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The layout of the third floor was quite different from the second. The first thing that caught Lucian's eye was a blue-and-white living room, with rows of wide windows on both sides that let the sunlight pour in, making the space exceptionally bright.
Although this living room was much smaller than the hall on the first floor, the casually arranged sofas, the round tables the size of coffee tables, the small black writing boards hung on the walls or behind the chairs, and the pots of verdant plants all gave off a peculiar sense of vitality amidst their disorder.
There were a dozen or so young boys and girls in the living room, the eldest perhaps fourteen or fifteen, the youngest only around twelve. They were either sitting on sofas bent over the round tables before them in deep concentration as they calculated, or gathered in groups of three or four in front of the small blackboards, discussing with solemn seriousness — making Lucian almost think he had stumbled into some kind of study salon or learning club.
Perhaps whoever had designed the third floor had considered not wanting people coming up the stairs to disrupt the atmosphere, because this living room faced the other direction, meaning Lucian and Tom could only see the teenagers' backs or profiles. The thick carpet also muffled their footsteps, so they didn't disturb anyone.
"Anik, this *Mathematical Principles of Arcane Philosophy* is really fascinating. The three fundamental laws of force-field magic inside look simple at first glance, but when you think carefully, they actually summarize the rules we follow when casting force-field magic — and they even seem to apply to certain everyday phenomena." A crisp, bird-like girl's voice rang out as she spoke in a low voice to her companion on the adjacent sofa.
They were sitting with their backs to Lucian and Tom on a semicircular arrangement of sofas just ahead of them. The boy with fuzzy, light-yellow hair raised his head and said, "Laylia, I heard Mr. Astal say that the contents of the *Mathematical Principles of Arcane Philosophy* represent one of the two great pillars of the modern arcane system. If you could thoroughly understand it, you might be able to become a formal magician!"
Another girl beside him with long, flaxen hair chimed in, "Laylia, Anik, have you two only read the first part? I skimmed through the whole thing a few days ago and found that the third part is what truly defies imagination. It attempts to use the concept of 'force' to explain the movement and phenomena of the entire world, including the stars, the tides, and so on. It even names the force between the stars and the earth 'gravity,' and from that derives the trajectories of celestial bodies. Won't this be useful as a reference when we study stellar magic later?"
Laylia had black hair tied in a bouncy ponytail that bobbed as she nodded. "Mm-hmm, it seems so. But I can't follow the derivation process at all, and those mathematical methods called calculus — I can't understand the calculations whatsoever. Hettie, Anik, what about you two?"
"Same here — I went through it like reading a fairy tale, and couldn't understand a thing." Hettie, with her long flaxen hair and a voice that seemed to curl upward at the end, answered without much concern. "But didn't Mr. Astal tell us when he gave us the *Mathematical Principles of Arcane Philosophy*? Before becoming a formal magician, we only need to memorize a few theorems and formulas — there's no need to fully understand everything. What we need to study right now are *Fundamentals of Arcane Geometry*, *The Mapping from Arcane Principles to Model Construction*, *The Symbolic Significance of Constructed Figures*, *The Elemental Equations Behind Arcane Formulas*, *Introduction to the Elements*, *Common Algebraic Problems*, *A Classification of Low-tier Meditation Techniques*, *A Brief Analysis of the Nature of Cold and Heat*, *The Role of Motion and Force in Arcane Magic*, and so on."
She seemed to be showing off her memory, rattling off the entire list of books they needed to study.
"Now that you mention it, Hettie, I remember too — Mr. Astal did say that if we could fully understand the *Mathematical Principles of Arcane Philosophy*, then after a year of systematic study of calculus, once our mental power is sufficient, we'd be qualified to attempt becoming mid-tier magicians." Laylia agreed with Hettie. "But all those arcane fundamentals you recited — I don't know when we'll ever finish them. Without a teacher's guidance, I'm afraid it would take me more than fifteen years. Right now I get dizzy just reading a few pages a day. Sigh, I wonder when I'll become a formal magician."
Any apprentice who didn't aspire to become a formal magician wasn't a good apprentice. Having passed the examination, they of course harbored ambitions of their own.
Anik scratched his light-yellow hair. "If it's all self-study, I don't know how long it would take either. But didn't Mr. Astal say that once we reach Alinor, the Parliament will arrange for formal magicians to teach us? That way, maybe in four or five years we could finish our studies and have enough ability to aim for the magician rank. And then…"
"And then we'll be city council members — gentlemen and ladies with servants of our own." Hettie's voice was full of longing.
Laylia was equally wistful as she added, "And the Parliament promised that once we become formal magicians, they'll bring our parents and families over to Holm, Collette, and the other nations."
The three fell silent for a moment, then sighed in unison: "A formal magician…"
Standing silently at the stairway behind their sofas and listening in, Tom's gaunt, gloomy face showed a rare smile. "Those three, along with Splinter, Ormos, and
As he spoke, he pointed them out — Splinter, the dark-red-haired boy instructing others at the blackboard; Ormos, the brown-haired youth writing and calculating quietly; and Katrina, the tall golden-haired girl discussing problems with the three young women.
"Fine young people," Lucian replied in the tone befitting a formal magician.
Their conversation caught the attention of the apprentices studying and discussing in the living room. They turned their heads or stood up to look over, then bowed politely: "Good day, Mr. Tom."
This Mr. Tom was a powerhouse at the Knight rank, so naturally he deserved their respect.
Facing these vibrant, somewhat naive children, Tom was less gloomy than usual. He smiled and said, "I want to sincerely praise you all for working so hard. However, the *Mathematical Principles of Arcane Philosophy* is the first work in which our Parliament Chairman, the greatest Archanist, His Excellency
Though he was only a Second-level Knight, having grown up in Alinor since childhood, he was far from lacking in general knowledge of magic.
"Thank you for your instruction, Mr. Tom." Splinter, who was around fifteen with a faint fuzz on his upper lip, stepped forward to respond. Handsome and somewhat defiant, he seemed to regard himself as the leader of these dozen-odd Magic Apprentices as he declared proudly, "I have never wasted a single moment. I already became a formal Magic Apprentice yesterday."