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"Good morning, class," Myrni called out abruptly as she marched purposely out of the back room that was her office and towards the front of the room. With the fifth year class on its own on this day, she once again could see how slight the roster was. But this was actually a positive in her mind, as it meant a more intimate discussion and class interaction. Before continuing, she looked at each student's face in turn. "Today we're going to touch on something that might be considered more advanced for your year, but I think you can handle it," she explained with a wink. "And I think it's still very important for your understanding of Arithmancy as you move forward in your studies."

She stepped over to the blackboard and pointed to where she had written out the day's topic. "We'll get to this in a moment, but I'd like to start with a little discussion." She paused and then looked the surveyed their faces again before continuing. "Pythagoreas said that numbers set a limit to the limitless; that numbers constitute the true nature of things and that all concepts can be expressed in numbers. Using what you have learned so far, what is your opinion of his thinking? Do you agree or disagree? If so, how so? If not, why not?"

In many ways, Arithmancy wasn't dissimilar from Divination - one of Sasha's least favorite (and least successful) classes.  Both focused on trying to predict the future but while Divination focused on inexact measurement tools (swirls in a crystal ball or globules in tea dregs just to name a few), Arithmancy utilized exact numbers, calculations and science.  And, it was one of a handful of classes (asides from Muggle Science, of course) where Sasha's continued math and science studies actually proved to be beneficial. 

Today's class was seeming to be no exception.  Sasha looked up from his notes as Professor Levartian's gaze scanned the room but shyness drew his eyes back down to his page a moment before her gaze landed on him. 

He jotted the question down on his parchment and jotted down a few notes before his hand slid slowly into the air.  Once acknowledged, he straightened in his seat and shook his head.  "For a lot of things, I agree.  But, I don't think that theory can be applied as absolutely as Pythagoras might have imagined.  I mean, the world was much ... well, simpler when he lived."  Unless, of course, even the Greeks had Seers amongst them.  Magic theory always just made things more confusing. 

"I mean, geocentric theory was the only theory - Heliocentric theory didn't exist, yet.  The Greeks made huge advancements in studying math and its relation to space but I'm not sure they really understood how ... well, vast and infinite space was.  Perhaps, no one did until we ... well, muggles ... began exploring it."  The theory, in Sasha's mind, worked in most applications but it just seemed the world had grown more complex since the theories origins.

Kat bit her lip upon hearing the Professor’s question. Exactly how much should she reveal she knew? She didn’t exactly want to divulge all of her passions to the class, but when posed with a question that required thought, Kat had no desire to back down. If there was one thing she knew how to do well, it was think.

“I both agree and disagree with Sasha,” Kat began, shooting a quick look at the boy. “I do agree that these times are infinitely more complex than Pythagoras’ times. However, it’s not because we suddenly discovered a heliocentric universe, but emotions have evolved. People have become more free-thinking, instead of females being told that they’re to be happy to be wed to a man, and men should think only of providing for their family. Now, there’s a bit of a chaos complex. There’s no sure way to figure out how someone will react to a particular situation; ten different people could react ten different ways. The muggles have this bit called the Chaos Theory,” at this Kat shifted, not wanting to seem fixated on the topic. “It basically states that you can know what’s happening, or where an action is happening, but not both. So even the muggles have determined that Pythagoras’ quote is wrong; not every aspect of life can be expressed mathematically.” Upon finishing her rant, Kat fidgeted uncomfortably in her seat. She began staring down at her blank parchment, determined not to open her mouth again for the remainder of the class.

Mentally, she berated herself for having spoken so much. Kat knew that she shouldn’t have said much, but from her observation of others around her, she knew for a fact that emotions were completely irrational; sure, upon seeing somebody’s reaction to a situation, one could determine the plausible outcomes, but the emotions themselves couldn’t be predicted. Even Seers had problems with such; revealing a prophecy could make those included either change their paths, thus voiding the prophecy, or they could disregard it, falling into Fate’s tangles. It was truly an interesting topic for Kat, as she loathed the unknowns of life.

