Fan Fiction ❯ The Year of the Phoenix ❯ Math, Magic, and Mutiny ( Chapter 3 )

[ Y - Young Adult: Not suitable for readers under 16 ]

It was the first day of classes, and Deanne had not slept at all well the night before. Despite Teluryon's intervention, the dementor's assault still did a number on her and she had not been provided with any chocolate of any kind. Dumbledore's touch was so obviously lost from that paltry meal Umbridge dared to call a feast last night. She had thought there might have been even a single mote of chocolate, but alas there was none. Her restlessness also was due largely to her inability to ascertain the purpose for the presence of the dementors at Hogwarts this year. After they had served as soldiers so willingly for Voldemort, why was it that the Ministry still employed them? For that matter, what need was there for dementors at the school? Did they truly think of the Second Round Table as that much of a threat?

Perhaps there was cause to, Deanne considered, letting the hot water of her shower splash upon her face, somehow cleansing her of some fatigue. After all, they did have an inside agent in the faculty along with a planned trusted student. None of that was known to the Ministry, of course, but their paranoia regarding the situation was not baseless. Secondly, the Second Round Table had already proven their penchant for open confrontation, both with the Battle of Hogwarts and Telarius' trial. Through the dementors, the Ministry could attack the Second Round Table while appearing to take no action at all. It was a move not without risk, but to expose the actions of the Ministry would be to expose their organization's existence. Once that happened the Ministry could legally send Auror's in, and Deanne doubted that they could stave off the might of the Ministry's crack squad, even with Teluryon's assitance.

With her fatigue somewhat sated, Deanne prepared herself for her first class. The list of supplies for Arithmancy was different than the previous years, including a graphing calculator as a required tool. She liked her new house leader so far, but she had not yet witnessed the teaching style of this Thomas Lichen. His age still surprised her. She hoped that his style of teaching would make the subject interesting for her. He promised to introduce the students enrolled into the new school of Arithmantic Theory. It sounded exciting enough, learning how and why wizardry worked.

It was important to her that she did well in this class. After comparing schedules through the nightly link last night, she had found herself to be the only Shadine taking Arithmancy. If this new theory was truly revolutionary stuff, then perhaps she could find her niche by learning it. If no one else but she in their organization knew the intracacies and workings of wizardry then she could at last have a role no one else could fill. Well, save for Telarius anyway.

Fearing that her train of thought would lead her back to him, she quickly finished her packing and headed off to the Great Hall for breakfast. Much to her regret, the options available were no more tempting than those she had the night before. The french toast looked exactly like that which used to be served for lunch at her old high school. Someone had sprinkled the powdered sugar almost apologetically onto the shrivelled sticks of badly microwaved dough. Still, the french toast was more appealing than the waffles, which seemed to come in two distinct colours: black and almost black. She begrudgingly consumed a filling portion of the french toast (after drowning the poor things in syrup, anyway) and hurried off to Arithmancy.

The first thing that Deanne noticed was the layout of the classroom. The room was a well constructed semi-circle, with the arced half being the half one entered from. As you continued on toward the straight wall, you descended down different levels of semi-circles, each level possessing rows of single chairs with tables which could be flipped up or placed to the side. Center of the would-be circle was a desk with piles of papers, a chair behind it, and then a blackboard on the wall itself. It was a traditional college lecture hall, but seeing it at Hogwarts gave Deanne a bit of a start. It was not at all traditional for wizards.

Desiring to do well, Deanne made sure to take a seat in the front row, right next to the aisle. After situating herself, she turned about to examine the other students. The red and gold colours told her that the Gryffindors would share this class with the Ravenclaws. She did not have time to formulate the question in her mind before she saw Hermione step through and seat herself on the other end of the aisle. She gave Deanne a look which caused her to avert her eyes. She now had no suspicions that she had done something which upset Hermione greatly.

Lichen was two minutes late, and he dashed into the room quickly, his hair in general disarray. After placing his sachel on the desk, he fumbled out a stack of papers and gave them to Deanne. "Would you please do me a favour and pass those out to everyone?" he asked, almost out of breath.

Deanne nodded, and took her time passing out the syllabi to everyone present, giving him time to catch his breath and organize his other articles. She promptly took her seat again after finishing, and Lichen appeared quite grateful and ready to start.

