Chapter 46 – A Growing Understanding

On Thursday, she found herself back in the large lecture hall for von Agrippin’s lecture, which this week covered the mathematical formalization of the transformation rules between Essence types.

Valentina sat next to Innogen in the fourth row and took notes. Von Agrippin stood in front of the slate board, half of which he had covered with an equation describing the symmetry operations by which the Leb-resonant configuration could be transformed into the Viur-resonant one.

“One important insight,” he said, tapping the chalk against a specific spot in the equation, “is that each of these transformations entails a measurable amount of additional burden, which is introduced by the symmetry barrier. That is, part of the energy expended does not go into the transformation itself, but is absorbed by the specific geometric restrictions of the target essence type. The restrictions are, so to speak, the price we pay for the specification. I call it the restrictive burden.”

He set down the chalk and wiped his hands on a cloth, which he then carelessly tossed over his shoulder.

“Which brings us to an interesting question: If the restrictions are the price of specification, what happens to the burden when we operate closer to the Grundgestalt, where specification is lower?”

Valentina felt her pulse quicken. That was exactly what her project was about.

She raised her hand.

Von Agrippin saw her and nodded, and again there was that barely perceptible sparkle in his eyes. “Valentina.”

She noticed that he had stopped addressing her formally weeks ago.

“If the restrictive burden is proportional to the distance from the Grundgestalt,” she said, “then that would have to apply not only to temporary transformations, but also to permanent applications. To interactions between architecture and patterns, for example, that must remain stable for decades. These permanently bear the full set of restrictions of their specific essence type, and the accumulated Essence loss over the lifespan of such a structure would be considerable.”

Von Agrippin crossed his arms and tilted his head, a gesture she had come to recognize as his sign that he was seriously thinking.

“That’s a point I’ve so far addressed exclusively in the context of temporary transformations,” he said. “But you’re right, the implication is logically compelling. Personally, I would have chosen an example of smaller artifacts, such as an Essence lamp, but the principle is the same, I guess. If we design a permanent pattern at a geometric level closer to the Grundgestalt, the permanent restrictive burden should decrease.” He raised a hand. “However, with one significant caveat: A permanent pattern that operates closer to the Grundgestalt theoretically has access to a broader range of possible states and thus also to significantly more opportunities to drift into an undesirable state, which can pose a stability problem.”

“But the stability problem could be addressed through a… a predictive analysis of the disturbances,” said Valentina. “If we could show that all, um, let’s call them disturbance states are decaying and not escalating, the pattern would also be stable in the long term, even at the more fundamental level.”

“If you can prove it.” He smiled, and it was a sincere smile, not one of his charming gestures. “The emphasis is on ‘if.’ But the approach is sound, and the question deserves to be explored. May I ask if this is purely theoretical interest, or if there’s a specific practical application you have in mind?”

“The Greystone Cascade,” said Valentina.

A brief murmur spread through the lecture hall. Two of the city scholars exchanged a glance.

“The Cascade.” Von Agrippin repeated the word with a mixture of surprise and obvious pleasure. “So that’s why the example with architecture. Well, that would certainly be an extremely spectacular use case. I’d be happy to discuss it further with you if the opportunity arises.”

“I’d love to,” said Valentina, sitting down.

Next to her, Innogen, smiling mischievously, traced a heart with her finger on Valentina’s knee, where only Valentina could see it, and Valentina had to bite the inside of her cheek to keep from laughing.

Von Agrippin had already moved on to the next question posed by Ignacio Flintside, but Valentina was only half-listening. Her heart was pounding, and she knew it wasn’t just due to intellectual excitement, even though she would have liked to convince herself otherwise.

“He just offered to talk to you about your project,” said Vyxara. “In private, if I’m reading him correctly. His support could be incredibly useful.”

“I know.”

“And he smells good.”

“That’s an argument that has no place in an academic discussion.”

“Who’s talking about an academic discussion?”

Valentina snapped her notebook shut, thanked Von Agrippin with a nod as she passed him after the lecture, and felt a familiar pulling in her abdomen. He really did smell good.

Out in the hallway, Innogen turned to her. “You’re glowing.”

“Um, yeah, I’m thrilled about math.” Valentina winked.

“Of course you are.” Innogen hooked her arm through Valentina’s. “Come on, let’s go pick up Crispin for dinner.”

~

Four days later, just as she was on her way home, Hoager was standing in front of her again.

Valentina had just come out of Veilford’s seminar, and her head was still full of rotational symmetries, when the cheeky boy emerged from a side alley and blocked her path.

“The pretty lady from Pinfeather Lane,” said Hoager, standing in front of her cockily, trying to look at least two heads taller. “I have a message.”

“From a friend of a friend?”

“Exactly.” The boy cleared his throat, apparently to lend his voice the necessary gravitas. “The second delivery is ready. Same spot as last time, same arrangement.”

Valentina nodded, reached into her purse, and gave him one more copper coin than last time.

Hoager flashed his toothless grin and then skillfully slipped the coins into the depths of his much-too-big jacket. “Tell me, have you actually signed me into your kiss book yet?”

“On the very first page, Hoager. In red ink.”