In Sasha's eyes, Arithmancy had another distinct advantage over Divination.  Like Muggle Studies, the class itself seemed to filter the students that chose to attend it.  They were the two classes that seemed to, consistently, be free of the usual bullies or troublemakers.  Sasha usually felt freer to get further into the conversations and discussions.  Today's class, so far, was certainly not shaping up to be an exception. 

Sasha swiveled in his seat to watch Kat as she spoke, enthusiastic about the prospects of discussing the topic rather than annoyed that she'd disagreed.  Hers was an interesting point and Sasha listened intently, looking away occasionally to jot down notes and thoughts.

"But," he started.  Approaching discussions and thoughts a little too literally had always been his weakness.  Sasha usually had to trudge his way through his own arguments to come to conclusions that didn't play by the rules he was used to.  It happened - he was willing to consider other ideas, it just took a little work to get there.  "But, can emotions really evolve?" Sasha asked.  "Evolution implies there's a strategical survival advantage to a trait - biologically, emotions aren't ..."  His voice trailed off as he realized he wasn't sure of his own argument. 

...Instead of females being told that they’re to be happy to be wed to a man, and men should think only of providing for their family.

Perhaps, people hadn't evolved as much as they'd like to think they had.  Gerhard wouldn't hesitate to agree, whole-heartedly, with that mindset and that was the case in Sasha's own family.  Sasha had been raised to believe it, as well.  But, something told him he was better off not pointing that out. 

Chaos theory?  Sasha smiled slightly - they were discussing chaos theory in Arithmancy.  "I don't think Divination likes Chaos theory," Sasha remarked with a slight grin.  "But - I don't think ... chaos theory or magic itself, really, doesn't make Pythagoras' theory wrong.  I think it makes it ... well, incomplete.  Numbers are, in themselves, an entirely human construct.  To think that the world is defined by numbers is a rather egocentric idea.  Pythagorean theory, chaos theory - all of that helps us explain a bigger picture.  One we don't fully understand, yet.  Maybe we aren't meant to."

Sasha watched Kat's bashful response to her own answer and found himself able to relate, completely.  But, with all his discussions - and all his time spent pondering many of these ideas - he was quite eager to discuss them.  Especially with no Slytherins around.  "It's like trying to play connect the dots with all the stars in the sky - as soon as you think you've got them all connected, you look closer and you can see more stars."

Kat’s eyes widened at being spoken to; giving her opinion was one thing, but actually holding a discussion… She turned slightly in her seat to face Sasha, not wanting to appear rude, but still couldn’t bring herself to meet his eyes. No, instead her eyes darted wildly around the room, looking for something to focus on. Kat was honestly surprised to hear Sasha talking so much, he seemed rather quiet in her other classes. Ah well, if Sasha could speak openly, she supposed she should too.

But, can emotions really evolve? Evolution implies there's a strategical survival advantage to a trait - biologically, emotions aren't ...

“I… I mean… Uh.” If possible, Kat turned a shade darker. She hung her head in embarrassment. There was finally a person willing to talk to her without the typical exchange of insults, if she couldn’t manage a friendly encounter… Kat shook her head and took a deep breath in. ‘You are braver than you believe, stronger than you seem, and smarter than you think.’ She told herself this every time a situation required more of her than she thought she had; it was, after all, one of her favorite muggle quotes, even if it HAD come from a children’s show.

“Erm, what I meant to say was th-that, while emotions themselves remained the same, but certain traits are more, uh, pronounced now.” Kat reminded herself to breath. “Society wants us to act a certain way,” breath in, “and the st-strategical survival you mentioned kicks in.” Now lets aim for a sentence in which you DON’T stutter, she thought, mentally kicking herself. A forceful exhalation later, she continued her train of thought, “The emotions nowadays are what allow us to survive. Look at the Purist movement… the children m-may only spout the ideas to blend in with their family. So, while emotions may not have evolved… the purposes and mentalities behind them have.”
Kat sighed, finally having finished her train of thought. See? That wasn’t too hard, she convinced herself. All it took was a couple hundred stutters and she could attempt a conversation. She sighed once more. I can at least pretend to be normal…

I don't think Divination likes Chaos theory

At this, Kat abruptly looked up at Sasha, just in time to see him grin. He actually knew what it was? Her mind was racing; even some of her mother’s colleagues, college professors by trade, had no idea of the theory, let alone how it affects the world around them. “No, I don’t think Seers like the Chaos Theory.” At this, she glanced at Sasha let a small smile grace her face, “Telling them they can’t predict every aspect of the future has to be a blow to their ego.” Yeah. Yeah! She could do this. Kat attempted to cover up the glee she was sure was showing on her face.

