The Lecture
A blackboard would never have served a crowd of this size, not if I meant them to follow the concept. I set the coffin that held Isabel's corpse down upon the floor, raised her by Enslavement, and transmuted mana into water, and that water into ice. Point, line, plane, and solid I formed in the empty air, one after another, and I interfered with the atmosphere itself so that none of them would fall.
"A point in which no concept whatever exists stretches out without number and becomes a line possessed of length. Those lines stack, layer upon layer, into a plane possessed of area, and that plane becomes a solid. The moment mages understood this, they grasped something else, however dimly. A figure bearing the concept of n—a concept we cannot yet know—must come into being by a similar course."
No one spoke.
"But that alone does not establish a hierarchy. Which is why, until now, we have always perceived the compositional formulas of magic by rendering them as equations."
Length, area, volume. These were nothing more than measures, a means of comparing how much mana a thing could hold. If an order of rank was to stand, one had to name the cause of such results—the proper chain of cause and effect.
"Then let us return, lightly, to the beginning."
I cleared away the line, the plane, and the solid. Only the point remained.
"A point in which no concept exists at all. A state barren of the concepts one needs in order to understand a compositional formula. But strew these points without number, as one dabs pigment for a pointillist painting, and they become a line possessed of length. From that moment, one can perceive the compositional formula of magic at the rank of Kether..."
I enlarged the line of ice and held it suspended in the air.
"Why, then, are point and line divided into the lower and the higher? Simply because the concept of length has arisen? No. And yet that answer is not wrong, either. It is nothing more than a byproduct of the result."
Still, the hall was silent.
"To put it exactly: a line that has length is a state that has wholly transcended the point's axis of time. It has become an omniscient being, able to observe everything about the point all at once. That is the correct view."
"Isn't the explanation too difficult? Too much of a tangle?"
The elder of House Roswell, seated toward the back, had spoken. I smiled bitterly and nodded.
"From here, I will unpack it in simpler terms."
I laid color along each portion of the ice-line hanging in the air.
"In the world of the line, no concept exists but length. A thing can exist only as a red line or a blue line, like so. Movement, too, is possible only to the left and to the right. So when a line of either color looks upon someone..."
I turned the line of ice end-on.
"...it sees a point."
The clever ones among them would have caught it by now. A line cannot recognize itself as a line.
"Add time as a y-axis, and the red line and the blue line living upon the x-axis will live by their own wills, and then they will die..."
I let the words trail. Then I greatly enlarged the stretch where the lives of the red line and the blue line were recorded along time's y-axis.
"A life like that becomes a sight no different from paint dragged in a zigzag across a sheet of drawing paper. Yes. In a word, a plane. Upon this plane, the beginning and the end of the lines are recorded all at once."
Express, in the same way, a plane possessed of both area and length as it flowed along a time-axis one might call z, and it became a solid possessed of volume. Which was to say:
I drank the black tea Alphonse had set ready beforehand, and I broke apart every figure I had traced in ice until nothing of them remained.
"I will take questions. Raise your hand."
"Hmm. This business of transcending the axis of time—I can't quite get hold of it..."
The elder of House Roswell threw the question out in the same breath as he raised his hand. I formed a great rectangle of ice in the air.
"Let us suppose that is a sheet of drawing paper."
"All right."
"And..."
In the midst of that great rectangle of ice, I incised a tiny square, neat and delicate.
"If that small square were to become a cube possessed of volume, it could no longer exist in the world of the paper. The instant it gains volume, it is flung out of that world. That is what it means to transcend the axis of time."
"By your account, then, if we—solids that we are—became something of a higher concept, we too would be flung out of this world?"
"In theory, yes."
"Hmm..."
"And from the standpoint of that higher being, the moment of our birth and the moment of our death could both be observed at once. Liken it simply to a figure, and it would look like this."
I drew them in ice—four-dimensional forms, the pentachoron and the tesseract—and set them turning so that everyone gathered in the hall might see.
"A figure for the concept beyond this one could be expressed as a form that takes the present figure for each of its cross-sections. But then the virtue of the thing, its intuitiveness, would fall away sharply. For ranks beyond Termiel, it will be more helpful to perceive a spell's compositional formula through equations, as we have always done."
