As Iris and her new friends sat down in the Arithmancy classroom, they could hear the Gryffindors they shared the class with eagerly chat amongst themselves.
"So…" Iris said, turning to where Daphne and Theo were sitting on her right, "I've been meaning to ask. How exactly does arithmancy manage to translate magical effects to spells? I could understand the basic theory for almost all of the other classes, but the Arithmancy textbook was really difficult."
"Honestly", Theo replied, "I don't really understand it either. It's supposed to be the theory behind all magic, but I haven't really read much into it, so I don't get it. Daphne probably knows though, don't you?"
"Well… it's actually a bit of a common error to say that Arithmancy is the foundation of all the magic. Arithmancy is actually just one of the two uses of the discipline we call 'magical mathematics', along with s–… certain types of higher-level spells that Arithmancy is based on. Arithmancy is considered the 'truest' expression of magical mathematics by… dominant academics though, so generally, you'll see the two equivocated."
"Now," she said, "as to what exactly Arithmancy entails… well I suppose you'll just have to wait and find out like the rest of the students, now won't you?"
After Theo playfully butted her shoulder, she clarified: "I'm honest, I don't know very much myself beyond the absolute basics, and I'm sure Professor Vector can explain it much better than I ever could. Be careful though, I've heard he's pretty biased against Slytherins, especially us… 'dark creatures'."
"Also, Iris, don't feel bad about not understanding the textbook. My mother is quite adept at Magical Mathematics, and she's repeatedly criticized Prof. Vector's choice of textbook as being far too advanced for a beginner's class."
As if summoned by Daphne's reference, the professor in question chose that moment to stride through the door, as a loud gong rang throughout the castle. Dante jumped from where he was lightly napping in his seat.
"Good morning class! My names is Séamus Vector, and I'll be your Professor of Arithmancy for the next seven years. I expect to be addressed as either 'Professor', 'Professor Vector', or 'Sir'."
"Now, before we begin, I'm curious, does anyone here feel that they can give the class a good, introductory definition of Arithmancy?"
Hermione's hand shot up immediately; Iris smiled at her fondly.
"Yes, Ms…"
"Granger, Sir!"
"Ms. Granger then. Could you give the class a brief summary of the field of arithmancy?"
"Well sir, arithmancy has to do with creating mathematical equations to describe the physical forms and effects of spells, to act as a map to express the mathematical equations of certain phonological–"
"I think that's enough for now, Ms. Granger, we don't want to give the whole semester's content away!"
Hermione blushed fetchingly and ducked her head as the whole glass chucked. Iris gave her a supportive nod and grin.
"Yes, as Ms. Granger said, Arithmancy describes the process of describing magical effects through the use of equations. However, what she did not tell you was that those equation are not the kind that our more newly-gifted students would find at their muggle primary school, or even most muggle colleges! Indeed, where muggle mathematics, with the exception of very high levels, only deal with the three physical dimensions, Arithmancy deals with the higher dimensions necessary to describe magic."
Ron raised his hand, and began to speak without being called upon.
"Sir, what exactly–"
"Patience, Mr. Weasley," the Professor said, slightly amused, "is a great virtue. If you'll let me finish, I'll most likely answer your question."
"Now, higher dimensions. I'm sure many of you, Mr. Weasley most likely included, are wondering what exactly what a higher dimension is, and how it relates to magic."
With a precise wave of his wand, the Professor summoned a chalkboard from across the classroom.
"Now", he said, drawing a straight dash on the chalkboard, "this, right here, is an object in a single dimension."
Danny piped up: "It's… it's a line? What does a line have to do with math?"
"Exactly Mr. Potter, a well-thought question!"
"You see class, this isn't simply a line, it can also be understood as a one-dimensional object. This means that there is only one axis of possible movement and manipulation in this object, the right-left axis, or, in Arithmantic parlance, the First Axis."
"I see many of you still look confused. Think of it in more practical terms. Imagine that you're walking down a narrow path, so narrow that it can only fit one person. Now, when you walk, the only way you can walk is forward or backward. This is the axis of movement, a path along which one can step."