Pythagorean theory, chaos theory - all of that helps us explain a bigger picture.  One we don't fully understand, yet.  Maybe we aren't meant to.

“Theories do allow us to explain the universe better, even if they are man-made creations.” Her eyes were once again looking anywhere except Sasha. “Numbers, however, already existed. Pi, for instance, always occurred in nature, repeating constantly in circles. Even Fibonacci’s sequence was observed in the mating rituals of animals…” Kat fidgeted, once again feeling as if she had talked too long. “All humans did was give them written and verbal identification. And sure, maybe we aren’t meant to understand all the intricacies of the universe, but the numbers lurking in repeated patterns are just… there. All it takes is an observant person to notice. As a Ravenclaw, you should know the lure of knowledge.”

It's like trying to play connect the dots with all the stars in the sky - as soon as you think you've got them all connected, you look closer and you can see more stars.

Kat was truly stunned at this bit of insight; not once had she seen somebody her age exemplify wisdom. She’d only seen girls fretting over dresses and boys chatting about quidditch. Kat had personally experienced this; her love of nature frequently brought her outdoors at night. The number of stars always directly corresponded with how hard one looked. “All you have to do is look hard enough. That’s all it takes to see the true colors of nature. Putting it into adequate words is difficult, and expressing it in numbers even harder, so perhaps you’re right. Maybe we’re only meant to enjoy life, not to analyze it.” And perhaps Kat should listen to her own words sometimes; the pull of knowing information would always overpower her ability to just exist, happy and in the moment.

Uniform.

Arithmancy wasn't that great on Razzy's standards. His only good class was Astronomy, really, because he stayed up all night. But the fact that he had other classes made him a bit sad. Razzy decided to actually show up to class, one of the last students there, and sat down in the very back so he could nap and not do anything. He was a true Chancelier, he was. Hard working and oh-so caring. Well, minus the caring. Since when did his family ever care?

The Professor already blurted out a question, and Sasha and Katarina were already blabbing about what the heck the teacher was talking about. Razzy really didn't care and was kind of angry that he had to sit through class. Especially with the smart people. He shouldn't have picked such a hard class. Razzy pulled his notebook out of his bag and tried to look like he was writing. He wasn't really, but who really cared to watch him, Reynaud Chancelier, and see if he were to be actually doing something.

Another few minutes past and Razzy became increasingly bored. The poor boy couldn't handle himself well. Minutes felt like hours and he really wanted to burst out of the room or into song or out of his MIND! Razzy took his notebook and threw it across the room, purely for enjoyment, hoping it would hit someone on the head and make him laugh for a few minutes, or for it to knock things over. He wasn't a cruel boy, he was just very bored.

Sitting at her desk, Meg took notes on a piece of parchment as the Arithmancy Professor talked. She decided to take Arihmancy back in her third year, since she knew that it had to do with numbers. Sure, it was way different than muggle mathematics, but there were ways which they were similar. For example, some of the information learned through a muggle school could help in the obscure subject of Arithmancy. While being a muggleborn could help her, it could go against her as well. After all, since she had no magical background, she didn't have too many people to discuss the classes with back when she had to decide which one to take. However, she did hope to get through everything with high marks.

Meg looked up as Professor Levartian posed a question to the class. Pythagoras was a well-known mathematician that was studied in muggle math. Clearly, she had no idea how he could pertain to Arithmancy, but that was exactly why she was in the class, to learn. She wrote down the question, and information posed to the class. As she did so, she heard both Sasha and Kat already voicing their opinions. As she finished writing on the parchment, she looked over at her two fellow classmates.

