the higher-dimensional coordinate vector and then calculate its projection in three dimensions, and then find its real projection and modulus—"

"-Isn't this just Hilbert space operations under special circumstances?" He suddenly realized that despite its complexity, even complex Hilbert space still has the properties, inner product and completeness of linear space, and calculation is not an impossible task.

"Then regard yourself as a point mass in a high-dimensional Hilbert space..." Xing Qingyu quickly sketched out a high-dimensional Hilbert space in his mind, and regarded himself as a point mass in a high-dimensional Hilbert space for calculations. Although he didn't know where he was, he knew where he was going.

It's just that his body structure is special. If an ordinary person were to do this, he would have died countless times.

Wait, would a normal person dare to soak their physical body in the sea of imaginary numbers?

Time lost its meaning in imaginary space. In the surrounding void, only Xing Qingfeng's thoughts raced. He constantly adjusted his computational model, experimenting with various possible mappings and transformations. Each step required extreme precision; the slightest mistake could lead to endless confusion.

He began to calculate rapidly in his mind: the addition, subtraction, multiplication, and division of complex numbers, the transformation of vectors, the folding and unfolding of space. Each step flashed through his mind like a revolving lantern. He felt as if he were in a vast mathematical maze, where every step could lead to a different result, and he needed to find the only correct path.

——The equations and matrices were interwoven into a huge network in his mind, and every node told him what to do next.

The sense of time became blurred in this numb state, and Xing Qingyu didn't know how long he had been thinking.

Finally, he calculated a path to the real world. Euler's formula became his bridge across imaginary space and real space, and Hilbert space pointed him in the right direction.

Although due to the uncertainty of his own coordinates, he didn't know what the coordinates would be like when he got out, but at least he was able to get out.

At least it won't throw him off the planet, probably.

He concentrated all his energy, remapping his coordinate vectors in high-dimensional space back to three-dimensional real space. The imaginary coordinates were rearranged in his mind, and the image of reality gradually became clear in his mind.

The next moment, he found himself falling from a high altitude somewhere.

The good news is that he is still on Earth. He is very lucky not to appear in space or in the mantle.

The bad news is, he has no idea where on Earth he is.

"It looks like... somewhere in the United States down there?" Xing Qingqiu squinted at the city billboards below and made his assessment. "It's all in English. I'm not sure..."

He tried to adjust his falling posture so that he could hit a deserted place to avoid accidentally hurting pedestrians. Otherwise, if he hit a passing high school girl, maybe there would be two more ninjas in the world.

--------------------------

"Is Xing Qingfeng not here?" Kenneth, who had just emerged from the inherent barrier, looked a little pale. When he heard Newton mumbling to himself, he couldn't help but ask.

"I asked him to calculate a coordinate conversion between two inherent barriers, and he ended up throwing himself into imaginary space," Newton replied casually, a hint of disapproval in his tone. His eyes narrowed slightly, carefully sensing the residual magical fluctuations in the air. "This kid does have some talent."

"?" Kenneth stood there in a daze with a puzzled expression on his face.

The guy who just started learning magic for less than a week is now diving in the virtual world of physical body.

"Wait, you said he entered the imaginary space just by calculating?" Kenneth asked impatiently, his voice filled with disbelief. "Is he imaginary?"

"No, imaginary space isn't exclusive to magicians with imaginary attributes," Newton scoffed. "It's just that magicians with imaginary attributes find it easier to perceive imaginary space."

"Most of them even manipulate imaginary space using a somewhat intuitive method." Newton chuckled disdainfully, a hint of sarcasm curling up his lips. "If it weren't for the black box nature of magic that allows even idiots who don't understand the principles to operate it, they would have died countless times over."

Kenneth was silent for a while, lowering his head in thought, trying to digest what Newton had just said in his mind.

After a moment, he finally spoke: "Then Xing Qing... 1 Ming () Erlong Si 帬"

"He forced his way in," Newton replied flatly. "He converted his coordinates into those of the complex plane, then entered the imaginary space the same way he entered and exited the inherent barrier."

"Now, let's get him out." Newton sighed. "Xing Qingfeng is just like any other person. He lacks the abstract understanding of mathematics. It's hard to say how long he can last in there."

Without knowing their actual location, retrieving them from imaginary space was a complex undertaking. Newton began to gradually confirm whether any coordinates contained any trace of Xing Qingfeng. The unobservability of imaginary space gave him a headache. Without precise instruments, searching alone was like looking for a needle in a haystack.

But just as Newton was calculating, a golden diamond suddenly appeared out of nowhere in the air not far away.

——This means that Xing Qing has come out, or maybe part of it has come out.

"Not bad." Newton raised his eyebrows and smiled with satisfaction, "This kid has made much greater progress than I imagined."

------------------

I tried my best to use high school knowledge to describe the imaginary space. Apart from Hilbert, the other parts should not be too beyond the scope.