"Now, to make things clearer, let's consider a two-dimensional object" He paused, and drew four more straight lines on the chalkboard, forming a square.
"You see, in this two-dimensional shape, the square, we've added another axis of movement, the Second Axis. If we're using our path example from earlier, this is like taking that path, and expanding sideways to form a large paved area. Not only can you step forward or backwards, you can now also step left or right."
"The physical world that we see, then, is filled with objects in three dimensions. We have our First Axis, walking forward and backward, our Second Axis, walking left or right, and our Third Axis, jumping up or falling down. Are there any questions so far?"
A Slytherin boy down near the front raised his hand.
"Yes, Mr.… Leopold?"
"U-um, Professor, how is it one-dimensional, if you can walk forward and backward. Wouldn't that be–?"
"Well, as it states in the textbook, one the very second page in fact, movement forward and movement backward along an axis can be considered simple mirror images of each other, one occurring in the positive direction, and one in the negative."
He looked around at the class. "As strange as it might seem to you all, in Arithmancy you must consider walking left not as walking in a distinct direction, but as walking negative right."
"Now," he said, turning back to the board and scrawling several names and dates, "many of you may be wondering, this is all well and good, but how does it relate to magic? Well, to understand that, we must first understand a bit of history."
"Before the publishing of Sir Francis Bacon's 'New Magic from the Fires of Righteousness', wands were merely used as a focus for magic, something to channel one's magic through. A wizard or witch would channel their magic through the wand, and into an object, in order to change or manipulate its outer form. Now, while this is indeed a powerful form of magic, it is not nearly the length or breadth of what magic could do, and so the field of magical mathematics was developed."
"What was so revolutionary about Bacon's work was his adaptation of the muggle art of algebra, used to describe the physical world, as the basis for an entirely new, magical form of mathematics he called Arithmancy, used to describe the properties and effects of magic."
"Bacon discovered that spells, in essence, could be understood as constructs in a seven-dimensional space, with their physical forms being described in the three lower dimensions, and their magical effects being described in the four higher."
"Now," he said, chuckling, "I don't expect any of you to gain an ability to picture the seven-dimensional forms of spells by the end of this year, nothing like that. I assure you, that ability only comes to those with years and years of Arithmancy training.
"However! It is the goal of this class, and your first year of arithmancy education, to be able to accurately understand and explain the equations for six basic magical effects: lighting, dimming, levitation, changing color, and force projection. You will also be expected to explain, but not demonstrate, how those five magical effects can translate into the components of wanded spellcasting."
To Iris's confusion, there were a few groans from the Gryffindor side of the classroom.
"Yes, yes, I know that many of your parents have told you that you will learn to design your own spells in this class. And you will, I assure you, starting in your fifth year."
"I would like to stress this point: experimenting with original spells unsupervised is dangerous. Even once we've learned how to translate these equations into incantations and wand movements, I do not want any of you to go around thinking you can use them to make your own magic."
He looked at the Gryffindors, who were doing their (frankly pathetic) best to mask their excitement. "I know it may seem like I'm just some stuffy old authority figure giving you a needless warning, because I don't want you to perform 'cool magic', as another one of my first years once put it, but I assure you, I am deathly serious. Anyone caught developing their own spells unsupervised even after fifth year, will be suspended from Hogwarts, and quite possibly expelled."
Well, the Gryffindors sure were looking a bit less enthusiastic now.
"Do you all know what happened to the last student that was caught experimenting with his own spells in Hogwarts? No? Well let me tell you. It was around twenty years ago, and he was a fourth year named Jesse Massen. He thought he could develop a color-changing variant of the lumos charm using all the arithmetical knowledge he'd gained in this class."
"Now, I'm sure Mr. Massen was thinking what many of you are right now: 'the lumos charm? How could experimenting with that be dangerous? It's just a little glow of light!' He believed that he was exempt from my warnings, because the spell he was altering was too simple to ever possibly hurt him."
"Do you know what happened to Jesse Massen, who was working on a spell too simple to ever go wrong? They had to pick him off of his dorm room walls."
The whole class was completely silent, with many students, even the Slytherins, looking quite queasy.
