Alchemy Principles of Type-Moon World

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NTR is actually a sensitive word, damn.

A patch was made to allow one of Ptolemy's Noble Phantasms to unfold in a more reasonable way.

I'll see if I can spare some time in the next two days to catch up on the overdue update.

New author, new book, looking for votes, comments and feedback. In fact, I would be very happy if you cast some free recommendation votes (

Volume 57: Alchemy Apprentice from the Fourth War: . Primal Life ① Mountain Cage IV Strikes

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"Is that meteor still there?" Xing Qingqiu, who had left the inherent barrier, subconsciously looked up at the starry sky. The shining meteor he had just seen not only did not leave the night sky, but became more obvious.

On a night on the Fuyuki Coast, moonlight shimmered like water across the shimmering sea, and a gentle breeze brought a touch of coolness. The waves gently lapped against the beach, emitting a low, melodious sound. The meteor Xing Qingfeng had seen earlier split the night sky, streaking across the horizon, trailing a long tail.

"Wait, that thing isn't coming this way, is it?"

The meteor didn't fade from the sky, but grew larger and brighter, as if possessed of some unstoppable force. Its tail burned like a flame, leaving a brilliant trail across the night sky as it moved. The meteor's light grew ever brighter, gradually dimming the surrounding stars and obscuring the moonlight in its dazzling brilliance. The entire Fuyuki Coast seemed engulfed in a sea of blazing light, the fine sand on the beach translucent in its reflection, like a vast silver ocean.

"Teacher, are you going to pull a meteor to hit someone?" Xing Qingfu was very calm. It was just a meteorite that he was going to pull to hit someone. He had seen a lot of things in the world. It was just a meteor that he was going to pull to hit someone.

He had never seen this before.

Xing Qingfu subconsciously prepared to change his coordinates and throw himself back into Iskandar's inherent barrier. He still wanted to see how Newton hit people.

However, because he had never accurately grasped the relative position relationship between the coordinate systems, and the relative position between the inherent barrier and reality was constantly changing, he could only estimate the coordinates of his target position in the inherent barrier.

If Xing Qingfeng had not calculated the accurate relative position relationship and the equation describing its motion, and had only used this ambiguous answer to deal with Newton, Newton would probably not only not give it to him, but would also double the workload.

"We still have to find a way to calculate the analytical solution." Xing Qingyu felt the fluctuations of magic power in front of him, "If we use Hilbert space to process it..."

Hilbert space is a generalization of Euclidean space, which is no longer limited to finite dimensions. Infinite-dimensional Hilbert space is a generalization of n-dimensional Euclidean space and can be regarded as "infinite-dimensional Euclidean space".

In this world, Newton told Xing Qingjiu that inherent barriers or alien spaces, etc., can all be processed and calculated through Hilbert space.

Does this mean that the mathematical expansion of "dimension" has practical significance?

Without more actual evidence, it cannot be solved.

His thirst for knowledge once again filled his mind, forcing him to fork out a thread to block out these distracting thoughts. Xing Qingfeng always avoided thinking about problems that couldn't be solved, locking them away deep in his mind. But no matter how much he blocked out the distracting thoughts and locked away the doubts, one thought always lingered in his mind:

If we extend the real linear space to the complex linear space, that is, introduce imaginary numbers into the calculation,

——Imaginary number sneaks.

Xing Qingfeng recalled the concept of imaginary space mentioned by Newton. He once quoted Leibniz, whom he had always disliked in his youth, to describe imaginary numbers:

"—Imaginary numbers are a wonderful and strange retreat for the gods, almost an amphibious entity that exists and does not exist at the same time."

To put it simply, the relationship between real numbers and imaginary numbers, if represented by a number axis, can be regarded as the horizontal and vertical axes of a two-dimensional plane, with real numbers as the horizontal axis and imaginary numbers as the vertical axis.

Xing Qingyu's fingers slid across the ethereal [Dream|^First Breath, as if touching the imaginary axis that was perpendicular to the real axis.

Then he fell into the sea of imaginary numbers.

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The impact of the laser cannons was like a blazing torrent, crashing down upon the Silver Shield's defenses. The sun blazed high, and the entire desert seemed like a vast furnace. The air was filled with a scorching heat, making even breathing difficult. The desert sand, shimmering metallically in the heat, seemed to burst into flames.

