Ancient Runes was wonderful, just as Remus had expected. The Ancient Runes professor, a stocky man by the name of Professor Finley, seemed to be a little wary of Remus—but he wasn't so obvious about it that James noticed, which was extremely lucky. Remus liked Professor Finley, werewolf biases or no werewolf biases—he was animated, funny, and seemed to be fiercely intelligent. It didn't matter if he didn't make eye contact with Remus all that often.

He started them right off with a vocabulary chart and a basic overview of grammar. "The hardest part at first is the alphabet. Ancient Runes has seventy-seven different characters, and many of them make exactly the same sounds. The pronunciation is heavily anglicized, but that doesn't mean that you don't have to learn the accepted modern pronunciation for each individual character."

Remus had already memorized much of the alphabet from the days stuck at home in between full moons, so he reckoned he had a head start. James, too, was staring at the list of characters leisurely; Remus supposed that he'd already memorized half of them. Sometimes, Remus envied James' eidetic memory... and then he remembered that he really didn't want to be any more unique than he already was.

That afternoon, after classes had ended, Remus and James met up with Sirius and Peter in the corridor. It was odd, having a different class schedule for the first time in their Hogwarts career. "Let's go flying," said Sirius. "Regulus is going out for Seeker this year, so Mum bought him a new broomstick. I've nicked it, and he'll never know. It's a good broom, too—Silver Arrow. I'll let you have a go, James…"

Remus happened to know that James had a Silver Arrow at home that he loved very dearly. His parents, though, wouldn't let him bring it to school—not after James had broken the first four—so James had to make do with the highest version of the Cleansweep. It was just about the same in terms of quality, but James always said that the feel of the Silver Arrow simply couldn't be replaced. Remus didn't understand, but he took James' word for it.

James' face lit up for half a second, and then he cast a sorrowful glance down the corridor. "Can't," he said miserably. "I've got Muggle Studies next, and then I have to go to Divination tutoring."

"You have Muggle Studies?" said Peter. "But classes are over."

"That's just the way that classes are arranged this year. Muggle Studies is a bit later in the day." James sighed. "Perhaps tomorrow? Or this evening? We could sneak out under the Invisibility Cloak and go flying during nighttime…" A wicked gleam appeared in his eye. "Or I could just skive. Muggle Studies can't possibly be very difficult. I'll just catch up next time and skip it today… after all, we never really learn much in the first class, anyway. I'll just tell the professor that I was ill or something. You lot will vouch for me, yeah?"

"You can't skive," said Remus. "Madam Hooch knows that you're taking all the electives. She'll see you flying during your Muggle Studies period and tell Professor McGonagall or something."

"Why would Rolanda know that I'm taking all the electives? I'm not even taking her class anymore. That's ridiculous!"

"First off, the teachers tell each other just about everything." Remus made a face. "About me, at least. I gathered that much from Professor Questus. Second, I heard Madam Hooch grumbling to Professor McGonagall the other day. She's worried that your studies will conflict with Quidditch. Typically, people on the team don't take all the electives."

"When did you hear this?"

"Breakfast yesterday, I think."

"What did Minerva say?"

"She said that she sincerely doubted that your studies would get in the way of Quidditch. She said that it was more likely that Quidditch would get in the way of your studies."

James let out a hefty snort. "And right she is. Thank goodness for Remus' superhuman hearing, eh?"

"Shush!" said Remus.

"Ah, stuff it. No one's around," said James. Then, turning back to Sirius: "I guess we'll have to go out this evening, after I'm done with Muggle Studies. Have fun without me, mate."

"Me? Have fun without you?" said Sirius dully. "That's unlikely. Come on, Remus and Peter… let's go to the common room and do our schoolwork, I guess. Nothing's fun anymore when it's only three of us."

Remus would never say so, but he rather agreed. Sirius' attitude without James around... well, suffice it to say that it often left much to be desired.

"I wish James hadn't taken all the electives," said Sirius. He was lying upside-down off of his four-poster, watching Remus try to handfeed a distrustful Francine. "Things are so much more boring without him. What does he expect me to do without him? Take a nap?"

"It's only two hours," said Remus fairly. "He's only got to go to two classes."

"It's a hundred and fifty minutes," groaned Sirius. "A hundred. And fifty. Minutes. That's so many minutes! How am I supposed to survive without James for a hundred and fifty minutes?"

"You survive just fine without him while he's at Quidditch practice."

"But I watch him practice Quidditch and cheer him on! You wouldn't know. You're always back up here in the dormitory studying. What a lousy friend."