He looked about at the students and smiled for a bit. "This is more students than I expected for my first class. That's excellent! I'm quite excited that all of you are interested in Arithmancy," he took out his spectacles from his sachel's front pocket and put them on, "As I said before the modest meal we were given last night, I'm Thomas Lichen, and I have a Doctorate in mathematics with a focus in number theory. For those of you unfamiliar with how the muggle education system works, a Doctorate is a muggle certificate which clearly states that I spent far too much time as a student."

Deanne joined the class in laughter and Lichen smiled to all of them. "I like to run a relaxed classroom, as it tends to produce far less stress. Believe me, the kinds of questions you'll be assigned to answer can, in the wrong environment, produce an exorbitant amount of stress. It's important to maintain a light-hearted attitude such that you can function at pique efficiency. For those reasons, any negativity you may be carrying with you must be left at the door as you would leave shoes in the mudroom of a fancy house. If at some time you feel as though you simply must be negative, just remind yourself that Professor Snape's Potion's class is only four hours off."

More laughter ensued. So far Deanne approved, but there was an amount of anxiousness within her. He seemed to be warming up the crowd, which could mean that he was about to hit them with something unpleasant. "It's my intent to treat you with the same type of respect one would give an equal. All I ask in return is that you refer to me as Dr. Lichen, my proper title. That being said... well, as some of you may have guessed already," he looked directly at Deanne for a moment before addressing the class as a whole once more, "I do have a mote of bad news: You all have a considerable amount of catching up to do."

It was amazing how quickly the mood shifted. The general feel of the mood was a slight despair, save for one individual. Hermione actually appeared insulted. If Lichen perceived this then he paid it no mind. "The new Arithmantic Theory is, indeed, a breakthrough in our understanding of how magic itself works. Not just wizardry, but the actual core body of magic. If you stay in this course, you will be amazed at how mathematical magic truly is. Of course, you are all of the fourth year level... and I'm expected to be teaching you fourth year material. To understand material at this level requires a mathematical base that none of you have ever been taught. I know; I checked the cirriculum of previous years."

Lichen reached for a rather large stack of papers as he continued speaking. "Personally, I'd love to take the time to bring each and every one of you up to the level of math you'd need to understand the first through fourth year blitz course that I have to teach this term. Unfortunately there's simply too much material to be covered. Because of that, I must now give you an exam to test your mathematical aptitude. Those who pass the exam will be allowed to remain in the course. If you do not pass, you may drop the course, or choose to enter into my Remedial Arithmancy class, which meets after this one. I go a lot slower in Remedial Arithmancy, so you'll only reach the second year level by the time you have to leave Hogwarts, but I still highly recommend it if you're interested in the subject but don't pass the test."

As Lichen passed out the tests, Deanne dispaired. What level of math would be required? She had never had problems with the subject, but it also was far from her favourite avenue of learning. The numbers and symbols all seemed so trivial and meaningless. Yet Lichen said that understanding math would allow one to understand how magic itself worked. This meant sorcery, wyld magic, wizardry, and even weaving. She knew that Telarius understood all these things, but she was not Telarius. She had not solved the Veritas Enigmatus. She could only hope that Lichen could teach the material in a way she understood.

First thing was first, though: pass the exam. She looked down at the stapled packet of papers on her desk and balked. There had to be thirty-something pages to this exam. Also, Lichen was now passing out several sheets of scratch paper to each student, meaning that there would likely be calculations involved that the calculator itself could not do. She decided to look at the first problem and see how it was worded.

1) An object is dropped from a position above the ground of exactly 120 meters. Which integer of seconds will be the first to be reached when the object be on the ground?

A word problem. It had been a long time since she had to construct any type of equation for dealing with these problems. She looked at the next problem to find the exact same wording, but with a different distance. She continued down through, page after page, until she realized that every problem was the same. With the amount of time it would take to solve one of these problems, multiplied by thirty problems, the two hour class would be well over before she could finish.

"You have one hour to complete all 30 problems. Begin," Lichen's tone was short and decisive.

Deanne suddenly felt the weight of her fatigue. How could anyone possibly do these problems in that amount of time? And how did running the same problem over and over again test one's mathematical prowess and aptitude? Was it not too repetious to...?

It dawned on her, and suddenly everything made more sense. She suddenly was aware of how long it had been since her last epiphany. This one was far better, she knew. The point was that no one could crank through all of the problems in the amount of time given. The test was meant to test a student's learning curve as well as their mathematical ability. After all, running the same problem over and over again did not test one's mathematical ability. Realizing this quickly would be learning the true intent of the test. What they were really supposed to do was devise a formula wherein the distance could be plugged in, the position set to zero, and the amount of time a variable to be solved for. It required knowledge of algebra to solve the equation, which was more than most magic students would have learned.