A brief stillness settled over the hall. No rank beyond Termiel existed. In all of history, that was as high as any mage had ever reached.
"I will take further questions. Is there nothing more?"
I let my gaze travel slowly over the assembly. Uriel raised her hand.
"...Speak. Professor Uriel."
"You said a higher concept can observe a lower one all at once, didn't you? But we're solids, and we can observe every face of a solid."
"Strictly speaking, one can observe them only as time passes, so the statement is wrong. Suppose there is a large die. To see every face of it, one must move in order to look upon the faces that are hidden, or else apply physical force and turn the die."
"You could just set a mirror there."
"The world a mirror reflects is, strictly considered, a plane. And once so many mirrors have been arranged, there remains the flow of time required to turn one's eyes and take each reflection into view, one by one..."
"Ah... I get it. I understand."
She cut me off before the answer was even finished. A truly ill-mannered bitch.
"Tsk."
I made a point of clicking my tongue loudly enough to carry. Objectively, what Uriel had done was rude, and the looks turned on her from every side were none too kind. Color climbed her face, and her shoulders drew in. That would do.
I took what further questions remained, and then I brought the lecture to an end.
"It—it worked...!"
The moment Ferzen finished the lecture and stepped out of the hall, the mages around him deliberately manifested spells, succeeded in perceiving those compositional formulas as points, lines, planes, and solids, and cried out in excitement. The more intuitive the concept by which one perceived a formula, the simpler it became to reverse it, nullify it, or alter its properties. How could they help but rejoice?
Uriel was hardly pleased about it. Even so, she quietly took in a spell manifesting nearby, perceived it through that same concept, and closed her fist tight. Not letting the pleasure show was, in its way, a point of pride.
More than that... There was one more thing she wanted to ask, and it gnawed at her that she could not. But what was she to do? She had been on edge for no good reason, snapped at him, and behaved in a way anyone would have called rude. She had brought it on herself.
Her heels clicked as she left the hall, returned to the main building, climbed the ramp, and stopped before her own office. The outside guests had been formidable company, but her body was in no state for a long round of greetings.
...Is he in? Right beside hers: Room 404. His office, with the name Ferzen von Schweig Ruerug written upon the door. Uriel shifted a step closer, took hold of the handle, and hesitated. Curiosity, in the end, was still curiosity. She knocked, heard his voice faintly from within, and stepped inside.
"Um..."
Perhaps it was the rudeness of the lecture still hanging between them. He had told her to enter, and then he did not so much as glance her way. At that chill she flinched, though she could not have said why.
"I'm sorry. I was feeling much worse than I thought, so in the hall I was rude without meaning to be."
"Treating illness as a letter of indulgence. A very comfortable way of thinking."
"Then why don't you try having a period yourself..."
Uriel pouted and pulled her brimmed hat down low. He was the one who had ruined a twelve-year-old girl's legs and offered not a word of apology, and yet here he sat playing the injured party. There was no hypocrisy to match it. She swallowed the words, and did not throw them in his face.
"So. Why have you come."
"From what you were saying, once you transcend the axis of time, you can advance from a lower concept to a higher one."
"That is so."
"Then if we accelerated at an overwhelming speed, we would..."
Ferzen had already caught what she meant. He nodded. So the people of this world, too, were aware of that faint correlation between speed and time.
"If, as you say, one accelerated at an overwhelming speed, and drew so near the speed of light that one truly reached it... one would be flung out of this world."
"Ah..."
"However, an object that possesses mass..."
"Can't go faster than light, so for now it would be impossible."
"You have picked up a strange habit of cutting people off. Uriel."
"I told you not to call me so familiarly."
Uriel frowned and glared at him. Ferzen let the look pass without expression, propped his chin on his hand as if to mock her, and spoke.
"In that body of yours, an acceleration of that degree would kill you long before you endured it. Strange, that you should be curious about such a thing."
Today her chest stood out with a particularly vulgar prominence. Ferzen spared it a brief glance, let a sneer slip, and rose. When he looked at other people he deliberately blurred his focus, and even that laid a considerable strain upon his eyes. How much worse, then, when a large bosom kept swaying and nagging that focus back into place?
