Luna was waiting for Harry and Hermione outside of the Great Hall for dinner. She was laughing very hard as they approached at seemingly nothing, garnering strange looks from other people as they went in. When she saw Harry approach, she laughed even harder.
"A death omen!" she said, laughing. "A death omen, Harry!"
Hermione wondered if Luna had overheard from someone coming from Divination to dinner, or if this was just one of those odd things Luna just seemed to know. Harry seemed unbothered by how Luna knew, and he just grinned.
"Is it a death omen, then?" he asked. "Am I going to die?"
"Of course not," Luna dismissed. "It's just a dog. It represents your godfather."
Harry froze.
"My what?" he asked, eyes going wide.
"Your godfather," Luna told him. "And no, I have no idea who that is. I just know that's what it means." She shrugged. "Shall we go in?"
Harry looked mildly disturbed, but Hermione let him go as she sat down at the Slytherin table. Draco's eyes went to her immediately, taking in the sling on her arm.
"Are you okay, Hermione?" he demanded. "I've already written my father – having a violent animal like that who attacks students is mad—"
"I'm fine, Draco," Hermione insisted. "I went to afternoon classes and everything – I just need the sling for a bit longer before the muscle is healed."
But Draco was shaking his head.
"You don't have to be so modest," he said. "There was blood everywhere. You saved my life again, Hermione. I owe you."
Hermione scoffed and set about awkwardly getting herself dinner while Pansy began ranting about Hagrid's unsuitability as a teacher. Blaise touched her arm slightly and subtly began serving her as well as himself, Hermione shooting him a relieved, grateful look.
"Why is Draco so set on this?" she asked Blaise quietly. "I very clearly didn't save his life."
Blaise's eyes flashed.
"Who knows," he muttered, but Hermione suspected Blaise did know indeed.
Herbology the next day was mostly a lecture and a tour – they would be permitted to work in Greenhouse Four, now, where some of the plants were nastier and more volatile. These plants, Professor Sprout explained, were all created by Herbologists cross-breeding different plants over the years. Hermione was fascinated by the idea. She'd read about Gregor Mendel's pea experiments in muggle science class, and the idea of getting to try something similar with Fanged Geraniums or some such plant was exciting.
She probably wouldn't get to try her own until after O.W.L.s, but still. That gave Hermione plenty of time to study these plants and see how it had worked, and to come up with her own plant breeding ideas beforehand.
Double Potions was a nightmare. They were doing a Shrinking Solution on their very first day back, and Hermione was dismayed to realize she couldn't do her half of the preparation with her arm still bound to her chest as it was. Professor Snape was busy berating Neville, Harry, and Ron – Neville's Shrinking Solution had turned bright orange, somehow, when it should have been a lime green, and Harry and Ron seemed distracted. Draco had sat right behind their table today, and he was smirking, clearly hissing things at them whenever Professor Snape looked away.
Hermione turned to Theo when Snape wasn't looking.
"Can you help me take my arm down?" she asked quietly. "I'm never going to be able to dice these daisy roots left-handed."
Theo raised an eyebrow. "Are you sure that's wise?"
"I would have gone to Madame Pomfrey to get her approval over lunch if I'd had the time," Hermione huffed. "Come on, Theo."
Theo sighed. "Let the record show that I don't think this a good idea…"
He carefully helped unhook the sling from around her neck and shoulder, peeling it off of her arm. Hermione stretched her arm and flexed her hand, testing the ligaments and muscles. To her relief, she didn't feel any pain, and she looked up at Theo with a smile.
"Thanks," she said, meaning it.
Theo shrugged. "It was nothing."
As she turned back to her ingredients, Hermione paused, glancing sideways at Theo again. To her astonishment, Theo's cheeks bore a hint a red.
Hermione was surprised to notice his flush. Theo was never ruffled – ever.
Her eyes narrowed. This bore further investigation.
She diced her roots neatly and evenly, relieved that the muscle memory in her fingers had remained over the summer. Across the room, Ron was still dicing his roots as he had been for five minutes now – Hermione was able to do a better job of it in under half that time. But then again, she had paid attention when Snape had demonstrated proper dicing technique, and Ron clearly had not.
"What's up with you?" Hermione murmured to Theo, putting the daisy roots in the cauldron.