There may be some loopholes in the details, but don't worry too much.

In fact, the original text of the mushroom's imaginary space actually said "challenging the field of negative numbers". No, man, these two are completely different concepts. Negative numbers are still on the real axis, and imaginary numbers are a separate imaginary axis that constitutes the complex plane. Most of the time, they can be used to express the value of the rotation. I was still quite nervous when I saw this paragraph (

By the way, is there any servant that is more in line with the Kyoto style for me to refer to?

New author, new book, please vote and give me some review suggestions, thank you!

Volume 59: The Alchemist's Apprentice from the Fourth War: . Fuyuki Senbei II

Xing Qingqiu slumped on the living room sofa, lazily basking in the early winter sunshine. The sunlight streamed in through the floor-to-ceiling windows, bringing waves of warm comfort. The trees outside were bare, with only a few stubborn leaves swaying on the branches. A gentle breeze rustled, bringing a hint of cool air, as if reminding him of winter's presence. Xing Qingqiu half-closed his eyes, savoring this rare moment of leisure.

In the living room, sunlight cast dappled shadows on the floor, and the air was filled with a faint woody aroma and the rich aroma of hot butterbeer. An open book and a glass of beer lay on the small coffee table next to the sofa. The aroma blended with the cold breeze outside the window, making it particularly pleasant.

The aroma of hot butterbeer, with its subtle sweetness and rich buttery flavor, added a unique warmth to this early winter afternoon. Qingjiu's eyes occasionally glanced across the pages of the book, then lazily shifted to the window, feeling the gentle comfort of the winter sun.

The midday news was playing on TV, and the anchor's voice came to my ears: "Now reporting international news. This morning, around 3: Japan time, an unidentified falling object suddenly fell from a high altitude in the afternoon sky of New York City, crashing into Wall Street and causing an uproar. According to eyewitnesses, the shape of the unidentified falling object resembled a person."

Xing Qingwu listened attentively to the reporter's description. He stretched, the beer glass in his hand gleaming golden in the sunlight. He took a sip of the hot butterbeer, savoring the sweetness and richness of the warm, mellow liquid on his tongue, bringing a long-lost sense of relaxation and comfort.

"The accident occurred around 1 p.m. local time. After the incident, local police and relevant departments rushed to the scene to investigate and deal with the matter. At present, there is no detailed information and exact cause of the incident. The police have blocked the area where the incident occurred and called on citizens to remain calm and not believe rumors." The voice of the news anchor continued to echo in his ears.

The atmosphere in the living room was exceptionally cozy. Sunlight cast patches of warm light on the floor, and the aroma of hot butterbeer filled the air, perfectly matching Qingjiu's lazy mood. Although it was a slightly chilly early winter day outside, the sunlight was warm enough, and together with the atmosphere of the room, he immersed himself in his own little world.

"It is worth mentioning that this falling object was called the 'Wall Street meteor' by those who were curious about it, and many people believed that it could bring good luck. This statement spread rapidly on social media, and even prompted some citizens to go to the scene to pray, hoping to be touched by good luck." The reporter added.

"A shooting star on Wall Street..." Xing Qingwu's lips curled up slightly. "Does this count as leaving a legend on Wall Street to some extent?"

Normal people leave legends on Wall Street through financial means such as stock trading, but this person left a legend on Wall Street through physical means.

In fact, when Xing Qingjiu escaped from the imaginary space, although the Uruk Cup, the source of magic, landed correctly on the beach in Fuyuki, his body inexplicably ended up in the skies above Wall Street. Without the magic, he couldn't return to Fuyuki through imaginary submersible navigation, so he had to rely on Newton to bring him back.

By the way, when Newton saw that Xing Qingwu fell on Wall Street, he had a sullen face for some reason, as if he was recalling some unpleasant past events.

I guess he was recalling the only defeat of Lord Niu.

Suddenly, the doorbell outside the Matou residence rang. The crisp ding-dong sound pierced the quietness of the room, interrupting Xing Qingjiu's thoughts. He sat up lazily on the sofa. The TV news was still broadcasting international events, but his attention was completely drawn to the doorbell.

He put down his glass, stood up, and peered out the window with a hint of curiosity. The courtyard outside was quiet and tidy. The bare trees swayed gently in the breeze, and a few withered yellow leaves swirled in the air before slowly falling. On the stone paths of the courtyard, sunlight and shadows intertwined, forming a beautiful winter scene. He squinted his eyes and tried to look towards the door.

——It turned out to be Waver Velvet.

Xing Qingfu, who was too lazy to move, manipulated the Moon Spirit Marrow Fluid to probe out from the crack of the door, opened the door for Weber, and let him in.

"What are you doing here?" Xing Qingfeng poured Weber a cup of hot beer and asked casually, "Are you in such a hurry to sign the agreement?"

