Advanced Spellcraft: Second Lecture
Arienael arrived at the lecture hall for Advanced Spellcraft with plenty of time to spare before class started, but the professor was already there waiting.
Professor Kauli, who taught Advanced Spellcraft, was dressed in his usual neat suit today as well.
"Good to see you all. Unlike last time, we're doing a proper lesson today, so pay attention."
Professor Kauli skipped roll call and dove right into the lesson.
"Everyone knows the three elements of magic, right?"
It was the same topic that had come up in Atwill's class just earlier. No one answered what felt like a question treating them like idiots.
Professor Kauli didn't wait for a response anyway.
"Right. Mana, mana circulation, and spells. So why are these the three elements of magic?"
Unlike the previous question, this one wasn't something most students had ever pondered, making it hard to answer on the spot. Of course, the Spellcraft majors knew the answer to this too.
"It's because the very definition of magic stems from these three. Magic means using mana as a resource, circulating it through mana circuits, and manifesting it via spells. If even one is missing, it's not magic."
Arienael, who hadn't delved deeply into magic spells despite being in the magic department, found the following content intriguing as well. The Spellcraft class hadn't gotten into full-blown formula disassembly yet, so it wasn't all that difficult.
"The holy spells used by priests and holy knights aren't actually magic. They use divine power as the resource instead of mana. Shamanism uses mana as a resource and takes the form of spells, but it's still not magic. There's no process of forming mana circuits to circulate mana. Swordsmen who reach enlightenment circulate mana through their own unique circuits in their bodies to strengthen themselves physically, but we don't call that magic either. No spells involved."
A few students started taking notes at this point. Arienael jotted down notes too, but a question popped into her mind.
What about spirit arts?
She didn't raise her hand to ask, but Professor Kauli addressed it soon after.
"Spirit arts are a bit tricky. They use the power of nature but also mana. The driving force is affinity with nature and spirit resonance, so mana circulation is sometimes there, sometimes not. There's debate on whether spirit summoning counts as a spell. Spirit arts are so different from other magic that we classify them separately, but it's not definitively not magic. More accurately, there's no consensus yet."
Arienael quietly summoned a spirit for a moment. The sensation was definitely very different from casting magic. She'd thought it was just because she was an elf feeling spirits specially, but apparently humans felt it the same way.
Not wanting to draw attention during class, she greeted the spirit and sent it back right away.
"But mana capacity has limits. You can increase it with effort, but the efficiency and ceiling of that effort vary by person. And those traits differ individually—you can't just change them on a whim. Mana operation is the same. Just like you don't need special tricks to move your hands or speak, talented people handle it freely without training. You can teach the clumsy ones to reach average, but you can't make the skilled even better."
Professor Kauli's words filled the Spellcraft majors with pride. Even non-majors like Arienael could relate.
Mana traits and capacity were mostly set from birth. Once you reached a level called a 'mage,' training just mana operation alone didn't mean much.
"That's why you study Spellcraft. The only thing you can overcome through learning is 'spells.' Plus, studying spells is the path to surpassing your own limits. The way to circulate mana efficiently is to construct formula circuits well. And with well-constructed circuits creating efficient circulation, you can get high output even with less mana."
But Professor Kauli's argument had a bit of self-contradiction. As a Spellcraft major himself, he overlooked the obvious fact that not everyone was equal in constructing spell formulas.
Just two days ago in class, he'd talked about a formula only one person in the world understood.
Professors at a magic university were ultimately experts in their field. Just as Kauli himself couldn't match Atwill in formula invention, he unconsciously ignored how his own level was unattainably high for most people.
"So how do you construct circuits? To learn that, you need to dissect every magic circle you've memorized so far one by one. As you all know, the most important part is the circle."
A large bright blue circle of mana appeared in the air, drawn with mana power.
Some students recalled spending hundreds of attempts in the academy just to draw a perfect circle.
"Barring a few exceptions, the basic structure of magic circles is a circle. Polygons or radial ones exist, but they're ultimately variations of circular formulas."
Professor Kauli drew an equilateral triangle, square, hexagon, octagon, and so on next to the circle.
He especially enlarged the hexagon for emphasis.
But there was no pentagon.
No one asked why; everyone knew.
Below them, he lined up several radial magic circles too. Clover-shaped ones, cross-shaped, hexagram ones—various kinds.
Again, none with five points.
"These irregular magic circles are only used in special situations. And since the basis of magic circles is 'circulation,' none deviate from rotational symmetry. There are more strict rules like that than you'd think. People say constructing magic circles is 'free and limitless,' but you can't just draw them willy-nilly."
Professor Kauli began drawing a few more shapes. They varied in size and form, but had one thing in common.
They were ellipses.