As soon as there was a momentary lull in their discussion, Meg decided that it was about time to express her own ideas. "I think that what was meant was back when Pythagoras developed this theory, it was hard to have differing ideas. Usually, if people didn't share the same ideas, violence would erupt. So, Pythagoras would have to make his theory conformed more to the times, rather than abstractly. Now, we are not held to as strict rules with our thoughts, and we could freely think what we do," she responded, looking at her two classmates.

"As for the actual theory, I would agree with it. All that happened was that we put names to the numbers. Numbers extend infinitely, as it is taught in muggle colleges. So, the infinity of numbers makes it possible for many things to be expressed with numbers. Nearly everything we do has some form of mathematics to it. Numbers already defined what we do, Pythagoras tried to sum that up in his theory," Meg concluded.

Myrni smiled as she listened to the back and forth conversation that the students were making. Clearly she was pleased that they did not require much moderation on her part to maintain order or steer its direction. She was impressed by the points that were being made, particularly because they exhibited the breadth of knowledge that her students truly possessed. She was thrilled that they seemed to be bringing in their outside knowledge to make their points more lucid and weighty. She found herself perching casually on the stool at the front of the class, content to continue listening. At one point though, she was about to compliment them on this fact when there was a disturbance that was clearly out of place.

She was reminded that Arithmancy was generally a class full of students who wanted to be there, since it was an elective. She didn't have much sympathy for the students who signed up for it and then insisted on contributing in a negative way. So with a stern raise of her brows, she crossed her arms in front of her and said to the disruptive student, "Are we boring you, Mr. Chancelier? If we are and you cannot possibly find any positive way to contribute to the discussion, you know where the door is. You're free to leave and we can work out how you may make this class up later. I leave it for you to decide."

Not really waiting for his decision, Myrni turned back to Sasha, Katarina and Megan, wishing to reassure them that she appreciated what they had to offer. Clearing her throat, she said, "You've all made some really great points and they lead in nicely to the next portion of our discussion. I think some of your opinions may already speak to what you think, but let me just ask this anyway. So Arithmancy is the language of numbers. Are you inclined to believe that this language is more of a science or an art?" She used her hands as if they were a scale weighing two options. "When you look at their use in this subject, do you tend to be more analytical or artistic in your approach?"

Kat was avoiding looking at Sasha - something Sasha was quite familiar with.  He was prone to doing so, himself, especially if the conversation started slipping into the realm of the awkward and uncomfortable.  Chances were, Kat was no stranger to Sasha's social awkwardness in class.  He wasn't immune to the occasional (or - regular) stuttering or incomplete sentences.  In fact, if Sasha hadn't spent the last couple months obsessed with the question of where magic ended and science started, Sasha would probably be demonstrating more of it, himself. 

He understood what Kat, and now Megan, were trying to say.  That, somehow, society had experienced enlightenment since Pythagoras' day.  To some degree, there was some truth to that statement, though Sasha wondered how much.  On a personal level, Sasha was very much in a position that Kat was describing - there was quite a bit he said while he was at home because it was just easier that way.  He knew the beliefs his step-father was looking for and he knew saying anything different would lead to trouble.  But, was that really all that different than back in the day?  Did they know?  Maybe things were different in the wizarding world than the muggle. 

Usually, if people didn't share the same ideas, violence would erupt. So, Pythagoras would have to make his theory conformed more to the times, rather than abstractly.

"Has that really changed that much?"  Sasha asked, glancing towards Megan.  "Isn't there still a tendency to sugar coat ideas or conform?  Certainly, it still happens in the muggle world.  And, purists still seem to do some of that in the wizarding world as well." 