Weber took the butterbeer and was about to say thank you when Xing Qingjiu choked on his words. Xing Qingjiu was an expert at bringing up irrelevant issues.

Before coming here, Weber had been constantly encouraging himself, preparing for every possible scenario. However, Xing Qingjiu's words immediately brought him back to his original form. Although his timidity had largely faded, Weber still seemed a little timid.

"I... I'm here to find Sir El-Melloi..." Weber's voice was low, almost a murmur, as if he was not sure whether he should come.

After hearing this, Xing Qingyu raised his eyebrows slightly: "Ah, he's upstairs, I'll call him down for you." He originally wanted to call Kenneth down directly, but considering that the other people in the Matou family were taking a lunch break at this time, he finally decided to knock on Kenneth's door with the Moon Spirit Marrow Liquid.

Soon, Kenneth came down the stairs. His footsteps were particularly clear in the quiet room, and each step seemed to beat against Weber's nervous heart. The sunlight shone through the window onto Kenneth's golden hair, and the glittering light made Xing Qingqi feel that his golden hair looked like a lemon gleaming in the sun.

Kenneth's eyes swept across Weber's nervous face and asked jokingly, "Weber, what's the matter?"

Waver took a deep breath and tried to calm himself down: "Sir El-Melloi, I..."

Kenneth interrupted him before he could finish, "You're not qualified to address me that way yet. Do you think you've graduated?"

"Keep calling him Mr.! I told you that in the first class. As a student, you've forgotten how to address your teacher. Do you expect me to teach you what a student's duty is?"

Weber was stunned and quickly changed his words: "Yes...Mr. Kenneth..."

Xing Qingqiu found the scene rather amusing, watching Weber's trembling expression. He leaned back leisurely on the sofa, continuing to savor his Butterbeer. The sun shone right on Kenneth's head, reflecting a golden light. From Xing Qingqiu's perspective, Kenneth's head looked like a lemon gleaming in the sun. This made him stifle a laugh, which was painful.

Kenneth poured himself a beer and looked at Weber sternly: "What's the matter? Didn't I ask you to come back to the Clock Tower to see me in a week? You can't afford the ticket back to England, right?"

Weber took a deep breath, forced himself to calm down, raised his head and looked directly at Kenneth: "I...I don't plan to go back to the Clock Tower so early."

"Oh?" Kenneth said disapprovingly, "Are you planning to break the contract?"

"I'm sorry, but even if you force me back, I'll find a way to escape..." Weber was quite uncharacteristically tough in front of Kenneth. "I have something I must witness."

"My king wants me to go from east to west, following the path he took to conquer the east, to witness the territories he conquered."

"Really?" Kayneth raised an eyebrow and asked with interest, "So you intend to break the promise you made to me and disobey the El-Melloi family. Am I right in understanding this?"

"No... I..." Weber's courage was shattered by Kenneth's questioning. "I will return to the Clock Tower eventually. I promise."

"Really?" Kenneth downed the beer in his glass. Just as he was about to get another from the pot, he found that Xing Qingfeng had already finished it. "It's just that he broke the contract for selfish reasons. Why bother to say it so righteously? Don't you agree, Xing?"

"Ah, this guy is trying to get out of this with me." Xing Qingyu quickly realized Kenneth's intention of throwing the topic at him. He thought to himself, "Why not just agree directly? Why go through so many twists and turns..."

"I think it's quite good," Xing Qing Liuba Jiuwu Xia Ling④ Lingwu Feng said. "He won't be able to extract much value from the Clock Tower now. It seems he can't even live independently. Unripe fruit is not worth picking." Xing Qingfeng yawned. "It's better to hang it on the tree and wait for it to mature before picking it."

"That's true." Kenneth nodded with satisfaction. "I agree. Thank me for my kindness, kid."

"Why, is there anything else?" Kenneth saw that Weber was hesitant, as if he had something to say but couldn't.

"Well, thank you for your generosity...it's just..." Weber was no longer intimidated by Kenneth, but rather felt embarrassed to speak. "I had almost spent all my money when I came here..."

"If you have anything to say, tell me immediately!"

"Um... could you..." Waver's face flushed with embarrassment. He hesitated for a long time before saying the following words, "Could you... lend me some money for the journey..."

"Huh?" Kenneth felt a little amused. "You stole my relics, took everything with you, and fled to Japan on a plane overnight—"

"—And then, you're asking me to borrow money for the journey?" Kayneth sneered, "Webber Velvet, I never thought your biggest gain from this Holy Grail War would be a thick skin."

"Yes...I'm sorry..."

"Ah, just go there, there's no need to pay." Xing Qingfeng gave another well-timed gift. "Give us travel expenses, and it'll become a school trip. I think it's great to travel while working."

"Well...if you're short of start-up capital, I can help a little." Xing Qingfeng wrote a note and handed it to Weber. "Just go to this address and wait for me. Go ahead."