"You don't see elliptical magic circles often. Many of you are seeing them for the first time, right? That's because they're rarely used. No reason to."
One student raised a hand.
"Do those even work?"
"Yes. Surprisingly, they do."
"Then why not use them? Seems convenient to stretch them out long like that."
"You're asking if you can't just draw big ones in narrow spaces because they're elongated?"
"Yes."
Because of their long, narrow shape, many objects couldn't accommodate large magic circles. Arienael thought of the sword from that morning's class. That ferocious sword gleam was still vivid in her mind.
"That's exactly the reason."
Professor Kauli answered fluidly, as if he'd heard it a million times.
"A magic circle's output depends on its size. Correct. The issue is 'what defines size.' Area? Or length? Circular ones grow in area as diameter increases, so no need to worry."
The conclusion was obvious to everyone. The professor had already said elliptical ones weren't used.
"But research on elliptical magic circles revealed this: length matters. Specifically, not the major axis, but the minor axis. An elliptical magic circle's output is determined by the length of its shortest axis."
The students, excited by the new knowledge, deflated.
"So forcing an elliptical one onto a long object is worse than just drawing a small circle. Easier to draw, more stable too."
Arienael imagined an ellipse stretched to dozens of times its minor axis. Even if there were advantages, she had no confidence in drawing it flawlessly.
"This was proven again in Professor Atwill's 3D formula research. His paper showed examples not just spherical, but elongated or flattened ellipsoids. Ultimately, even in 3D, the shortest axis determines output."
Arienael, starting to feel bored, suddenly snapped awake.
She'd let her guard down, and Atwill's name popped up again.
Right after this class, back to Atwill's lab. Not even a week into the semester, and her future already looked bleak.
What’s that guy doing right now?
"So, what did you come to ask?"
I'm sitting face-to-face with Stella Rackton at a campus café.
Since Arienael left for class, our conversation had been nothing but pointless small talk.
She'd build up like she was leading to something important, only for it to fizzle into chit-chat.
Thanks to that, I learned she's the eldest daughter of the Count of Honlake territory.
No wonder the name Rackton rang a bell.
Honlake wasn't far from the university.
I might've been interested up to there, but she didn't stop. I ended up knowing she grew up spoiled despite being the eldest because of her two older brothers, and that she dotes on her two younger sisters—useless info.
She's currently in her third year of the magic department, same age as me.
Wait, why do I need to know any of this?
She started like she was confessing some family secret I couldn't interrupt, and I missed the chance to cut her off.
In the old days, I'd have stormed out regardless of lady's etiquette, but as a professor now, I didn't want to insult an undergrad like that.
"You still haven't gotten to the point."
Same age, huh. I got my degree faster than peers, sure, but at my age, undergrad should've been done.
People do enter late and graduate late sometimes.
But she's nobility. If nobles send a daughter to magic university, it's usually right after academy.
Otherwise, age catches up. Stella's old enough that being married three years ago wouldn't be weird.
For a count's daughter to enter magic university so late and still be in undergrad past twenty? Unnatural. Family doesn't seem strapped for tuition either.
"There must be a reason you called me out."
"It's refreshing hearing you talk so casually! Makes the rumors seem true?"
She's propping her chin on both hands, grinning ear to ear.
Opposite of me leaning back, she's bent way forward. The table's so small her head's halfway over it.
"Rumors?"
"Arrogant, rude, self-centered, prickly weirdo?"
"......."
"Ah! Sorry. Shouldn't say that to your face."
"Whatever. Get to the point."
My reputation's been in the gutter forever. Didn't even feel rude.
She thinks it's a joke, probably.
Why drag it out like this?
Her actual purpose was, predictably, outside my expectations.
"You know your way around swords?"
I wondered what it'd be. Thinks I'm some illiterate sword-slinger? Major insult.
"Do I look like it?"
"No!"
"Then why ask?"
"That one you showed in class—it wasn't ordinary, right? I could tell."
Curious about that, huh.
Origin's no big secret, so I answered honestly. No way she'd ask to see it drawn here in a café.
"Yeah. Imperial Knight Order sword. Got it while studying at Imperial University."
"You got that? How?"
"Does it matter?"
Odd for a girl her age to fixate on a sword like this.
Should've left it behind if I'd known it'd cause hassle.
"Not illegal or anything weird. Legitimately obtained. But not something to blab about."
"You took it fair and square from a knight? A mage from a knight?"
Stella Rackton kept her bubbly, lively tone to the end.
Like insisting it was pure curiosity. No hint of blame or scolding.
But I'm no fool to miss her intent from word choice alone.
She chased me down over that one sword and spun all this yarn.
Whatever her goal, feels like trouble brewing.
Arienael was here, I'd have dodged with research talk.
Wonder if she's paying attention in class.