8. Magical Math

— Clara POV —

After my fifth unofficial birthday I started to learn arithmancy and at the same time also calligraphy, as that is kind of a soft lock, before you can really start anything concerning arithmancy. I also started with basic math, instead of jumping into arithmancy. In the following six months i concentrated wholly on muggle maths and a little bit of calligraphy, if I got bored of maths.

I also started to transition from sleeping to meditating over night, as it is even more effective, after you have enough normal practice in it. This freed up very much time, as while I couldn't do an apprenticeship, I still wanted to be on the level of a master before joining hogwarts, even if I didn't take my master certification before it, which could lead to consequences down the line. The mid arts guild, which since this year no longer has a branch in Britain, due to it being considered dark magic, places importance on privacy and secrecy, so everything could go smoothly. I doubt this though, as my life is way to weird for something like that to not happen.

In these six months my maths skill was brought to an early university level, at which point I thought, that I had a good enough foundation to start arithmancy, as most third years in hogwarts start with just a rudimentary understanding of maths in general, you could even say that I am overqualified, though I think you need to build foundations in every area of your expertise, before you can jump into harder thing. You need to take everything step for step. That will help in the long run, as you don't find knowledge gaps, which can largely be avoided if done this way.

While I say this, I had already read about some basic principles of arithmancy. Like three and seven being magical numbers, which is why the tripod of my planned foci part builds upon those numbers. The end foci result will also be a trifecta of the two foci materials and the third foci part, which will help with the harmony of the construct. In what I didn't delve yet, was calculating your personality, lifespan and talent in the magical art, depending on a few factors like age, magical amount and strength, birthday, age and so on. Some calculations even needed your favorite color, which would be red for me.

Arithmancy in its base is calculating with numbers, real letters, images, concepts and so much more, which you couldn't do with sole maths.

I started with calculating my personality through the standard formula and understanding the why, how and what behind it, which was interesting to say the least. According to the result, I should be an outgoing and friendly girl, with an interest in reading and learning, which meant it was right for 50% and knowing that my harrowing first three years of my life weren't included in that standard formula, it made sense. At that point I started changing around things, to work from my actual personality back to the formula. This basically meant, that I tried to include the first few years of a person into this already existing formula. After realizing that five years at once might be too hard for now, I tried from both ends simultaneously, using a ton of parchment and later paper, after parchment annoyed me so much, I asked my parents to get me some. And it went pretty well from there. I only needed to find a set of variables, which could work with the idea I had and could also summarize a year of your life. The set of variables included things like loved, disastrous, normal, quiet, loud and many more. This set of variables also needed another formula to be calculated, to be exact and detailed. I made two approaches for that. One, which went from months and calculated 12 months up to a year and another one which, depending on the first one, first calculated the days into months and then into years, though the application of this one would be way more useful for specific cases, as close to no one can remember every single day, especially of their first few years of their life.

After the initial formula stood, I tested it with various sets of data, which I fabricated. While this wasn't the perfect way to test it, it was the only real applicable way at that moment. Through this I found multiple mistakes and needed to make many adjustments, through which the formula got more complicating and after which I also started splitting it into the other formulas I talked about. This also meant, that I needed to do a lot more testing and even though it took much longer than I fought, I slowly but surely perfected all those smaller formula, till even the large one was perfected to a satisfying degree, through a loop of testing with old and new data sets, followed by correcting mistakes and making adjustments in some constants, followed by more of the same. I also meticulously recorded every little step of the way, so I would be able to publish it in the future.

This whole process took four months and was only possible, because I already had a foundation from muggle maths, as no normal beginner could do anything like that. I also started combining it with mind arts, after I completed the formulas down to every second of your life. This was accomplished through making an archive in my mind, which detailed every single second in my life. I was still building my defenses at the start of these four months, but as those were already pretty good and kind of self expanding, I changed to making a memory storage system.

My defenses currently are a number of imaginary graphene like atoms, which can form into molecules which then have many functions like detection, repair, defense, counterattack and so on. These molecules can also snap together to form constructs, which were then layered around my inner core, which basically looked like a very complex but empty beehive at the moment.

So I started designing and then building a kind of library structure. This worked through some not yet overly complex calculations, so I could find the stored memories and a lot of the empty space of my beehive. At the start I wanted to sort memories after months, weeks, days, hours and minutes, until I finally settled for seconds, as the storage of these small data units was easier to store and navigate to, while also being easier to expand upon. While this did have huge performance issues, big data units had the same problem. The ultimate plan was to have multiple, interconnected systems for each of these units, but I started with deconstructing my current unsorted memories into seconds first.

These seconds were saved in a small octagonal library, with 8 different sides, which was also spatially expandable so suit my needs at any point in time and also be reusable for bigger projects. I used 1 side for each of emotions, sensations, primary information, secondary information, the whole second in itself, thoughts, actions and lifeforms like persons, animals, ghosts and organisms for every single second of my memories.

I was not even near completion, I was at approximately 20%, of this first step, but after I had sorted all my memories into these smallest bits of data, which will then be scaled into minutes, hours, days, weeks, months and years. I don't know if I will go any bigger, like maybe decades but I don't necessarily need it to conform to current physic rules, as I could also upscale it into irregular timeframes in which I researched a singular topic, though that is unlikely, as I have another plan for that. Though it will take me approximately 2 years to complete sorting everything into timeframes, after which the next point on my agenda would be sorting the main and secondary information into content packages, which will be another can of worms, as the arithmancy calculations for that step are immense.

