My quill scratched against the parchment as I finished transcribing my rough draft from the slate I secretly borrowed from my mother. It was a cold and rainy day out now that winter had arrived, and a fire crackled in the hearth. I had broken back into my own house after my parents left for work instead of spending my day getting wet around town or hunkering down in the Church. That was my usual routine lately as I worked on my personal studies.

I wiped the slate clean and looked over my various works. I had three different projects I was working on at the same time, two of which I had seen through to my current limits.

The first was my bestiary. I was recording everything I knew about beasts and beast evolution. I divided my parchments into three columns. In the first, I was recording all the details I could think of for the beasts; description, habitat, temperament, and so on. The second column was information about the beasts’ evolutions, which still had many blank spots. The third column was even more sparse, describing what I had seen in the dungeon. I had a series of pages for the beasts of Mirut Jungle, which included the beasts I encountered within the city as well, and another series of pages for the beasts of the western sea, which was much shorter.

I was recording my thoughts in my native language, and not the language of the Horuth Kingdom, just in case my parchment was discovered, though it always stayed in my inventory when I wasn’t working on it. When I was older, I would translate it so that I could share the information with others. Despite writing in an Earthen language, I was trying to break a habit I had developed of comparing this world’s beasts to Earth animals. Using proper, descriptive language was hard, and I drafted several versions on the slate before I committed anything to parchment.

The second project was my collection of recipes and ingredients, transcribing the things I had learned from Belat about brewing, plants, and a page about ink. It was nowhere near as thorough as I had hoped, so I would have to go back to her shop and sneak another look at her book. I had one major leg up on her, which was my ability to appraise the plants I collected in my inventory, so I was recording the specifics I learned from that. I started doing more potion experiments in the kitchen to expand my knowledge and had come up with a few potion recipes of my own.

The third and main project was my future grimoire. I recorded everything I knew about magic. I combined everything I knew together, because there was interplay between the different circles that got lost when I separated them out into distinct classes. It was tricky to separate some of my magical habits from my other, non-standard skills, though, which encouraged me to turn my study towards some more theoretical ideas.

I was fighting an educational war on two fronts. The first was the study of magical, non-circle skills and attempting to classify them in ways that found commonalities. In the past, some mage realized that fire, air, water, and earth magic were all aspects of a larger, general class of elemental magic, and the skill evolved into 4-point magic. I was hoping to do the same with some of my own skills as I learned more. The second was the study of magic circles themselves, to see if I could learn more about the “vocabulary” of magic in order to use that to my advantage.

I had prepared a few experiments to test my theories.

Sitting cross-legged on the floor, I laid out a number of magic circles that I had prepared for my first experiment. I had my three standard magic circles made from shaped stone: one which contained a square for 4-point magic, one which contained a pentagram for 5-point magic, and one which contained a hexagram for 6-point magic. I was adept at using these now, and had started to take them at face value, but was finally revisiting the thoughts I had initially when I learned about magic circles.

A square was a regular, convex polygon. Each point connected to the next, a step of 1 with no jumps. As such, it could be written as {4/1}, which is reduced to {4}. It was, more or less, the only way to draw a 4-point circle. A pentagram, on the other hand, was a regular star polygon, also known as a regular polygram. It was written as {5/2}, five points connected by every second point, which was irreducible.

In the realm of 5-point shapes, there was also the pentagon, a regular and convex polygon like the square. Like the square, it could be represented as {5/1} and reduced to {5}. Why didn’t 5-point magic use pentagons instead of pentagrams?

I placed a new magic circle on the floor in front of me: a pentagon within a circle.

Bracing myself in case things went wrong, I attempted to channel 10 MP into a small light. To my surprise, it worked without issue, although the light seemed slightly weaker. I tested it against my usual pentagram, which I ensured was otherwise an identical size, and saw my light was brighter with the accepted shape.

I didn’t think this had anything to do with geometry. It seemed like an aspect of a common language. For example, one could read the word “fox” and one could read the word “phoks” and get the same sound, but one word brought to mind a more immediate and familiar understanding, whereas the other required some thinking to glean the meaning of.

I wagered that, with practice, I could use a pentagon just as well as a pentagram. There was no reason to use convex polygons, though. The more points a convex polygon had, the closer it approached a circle. The main reason to use a star polygon instead of a convex polygon was readability, which was undeniably a factor in how a mage channeled magic. It would simply confuse a mage to try to use convex polygons in place of star polygons, particularly with higher-point magic.

That brought me to 6-point magic and the hexagram. I placed a new magic circle containing a hexagon, the regular and convex polygon version of a 6-point magic shape, and cut myself with my knife to test that as well. As with the 5-point experiment, it worked, but was less efficient. With that out of the way, I turned myself back to a question I had when I was four years old.

The star polygon version of a 6-point shape was slightly different from the 5-point shape. When written as {6/2}, it actually could be reduced, and written as 2{3/1} or simply 2{3}. A hexagram was called a compound polygon, in that it could be separated out into two lower polygons, in this case two convex 3-point polygons, or more simply, two equilateral triangles. I pulled out yet another experimental magic circle, a 3-point magic circle containing a single triangle.

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I cut and braced myself again, and tried to heal with the 3-point magic circle.

Nothing happened.

I smiled, and healed myself normally through the 6-point magic circle nearby. That had been the expected result. Magic circles didn’t have anything to do with the shape itself so much as the number of points. With magic, {6/2} was irreducible, unlike in geometry.