Remus ignored the jab, even though it stung considerably. Sirius always got like this when he was angry. "I'm fun too, aren't I?" he retorted. "I bet that you, me, and Peter could have just as much fun as you do with James. Maybe more."

"Yeah?" said Sirius. He sat up and stared Remus dead in the eyes. "Prove it."

"Sure," said Remus. "Let's go to the library."

Sirius flopped back onto his bed and groaned. "Remus! That's not fun!" Then he sat back up. "Unless you're planning on playing a prank on Madam Pince?"

"Erm, no."

"Ughhhh. Any other bright ideas? Preferably ones to do with sneaking and spying?"

"We could sit outside the Muggle Studies classroom and listen in to the lesson."

"Extra school? Why would I want to do that?" moaned Sirius. "Anything to do with hexing people?"

"We could practice duelling. I'm getting rather good at nonverbal Disarming Charms, and the duelling club is going to start up anytime…"

"I don't like duelling with you. You get too serious about it. Anything to do with inconveniencing Slytherins?"

"We could… I mean… hm, no."

"Argh! You don't even know what fun is, Moony."

"We could go to Hagrid's," said Peter quietly. Remus had almost forgotten that he was there.

Sirius paused. "Actually… yeah, that's better than all the boring nonsense that Remus was suggesting." He hopped out of bed. "Let's go, then."

Remus smiled, put Francine back into her container, and then tucked the container under his arm. "Good idea, Peter," he said, and then the three of them started trekking across the grounds in the direction of Hagrid's hut.

"You were only joking, though, right?" whispered Peter to Remus—the two of them were lagging behind Sirius, who was much healthier than Remus and had far longer legs than Peter. "You didn't really think that going to the library is fun enough to hold Sirius' attention?"

"Er… it's not my fault that Sirius' attention span is that of a hyperactive rabbit," said Remus.

Peter erupted into hysterical giggles. "Merlin's beard, Moony, you did! You actually thought that he would go to the library with you! Sirius Black, set foot in a library? I can't believe you, Moony!"

Remus elbowed Peter in the side, but he couldn't stop smiling.

It wasn't long at all before Hagrid saw them approaching and ran out to greet them. "Sirius! Remus, Peter—Come on in, yeh three! Wan' some tea or summat?"

"No, thank you," said Remus politely. "Sirius has just accused me of "Not Being Fun", and I'd like to redeem myself in his eyes."

"He has a worse sense of fun than a Dementor does," muttered Sirius. "I asked him for suggestions of fun things to do, and do you know what he said?"

Hagrid huffed a laugh. "What?"

"He said 'the library'. And then he suggested practicing our wandwork and extra school. Ridiculous!"

Hagrid started laughing harder—a great, booming laugh that hurt Remus' ears a little. "O' course he did!"

"I'll have you know that I am very fun," said Remus. "Just because you're cleverer than I am and don't have to study as much doesn't mean I'm not fun. I am thoroughly convinced that Peter and I can succeed in entertaining Sirius for the next hundred and twenty-five minutes or so. James is in Muggle Studies—"

"—and he has Divination tutoring right afterward—"

"—so Sirius needs something fun to do while he waits. Do you have a dangerous magical creature, perchance? Preferably one that bites or flies?"

Sirius poked Remus in the arm. "Found one!" he said gloatingly.

"Don't be ridiculous, Sirius. I don't fly, and I don't really feel like biting anyone right now." Remus looked around Hagrid's hut, looking for inspiration. "Animals? Plants? Any ideas at all, Hagrid?"

"Well, I've just picked up a batch of Flesh-Eatin' Slug Repellent for me pumpkins. Yeh could help me apply that, but it's a bit gross."

"Gross!" said Remus, snapping his fingers. "That's it! Sirius will love that."

"I guess," mumbled Sirius.

Sirius was reluctant for a while, but it turned out that Remus had been right—as soon as Sirius got to spray Flesh-Eating Slug Repellant directly onto the slugs and watch their skin melt away, he was once again in a wonderful mood. Downright gleeful, in fact.

Remus rather thought that Sirius was the one without a normal sense of fun, but he didn't say so.

"I'm kind of angry with James for taking so many electives," Sirius confessed over supper. "It's not as much fun without him, and he knew that it wouldn't be. He's abandoning me to do things that he doesn't even like!"

"James likes showing off his skill," said Remus. "As annoying and irresponsible as he can be, I'd reckon he's the brightest one in the school. Not many people are clever enough to take all the electives, and I think he just wants to prove himself. Quidditch Captain, taking the most classes, et cetera… you know he likes all that."

Sirius shoveled a bit of pork into his mouth and chewed thoughtfully. "But why is it more important than me?"

