He flipped a coin between the fingers of his right hand, the gesture not so much the result of practice as the sublimation of host of nervous ticks. Sitting with his flat-top trunk in front of him, atop it a quill and a notebook, he was contemplating an arithmetical riddle, manipulating an approximation of the problem in his head, occasionally writing and scribbling out equations with his left hand, the knut still making its rounds in his right. Eyebrows scrunched together, he thought deeply for what felt like an excruciatingly long time. Finally, there was a click– and not a metaphorical one. He heard it clear as anything - felt it too, a sort of abstract synesthesia; all of reality shifting a millimetre like he was at the centre of some incomprehensibly vast dial.

He knew the lay of the territory, now, finishing off the rest wouldn't be much of an issue unless something unexpected came up, the click becoming a discordant siren. Though that didn't seem likely to him, then, as he began to sketch a proof, which is a spell of sorts, inducing that same click in all those minds that can comprehend it. A spell and not a spell. A proof and not a proof. Arithmancy is a strange art few have the capacity to truly understand – fewer still bother to develop this capacity beyond what's required for one's NEWTS, yet if you want to know spells – not understand but know them as one does a friend - you have to study arthmancy. It models the structure of that stark edifice beneath magic and allows a practitioner not to create spells (as one cannot create spells) but rediscover them, find the connections between what magic exists and what was lost since its creation, and a means to derive the one from the other.

"Excuse me," he heard a girls voice say. He heard that voice and remembered that he was on a train, and across from him an attractive girl sat, an attractive girl with brown hair and these devastatingly sharp eyes. He remembered how excited he was to see her when she first stepped into the compartment and he wondered why it was he could always lose himself in arithmancy, even in the presence of a friend he hadn't seen in months.

But he already knew the answer: his love of magic. He had felt it so long he couldn't remember its absence, a mechanical urgency that dripped in time with his thoughts, but only his thoughts of magic. It was a beautiful, addicting sensation, relief combined with pleasure, the sensation of tonguing a sore tooth and eating a sweet joined as one. It was certainly pathological, the way this ticking compelled him, his head in a cloud of theory, abstraction and arithmancy, tempered only by the disciplined physical practice of wand movements combined with subvocal incantation. It was an unhealthy obsession, but a productive one - and so unlikely to be remedied.

"Excuse me," she said. "You know we were talking just then, before you zoned out on me. It's not healthy you know, staring at the parchment and ignoring your friends". They'll be time for studying when we are at Hogwarts," this meant something coming from Hermione, as she was near as interested with magic as he - though hers more like a deep abiding curiosity than an obsession.

"I wanted to work up something clever to show Vector,' Harry said, just as Ron walked into the compartment the two were siting, sat beside Hermione and kissed her lightly.

"The way that women swoons for you," Ron said, his brown eyes twinkling as he did, "I'd swear you've spent half your career at Hogwarts underneath her desk." Hermione smiled lightly and slapped him on the chest.

"Slow, concentric circles," Hermione said, her voice now a perfect imitation of Vector's breathy, ironic drawl.

Harry grinned, " So that makes two of us, then. Or do you just share a preference?"

Hermione blushed and Ron howled.

It was almost depressing how well they had known each other. Sorted into Gryffindor, among the brightest students in their year, they spent hour after hour together in the library, then hours more practising spells in their common room, and after sleeping they'd get up and take mostly the same classes, always sitting together. When lectures got boring Harry would devise ruthlessly difficult Arithmancy problem, Ron solving most of them with a sort of unflappable determination, Hermione solving all of them with a casual intensity. After five years of this, Harry knew Ron and Hermione more than anyone, this including his sorry excuse of a family. He envied them their relationship, the two of them falling together so simply and without thought.

Everything came so easily to them - well, everything save for Arthmancy, but they did well at that, too, with a little work.

"Time to get changed then," Hermione said after a time, dragging a deep black robe over her muggle shirt and jeans. Ron was already wearing his Hogwarts clothes. Harry waved his wand, casually performing a switching spell, his muggle clothes instantaneously replaced with his Hogwarts robes, which only moments before were inside his trunk.

Hermione raised an eyebrow, "A switching spell, Harry. Without line of sight?"

Ron butted in, "How'd you pull that off."

Harry spent a pleasant few minutes explaining what had taken him only moments to do.

"So you cast Henfeather's Eldritch Sight and then combined it with switching spell," Hermione said, she then waved her wand and switched her Hogwarts robes with the dress robes in her trunk, then waved her wand again and swapped them back. "It's not half as clever now that you have told me how you did it. Is this is what you were working on for Vector?" The train slowed down and stopped, and the three of them walked out of their compartment and left the train, Harry explaining that he was working on pure (not applied) arithmancy for Vector.

"I got the idea for the switch when I was reading about Grindelwald. He used to switch peoples hearts with heated stones," Harry said. Ron grimaced. "Best as I can tell that's how he did it."

Harry was tall and thin, had the build of a seeker but no interest in Quidditch. He wore fine robes, but they were poorly maintained, as he never bothered to cast the standard charms fashionable kids used to keep their robes from wrinkling and fraying. He never quite understood fashion. It all seemed so arbitrary. Ron had a head for it. He should probably ask for his advice this year. If he was to be a lonely obsessive, he may as well look good doing it, he thought, but soon enough he felt the tick in his mind, and he began to think about transfiguration and its obvious connections with animation charms despite a completely different developmental history-

"Are you even listening to me," Ron said.

"What?

"The boats, remember when we were first years, and had to get in those boats. I was bloody terrified," Ron said, pointing at the large group of first years, each of them lining up behind a group of prefects who were set to lead them to the traditional first-year trip across the justly named Black Lake. "Fred and George had told me about the giant squid, neglecting that the things bloody harmless. "

Harry chuckled, "I didn't know what was going on. Was too confused to be scared."

"I had read all about it all in Hogwarts a History," Hermione said in the bossy tones of her younger self, "so I wasn't scared or confused. I knew exactly what was happening." They all laughed together. The three of them continued chatting about their early years of Hogwarts, continuing to do so as they stepped into a horseless carriage and made there way at relaxed pace down the cobblestone path that leads from Hogsmede station to Hogwarts School of Witchcraft and Wizardry.

OOOoooOOO