The head magic researcher at the institute where my mother worked, Master Vorel, had told me as a child that 3-point magic didn’t exist because it was simply a “half” of 6-point magic. Clearly, that wasn’t correct, because if so, other convex polygons like the square wouldn’t work, as they were halves of higher order, reducible compound star polygons. I strongly suspected that 3-point magic was a possibility, though I didn’t yet know what. Still, I felt like there must be some relationship between 3-point and 6-point magics.

6-point magic had a direct effect on my stats. It affected HP and status directly. The main limitation of 6-point magic, and part of why it was forbidden, was that HP and MP were usually hidden, which caused novice casters to overspend on MP while attempting to heal, which caused the magic to draw from the caster’s HP and could lead to death.

My appraisal skill fixed that. Appraisal was one of the skills I acquired through my metasystem, and as far as I could tell was separate from the physical world. It was… information magic, I supposed.

I felt my heart start to pound at the implication. The number three did have meaning in my old world. The third eye. Clairvoyance. True sight. I pulled up my skill list and looked at the other information-based skills I had. My map skill was pure information and sight beyond my eyes, a form of scrying. The most recent skill I gained from my metasystem was telepathy, which was the direct transmission of information through magic.

I cupped my 3-point magic circle in my hands and looked at Treepo, who was curled up near the warm hearth. Instead of appraising him through my metasystem, I channeled some magic through the circle and tried to cast appraisal as a spell using MP.

Instead of the usual window appearing, I felt a deeper understanding of the knowledge flow through my brain. I could intuit his health, his magic, his species type, and something else. A potential, maybe, that was yet unseen. As the knowledge passed through my brain, I also felt the familiar pressure of a notification from my metasystem.

Skills {Appraisal (2/100), Map (0/10), Telepathy (1/10)} converted to new skill: 3-Point Magic

Skill acquired: 3-Point Magic

16 SP reassigned to converted skill.

I did it. I created a new form of magic.

A giggle burst from my lips and Gregory lifted his head with a start from his nearby nap, and I fell back onto the floor and stared at the ceiling. My heart was racing at the implications.

I had made a new form of magic. Could I make another? Did I need to already have the skills learned, or could I create novel magic just from my Earthly knowledge and creativity?

I checked my skill menu, and saw that my new 3-point magic skill had combined all the points I had across the three former skills into one. The skill was already advanced and displayed 6/100. It did seem to cost me one of my banked SP to gain 3-point magic in the first place, but that was a fair trade. I hadn’t spent anything to learn the three skills in the first place, as they were given to me by the metasystem. The ten points to advance my appraisal skill were also a cheat. Still, I was glad the few extra skill points that had naturally been assigned through daily use carried over as well.

I gathered myself and left the house, wandering down the street to test my new skill. I channeled some MP through the 3-point magic circle and started trying to appraise things. A huge grin broke out on my face as I realized I had broken through a massive former barrier.

In the past, I could only appraise people, my own familiars, and items that I stored in my inventory. Now, I could appraise anything that I saw. It cost MP to do so, but it was a negligible cost and was so, so worth it. I would be able to learn so much more about the world now. I could identify beasts before I killed or tamed them. I stumbled a bit when I realized I would probably be able to identify beasts in dungeons, as well, which would make them so much more accessible to me. This is huge!

On my way back home, some of the other implications started to land. Magic circles were teachable. I had no way to teach something like appraisal or telepathy before, but I could now. It might also be the case that now that the 3-point magic skill existed, others could learn it on their own. Appraisal let me learn about other people’s skills. While this new, MP-charged appraisal was slightly different, it could still reveal to others what my own level and skills were. Most importantly, it could reveal to the Church that I had the forbidden, 6-point magic skill.

The Church would probably forbid 3-point magic as well when they found out about it. I could end up in a lot of trouble. I would have to play this very close to the vest until I had the strength to protect myself or escape the kingdom. Even if I could, I wasn’t sure how far the reach of the Church spread.

If I could find a safe haven away from the Church, the spread of 3-point magic could be a paradigm shift to the people of this world. Understanding my own stats and skills gave me a huge leg up and helped me to uncover many mysteries of this world. How much further could this world advance if researchers and scientists could use this to seek more knowledge and truth?

I was a little worried about the cost to the caster, but it certainly seemed like 3-point magic was pretty easy on my MP. Some appraisals cost no MP at all, but that was likely due to my advancement, as was the case with some of my other advanced magic. Unfortunately, I could never know what it would cost a true novice caster without teaching someone else, which would have to wait until I met someone totally trustworthy.

Even if the costs were high, the existence of a magic circle for these skills had secondary implications. Magic circles were a core part of item enchantment. I still had a lot to learn before I could tackle enchantments, but I was already dreaming about the possibilities. Two-way enchanted communication devices using telepathy? It would be a telecommunication revolution! Could I leverage both information magic and illusion magic to replicate stats screens? It would be so useful for tamers to track the progress of their familiars.

As with all progress, there would be two sides to it. All new technologies, which magic more or less was in this world, came with upsides and downsides. The good came with the bad. I hoped I hadn’t just invented the equivalent of a magical nuke. Even if 3-point magic was benign, well…

I wasn’t even close to being done pushing the boundaries of what magic had to offer.