For the current formula I use, I have made another structure, not unlike the octagonal library, just with a desk in the middle of it, which takes this smalest unit of data and calculates it into a value usable in arithmancy which is then saved in its 8 sides, though I should probably split the working and saving apart, so that I have working structures and library structures, instead of mixing them. Now I only need to find a design to match this working structure. Well, that is another plan for the future, as I currently have only one of these anyway, though I will probably populate my mind with many more, after I have found the design and a good way to save the information. Now that I think about that, maybe I could build a pedestal in the middle of the libraries, to hold the values, no never mind, that won't work. I will need to think more about that. I should first finish the current projects before planning and starting new ones. Back to the current working structure, it basically displays the end result of all the smallest units of data according to my improved version of the personality formula.

Fun fact, the original formula already took leap-years into account, so I at least didn't need to implement that.

While I learned a lot about arithmancy, I was still nowhere close to calculating my foci part, so I devoted the next 10 months the lifespan equation, which was a lot more complicated than the original personality one. While I understood the original lifespan equation and there was no way to know, if it was exact for me, I still wanted to mess with it a little bit, which in the end escalated into the timeframe of 10 months. I started with downgrading the lifespan equation, which worked on many magical factors, to a pure muggle lifespan equation, basically taking out any reference of magic. I could also test this equation, with data from human hospitals on recently deceased elderly, which I got through Henry, as he got contacts in those circles. I also requested information about this from archives of multiple Ollivanders. After I achieved a 90% success chance on muggles, I tried to upscale the new formula, which had a better success chance than the original one, to work with magic. I started with modifying it for muggleborns, as that was the easiest, followed by half-bloods and then pure-bloods, though in the end I combined all four of those into one, with a success rate of 70%, which was only 1% better than the current one, as there were way to many variables for a formula like this. The combining step alone took me more than 3 months, totaling 5 months with bringing the other three formulas to a rounded success chance of 90%, 55% and 70%. The difference between the half-blood and pure-blood equation being the many variables, while I also realized mid way through, that it combines most parts of the other three formula, after which I shelved it. I only used it for some anecdotes for the fusion of all of them, so I didn't need to do it again, though if I want to ever publish it, I would need to do it properly.

The remaining month was used to recalibrate the lifespan equation to be applicable to normal and magical animals alive. While I succeeded in fusing the two of them, I also tried to fuse the end result with the end result for humans, which while possible, is not really practical, as it is way to complex. That is why i shelved that idea and also why I didn't sink another 10 months into the lifespan equation.

I also celebrated my sixth unofficial birthday, which was not really any different than the last ones, except that the books were more advanced. I also got a coupon for a free artifact from a Celine Ollivander. This year I got no rock or literally anything without a sender sadly, so the question of the stone still stumped me.

The next project for this month was an idea I got, after seeing the coupon for enchanted clothing. The idea was something like second skin, which would stimulate my personal forth talent, which I have dubbed hypersensitivity, as it no longer improved automatically and I don't want to wast any potential of that power.

The design for it was an invisible second skin, which also reaches inside of any opening, like mouth, ears, nose. Into it should be incorporated feelings and sensations, just with the twist of being reinforced and amplified by a factor, through a direct link to my magic and inner core, to calculate the needed factor.

Preliminary sensations include being drowned in mud or other things, getting tickled at every part of my body, physical and magical pressure, reverse physical and magical pressure, not unlike a vacuum, itchiness, wetness, cold and warmth, seasickness, vibrations, magical resonance, ants or other insects/animals walking over my skin and maybe even emotions for my empathy, as the effect of my empathy gets amplified by my hypersensitivity.

There will also be various sounds, smells, tastes and I pondered over sight, but decided to make that feature toggleable, together with a whole mode for illusions, which I will use while meditating or alone. Everything will also be interchangeable, switch at random for a random amount of time until the next switch and so on. Henry called it a torture device, the first time I told him about it and while he is probably right, I couldn't care less.

I made most calculations for this second skin myself, while also acquiring buckypaper, as that is the material I decided on for it, though the end result will be of the same consistency as normal skin. The only problems were implementing an emergency shutdown for e.g. fights, a self healing function for the second skin, that I can feel the normal sensations through this second skin and different modes, depending on what intensity I want. I also decided to not implement a normal turn off button, as the minimum setting will be, where my hypersensitivity just barely advances. That one is titled easy, followed by medium, hard, hell, nightmare, impossible and full dive illusions for a total of seven modes, changeable through a mental command. I could have just named them mode one to seven, but that is way too boring and in no way intuitive. Additionally it also enhances external stimuli by a larger factor than the current selected mode, so I am still conscious of my surroundings.

I also gave it complete access to my memories, so that it could automatically advance its techniques depending on my experiences and reactions.

It took another day to find or better create the perfect one on one oath, as I wanted no one to know any details regarding my dealings with Mrs. Celine, as that second skin could be counted as an enormous weakness. Even Henry new only of the basic idea, a tool to advance my hypersensitivity, not more.