“Very good.” He puffed out his narrow chest. “Then all I have to do now is get old enough.”

“Time is working in your favor then, isn’t it?”

He grinned again, gave a small, surprisingly elegant bow, which he’d probably copied from someone, and vanished just as quickly as he’d appeared.

Valentina watched him go with a smile. Then she set off to pick up her delivery.

On her way to Candleway Bridge, she didn’t take the usual route this time, but instead went through the neighborhood behind the tanneries, through a narrow alley that reeked of wet leather and lye, and then along the river toward the east.

She stopped twice, once at a street corner where she pretended to adjust her garter while watching the street behind her, and a second time at a trough where she washed her hands while looking around cautiously. But she wasn’t being followed.

Under the Candleway Bridge, she found the loose stone with the barely visible chalk mark and pulled the package wrapped in oilcloth out of the hollow. It was quite a bit heavier than the last delivery.

She unwrapped one corner of the oilcloth just enough to check the contents. Inside was a single sealed vial, and the liquid inside shimmered oily and iridescent.

Corrupted Essence.

Valentina hadn’t even opened the vial yet, hadn’t even activated the Sight, and yet she could already feel the faint nausea and slight dizziness rising uncomfortably behind her eyes, as if something in her perception were resisting what she held in her hands. Like a headache that was coming on but never quite arrived.

She carefully wrapped the oil cloth back around it and hid the vial under her coat.

~

Once home, Valentina locked the front door behind her, climbed the stairs, and entered her study. The shutters were still closed, just as she had left them that morning. She lit the tallow candle and placed the vial on the desk.

Only then did she activate the Sight. Her gaze shifted, and the familiar protective structures of the demonic configurations in the walls glowed dark and dense.

The Corrupted Essence in the vial looked completely different when viewed through the Sight.

The shimmer was there, yes, the normal, pulsating shimmer of Distilled Essence she’d known since she was first able to see it, but it was simply wrong. It was like looking at a familiar face in a warped mirror. All the features were there, but the proportions were off, and the longer she looked, the stronger the feeling grew that something fundamental was twisted.

And it was beautiful in a terrifying way. The iridescent shimmer shifted between colors that no Distilled Essence ever took on, and tugged at something deep within her perception, a place she hadn’t even known existed until she had learned the Sight.

“Yes, it looks beautiful, but you’d better not touch it,” said Vyxara. “And we should keep it separate from the Eye and your regular Distilled Essence. Preferably in its own container. The orientations must not influence each other.”

Valentina dropped the Sight and rubbed her slightly throbbing eyes. Then she took a small wooden box from one of her locked cabinets, placed the vial inside, closed the lid, and then cast Vyxara’s dampening patterns over it until the box became almost invisible to her perception.

Then she locked the cabinet, weaved protective pattern over the lock, and took a step back.

“All set,” said Vyxara, and there was a certain tension in the demon’s voice, or perhaps anticipation.

“Let’s hope so,” replied Valentina.

~

But first, she had to work out that damn mathematical foundation Professor Whitehall wanted from her.

She had spread out von Agrippin’s lecture notes to her left and her notes on the Greystone Cascade, which she had brought with her from Dusktown, to her right. On the sheet in the middle, she was trying to somehow bring the two together.

In her own sketch, she was trying to reduce, step by step, the specific restrictions of the Leb-resonant geometry of the original patterns of the outermost ring of the Cascade, thereby shifting the pattern closer to a more fundamental symmetry.

It was tedious. The idea was right, she sensed that with unshakable certainty, but the formal proof that the optimized patterns would remain stable in the long term required a mathematical rigor that did not come easily to her. Someone like Veilford, or perhaps even Crispin, could probably have written it up in an hour, but it took Valentina the entire evening.

But when she managed to truly immerse herself in the work, and when the numbers and geometries stopped to be mere symbols on parchment and really began to take shape in her mind as three-dimensional structures that she could rotate and stretch and view from all sides, then suddenly everything made sense and felt downright intuitive.

“The restriction at this point in the first ring,” Vyxara said sometime during the second hour, referring to a specific axis of symmetry in the collection pattern, “is not independent of the one in the next ring. If you reduce one without taking the correlation with the other into account, the stability at the interface suffers immensely and you risk collapse.”

Valentina stared at her notes and saw immediately that Vyxara was right. Damn. The two restrictions were definitely coupled.

“That complicates the proof by a lot,” she muttered.

“Don’t complain. Actually, it works to your advantage. If the restrictions are coupled, that means you can reduce them together, which would make the efficiency gain even greater than you had previously assumed.”

She scribbled a correction into her calculations, then another, and then she realized that another connection was emerging, on a level she hadn’t seen before. The linked constraints also followed a pattern. But which one?

Valentina leaned back and rubbed her tired eyes. She had to stay focused and not let the complexity discourage her.

“Go to bed,” Vyxara said in her mind. “There’ll be plenty of time to work on this tomorrow.”

“I’ll probably have to work on it the day after tomorrow, too,” Valentina muttered.

“You definitely won’t finish today.”

“Do you think I’ll even be able to do this at all? Please be honest, Vyxara.”

“Go to bed.”

“Okay.”