I wrote this story for the Creative Writing contest on Spacebattles a year and a half or so ago. I've been meaning to transfer a copy to this site for quite some time, but I only just now actually sat down and did it due to the way that this site goes out of its way to be as difficult and impractical to use as possible. The theme of the contest this oneshot was written for was "lessons learned."
After reading a few Harry Potter fanfics that used a fairly common fanon version of what arithmancy is and what It is for, I had the following idea of my own. Then I remembered the CrWri contest that was going on at the time on Spacebattles and realized how well it fit, so I decided I might as well give it a go.
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As Hermione waited for her first class full of students she ran her fingers along the edge of the familiar blackboard. She had once thought of getting a job at the Ministry, but when the position of Arithmancy Professor was offered to her she simply couldn't turn it down. The subject always fascinated her, the way that it seemed to make sense where so much of magic didn't, and then suddenly took that one crucial step into the illogical. It was only because of arithmancy and its pretended adherence to the laws of physics that things like the wizarding wireless of her student days, or the new 'wizardnet,' as people were calling the Wizarding World's new adaptation of the internet, were possible in such magic-saturated places.
She sat down in the chair behind the familiar desk, on which sat a familiar arithmantic clockwork bell that had signaled the beginning to so many classes, and remembered her own first day in one of the desks facing her.
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Hermione almost squirmed in her seat in anticipation as she waited for Professor Vector to start class. Shortly after the last student found his seat a small bell on the Professor's desk let out a surprisingly deep chime, bringing the class's attention to the front of the room. Professor Vector stood and pushed in her chair before she began their first lesson.
"Hello, I am Professor Septima Vector. I can see that everyone is here, and it looks like I have a majority of Ravenclaws this year, as seems to be usual. Before we start on learning arithmancy, I would like to ask you all a question about it. Tell me in your own words, what is arithmancy?" She pointed to a Ravenclaw student with her hand in the air. "You please, first your name, then your definition."
"Claire Miller. Arithmancy is using numbers and math to predict the future and understand the nature of spells, or even to create new ones. We use it most with ancient runes to create stronger wards and enchantments, and cursebreakers use it to help break them."
Professor Vector nodded, but she didn't give out any points. "You are half right. Arithmancy can be used to predict the future much more clearly and reliably than divination, although it has a number of disadvantages. One being the fact that, unlike with divination, predictions made with arithmancy are always predictions of what is likely to happen, rather than what is certain to happen. We do use arithmancy little bit with runes and erecting wards. Arithmancy however, cannot and will not be used to understand or create most spells." She paused slightly at the looks of dismay she was receiving before she continued on. "This is not to say that one cannot do magic using arithmancy, or even that the magic in question will look any different from what you might learn in a different class. Nevertheless, you will never be able to create an understandable equation that describes a spell such as Stupefy or Accio. This is because Arithmancy is an entirely different way of doing magic."
She touched the blackboard with her wand and it flipped over, as if there was an empty space behind it in the wall to which it was attached. On the other side was a rather odd, if simple, looking equation with sketches taking the place of two numbers. "Purely non-arithmantic magic, if rendered into an equation, might look something like '2 + igloo = cheese,' as you see here. This kind of magic forces the world to work entirely differently from how it normally would, which makes things like more advanced muggle technology stop working or even break down if it there is too much of it." She pointed to Hermione, who had her hand up. "Your name, then your question please."
"Hermione Granger. Is the way that the magic we have been learning eventually stops working, like transfigured things eventually going back to what they were originally, a result of that?"
Professor Vector smiled. "Five points to Gryffindor. Yes, because of the brute force approach taken by that kind of magic it will sooner or later come undone when that part of the world goes back to normal. You have forced the world do change to what you wanted, and it doesn't stay changed forever. With arithmancy however, you instead work with the way that things work, but you use the rules in a way they aren't supposed to be used. For instance:" She tapped the blackboard again, and it flipped again to show am equation and diagram that had not been there before she flipped it the first time.
The professor pointed to a pair of differently sized rectangles. "Say that you have two boxes. One is very tall but thin and the other very wide but short. If you put one on top of the other you get a box that is tall with a wide part sticking out from the bottom," she said as she pointed to the next image of an irregular hexagon. Then she moved on to a fourth polygon. "If you use arithmancy however, you can convince the world that you are 'adding the height of one box to the width of the other,' getting a single, normal box that is both as tall as the first one and as wide as the second, and has much more space than the two of them combined actually would. Of course, a real arithmantic spell would be much more complicated than that, and it would be much closer to how things actually work. That brings me to my next point."
Professor Vector tapped the blackboard again and it flopped over one last time to show a single sentence underlined several times; a sentence that she then proceeded to read aloud. "Arithmantic spell equations are ALWAYS wrong!" She turned back to the class. "Now, this isn't to say that they don't look right. A proper arithmantic equation must be very close to being accurate, which is why it is important to know as much about mathematics as you can. Muggles have made many advancements in mathematics in recent centuries that can help us to…"
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The chime of an unnaturally deep bell brought Hermione from her reminiscing. She stood and pushed in her chair. As she did so, Hermione counted the third years before her and found no less than she expected. Good, that meant no one was late to their first lesson.
Taking a deep breath, she began her class. "Hello class, I am Professor Hermione Granger. I see that everyone is here, but before I start teach you any arithmancy I want to ask you all a question about it. Tell me in your own words, what is arithmancy?"