Remus sighed, frustrated. "He's not choosing classes over you, you absolute nimrod. He still spends nearly every waking second with you. He's in all of your classes, even though you're not in all of his, and he'll come right back here when he's done with Divination tutoring. Let him be his own person, for heaven's sake."

Remus finished off his glass of water. Sirius was staring at him with a very queer look on his face. Remus wondered if he'd said something rude... well, excessively rude.

"I… I'm sorry, I didn't mean to be so harsh," tried Remus.

"No, no, it's fine," said Sirius. He was laughing now. "It's just… for a second there, you sounded exactly like John Questus."

Oh. Remus wasn't sure whether that was a good thing or not. He suspected not.

"You're getting a lot braver, you know," said Sirius. "You were a bashful little coward in first year. It's a lot more fun spending time with you now than it was then. You're cooler. Unlike Peter, here," finished Sirius, jerking thumb in Peter's direction. Peter blushed and looked away. "See? Peter's still just like first-year Remus. Worse than. But you're funny—well, you've always been funny. But now you're louder about it, you know?"

"I don't know what you're talking about," said Remus primly. "I've always been loud about it. Loud and outgoing, that's me."

Sirius laughed and threw a pea at him, but Remus, whose reflexes had been drilled into him by Professor Questus in his first-year duelling lessons, caught it expertly and threw it back. Nearly Headless Nick gave them a dirty look, so Remus and Sirius stopped throwing peas and left the Great Hall, giggling and laughing, so that Remus could finish feeding Francine and get a start on his Arithmancy homework. Hagrid had given him a few tips about caring for Bowtruckles while they were at his hut, so Remus felt perfectly prepared to try to wring just a bit of affection from Francine.

It wasn't until James was back and Remus was trying to fall asleep that night that he realized.

Sirius had insulted Peter, and Remus hadn't defended him. Hadn't even tried. Hadn't even checked to see if Peter had been laughing, too. Hadn't even thought about it.

Remus had always felt responsible for Peter's inclusion into the group. He'd always felt responsible for making Peter, who was so quiet and nervous, feel good about himself. He was Peter's best friend in the whole world, and he was always sure to act like it whenever he could. But he'd failed, and he hadn't even noticed... and right after nearly insulting Peter the other day, too. Remus felt very guilty.

But Peter had laughed a little, hadn't he? Remus couldn't really remember, but he must have; otherwise Remus would have surely defended him. Besides, Remus had been having a good time. Peter could pull his own weight, couldn't he? They were all friends. They were all on equal footing. Remus was not responsible for Peter's happiness, and he was certain that Professor Questus would agree.

With that semi-comforting thought, Remus rolled over and went to sleep.

"Today," said Professor Craff, looking anywhere but Remus, "we are going to be learning how number charts are created. Now, remember: there are no mathematical equations that correspond with these charts. Like mathematical equations, they can predict future events—purely through logic and reasoning—but unlike mathematical equations, they are completely unpredictable. We get these charts through experimentation, remember?"

She took out her wand and Summoned a small item from the inside of a cupboard.

"What's that?" whispered James.

Remus inhaled, and the scent of chocolate filled his nostrils. "It's a Chocolate Frog, I think," he said.

"This is a Chocolate Frog," said Craff, confirming Remus' inference. James high-fived Remus under the table. "Chocolate Frogs are predictable, yet simultaneously very unpredictable. The hop of a Chocolate Frog can be predicted through Arithmancy, but not though any other means." She walked up to the blackboard and drew a neat grid with the tip of her wand. The lines on the hand-drawn grid, Remus noted, formed perfect right angles—if that wasn't magic, he didn't know what was. Remus' hands had never been that steady.

"This number chart will predict the direction and height in which the Frog bounces," she said. "Typically, there would be more boxes on this grid, so that we could take into account other factors. Can anybody name a factor which we may have to consider?"

"Temperature," said Evans.

"Yes, Evans, perfect. That's usually the first one that I ask students to consider when they're stuck."

"Surface material," said a Slytherin girl.

"Exactly, Thomson."

"How far the Frog has already jumped," said James.

"Perfect, Potter."

"Wind speed," said Remus.

"How long ago the Frog was made," said Snape.

"Very good, Snape. Now, fortunately, Chocolate Frogs only have one good jump in them, for the most part—so we won't have to calculate for fatigue of the Frog, which would complicate things immensely. But we will be trying to solve for the direction in which the frog will jump and the length of the jump, and I assure you that those variables should be difficult enough to keep you busy."

"Can we predict the card inside?" asked a Gryffindor boy.

"No, because the card inside is not dependent on magic. Arithmancy can only predict magic. Prediction of non-magical events rests on Divination or the Muggle sciences."

