Advanced Spellcraft Orientation (1)
After finishing the lecture, Arienael approached me.
"Professor, you're surprisingly good at speaking."
"Surprisingly?" Her tone made it sound like I usually spouted nonsense. My professorial authority really was in the gutter.
"Honestly, I was a bit shocked. From the way you talk normally, I figured you'd just phone it in during lectures."
"Not far off, is it? What I said wasn't wrong, but it's the kind of thing you could say in any class. Even if I were teaching Spellcraft, it'd be pretty much the same content."
"Is that so?"
"Think back on what I said. 'There are so many factors involved in magic, and the qualities needed to become a great mage are endless, so even if it doesn't seem immediately useful, you should take this course.' Something along those lines. It's not a lie, but it's generic enough to slap on anywhere."
"Still, that makes you seem more serious about teaching methods than I thought."
Her tone had been grating on me from the start. What kind of professor did she think I was? Probably some sleazy type who couldn't care less about lectures and just exploited his students to churn out papers. To think I'd be saddled with such an absurd misunderstanding.
"It's not teaching theory—I'm serious about magic. That's genuinely how I feel. The biggest reason I reached this position at my age is that I acquired and utilized knowledge from all sorts of fields."
"Hearing you say that yourself..."
"It's not just me. Most great mages whose names live on in history were the same. You can't use what you don't know."
"So, if you want to create something new, you should first build up existing knowledge?"
"Exactly. So-called great inventions often don't have ideas that are all that groundbreaking when you look closer."
We'd arrived at the cafeteria while chatting. Since I'd ended class early, there weren't many students yet.
"Is that right? Whenever I see those kinds of things, I wonder how they even came up with the idea."
"That's because you're only looking at the end result. If you dissect the knowledge they learned and the processes they researched, it's an obvious conclusion. It's not 'How did they think of that?' Coming up with it when you already know the pieces is easy. It becomes 'How did they know all that?' Usually, they didn't set out to accumulate that specific knowledge on purpose. They piled it up, and then the ways to use it became clear."
"That sounds too complicated. Honestly, I don't quite get what you just said, Professor."
"Everyone says that. You'll understand once you study more."
"...Are you giving me more papers today too?"
"Of course. Don't want to?"
"No... I like it......."
Arienael's expression as she said that didn't look remotely pleased. She wanted to study but was too shy to admit it outright.
Before the first Advanced Spellcraft class began, Arienael arrived early and took her seat in the lecture hall. The professor in charge was already there. With thick-rimmed glasses and a neat suit cape, the middle-aged professor exuded a scholarly aura just from his appearance.
The atmosphere among the students was different from the previous class. Most of those taking Advanced Spellcraft were master's and PhD researchers. The youngest were graduating undergrads. Everyone was from the magic department, and more than half specialized in Spellcraft.
This also meant Professor Atwill had recommended Arienael for an excessively advanced lecture. But she was too overwhelmed by the vibe to think of that.
The professor, who had a stern rather than severe impression, didn't even take roll before starting.
"Pleased to meet you all. I'm Clyde Crowley, the professor in charge of Advanced Spellcraft. I assume everyone here has taken most of the undergrad Spellcraft major courses."
Arienael realized from this that professors didn't check prerequisites. Anxiety bubbled up inside her at the same time.
"I won't bombard you with convoluted magic circles right from the first class. No need to be disappointed, though. Haha. You'll see them until you're sick of it."
It was meant as a joke to lighten the mood, but it drew light boos from the students.
"You all seem thrilled. Today, I'd like to briefly cover the history of spell formula development. You've heard it many times before, right? But let's dive a bit deeper. Knowing the evolution makes it easier to understand the complex formulas we'll dissect one by one."
Some students' eyes lit up, while others looked bored, like they already knew it all. Arienael, unfamiliar with the topic, fell into the former group.
"The magic circles we use today haven't been around that long. Just two hundred years ago, they were incredibly simple. Like this—a single circle with a few lines scribbled in."
As he spoke, Professor Crowley drew a magic circle in the air, and it was indeed extremely basic: a small circle with an inscribed regular hexagon and equilateral triangle, and an inverted triangle inside. The kind of formula taught to low-year students at the academy.
"They didn't even have runes. Many formulas from that era had none at all—maybe one or two at most, six if you were lucky."
He paused briefly before posing a question.
"Why do you think that was?"
As an elf, Arienael could hear a student in the front row mutter "paper" softly. Professor Crowley, nearby, didn't miss it either.
