We took down the barrier, delivered the final few letters, and found Agnia waiting for us at the practice field. She was sitting on a bench, frowning at a stack of paperwork. No doubt, it was the paperwork that she had just caused for herself.

Without even glancing at us, she called out to us. "You two, come over here."

We walked over, and she addressed us while slowly running a pen over the topmost document on the stack. "You two are familiar with—"

"Professor," Natsuki interrupted. "What was that device you used back there?"

Agnia paused, but didn't look up. "...That's a REM, a remote electrogram monitor. It can detect electrical signals, so I was using it to check their heart rhythm. Which didn't exist. Because they were reanimated corpses. Any more questions? I will not answer any about necromancy, as it is illegal."

Natsuki scratched her cheek, and then smiled. "How does the REM work?"

"Lightning-trigram magic or something. Anyways, let's continue. You two are familiar with the basic logic of the eight trigrams, right?"

"Ob-viously." Natsuki let out a hmph. "The eight trigrams are the building blocks of magic, after all."

"Okay, then let's make sure." With one hand still holding the pen, she brought her other hand forward, and within that palm spawned a small fireball, the same kind as we generally call Firebolt. "What trigram is this magic?"

"Ob-viously, it's fire."

"It's lightning."

Wait, what? What about that is lightning?

—Agnia snuffed out the fireball, and from her palm arose small sparks, dancing in the air like falling flower petals. "What trigram is this magic?"

"It's..." Natsuki's voice came out quieter this time. "...fire?"

"It's wind." Agnia caught all the sparks in her hand, and lit a brightly burning flame at the tip of her index finger. "What trigram is this magic?"

"It's..." Natsuki gave up on answering, and I didn't dare answer either.

"It's fire." Agnia sighed. She snuffed out the flame, then moved the topmost document off the stack and onto the bench and started working on the next one. "Well, this isn't what we really need to do today, so I'll just give a quick explanation. The eight trigrams are an abstract system composed of four opposing pairs. Heaven and earth, symbolizing creation and destruction, associated with white and black—"

"Wait," Natsuki interrupted. "Isn't earth supposed to be purple?"

"The 'black light' that earth-trigram magic releases is, in scientific terms, ultraviolet, and therefore often appears to humans as purple. To continue. Fire and water, origin and evolution, red and blue. Wind and lightning, eternity and instantaneity, green and gold. Marsh and mountain, reception and rejection, cyan and orange. Whether you make flames or floods with your magic, the eight trigrams are only concerned with how you use them."

I had, in fact, heard these words before, but I had still assumed that magic that creates fire would necessarily be fire-trigram magic. I guess that assumption was a bit naive. Yesterday, when I was watching Agnia use her magic, I didn't see any red mana, despite all her magic being fire-based. I suppose that's because it had nothing to do with... "origin" as a concept.

"Professor, does that mean that yesterday, when you were showing us fire magic, the reason there was no red mana was because it wasn't fire-trigram magic?" I asked, to confirm.

"That is correct. The fire trigram is, in the first place, not suited for attack magic, which is primarily based on the lightning and earth trigrams, and secondarily on the wind and water trigrams. Well, I suppose that biological weapons magic is based on the fire trigram, but if you try doing that, then the God-Emperor will punish you in person."

"In person?" Natsuki repeated doubtfully.

Agnia looked up from the stack of papers and stared us both directly in the eyes.

"The God-Emperor will, in person, descend from the Inverted Castle, and, in person, exact divine judgement."

"Uh, if you say so..."

Divine judgement for... biological weapons magic? That sounds vaguely like some fable or another from the Gospel, but... isn't the condition a bit too specific? Normally it's like, if you use magic to do evil then you'll get bad karma, but... biological weapons? I had heard that the Church sometimes makes up fables and rules to the end of controlling people, but biological weapons... what kind of person would be influenced, one way or another, by a religious fable about biological weapons?

Agnia looked back down at her paperwork.