Under the impact of the laser cannon, the Silver Shield Soldiers struggled to resist the destructive energy. Their shields burned intensely in the heat, their silver surfaces distorting with a harsh hissing sound. Sweat covered the soldiers' faces, dripping like raindrops and evaporating quickly on the ground, forming a series of blurry vapors.

Waver stood behind the formation, his hands clenched, a feeling of powerlessness filling his heart. He had already used up his remaining two Command Seals: one to repair Iskandar's body and restore his mana, the other to simply supply his magic. He stared at the blazing beam of light before him, a deep sense of shock and fear filling his heart.

"How can there be such a huge amount of magical power..." Waver muttered to himself, his voice almost choking.

He couldn't understand how the other party possessed such immense power. Just now, their own forcible use of magic to liberate Ptolemy's Noble Phantasm had nearly exhausted Iskandar's stored magical energy. And now, the other party's output was fourteen times that of Ptolemy's Noble Phantasm, and it was still increasing.

It's known that a single day's sleep at a Spiritual Vein node provides roughly the same amount of magic power as Iskandar needs to free himself from his spirit form. Let's assume that fifty Webers would need to sleep at a Spiritual Vein node for a single day to power Iskandar's King's Army.

In the original novel, Iskandar's battles and the two deployments of the King's Army, including a major battle with the sea monster, all relied on Iskandar's own stored mana. Therefore, we can assume that Iskandar's stored mana is at least equivalent to the amount of mana provided by one hundred and fifty Webers sleeping in one day.

As for Ptolemy's recent shot, let's calculate it at 100 Ve. Assuming Newton's output rate increases by 12600% every half minute, the amount of magic power released by Newton so far is approximately Ve.

The answer is the 10,000-strong Weber army vs. the King's army!

Fierce winds whipped up yellow sand, sending clouds of dust dancing across the sky, as if foreshadowing impending destruction. Under the onslaught of the laser cannons, the Silver Shield soldiers' steps grew heavier, their shields and weapons scorching from the intense heat.

"Concentrate! Never retreat!" Iskandar's voice was like thunder, echoing over the battlefield and inspiring the morale of the soldiers.

Strategy: B, which grants favorable bonuses when using your own anti-army Noble Phantasms and countering those of the enemy. Iskandar decisively ordered the reorganization of the formation just before Newton's arrival, significantly improving the formation's defense against subsequent laser cannon attacks.

The power of the light cannon grew with each passing moment, its destructive force raging through the army like a giant dragon. The Silver Shield soldiers' defensive formation gradually weakened under this fierce attack, and the magical patterns on their shields began to flicker, as if they would collapse at any moment.

The desert sand began to transform under the intense heat, its loose grains gradually congealing into hard, glassy masses. The sand on the ground became scorching hot under the blazing sunlight, and the air was filled with a scorching smell, as if it would burst into flames at any moment.

The soldiers' arms holding their shields grew heavier, their armor gradually deformed in the heat, making it difficult to move. The sand beneath their feet became sticky in the heat, as if it was sticking to their footsteps.

"That Caster guy's offensive is still growing," Iskandar sighed, his gaze fixed on the terrifying magic power that was constantly gathering in the distant prisms. "He has bound my army here, yet he doesn't restrict any movement except displacement—I don't know if he's being overestimated or underestimated."

His voice sounded particularly firm under the scorching sun, but the sweat on his forehead revealed his inner nervousness and excitement.

"King, given the enemy's increasing damage output, we can only hold out for three minutes at most." Eumenes stood aside, his tone heavy, "If there is no other way to break the deadlock."

Iskandar roared with laughter, his voice echoing through the desert. "Hahahahahaha, so strong! That guy is too strong!" His eyes gleamed with an undying fighting spirit. "To be able to challenge such a difficult challenge after death is truly thrilling!"

Iskandar's bold words were met with a chorus of roars from the soldiers. Their roars shook like thunder, echoing across the desert. Every soldier gritted their teeth in the scorching heat, holding their ground. Their hands gripped their weapons tightly, their eyes burning with determination to fight alongside their king.

"Hahahaha!" Iskandar patted Waver, who was hiding behind him, his voice full of pride. "Hey, kid, remember this!"

"It's because it's out of reach that we have to challenge it, it's because we can only look up that we have to climb it—"

“—This is ‘Glory is in the distance.’”

Waver watched nervously, his face covered in sweat. He clutched Iskandar's cape tightly, as if this could provide him with a little comfort and strength. He knew they were facing an unimaginably powerful enemy, and Iskandar's bold words were undoubtedly his greatest encouragement.