Kat seemed surprised by Sasha's star comment and it was his turn to be slightly bashful.  A slight hint of color blossomed on his cheeks and he turned to his parchment under the guise of jotting down a few notes.  The notes that ended up getting placed on the page were vague and rather unrelated.  He certainly hadn't meant to give the impression he didn't see the need or reasons behind analyzing the world - goodness knew, he did his share of it.  But, he liked to think that wasn't all there was to it - that there had to be more than what humans were able to label or define.  "Well, I think, analyzing it is human nature - but, I think it's more complicated than that, you know?"  He forced himself to look back up though his quill continued to doodle random shapes on his page.  "Maybe there are patterns in nature but maybe there's more to it than the numbers we assign to it?  Maybe we limit our abi-"

His sentence was cut off as something connected with the back of Sasha's head.  He looked up and over his shoulder at the notebook crumpled on the floor and the young man who now sat notebook-less at his desk.  He blinked, confused at the young man before, awkwardly, turning back towards the front.  He scowled at the young man as his fingers passed through his hair, ensuring the collision hadn't mussed up his hair too badly, but Professor Levartian was already questioning the Razzy's motives. 

He turned back forward and turned his attention to the new question.  It was an interesting question; Sasha was definitely prone to approaching most learning in an analytical manner.  But, languages were an art form.  Slowly, Sasha shook his head.  If he was being honest, though, "I'm probably more analytical.  I always am.  But, if it is a language, it's probably better to approach it artistically."

Kat knew about conforming, but more specifically, the repercussions of NOT conforming; when she was eleven and had just gotten her letter from Hogwarts, her best—muggle—friend had left her alone because, as a witch, she was the spawn of something unholy. She could have taken them up on their offers to adopt her, to take her out of her mother’s household, to be normal; indeed, conformity was still in the muggle world. Instead she chose her true nature over becoming somebody she wasn’t; the same reason she and her mother had a strained relationship. Kat, personally, thought it ridiculous that a muggleborn, neigh, mudblood, wanted her half blood daughter to conform to Pureblood agenda. She had, once again, refused to become a brainless chit. At the thoughts of her mother, Kat stared down at her parchment, deciding it needed decorating. Anything to distract her from her current train of thought. She dipped her quill in the ink pot and began to sketch foxes frolicking around the edge of the parchment. Kat continued her actions until she heard a loud thud; immediately she looked up, in time to see Sasha grabbing his head and looking around. She saw the notebook laying on the floor behind him and was able to deduce what had happened. Kat whipped out her Hawthorn wand from her sleeve (yes, who had a need for wand holsters?) and muttered Wingardium Leviosa, then proceeded to flick her wand a little violently towards the Chancelier boy. The notebook hit him in the chest with a muffled thud before falling back onto the desk. Kat wasn’t confrontational, by any means, but surely the boy needed his notebook back, right? She glanced once more around the classroom to see if anything else had been thrown. When her search yielded no more potential projectiles, she went back to her doodles.

When Levartian posed her new question to the class, Kat immediately knew her answer. In fact, she had to bite back a grin at hearing Sasha’s conflicted answer, as there truly wasn’t just one correct answer. “Well, the language of numbers itself is beautiful, however, to truly appreciate it, you have to approach it in an analytical way. Only through working with the formula, and watching as numbers cancel out and reduce can you really grasp how amazing it is. However, anybody can appreciate the general beauty of Arithmancy; after all, it’s the only thing in life that has concrete answers with predictable results.” Kat was proud of her stutter-free ramble, now if only she could manage that while looking somebody in the eye. Ah well, she sighed quietly, for now, her foxes could use more detail.

It seemed that no one even noticed Razzy throwing the book. How queer! He frowned and slumped down in his chair. Nothing was fun anymore. He felt like he was going to explode at one point and hurt everyone and anyone that crossed his path. But Razzy hated to think that way... He was a good boy. Or so he believed. At least he got some joy out of the thing hitting the back of Sasha's head. The guy was a know-it-all, anyways. He didn't need those brains.

"Are we boring you, Mr. Chancelier? If we are and you cannot possibly find any positive way to contribute to the discussion, you know where the door is. You're free to leave and we can work out how you may make this class up later. I leave it for you to decide."