"That is why, students, you will be suspended for experimenting with spell creation. Not only for your own safety, but for the safety of others. What do you think would have happened, if Jesse Massen had decided to work on his spell when some of his dormmates were present?"
"Yes," he said to the gasps of the class, "exactly."
After around thirty seconds of silence, his glare receded, and he turned back to the chalkboard.
"Well! Now that we've covered that bit of nastiness, let's resume where we left off!"
He turned towards the Slytherin side of the classroom. "Mr. Leopold! Since you were so eager to interrupt during my lecture, perhaps you could help me pass out these copies of the course syllabus?"
The rest of the class proceeded without further gruesome interruption, covering the goals and requirements of the course in further detail, and the magical effects they'd be learning to describe.
"Iris! Iris! Hey, Iris!"
Startled by the call for her, Iris turned around, and saw Hermione frantically motioning for her.
Iris's face broke out in a beaming smile."Hey, Hermione! How are you! I haven't seen you since the train!"
"Oh my word Iris it's been incredible! You know I don't think magic being real had really sunk in until now, it's like I knew that it was, but I didn't know it, not until I got to Hogwarts where everything was just so, well, magical! I'm so excited, Hogwarts has one of the largest libraries in the whole world! I can't wait to go explore it, there are just so many new things about the magical world that I have no idea about! Did you know that they actually still have Lords in charge of their government here? There's jus so many new and different things, I can't wait to get to know all about it!"
"I know!", Iris said, Hermione's exuberance beginning to affect her, "Isn't it so wonderful? It's like, all our lives, we've known that we were different, and now we finally know why! I can't wait to learn everything about magic!"
Hermione frantically nodded her head at each of Iris's points.
"I know! I was so worried about being behind because my parents don't have magic, but everyone in Gryffindor tower is just so nice and helpful! They told me that most of the students from families with magic won't know any more than I do, so I should be fine! It's actually really funny, they all seemed so curious and excited about the muggle world, almost as much as I am about the wizarding one!"
Iris's smile grew strained at the mention of muggles, but was soon replaced by a genuine grin at Hermione's adorable earnestness.
"Yeah," she said, looking around for her Slytherin friends, "I actually made a bunch of friends in my new house, they've all been really helpful in understanding my new world and culture. Oh, there they are! Hey guys, come over here!"
Iris waved the rest of the Slytherin sixsome over, ignoring their guarded looks.
"Hermione, these are my new friends, Draco Malfoy, Theo Nott, Daphne Greengrass, and Blaise and Dante Zabini. Guys, this is Hermione Granger, I met her on the train."
When she saw none of the others were making moves to greet Hermione, Blaise stepped up, and introduced herself with a tight smile. "Hello, Ms.… Granger, was it? I'm Blaise Zabini, it's very nice to meet you. While I'd love to talk to you, and meet one of Iris's other friends, we really must be getting to our charms class with the Ravenclaws."
Shelving their obvious reluctance as an issue for later, Iris turned back to Hermione. "Hey, Hermione, it was so great seeing you, but we really do have to go. Do you want to meet up in the library sometime, so we can explore it together? How about Saturday?"
Hermione, seemingly oblivious to Blaise's coldness, nodded enthusiastically. "Yes, I'd love that! It was so nice to meet you Blaise, and all the rest of you too, you should all come with us! I'll see you on Saturday, Iris!"
As Hermione scampered off to join the retreating Gryffindors, Blaise turned to Iris with a serious look on her face.
"Darling, I'd be… careful with that one, if I were you."
"What? What do you mean?"
"Iris, she's a mudblood", Dante said, an uncharacteristically serious look on his face, "she may seem all bright and eager about magic now, but I'm telling you, in five weeks she'll be talking about how 'backwards' the magical world is, and how all the 'dark wizards' need to be kicked out of Hogwarts before they can sacrifice her in a blood orgy, or whatever other bloody nonsense they'll tell her up in Gryffindor tower."
"What? Hermione's not like that! She's nice, and wonderful, and really caring! Sure, she can get excited sometimes, but that's no reason to say she'd believe awful things like that!"