"What do you mean, what's up with me?" Theo deflected, skinning a shrivelfig with unnecessary concentration.
"You're blushing," she informed him. "And you never blush."
Theo gave her a look. Hermione raised her eyebrows and folded her arms, not to be denied. Theo sighed.
"My father sent a contract to your father over the summer," he muttered. "I didn't even know until Malfoy told me – his father had heard from my father."
Hermione blinked. "And?"
"And, it's embarrassing," Theo groaned, tossing the shrivelfig in. "I didn't even know my Dad was trying to arrange a betrothal for me already. Let alone to you."
Hermione's eyes narrowed. "What do you mean, 'let alone to me'?"
Theo caught her tone of voice, and he quickly clarified.
"I'm not implying you'd be an unsuitable match," he said. "But – realize, Hermione, most of the time when these contracts are made, you don't know the person you're matched with. Generally, guys end up contracted to girls who are a few years younger, so the guy will have time to start earning a living to provide for a family by the time they form a marriage bond."
Hermione tilted her head.
"You're telling me you'd have to work for a living?" she said sardonically, and Theo flushed a bit darker.
"Not all purebloods are Sacred 28," he muttered. "It's the custom of the thing, regardless of whether or not it plays out that way in practice."
"So you're more embarrassed by the fact your father would engage you to me while you'd still be expected to work with me in Potions?" Hermione summarized. "Wouldn't that be better, though? You'd actually get to know your affianced, then, instead of meeting some unknown ingenue at the altar."
Theo's eyes bulged, and he gave her a horrified look. "Merlin alive, Hermione, just what do you think a wizarding marriage ceremony entails?"
"I—"
Hermione paused. Theo had gone pale, and his eyes were large. He looked tense and alarmed, and Hermione had absolutely no idea why.
"Nothing I said I thought would provoke that reaction," she admitted. "Why don't you tell me what I got horribly wrong?"
"An altar," Theo hissed, stirring their potion rapidly. "Circe, no one's openly admitted altar use in years."
Hermione bit her lip.
"In muggle culture, an altar is a religious thing," she said quietly. "It's at the front of a church, the place where a couple gets married. It's not—it's not some horrible thing. That's all I meant."
Theo nearly wilted in relief.
"In magic, an altar is most commonly used when someone is making a ritual human sacrifice," he told her quietly. "They are not common, not used, and not discussed publicly."
"Understood," Hermione said weakly.
Hermione made a quick detour to the Hospital Wing to get the go-ahead from Madam Pomfrey to leave the sling off before Arithmancy. Madam Pomfrey was mildly dismayed to discover she'd taken her arm down herself ("Honestly!" she'd cried. "You, of all people, I would think would be more responsible with your wand arm, Miss Granger!"), but she confirmed that the muscles had indeed healed correctly, and she was in no more danger from the injury anymore.
Arithmancy was taught in a classroom far away from the main hallways of Hogwarts, to her surprise. By the time she finally got to the classroom, it was nearly full, and her eyes scanned the class.
Blaise was there, as were Draco and Theo. Daphne was also there, but to her somewhat surprise, so was Harry. As she scanned, Harry seemed to be the only one from Gryffindor there, looking very uncomfortable. With an odd number of Slytherins, one of them would be the odd one out anyway, Hermione figured, and she slid into the seat next to Harry with a smile.
Harry nearly wilted in relief.
"Can you believe no one else in Gryffindor took this class?" Harry complained. "No one. Not even Sally-Anne Perkins, and she's Muggleborn."
"It is supposed to be a difficult class," Hermione said, shrugging, and Harry rolled his eyes.
"It's just maths," he said. "Maths and magic, right?"
At that moment, Professor Vector entered the classroom. She was very tall, with long dark hair and a pronounced widow's peak. She wore robes of red suede and a matching tall, pointed red hat, completely uncaring that very few people wore hats day to day.
"Welcome to Arithmancy," she said. She looked out over them all, evaluating. "Arithmancy is the discipline of studying the magical properties of numbers, numerology, and using numbers to predict the future." She paused. "Is everyone in the right class?"
Everyone glanced around, before looking back to the front. Professor Vector looked satisfied.
"Very well," she said. "In that case, I look forward to having you in my class."
Hermione had been somewhat afraid that Arithmancy, despite its name, would be a lot of numerology and wishy-washy fortune telling. To her pleasure, Professor Vector immediately squashed that worry.