"Um..." Razzy stared at the Professor, completely unfazed by her words, "Fine enough by me." He stood up and picked up his belongings. He would probably drop the class and possibly drop out of the school. He was slowly just beginning to not care at all. Though class had just began, he was already being kicked out. A new personal best. Razzy walked over to Sasha, gave him an unnecessary scowl, and picked up his notebook.

"This class is so boring, anyways." He mumbled before departing the class with the biggest internal victory he ever had. Now he could go back to pacing in his room and doing completely nothing. His life was definitely going places.

Again, Myrni was impressed by the astuteness of her pupils. She settled back in her perch on the stool, crossed one leg over the other and she clasped her hands together at her knee. "I definitely feel there are merits to looking at what we do in this class both analytically and artistically. Numbers by nature are logical. And yet the language and meaning they sometimes portray is very much open to subjective interpretation."

After a pause, Myrni continued, "For the rest of our session today, you'll be working on an in class assignment. I'd like you to consider this discussion as you are working and try to bring in both analytical and artistic elements into your approach to it."

Myrni sought her wand and aimed it to the board and after a bit, the following instructions had been scrawled:

1. Select a number significant to Arithmancy (1-9, 11, 22)
2. Find its symbolism and meaning (both in Arithmantical terms and any others you wish to touch on)
3. Provide examples or evidence where appropriate

Turning back to the class, she told them, "The rest of the class is yours. If you finish your work, you may deposit your work with me or turn it in before the start of the next class." Another pause. "This will likely lead us into our next topic of Comparative Numerology. If you'd like to get ahead, feel free to look over the Chaldean System."

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OOC: It's been a really great class...hoping this will head toward a close! Credit for the "assignment" will be given to those who do a post a) talking about how they're going about working on it, b) an excerpt from what they'll turn in, or c) some funky hybrid of both! 

Useful Links
Arithmany World (How To)
The Meanings of the Numbers

Meg noted how the issue at hand could essentially take up the entire class time, with all the discussion that blossomed out of it. Sure, the discussion could be forced into a shorter time frame, but then, what would be fun about that? Absolutely nothing. Certainly, an open debate should be greatly appreciated, especially in such a class that could be open to different interpretations at times. Well, that was how she felt anyway, and who knew how anyone else would think of it, especially since that idea came from her own mind, in her own little world.

Glancing over at Sasha, Meg tilted her head to the side a little at his question. Dissenting opinions have came a long way, especially with how vocal some of them could be. "In the sense where most people would not kill someone else just for a dissenting opinion. The tendency of sugar coating, I feel, tends to depend on everyone, since some people tend to sugar coat more, while others are more abrupt. I don't think you could label society, with everyone sugar coating. Conformity and nonconformity are really the same thing with everyone's ideas, since people would conform or not conform based on what they think," she responded.

As a notebook hit Sasha, Meg frowned, but glanced down at her own notes, and decided that it wouldn't hurt to flesh them out more. Taking her quill, she jotted down a few notes on the parchment. She looked up, as she noticed Razzy leaving. She had barely even noticed that he failed to contribute to the class discussion. She shrugged lightly, not really fazed by his departure. When Professor Levartin posed a question to the class, she thought for a moment. "Numbers can be used for different forms of expression, so I guess artistic."

Meg's eyes looked up to the board as the class's next assignment was up. After Professor Levartin finished explaining the assignment, she thought of which number to chose to write about for her work. After a little bit, she decided to pick eleven, which so happened to be a prime number, as it was shown back when she was in a muggle school.

Taking out a fresh piece of parchment, Meg dipped her quill into her inkwell, and started writing about the meaning of the number eleven in arithmancy.

While eleven is not apart of the standard arithmancy chart, it is used in both the special traits number, and the life path number. Both occurrences mean the same thing, as leadership. Known as the "number of light," eleven represents the "knower." This known stands for one's self, and it refers to the Christ-self, as Christ is worshiped by Christianity from muggles. The number one is associated with wisdom, intellect, and spirituality... (The Meaning of Numbers and parts from How to Do Arithmancy)

Pushing a piece of her brunette hair out of her eyes, Meg continued to write the assignment.