As they left the dungeon for an aerial scouting trip, I flicked open the notebook, my fingers brushing over the cramped handwriting. It was clearly not written by someone who was concerned with precision … or any kind of order.
The notebook was filled with half-complete sentences, random observations, and weird formulas. I was glad that Maria's earlier explanation had given me some kind of a basis, or I might have just skipped all of the relevant sections.
However, as I read, I couldn't help but frown. In many places, I could see the references to the connection with the dungeon staying weak and controlled, even with a few sentences that implied that the weak connection significantly limited the potential connection with the dungeon.
But, as he described the way it worked, I couldn't help but close my eyes, and focus inwards to create the simple rotating feeling from Meditation, which didn't count as a part of the no-experimentation rule, as I had repeated that trick thousands of times.
I repeated it, simply because the pain I felt from Maria's botched attempt was very similar to what I felt when I botched Meditation while trying to reverse it … at least, the first portion. The Health damage was absent, but then I hadn't let mana loose in my body.
"This isn't experimentation, just observation," I muttered, though I was glad I didn't need to explain it to them. I had a feeling they wouldn't appreciate the distinction I was making.
I carefully examined the surface for any imperfections, but there were none. However, as I examined it more and more, I finally felt something.
A direct connection to the center of the sphere.
"That can't be good," I said even as I mentally touched the bond for a fleeting second. The bond felt faint … but it wasn't weak. It was like touching one of the invasive weeds with twenty feet of root into the ground.
I ignored the temptation to touch it more, and opened my eyes. "The connection is … intense," I muttered, glad that we didn't try to cut it easily. I had a feeling that it wouldn't do any good.
However, I had a feeling that I was already beyond the method described in the book. The unfortunate mage's method had taken great care to avoid the deeper connection, emphasizing the importance of keeping the bond weak, keeping it as one way as possible.
I couldn't say I blamed him, especially since, across all the notes, he treated the dungeons as an extremely dangerous and volatile entity, and rightfully so. I still didn't have any idea about where the dungeons came from, but anything that casually violated the rules of time and space couldn't be something trivial.
Not even in a world where magic was commonplace.
"I have a feeling I have to look for something more permanent," I muttered. It was a baseless statement, more of a hypothesis born out of sudden inspiration than anything else.
I flipped to another passage, reading about how he planned on using pillars of mana to stabilize the temporary connection, hoping to find some inspiration. As I read, I was glad that Maria had dealt with it first. The notebook didn't have a coherent approach, and without the notes she scribbled on the sides, using my notation, I would have required months to properly decipher what was going on.
I didn't bother with the calculations, trusting her to do them better than me, and instead focused on the core, repeating principles of control, containment, and caution.
I leaned back, tapping my finger against the notebook's edge. The logic was sound, but it was built on a foundation of a temporary approach. It was clear that he saw the connection as something negative, something to be dismissed once the dungeon was breached.
"I just hope that it means a permanent connection is a good idea without that need," I muttered. It was a bit of a stretch, but it implied that the technique was initially designed for a more permanent connection which was modified by his destructive usage.
It was not exactly an incredible piece of evidence, but considering the bond was already in place with no idea on how to sever it, I chose to believe it.
Flipping back to the earlier sections of the notebook, I scanned the notes on the initial bonding process, this time focusing more on Maria's notes to better understand how to regulate the connection between the individual and the dungeon.
I sighed even as I started taking my own notes. Unfortunately, those notes were less about clever adjustments and solutions, and more like a long list of questions I would ask Maria.
"It's time to switch," I muttered at one point, and instead opened Maria's sealed notes about her meditation technique. Her notes were far more impressive than the ramblings of the enemy mage, especially since she had gone through enough effort to write everything based on our shared notation system.
It was a far more acceptable challenge, even though I sincerely doubted I could actually apply even a part of those transformations to my own abilities. Maria could use them, because she had both the skill and Intelligence to guide her.
In their current form, it was impossible to implement them. "But, that doesn't mean that there's no alternative method," I muttered even as I started working on the formulas, trying to find a more generalized expression.
The only reason I even dared to do it was that math was still holding up as a universal constant. Unfortunately, considering I didn't know how it held up at the extremes, some of my favorite methods, like proof by contradiction or induction, were not available.
In the end, I found myself mostly relying on constructive proof, which was to create a wider expression, before going back to check if it worked for every unique formula she had provided. Which, even with my familiarity with high-level mathematics, was not exactly easy.
I never liked constructive proofs, as they were usually not 'elegant', a word that every doctorate student of mine hated. Also, finding the right construction was never trivial. Sometimes, it took weeks to come up with a valid construction, and then it took months to prove that generalization held true…
"At least, it's not proof of exhaustion," I muttered. It was one method I was happy not to be using.
However, the more I worked, the more I found myself lost in various topological transformations. Ultimately, the practical applications of mana were utterly reliant on mana. Of course, Maria's constructions were always focused on three dimensions, but it was hardly the only way.
I found out that inventing extra dimensions to resolve those structures was surprisingly stable. At least, at the first glimpse. Actually solving them was not exactly something I could achieve. Maybe, if I could prove that Group Theory holds correctly…
"What about ..." I muttered even as my pencil started to dance on the paper with sudden inspiration: a formula to reconcile the flow of mana with the higher-dimensional theories that theoretical physics loved so much.
It was so tempting to try. I might have even ignored my promise if it wasn't for the excruciating pain I felt when Maria managed to take over the dungeon. I was still reluctant to put a name to it, but it was clear that Meditation and Dungeon Connection relied on the same thing.
And, I almost killed myself trying to reverse the direction of Meditation in the past. Trying to somehow project it with more dimensions than we could perceive didn't seem like a good idea.
"But, creating a denser mana structure is different," I muttered as I suddenly went back to the generalized solution for the dense mana I had created for my skill. If I combined the two, there was a chance that it could help me create another, stronger variant of epic alloys.
One that could potentially unlock the next stage of the skill.
I began to trace in the air, trying to envision the idea in a way that was more than just a formula. A mere n-cube alone, even as its most common expression as a tesseract was not trivial, and I didn't dare to actually form that as a core for my meditation.
However, the principle idea was very simple. A two-dimensional cube was merely a square, and a three-dimensional one was an ordinary cube. A tesseract was a four-dimensional cube.
Mathematical properties were easy to define. Where a cube had eight vertices, a tesseract had sixteen. A cube had twelve edges, whereas a tesseract had thirty-two. A cube had six faces, whereas a tesseract had twenty-four.
Unfortunately, trying to imagine it as an actual construct was far more difficult.
"I feel like a poor student," I muttered even as I tried to tangle with the idea, like some of the visual learners did in more complicated undergraduate math classes, only to learn that, without the abstraction the mathematics provided, some of those concepts were plain impossible to comprehend.
Too bad merely experimenting on the idea would have likely killed me. I returned to the safe world of formulas and abstractions, once again hunting for a more generalized solution —
Only for my thoughts to be interrupted when Maria burst into the dungeon, her clothes ripped and bloody, not even bothering to step down from her griffin. And, it was sooner than I expected.
It was clearly not good news.