But how hard would the equation be to produce? She looked up in thought to notice that Lichen had written on the blackboard to use the approximation of 9.8 meters per second squared for acceleration. She began to jot down notes on the scratch paper. The goal was to find how at what integer of time the object would be at a position less than or equal to zero. Obviously the object did not go through the ground, but since the wording was at what integer of seconds, an answer of 3.2 seconds would not cut it. In other words, the number would always have to be rounded up if there was a decimal. In this case, the object would not be on the ground at 3 seconds, but would be at four seconds. Therefore four seconds would be the first integer of seconds reached after the object was on the ground.

She knew that acceleration was a change in velocity over time. 9.8 meters per second squared meant that, after one second, the object would reach a velocity of 9.8 meters per second. After two seconds that object's velocity would be 19.6 meters per second and so forth. This meant that, at any given number of seconds (t) the object had a velocity equal to 9.8 times that number (9.8t). Once each full second passed, another 9.8 meters per second was gained onto the velocity of the object. Since the object had no initial velocity, that means that, in the first second, it went from 0 meters per second to 9.8 meters per second. The question here was how much distance would the object have covered during this time? Well, since it began at 0 and ended at 9.8, the average velocity over that second was 4.9 meters (0 + 9.8 all divided by 2), as gravity is a constant acceleration rather than a spontaneous acceleration. It made sense that the object then travelled 4.9 meters in this time.

Now she would have to find a relationship of some sort. She noted down 4.9 as t = 1 (meaning that the object traveled 4.9 meters in one second's time). Then she thought about the next second. Well, the velocity would start at 9.8 meters per second this time. Added to this would have to be another average velocity due to acceleration. If the average velocity from one second was 4.9, it would stand to reason that, after two seconds, it would have to be twice that or 9.8. Since every second the object accelerated 9.8 meters per second, the average velocity obtained from this would be 4.9 times the number of seconds, since the velocity starts with no change and gains 9.8 (0 + 9.8 every time, therefore 4.9t from acceleration every time). However, at the third second she would have to take what was gained from the previous and add it. During t = 2 the velocity began at 9.8 and gained and additional 9.8 (4.9 * 2). This meant that the third second would be calculated as 9.8 plus 9.8 plus 4.9t.

Using her calculator, she computed and marked down the total change in position at each second from one to five. She found that each time she had to add an increasing amount of 9.8 units. For the third second, the formula was 9.8 * 3 added to the 4.9t. The fourth was 9.8 * 6 added to the 4.9t, and the fifth 9.8 * 10 added to the 4.9t. She was not getting a steady formula, but rather an increasingly large computation. Frustration hit her at this moment, as her goal had been to make the problems easier to solve.

She took a deep breath and looked at her results. At one second the object went down 4.9 meters, at two 19.6 meters, at three 44.1 meters, at four 78.4 meters, and at five 122.5 meters. She already had the answer to the first problem! After five seconds, the object would be on the ground. Perhaps she could still finish the test in time if she simply computed an amount of seconds that would cover any distance. After all, the numbers got increasingly larger and larger. How high would she need to go?

She looked at the next page and found out that the distances started being represented in kilometers, and got increasingly larger. She would have to compute over 100 of the seconds in order to do it that way. There had to be a formula to the decrease in position with relation to time that made these significantly easier.

But where was the relationship? The numbers just weren't talking to her. The only thing they had in common was that 4.9 evenly divided evenly into all of them. She paused for a moment, thinking that thought through again. If 4.9 divided evenly into all of them, then perhaps there was a noticeable relationship in the numbers produced. After dividing them all by 4.9, she produced 1 for one second, 4 for two seconds, 9 for three seconds, 16 for four seconds, and 25 for five seconds. It did not take a mathematical genius to realize that each number produced was the perfect square of the time interval. The amount of distance the object travelled over any given interval of time would always be 4.9 times the square of the amount of time (in seconds).

One more intellectual leap was made on her behalf from that (more of a small hop than a leap really), and she wrote down that the position of the object (S) was equal to it's initial position (P) minus 4.9 times the number of seconds (t) squared (or S = P - 4.9t^2). Since she needed to know the time when the position equalled 0, she rewrote the equation as t^2 = P/4.9. In other words, all she had to do was take the position she was given, divide it by 4.9, and then take the square root and round up her result. That was her answer.