"Look, the light is higher than the Hindu Kush peaks and hotter than the hot sands of Makran!" Iskandar's voice was filled with endless excitement and anticipation.

At this moment, what filled his heart was not the open-mindedness that came from understanding the insurmountable gap in strength between the enemy and himself, nor was there any sense of giving up or despair at all.

——The only thing that was beating in his chest was the excitement of seeing that unattainable goal.

This heroic sentiment, this bond of trust between the king and his soldiers, was deeply etched in Waver's heart. Tears welled in his eyes as he gazed upon the king, who stood tall and unwavering under the blazing sun.

"But it seems we can't hold out for more than three minutes." Iskandar narrowed his eyes slightly, gazing at the distant sky. Amidst the blazing light, an asteroid was hurtling towards the army formation, its trail slicing through the sky, bringing with it a foreboding of destruction.

"Hey, kid!" Iskandar suddenly said in a serious tone, "I suddenly remembered something I must ask."

"...What?" Weber raised his head, the tear marks on his face gleaming in the sunlight, and his voice trembled slightly.

"Webber Velvet, do you wish to serve me as a subject?"

"Ah..." The sudden surprise overwhelmed Waver's mind. He trembled with excitement, and even tears welled up in his eyes. His heart was beating so hard it seemed like it was about to jump out of his chest. He nodded vigorously.

"Hey, kid, why are you crying again..." Iskandar looked at Weber's excited expression, but a hint of tenderness flashed in his eyes.

"Only you are my king!" Waver replied passionately, not even bothering to wipe away his tears. "I am willing to serve you and sacrifice for you. Please guide me and let me see the same dream as you!"

"Very good!" Iskandar patted Waver's shoulder with such force that Waver stumbled. "But you're still a little unqualified!"

"Your vision is still too narrow. I was hoping to broaden your horizons in the Holy Grail War, but it seems there's nothing else interesting to see besides this final battle."

"Then I..." Weber was a little overwhelmed, his hands clasped together tightly, as if seeking a little comfort.

"Hahahaha, I already acknowledge you. You just need more experience," Iskandar consoled Weber. "Remember this scene in your heart. Live well, witness it all, and then tell the story of it all."

Endless gratitude and determination surged in Waver's heart. He nodded vigorously, tears streaking down his cheeks.

"Start your journey from this place in Japan. Head westward, from Asia to Europe, and follow the path of my eastern conquest. Witness the roads I once conquered, and return to my homeland."

"Yes... yes!" The tears in Waver's eyes could no longer be stopped, and they flowed down continuously. His voice trembled with excitement, but his tone was firm.

"Alas... If you want to be qualified to be my subject, the first thing you must do is to stop crying so easily!" Iskandar smiled and slammed his head on Weber's forehead with great force but full of tenderness.

"I will send you out of the inherent barrier before the last moment arrives."

"Until then, you just stand here and bear witness." He turned around and looked back at the still dazzling light with a fearless smile on his face.

Asteroids in the sky, trailing fiery trails, hurtled toward the army at astonishing speed. A flicker of determination flashed in Iskandar's eyes. His lips still wore that heroic smile, but his expression grew even more resolute.

"Everyone, prepare for defense!" Iskandar's voice resounded like thunder across the battlefield. The soldiers quickly adjusted their formation. The shield soldiers beside the silver shield soldiers raised their huge shields above their heads, forming a solid line of defense.

Under the reasonable arrangement of the military formation, the silver shield soldiers were responsible for dealing with the impact of magic, while the shield soldiers were responsible for dealing with physical impact. Together with the cavalry in the team, the coordination of different types of soldiers constituted the invincible combat effectiveness of the Macedonian phalanx, and finally swept across Europe under the leadership of Iskandar.

However, this time they are facing an asteroid.

To be honest, during the heyday of the Age of Gods, only a very small number of astrologers could accomplish this.

Only those who have reached the pinnacle of celestial magic can interfere with celestial bodies with the help of the magic power in the sky.

However, Newton did not use any force at all. He pulled an asteroid down, changed its coordinates when it was about to land, and threw it into the inherent barrier.

As the meteorite approached, the air grew unbearably hot, and the ground shook violently. The moment the meteorite streaked across the sky, the entire heavens seemed to be torn apart, and a fiery light illuminated the entire desert. The flames illuminated the surrounding yellow sand, which shimmered in the heat, flowing like molten metal.