"But…" said Remus, but then he changed his mind. He considered writing down the question and making James ask it, but that hadn't really worked last time.

"Remus sounds like he has a question," said James, and Remus briefly considered throttling James.

"…Yes?" said Craff after a long moment of apparent discomfort.

"Cooking and baking aren't exact arts, are they? Even if the Chocolate Frogs are meant to have, say, a cup of sugar, the measurements won't be perfectly exact if they're added by hand. So our model will only work if the ingredients were added… by magic." Remus' cheeks flushed as he realized that he'd answered his own question. He hadn't really thought it out before asking—how could he have? James hadn't given him a chance—and the answer was so obvious. Of course the ingredients were added by magic, because Chocolate Frogs were magical. Duh.

"They were," said Craff stiffly. "Yes, it is important to do your research and find out every single factor which can influence the outcome, but it's not relevant in this case."

Remus nodded, cheeks still red, and stared determinedly at the floor.

"These charts are a bit like graphs. Think of this as the X-axis, and this as the Y-axis… the only difference is that there are numbers instead of points, and that the numbers have no logical correlation. And there are often even more axes, as well, though not in this case. We'll fill in numbers and measurements as we go. The charm placed on Chocolate Frogs, since they are so simple, can be predicted through two main factors. I shan't be telling you what they are: we'll have to figure it out through experimentation."

The remainder of class was spent plugging numbers into the chart. Remus' brain hurt. It was such a lengthy, painstaking process—they had to start over every single time they wanted to consider a new factor. There were so many combinations. Fortunately, Craff knew a spell to put the Chocolate Frog back into its wrapping so that they wouldn't have to waste a hundred Frogs.

It was James who finally figured out the final factor, of course, and Snape who figured out the first. The two factors were surface material and position in relation to the edge of the surface. It was all terribly complicated, and it took hundreds of trials before they managed to fill in the entire chart. Craff had been right—the presence of a magical factor really did make it difficult to predict things.

Craff proceeded to hand out Chocolate Frogs to each of the students. She gave two to James and skipped over Remus completely—James was livid and looked as if he wanted to slap Craff all the way to Canada, but Remus gave him such an intense look of warning that James backed down and settled for loudly saying, "You must have made a mistake, Kirsten!" and handing the Frog to Remus.

"Based on this chart," Craff said, ignoring James, "I want each of you to guess which direction and how far your Frog will hop. That will be your grade for today."

James' hand waved in the air; it almost hit Remus in the face. "Kirsten! Can we—"

"Yes, Potter, you may eat the Frog when you are finished."

Frogs hopped willy-nilly across the room, and students shrieked. Both Remus and James were correct in their predictions—though Remus wondered if anybody could possibly be wrong after so much experimentation.

"Good," said Craff once everybody had finished. James grinned and stuffed his Frog into his mouth, letting the legs hang out and waggling his eyebrows at Remus. "Now, Arithmancy, being a high-level, cumulative course that is rooted in experimentation, will require each of you to do a personal project. Over the next week, I want you to start thinking about a kind of magical outcome that you want to be able to predict with a high level of accuracy. You'll be able to change your topic, of course, but this project—a number chart and a written essay—must be completed by the end of your fifth year.

"If you finish the project early, then you'll have next to no homework from me from here on out, save for preparing for exams—but I warn you that the project will take a very, very long time. Good time management is paramount. I will be grading on a scale of zero to infinity percent." She smiled slightly. "That means that the harder your project is, the more points you will receive. If you do a simple project, then the highest you can earn is an eighty percent. The record, currently, is a 739%, held by a Hufflepuff girl who predicted the passwords to the Slytherin dormitories for ninety-three years into the future. The passwords are set by humans now, so her charts are obsolete, but you must understand the level of attention to detail that coordinating numbers to letters of the alphabet with infinite combinations took. It was highly impressive indeed."

"I wish I could do that," whispered James, crossing his arms. "Entering Slytherin dorms whenever we want to would be so much fun."

"You won't be able to start until you know a bit more about Arithmancy, and you'll have to alter your project as you learn more. But start thinking about it now, please. Class dismissed."

Remus munched on his Chocolate Frog solemnly and thought about magic. It was a lot more complicated than he'd originally thought, but that just made it all the more interesting. Remus hated being a werewolf, but he loved being a wizard.

AN: I adore coming up with curriculum for Arithmancy! I took a lot of Physics classes in school, and I like thinking of Arithmancy as magical Phsyics/statistics with a touch of Divination. The Chocolate Frog lesson seems exactly like something one of my Physics teachers would have done :D