"Arithmancy works primarily through the construction of magical tables and prediction trees," Professor Vector said. "The difficulty comes in knowing which numbers to use, how to gather your variables, and what equations to use to create your trees. Observe."
She wrote on the board What color robe will the Headmaster wear to dinner tonight?
"This is a very simple example problem," she said. "First, we must determine the possible outputs."
She drew a chart, labeling the rows with various colors: blue, green, red, yellow, purple, black, brown, orange, silver, and gold.
"Now, we must determine what the Headmaster has worn historically to give us more accurate data," she said. She added several columns to the chart, labeling them Tuesday, Wednesday, Thursday and so on. She turned to the class, raising an eyebrow.
"Does anyone remember what color Professor Dumbledore was wearing yesterday?" she asked.
Hermione did not. Mandy Brocklehurst, however, did.
"It was blue, Professor," she volunteered when called upon. Professor Vector nodded approvingly.
"It was indeed," she said, making a mark on the chart. "Who recalls what he was wearing the day prior?"
More people remembered this one – it had been during the Sorting ceremony. Hermione raised her hand, and to her pleasure, Professor Vector called on her.
"A dark silver robe," Hermione said.
"Very good." The Professor made another mark on the chart. She turned back to the class. "We have some historical data, now. Do we think this is enough to draw conclusions about?"
Most of the class looked baffled, but Hermione was starting to follow along, and she raised her hand.
"We don't know the odds of which robe he might wear because we don't know how many of each robe he has," she said. "If we could know that, we'd have a much better chance of predicting it, right?"
Professor Vector nodded approvingly. "Very good. Let us gather that information, then."
She began to write very rapidly on the board, the chalk clacking loudly as she wrote what looked to be a long, complicated equation. Some of the places for numbers had what looked like runes, and there were operators in it that Hermione didn't recognize. As soon as she was done, she tapped the equation with her wand, and the class watched as the chalk turned into tiny gold streaks and flew off of the board.
"This is what is called an Arithmantic Query," she told them. "Queries are a more advanced tool of Arithmancy. We will get to them later; for now, know that it is a way of using Arithmancy to get concrete numbers for other equations."
Hermione and the class watched as tiny streaks of gold began to return, splashing back onto the board into a new column. As each one splashed onto the board, a new chalk number appeared, announcing how many robes of a particular color the gold streak had discovered.
"It seems Dumbledore has a varied wardrobe," Professor Vector said. "But you will notice that the numbers are somewhat skewed, and he has more colors of some than others."
It looked like Dumbledore favored brighter colors, but not too bright. He had several blue and red robes, as well as silver, gold, and orange. He had the most purple robes, and the fewest green and yellow. He also had very few black, which Hermione guessed would be ceremonial robes for certain functions.
"Now," Professor Vector said. "With this data, we can begin to construct an equation."
She began writing on the board once again, this time using letters as variables instead of runes, which Hermione could match to the first letter of the colors on the table. Again, she didn't recognize all of the operators, but she could tell it was some sort of probability equation.
"And now," she said, "we solve."
She tapped the equation with her wand, and the class watched in astonishment as results began to collect on the table below.
"Our data tells us there is an 82% chance that the Headmaster will wear a purple robe tonight," Professor Vector said. "There is a 10% chance of him wearing a red robe, and other colors have decreasing odds from there."
She looked at the class, folded her arms, and smirked.
"You could use Divination to try and predict the behavior of the Headmaster," she said. "You could read tarot cards or try and crystal gaze, but you would likely end up with vague, uncertain answers. This," she said, tapping the board sharply with her wand, "is not vague and uncertain. When you want to know the possibility of the future and you want a definitive answer, you turn not to Divination, but to Arithmancy."
"Oh," Hermione breathed. Professor Vector began erasing the board, constructing a new table, and Harry turned to her quizzically.
"'Oh?'" he whispered. "What?"
Hermione grinned sheepishly.
"I think I like her," she said, nodding at their professor. "I think I'm going to like this class."
And of course, when Professor Dumbledore appeared at dinner that night wearing a violet robe with lilac piping and detailing, Hermione's appreciation for Arithmancy was solidified. Anything that could help her figure out her odds of success in the future, magically, would be an excellent tool to have.