"Boom!" The meteorite slammed into the center of the army formation, creating a deafening explosion. The powerful shockwave instantly ripped through the Silver Shields' defenses, sending debris and dust flying. The entire formation was completely shattered. Soldiers were blown away by the massive shockwave, their shields and spears scattered to the ground. A deep crater instantly appeared in the ground, and the scorching air currents swept up the surrounding sand, creating a misty cloud of dust.

"Okay, kid, that's it. Remember everything you have witnessed and live well!" Iskandar's voice was still clear in the smoke and dust. His firm gaze penetrated the dust and looked into the distance.

The formation's structure was completely shattered, and the Silver Shields, unable to maintain it, were forced to bear a greater impact than before. Their equipment began to melt under the intense heat, molten liquid dripping from the metal surface with a harsh sizzling sound. Grimaces of pain crossed the soldiers' faces, sweat mixed with blood, streaming down their cheeks. A wave of intense heat swept through, and the air was filled with the smell of burning.

The Silver Shields' defenses completely collapsed. The intense light engulfed the entire formation, its scorching heat distorting everything. Soldiers groaned in agony under the blazing light, and the battlefield became a sea of fire. The sand on the ground was melted into glass by the intense heat, and the shattered glass reflected the glaring light, as if the earth itself were weeping.

Iskandar remained standing, his figure steadfast in the light. Flames and light swirled around him, but he remained unmoved.

Ultimately, the power of the laser cannon completely destroyed the army, dissolving the entire formation in a haze of light. The soldiers' silhouettes gradually blurred, eventually vanishing into the light. With Iskandar's disappearance, the inherent barrier collapsed, releasing Newton and Kenneth.

"Ha, now I understand why that astrologer from the Wandering Sea always loves to drop meteorites on people," Newton said with a refreshed expression. "No matter what formation the enemy has laid out, throwing a meteorite down can wipe it all out. It's truly a very satisfying approach."

Newton looked around but couldn't see anyone else who was supposed to be there.

"Where did that Xing Qingfeng kid go again?"

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I have tried to make the mathematical expressions in this article as simple as possible, so I have omitted a lot of details, but it should not affect understanding.

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The emperor left the stage just like that. I feel quite satisfied with the character creation. What follows is the end of the Holy Grail War.

By the way, it's time to put together the detailed outline for the next volume. The plan is for an original Kyoto Holy Grail War. Although the direction of the plot is roughly planned, I haven't decided on the candidates for Lancer and Bercerker yet. I wonder if anyone has any ideas. You can chat about it in the book reviews or in the thread. Thank you!

New author, new book, please vote, comment and feedback, thank you!

Volume 58: The Alchemist's Apprentice from the Fourth War: . Mathematical Bridge, God's Formula

I can't see anything.

How can I describe this feeling? Dark? Murky? Dull?

No, none of them are right.

It's not so much the feeling of being in some deep place, but rather the feeling that what you can see doesn't exist at all.

I couldn't even tell if my eyes were open, except that I was thinking and calculating -

——I can’t even sense whether my own body exists.

He tried to sit up, but he had no idea whether he was standing or lying down. He wanted to make a sound, but he had no idea how to move his throat.

Unknowable and unfeelable.

The most intuitive way for humans to understand the world is to directly understand it through the five senses, and the same is true for the understanding of mathematics.

A stone plus a stone equals two, just like adding the two stones upside down.

A simple understanding of the commutative law of addition.

With this, humans established the first mathematical system, which was established through simple observation of the world, summarizing and "abstracting" it.

Although there was abstraction, the mathematics of that era was always based on intuitive cognition, and a considerable number of mathematical theories at that time relied on the method of "combining numbers and shapes" to be proved.

This is why, even though negative numbers have long been used in practical calculations, humans have always found it difficult to accept their existence. Negative numbers weren't defined until Peano formally defined integers, and that was less than 300 years ago.

Humans accepted the concept of negative numbers, which had no intuitive basis in reality, and realized the non-intuitive nature of mathematics. They finally accepted the fact that mathematics was not entirely based on reality and that its field could not be described by human intuition.

Because of the rise of financial concepts, and the concepts of debt and deficit are deeply rooted in people's minds, we may be able to imagine a "negative" stone -

——But we cannot imagine an “imaginary” stone.

Therefore, for the intellectual individual, the so-called "imaginary space" is unknowable and unperceptible. We cannot intuitively understand imaginary numbers, even though imaginary numbers have applications in physics.

——It is essentially something that does not exist in reality.