Rook stomped out of the entrance hall, up the stairs and down a corridor, all in a fury until she came to an empty passage, leaned against the wall and started to cry freely. Her first day, and already she was overwhelmed by it all: Madeline, her workload, her lack of sleep…and now she was probably going to end up being late to her first class. Why did she think she could do this? Oh, wait…she hadn't thought that, everyone else did! And how could she let them down now?

Rook let herself cry a few seconds more before taking several deep breaths. When at last she looked around to figure out where exactly she'd taken herself, her eyes met two clear blue eyes. She jumped.

"H-how long have you been standing there?" Rook asked the girl staring at her.

"I followed you from the Great Hall, after you shouted at the Malfoy boy," Luna spoke in her calm, dreamy manner. "I wanted to speak to you before, but I hadn't the chance."

"Oh…" Rook said, trying to wipe away her tears as discreetly as possible. "Um, I'm sorry. I don't want to make you late."

"I don't mind being late. I often am. I tend to get lost, you see."

Rook smiled slightly. "I do too. So, um… what did you want to talk about?"

"I just wanted to say that I'm sorry about Madeline. I know it must be hard for you, since you two seemed to get along nicely. I've always wanted a friendship like that…"

"Aren't you friends with Madeline?"

"Only when no one is around. Honestly, watching the two of you earlier reminded me of…" Luna trailed off. Her face didn't really change, but Rook sensed a sadness in her. "It reminded me of when I first came here."

"You know… I still want to be friends with you, if you'd want that," Rook offered uncertainly.

"It is kind of you to offer, although you may want to reconsider."

"Why?"

Luna blinked and stared at Rook blankly. "The same reason everyone else does, I suppose."

Rook wasn't sure what to say to this. Luna was three years younger than herself, but she was clearly very intelligent and quite discerning. Rook recalled herself at twelve: scrawny, quiet and awkward. Her peers had certainly enjoyed teasing her, but it never lasted very long. The news of Luna's unpopularity did not come as a surprise to Rook, but it seemed like such a waste.

"Luna, I want to be your friend," Rook assured her. "But right now, I should probably get to…" she consulted her schedule once more, "Charms."

"Oh, it's this way. Come on—I'll take you."

Rook followed Luna to the third floor. Thanks to Luna, Rook managed to run into the classroom along with the last of the stragglers. She turned to wave to Luna once she was inside, but Luna had already gone.

Charms was an awkward affair, what with Rook once again being the only fifteen-year-old in a sea of eleven-year-olds. She made a note to not arrive late to any of her other classes, so that she might choose the least conspicuous seat in each room. Her inconvenient placement in the front row of desks made her extremely self-conscious, and was a hindrance to the first-years unfortunate enough to be seated behind her. Ultimately, Professor Flitwick directed Rook to switch seats with a particularly tiny, curly-haired Hufflepuff seated at the back of the classroom.

Rook rushed out of the classroom as soon as Professor Flitwick had dismissed them. Her next class was on the seventh floor, and even though she had a head start, she just barely made it to the classroom on time.

Before the school year had begun, after Rook was given her first aptitude tests, Dumbledore had suggested that Rook be allowed to take Arithmancy along with the core subjects taught at Hogwarts. Rook had shown a remarkable knack for Arithmancy, and Dumbledore decided to advance her past the third year class. Professor McGonagall had voiced her disapproval of this decision directly to Rook herself, which made Rook very apprehensive.

Rook took a seat at the edge of the classroom before directing her attention to the professor who stood in front of the room with her arms crossed in front of her. She was an older witch, perhaps in her late fifties or early sixties, with silvery streaks in her long brown hair, and she wore rust-colored robes. She took a moment to eye Rook with some interest as she unpacked her Arithmancy textbook and other supplies. Rook noticed the professor watching her out of the corner of her eye and wondered if she should try to introduce herself. She decided against it and kept her head down, scribbling numbers in the corner of her parchment.