"Yes, correct. At that time, there was no technique for drawing magic circles in midair like we do now. More accurately, they hadn't figured out how. For centuries after magic's invention, even after drawing magic circles, they were all physically inscribed on paper to activate. Or on walls or floors if not paper. The key point is they drew them directly, physically."
Crowley drew a few more magic circles in the air. All used thick lines like the first, rough and simple overall. Most lacked runes. One had just three runes in bold script.
"That's why complex formulas were naturally difficult. Modern intricate magic circles are affected by every detail: line thickness, color, size, placement, everything. As you know, even a slight mistake means it won't activate, backfires, or causes unpredictable results the caster doesn't anticipate. Knowing the risks, people back then preferred simple ones."
So that's how it was. Arienael had assumed they just lacked magical knowledge to draw complex formulas.
"Embedding hundreds of tiny runes like today? Impossible. They were already drawing directly on expensive parchment, which was hard to revise. Now we can check and fix instantly as we draw, but back then it took days. If the magic left traces on the paper during activation, you had to start over from scratch."
Making one parchment scroll required slaughtering dozens of lambs. Failing a single spell back then carried that much burden.
"That's why magic wasn't used for everyday trifles like now. Elemental magic dominated, mostly for combat. No need for precise mana control or complex formulas. Instead, surveying techniques and construction methods—the most crucial back then—advanced."
Attempts to express the most precise formulas possible within simple shapes. Those efforts laid the groundwork for today's complex formulas.
"Plus, as you all know, the most important way to boost magic power is the magic circle's size. They needed huge paper for larger circles. Some nations even carved them across entire castle marble floors."
Even in modern times, with advanced mana control and spell formulas, a magic circle's absolute size remains vital. Back then, it was the only way to increase output.
"This spurred papermaking advancements too. Thanks to developed paper and printing, we could publish magic papers like today. Mages dedicated their lives to vivid colors—the founders of color theory, they say."
The students thought something like "Life must've been tough back then," but Arienael recalled, "Come to think of it, paper's easier to get now than when I was little."
"This is where spell formulas underwent a revolution. Up to then, mages trained only absolute mana quantity and spell proficiency—nothing else available. But having too many options became a problem. Suddenly able to freely mix countless circles, polygons, lines, and runes, mages fell into chaos."
Professor Crowley drew several much more complex formulas than the earlier ones. The early ones were just slightly more geometric than ancient circles but far simpler than modern ones. Later ones grew increasingly intricate and detailed. No single circles anymore. Smaller circles, countless triangles, squares, hexagons filled the largest circle. Spaces between shapes brimmed with runes.
"Eventually, they concluded individual research had limits. That's when systematized mage societies formed to share knowledge. Before, researchers holed up in personal labs; the largest unit was a mage tower, far smaller than now. Magic universities reaching this scale is recent too."
Meaning modern magic research history was shorter than Arienael's lifespan. As a child uninterested in magic, she hadn't known.
"And without the ground-drawing constraint, magic circles gained another advantage: stacking multiples."
Crowley drew more circles in the air. Unlike earlier ones lined up on a plane, these were on separate parallel planes. Connecting their centers would form a single line.
"Combining different magic circles in layers like this—obvious to you university students, right? But it hasn't been obvious long. Layering 2nd-generation circles birthed 3rd-generation ones. That's the full evolution."
As the professor wrapped up, a student raised a hand.
"Yes, you there. A question?"
"Isn't there one more stage?"
Crowley chuckled softly, as if expecting it.
"I wondered when this would come. Yes, magic's progress doesn't end. Spell formulas faced another revolution by some genius. As Spellcraft majors, you've all heard the name."
Arienael, unfamiliar with Spellcraft figures, waited half-doubting. Maybe someone she knew. Perhaps glimpsed in a textbook corner.
Crowley's next words met her expectations. The great scholar who opened new horizons in Spellcraft was a name she'd heard endlessly lately.
"Correct. Dr. Atwill, now Professor Atwill at our school. Since his research is unfinished, I thought of it as future rather than modern, so I skipped it."
Arienael gasped at the familiar name in this unexpected spot.
What?
"Professor Atwill's idea was simple. 'If we're floating them in midair instead of paper, do they need to be planar? Isn't the core circulation, not the circle?'"
Finishing, Crowley floated a small orb-like shape in the air. Inside mixed polyhedrons and complex runes—so intricate it was hard to discern.
"The result: the birth of 3D formulas."
Arienael was still reeling from the shock.
"Someday, we might call this 4th-generation."