"Darling", Blaise cut back in, "I know that she probably seems that way now, but she's a mudblood in Gryffindor. You know what the muds think about vampires, do you really think that the Gryffindors will discourage that notion? I guarantee that by Samhain, she'll spend all your conversations telling you about what an 'awful shame' it is that 'dark creatures' like me are allowed to prey on 'innocent light witches and wizards'."
"Iris," Dante interjected, "for Circe's sake, the muds will even racially discriminate against other muds, and they're the same bloody race! How do you think they react to races that are actually different? And not one that claims to be the same as them, like the Nic sorcerers!"
Iris was shocked. She understood where her friends were coming from, she really did, but were they really ready to judge Hermione based on what all those other mudbloods had done? They didn't even know her!
"Morgana, darling, think about you," Blaise said, grabbing Iris's hand in concern, "How do you think she'll react learning that you could 'steal her face' whenever you wanted? The mudbloods are the chief supporters of that 'Talent Registry' Dumbledore proposed!"
"Blaise…" Iris said, shocked, "I… I don't think that Hermione's like that at all. She's so wonderful, I can't see her acting like any of those other mudbloods. I mean, isn't one of the biggest Rell policy goals to take mudbloods away from the muds? If you believe that, then you can't believe that she'd believe those awful things just because she's a mudblood!"
"Iris" Draco said, "I get why you'd think that, but the mudblood adoptions… They're adoptions. It's not… it's when they're babies, not when they're twelve! Once they start Hogwarts, they've already gotten all those mud ideas about hating other races rattling around in their heads, and then they all get swept up by the Nics, who start prattling on about the muds' 'superior culture'! You really think that little mudblood will be different?"
"She's not 'my little' anything Draco!"
Realizing she was almost yelling, Iris took a deep breath, and composed herself. "Look guys, I realize that you're only looking out for me, and I really appreciate that. But I promise, Hermione is different. Even if she does start talking about how we're all evil, I'll be there to explain things to her, and set her straight."
"Alright…", Dante said, raising his hand and cutting his bond-mate off, "we believe you, Iris. We just… we just don't want her to go breaking your heart or anything, alright? Promise you'll come to us wh–… if she really ends up hurting you?"
Cracking a slight smile at Dante's protective tone, Iris nodded. "Alright Dante, I will, I promise."
Shocking both herself and Dante, she leaned over, and embraced Dante in a brief hug.
"Thank you, really."
"Alright!" Draco said, either not knowing or caring about the stunned faces of the rest of the group, "now that we're done fighting, let's go! We're gonna be late for charms, and I wanna make a good impression on Professor Flitwick! He's a quarter Coblynau, you know!"
The rest of the group laughed as Draco shot off down the hallway, as the rest of the group followed, walking closely together. Realizing Blaise hadn't let go of her hand, Iris was about to pull back, until she paused. After a moment, she relaxed her arm, and allowed Blaise to pull her the rest of the way to class, rubbing slow circles on the back of her hand.
AN: Chapter title comes from the book by Archimedes of the same name, which is one of the first major mathematical texts ever written. I've always thought it was way too badass of a name to use in a math paper, so I'm using it here.
Seriously, it sounds like an epithet for Death. Like, he reckons the sand falling in the hourglass of your life, or something.
—
Fanfic Rec is Rebirth by Athey. She writes perhaps the only realistic, non-creepy HP/LV slash I've ever seen. With anyone else, the age difference makes it creepy real fast, but this fic, along with a few of her others, have several inventive, original way to make it work quite well.
—
Yes, Vector is a man in this fic, with a name change.
Firstly, if you haven't noticed by now, there's a pretty significant gender imbalance among prominent Nics. Their values say that women should be homemakers first, remember? Sprout is actually only female professor in the school, and that's only because Herbology is a 'woman's discipline'. You'll find several prominent female characters from canon have been gender-swapped in this fic.
Secondly, it's not the masculine version of her canon name, "Septimius Vector", because that's a name coming from a Roman emperor, and that is a very seclusionist type of name in this fic. Séamus is the Irish from of James, a popular Integrationist name, as evidenced by James Potter. If I'd kept Vector as a women, I'd have made her "Sheena".