In the moment that she took to be amazed and thrilled at her discovery, she felt a hand upon her shoulder. Quickly turning, she noticed Lichen bending down to whisper into her ear. "Well done. You can stop now and wait for the rest of the class. You passed."

There was a certain amount of pride in his voice which made her chest swell slightly. She did not even like math, but she was able to think the solution through and, in hindsight, enjoyed the fact that she was capable of doing it. She wondered what level of mathematical complexity she had just engaged in, but the point was moot. It was enough to remain in the class. She genuinely hoped that the amount of work per assignment would be less. Having to come up with an equation like that, thinking through all the nuances of it, was mentally taxing.

After forty minutes, Lichen was in the front of the room again, the smile on his face priceless. "Congratulations. All of you by this time have been informed by me that you have passed the test and may remain in the class," he looked about the room during his pause, "That is, if you wish to remain in it. If not, please inform me after we have adjourned for the day. Now, why do you think I would give such a test?"

The class was dead silent. His smile faded. "Come now. Think about it. I want to see hands and ideas. No answer is a wrong answer, since I asked what you thought. It's almost impossible to be incorrect about your own thoughts."

A few hands came up at this point, Deanne's included among them. Lichen did not call on her, however. He pointed to another student, farther back, who suggested: "Because coming up with the forumla demonstrates a certain amount of skill?"

Lichen nodded. "Indeed. All of you found that the amount of time necessary for the object to land when dropped from any distance was equal to the square root of the object's initial position over the constant 4.9. Why else?"

More hands and more answers were given, and it got to the point where Deanne was out of answers and Lichen was still asking for them, seemingly avoiding calling on her. She wondered why he would do this. He obviously noticed her hand up when it was, but he seemed to be waiting for something. What did he think she would discover?

Well, why else would he hold the test? What other, underlying motive could there be to his actions that was hidden underneath the other, more perceptable intents?

Her thoughts turned to Telarius and her hand shot up. It seemed to be the cue Lichen was waiting for. "Yes, Miss Ember?"

"To prove a point," she made certain that her answer was a definitive statement rather than an answer.

Lichen had his smile once more. "Brilliant, Miss Ember. Absolutely brilliant," he paced about the front of the room, "All of your answers were excellent, and all true, but one of your classmates has finally found the deepest, most underlying intent to this test. I wanted to prove a point to all of you. Now, what might that point be?"

This question was obviously rhetorical, and the class allowed him to continue without suggestion or comment. "How many of you consider mathematics to be difficult? A show of hands..."

It did not take long for every hand in the room to shoot up, save Hermione's. 'What an insufferable suck-up,' Deanne thought. She then took some measure of satisfaction that she, not Hermione, was the first to find the solution.

"Alright. How many of you believe that you could learn the complicated form of computation known as calculus?"

For a time where were no hands in the air. Hermione's went up soon thereafter, and Deanne thought on it. Calculus was a mystery to her. Telarius often spoke lovingly of it, and she had always considered herself someone with the ability to learn it if she so desired. She had never desired to in the past, and did not now either, but she did believe she could do it if she had to. Her hand came up to join Hermione's. They were the only two.

Lichen nodded. "Very well. My objective today is to disprove some myths about mathematics which have circulated far too much over the centuries. I wish to disprove them because they'll get in the way of our learning if I don't, and I don't want that. The first myth is simple..." he turned to the blackboard and wrote 'Math is Hard' on it.

After setting down the chalk he turned back to the class. "This is, to be perfectly frank, complete bullshit. Most of you consider math to be difficult, and most of you believe that you couldn't ever learn calculus. This may come as a shock to some of you," he got a sort of giddy grin on his face which was kind of cute, "But what you all just did in that test... WAS calculus."

He paused for effect, and the effect was there. "That's right. The most popularly known complicated form of computational analysis was performed by each and every one of you in forty minutes or less with no tutelage in the subject whatsoever. Once you finished, it was actually really easy, yes?" there were nods from various students, "What if I told you that, after learning calculus, you could come up with a formula for any acceleration, position, initial velocity, and unit of measure, and do it in a minute's time? It's there folks. It exists. I don't make this stuff up. Mathematics can't be hard if you just did calculus without even knowing it in forty minutes. If you did it in less time, give yourself a pat on the back. You've earned it."