Once all the students had arrived and settled, the Professor began a lecture on the properties of the number twelve.

"Now, we've all discussed previously that when analyzing and implementing the use of multi-digit numbers, it is important to consider each digit separately, as well as…" the Professor trailed off, awaiting a raised hand to complete the thought. Rook looked around the class, but no one present seemed eager to jump in. Rook raised her hand tentatively and noticed her heart start to race nervously.

"Yes, Miss Rook."

"The interactions between the two numbers…?" she guessed.

"Naturally, though we typically refer to this as the relationship between the digits. Three points for Gryffindor."

Rook nodded and lowered her head once more, taking notes.

"Now, who can wager a guess as to the properties of twelve by considering the properties of one and two individually, and their relationship in this configuration?"

Rook looked around once more. Once more, there were no volunteers. Rook raised her hand again, a bit braver this time.

"Miss Rook."

"The number twelve, being a combination of one followed by two, seems like it might be a, um, naturally balanced number, maybe? One is calm, still and contemplative where two is full of movement, action and represents externalized communication. One and two are in direct contrast to one another, but are able to work in harmony where other numbers might have difficulty. Together they have great insight, and create spiritual balance. These attributes, as well as being both an even number and divisible by three, make twelve a uniquely harmonious number. I mean—I think…"

The Professor raised her eyebrows as Rook spoke. "What gives you the impression that the number two is representative of external communications?"

"Because… because with one person there isn't necessarily the need to speak aloud, or even to communicate through gestures or expression, whereas with two people, external communication is generally a given…" Professor Vector stared at Rook, neither confirming nor denying Rook's supposition. "Well, and…" Rook went on, feeling the need to say more, "Two always talks a lot."

The Professor's eyebrows shot up at this. "Excuse me?"

Rook blushed. "Um… Nothing."

Professor Vector stared a bit longer before continuing. "You're correct. Twelve is considered among the most harmonious numbers in Arithmancy. As such, it has often been considered a holy or divine number. Twelve points to Gryffindor, for your detailed reasoning."

As the lesson progressed, more students began answering questions, seeming to readjust after the long break. They were instructed to complete a set of practice exercises individually to prepare them for their first homework assignment. As the students worked, the Professor passed their desks, making corrections and suggestions to the students as she went. When she arrived at Rook's desk, she seemed to examine Rook's work silently for several moments. Rook's work was on the same scroll of parchment she had been using to take notes, which were also covered in several doodles. Rook grew self-conscious as the Professor hovered, and tried to focus on the problems in front of her.

"Miss Rook?" the Professor interrupted. "What are these here?" She indicated the doodles of two people standing next to one another on the page.

"Oh, uh… While you were lecturing, I was taking notes, and—"

"This pertains to the lesson?"

Rook nodded. "That's twelve. Or rather, One and Two together."

"Really? May I?" The Professor reached for the parchment and Rook nodded. She lifted the parchment to examine the figures more closely. "What gave you the idea for this?"

"Nothing, really. It just kind of happens whenever I'm doing math."

"Really? I understand muggles practice some very complicated maths, and I've always been curious. A lot of the muggle-born students who liked maths in primary school end up in my class, and one of them introduced me to algebraic expression. It's fascinating!"

Rook looked up at the Professor. She was childlike in her excitement, and Rook wondered if this could really be the same strict Arithmancy professor Malerna had warned her about.

"So this, the numbers as people, this just happens naturally for you?"

"Actually, there's a word for it that my aunt told me… I think it's synesthesia? But this is a very specific type, where my numbers have always acted like people in my mind. I can't help thinking them as people."

"Miss Rook, I would like to give you an additional assignment. I would like you to draw each of these numbers as people, and list their character traits. I'd like you to turn it in by October first, if you don't mind."

"Yes, Professor… um…" Rook trailed off, realizing she still didn't know the Professor's name.

"Vector," she replied, smiling kindly. "It's good to have you, Miss Rook."