Uriel, who knew none of this, flushed. She jabbed a finger at him as he came closer and shouted.
"Y-you, really! Every time you look at me you harass me like that! Don't tell me you actually have designs on me?"
"It's exactly like little boys being mean for no reason to the girl they like. Your behavior is childish beyond belief."
"If I had harbored designs on you, I would not have wrecked the betrothal back then."
He left only about a single step between them, and pushed her brimmed hat down hard.
"You think far too much of yourself. Uriel."
"D-don't touch me...!"
"And who is it blocking the door, that you should say such a thing?"
Uriel said nothing. She straightened her hat and stepped aside. Ferzen went out, then looked back at her, still standing inside his office.
"Are you not coming out? What do you mean to do in an office with no master in it?"
She started. The words must have struck even her as strange, for she scurried out—and as she went to shut the door, the rough jolt sent pain through her chest. A groan escaped her, and she sank to the floor.
"Ah, it hurts... I'm sorry, but could you close the door for me..."
"One thing after another."
Ferzen let out an incredulous little laugh, shut the door, and turned on Quantification so that he might set the handle back to a proper horizontal. Then he went down to the first floor of the main building, stopped by the department office, received the revised schedule for when the corpses to be issued to the students were due to arrive, and headed for the parking lot.
The time... It was already past ten-thirty. By the time he arrived, it would be about ten-fifty. If he ate his lunch, took Euphemia to bed while she was in her fertile days, and then slept with her gathered in his arms, the warm sunlight for a coverlet... it would be a day of comfort beyond compare.
"I-I'm all ready."
It was a pale-pink lolita dress, the sleeves and the pleats beneath the skirt sweetly finished in frills, the cloth embroidered with beautiful flowers. White was worked in among the pink, and together they made a fresh, peaceful harmony with Euphemia's fair skin. The sunlight was a little strong today. Wearing a hat and holding a parasol, she shyly took up a basket of sandwiches in her free hand and called for the maids.
After she had gone about the capital with Ferzen, Euphemia had taken a certain interest of her own. She had picked up, in passing, that riding a ferry on the Tisbe River was one of the famous sights of the capital, and today she meant to do it. The sandwiches were for a simple lunch while she sat aboard and looked out on the beautiful scenery.
When the maids drew near, Euphemia left her room, came down the stairs of the mansion, and stepped out into the bright garden.
"Ah..."
A fresh wind blew rather hard from behind. The hat on her head lifted helplessly, flew, and dropped with a soft tap some distance off. But the one who picked it up and brought it back was not one of the maids at her side. It was Ferzen, returned at a remarkably early hour.
"You meant to go out."
"Mm..."
Fatigue lay thick across his face. The faintly furrowed look seemed ready to spit some harshness at her—do nothing useless, and shut yourself quietly in your room. But she had prepared so earnestly, had even made the sandwiches with her own hands. Euphemia gathered what courage she had and caught the hem of his clothes in a tight grip.
"I... I prepared. S-so hard..."
He did not answer.
"J-just for a little while, if I go out and..."
She even lifted the basket of sandwiches a little, appealing with all she had. But Ferzen's silence, to her, had almost always meant no. She could not bring herself to finish. As if she had quietly given up, she let both hands fall, strengthless, to her sides.
"Go, and come back."
In that moment Ferzen, still holding the hat he had retrieved, set it gently upon her head and gave his leave. Euphemia's eyes went wide. A blank, uncertain look crossed her face.
"What is it? Did you think I would tell you to do nothing useless, and go quietly up to your room?"
She did not answer.
"I know that what I am keeping is a person, not some animal like a dog. I have no intention of shutting you away until you wither."
"Th-thank you..."
She answered awkwardly, slipping into a formal tone.
"A dog, however, comes out to meet its master when he returns, and wags its tail as if it were glad..."
Ferzen let the sentence trail, dropping the hint without quite saying it. Euphemia hesitated a long while. Then, in a very small voice, she murmured it.
"W-welcome home..."
"Good. Then see that you are back before the sun goes down."
So lightly that her nervousness seemed almost wasted, Ferzen passed her by and went into the mansion. And beyond the door as it closed, his back slowly vanishing—Euphemia remained where she stood, and for a long while she watched.