"Myth number 2: Math is Boring. I encounter this one all the time. All mathematicians are bearded old men with brittle hips who sit around in chairs smoking their pipes and listening to prohibition era jazz..." Lichen paused a moment, "Mind you, there is nothing wrong with that music, but I like to think that grey hairs aren't in my near future."

He smiled at everyone's reaction. "I love math. I have loved math my whole life, and thus have dedicated a good chunk of my life to it. You don't need to dedicate you life to it to enjoy it, though. Each and every one of you beamed with pride and joy when I told you that you'd passed. Math did that. If you can get that feeling of satisfaction from math, then how can it be boring?"

"Now I'm not going to stand up here and tell you that math cannot be tedious and downright troublesome in its more complex variations. Goodness knows I spent sweat and blood to keep up my GPA all through college," he paused and shook his head a moment, "Didn't always do the best, but academia can only entertain for so long," he removed his spectacles to look at the students with his bare eyes, "But the work is worth it."

"And that brings me to my next myth. Myth number 3: Math is Pointless," he paced about the room now, one end on his glasses hooked in the corner of his mouth, "Everyone in this room knows this one. It is, as they say, merely a bunch of numbers and symbols. They also say that they're never going to need to have the level of math that is required of them. There is a push now in muggle universities to lower the required mathematics necessary to complete other majors. Since I received my first degree, I have fought tooth and nail to keep the math regimen as it stands. Sometimes I have even joined the call to push for more math to be required. Why would I do this? Am I some kind of sick, sadistic old hack who takes pleasure in the suffering of others?"

"That's what these young students would have you believe. And why not? They believe it themselves, so why shouldn't you?" he put his glasses back on and stopped his pacing, now addressing the class as a whole body rather than a large group of individuals, "Look at what you see before you. I'm not old, and I like to think I'm not sadistic. They have allowed the first two myths to perpetuate their belief in the third, and I merely am trying to open their eyes to the wonderful, glorious truth. That truth is simple, concise, and easily stated: Math is everything."

He smiled his warm, knowing smile. On any other man, with any other tact, the smile would seem arrogant. Lichen wore it with a kind of humility unknown to Deanne. "I know what all of you are thinking right now. Of course I'd say that. To me, math is a significantly large part of my life. Just humour me for a moment. Physics, chemistry, logic, music, law... all of these would not exist without the innovations in mathematical thought made by the ancient greeks up through our current time. It was math that allowed for the discovery of the twelve tone basis for western music, and math that later allowed for the innovation of the avant-garde twelve-tone compositional style, known for its planned disarray... and the rythmic complexity of some of the best jazz and rock solos of all time owe themselves in some way to mathematics. Physics, chemistry, and all of the natural sciences require an understanding of math. The better your mathematical knowledge, the more science you will be able to absorb and understand. Logic is purely mathematical in nature, and laws are made and defended by it. The very fabric of our civilization, our universe, even our souls can be broken down into the most finite, smallest pieces... and those pieces will be numbers, equations, ratios, derivatives and integrals."

"While I would love to teach a course on that subject, which is called Mathematical Cosmology for those interested, I do not get my paycheck and thereby my meals for that. I'm here to teach you that magic is bound by the same laws as all the aforementioned aspects of our day to day lives. Magic is woven from nodes of primes and geometric links between them to establish a mathematical relationship which transfers itself into the world physical via the unity of a physical and spiritual medium conjoined. The matrix of each spell, regardless of classification, is intensely mathematical in nature. An exceptionally brilliant individual recently taught us this truth and whole universes opened up to the mathematicians of the wizarding world. It is a shame his knowledge cannot be tapped further on the subject, but that is the way this administration has chosen to handle his unique situation, right or wrong."

The class was dead silent. He had just left-handedly shown support for Telarius. Telarius, the most feared criminal in all the wizarding world. The man who had slayed Voldemort and obliterated his once-immortal spirit. That kind of talk had been expressly forbidden the night before by the Headmistress herself. Deanne decided that moment that she liked this man.

Lichen looked at the clock in the back of the room, where no other eye was trained, and gasped. "Dear me! I've made you all late for your next class!" he scrambled through his satchel for some more papers and began to hastily sign them and pass them out to students, "Part of the new proceedure," he explained, "Have to sign excuses to confirm that a teacher is at fault for the student's tardiness."

Each student received their slip and were on their way. Deanne found a bounce in her step that the breakfast could not have provided. The bounce faded as she realized her next scheduled class for this day.

It was Defense Against the Dark Arts.