"Anyways, that's not what we need to focus on today. Yuki, I want to give you a basic idea of spellsword technique. Humanity's understanding of magic has advanced far faster than our ability to smith swords. Today, a master swordsman without magic could not even defeat a student at the Institute. If you do not learn how to mix magic into your sword technique, you cannot become a proper adventurer. Draw your sword."

I drew my sword, holding it with both hands in middle stance. "Professor, do you know swordcraft?"

"No, I don't. Now, put your sword... up."

"High stance?"

"Is that what you call it?" Agnia completed another document, and put it aside. "Put it where you can immediately swing it down."

I raised my sword so my hands were just above my head and the sword was parallel to the ground, pointing backwards. Natsuki stood right to my side and, unlike Agnia, watched me.

"That should work. Next, you need to bring your mana to your hands, and then move it to... the pointy part of the sword."

"The kissaki?"

"I have no idea what that means."

"It's the pointy part... I guess..." I drew my mana into my hands, like when casting magic, and then ran into the all-too-common problem of knowing what to do but not how to do it. "Uh, how do I move the mana from my hands into the sword?"

"How... Hmm... I guess you can... Hmm..." Agnia's pen stopped moving.

"Yuki." Natsuki put her hand on my shoulder. "When you wield a sword, you must consider it as a part of your own body. If the sword is part of you, then you can move your mana into the sword the same way you moved it into your hands."

Natsuki was the one who taught me how to wield a sword, so perhaps I shouldn't be surprised that her words cut through the problem so easily.

I felt the length and extent and rotation and position of the sword. The same way you know where your arm is even if your eyes are closed, I could tell where the sword was even though it was out of my sight. And the same way you draw mana into your hands in order to cast magic, I drew my mana down the length of the sword.

"Yuki, you're—"

Agnia tried to say something, but Natsuki interrupted her.

"Yuki, around halfway down the sword, your mana is leaking into the air. Remember. If your sword is part of your body, then you can feel the mana flow down its edge the same way you can feel your muscles tense and relax."

I focused once more, and restrained the leaking mana the same way I would restrain my breath. My mana flowed down the blade, and settled at the tip.

"Okay, that's good." Agnia didn't look up from her paperwork. "Next... you know how when you swing a sword, it makes a circle? Make the mana you made collect at the tip of your sword make the sword make a circle."

I was barely able to comprehend the syntactic structure of her words, and even less the meaning. All I could say was: "How?"

"Align the mana with water and lightning trigrams, then use it to create a force that pushes the sword along an approximately-circular path. Do note that you'll generate the greatest torque when the force is applied at the tip of the sword— that is to say, the point with the largest distance from the center of movement— in the direction perpendicular to the vector describing the difference between that point and the center of movement, which I suppose would be your shoulders. The centripetal force should be provided by the structural integrity of the sword itself, so keep in mind that as your technique develops, it will become necessary to work with swords less prone to collapse under stress of high tension."

I understood even less.

"...How?"

"Yuki." Natsuki spoke while holding back laughter. "In both spellcraft and swordcraft, the most important thing is attitude. Don't worry too much about the details. You want the sword to move in a circular path. That's all you really need to think about."

I understood a little bit.

I had a good sense of how the sword should move, and I had a good sense of the circular path that the tip of the sword should travel through. So all I needed to do was move the sword, but let it be guided by the mana at the sword tip as well as by my arms.

I brought the sword down, and felt a heavy weight at the tip of the sword, which speedily carried it along the circular path I had envisioned. The sword moved faster than I could normally move it, the same kind of feeling you get when you run full force down a hill. But it was magic, not gravity, which carried it along.

—Suddenly, I felt my left hand slipping off the handle of the sword.

When your left hand slips, it means that the sword has dropped too far. A simple stroke should end with your arms straight and the sword in line with your arms, 40 or so degrees downwards from parallel with the ground. I looked down and saw my sword falling further and further, carrying me along like a rabid dog on a leash. When it collided with the ground, I lost my balance and collapsed.