Discorded Lessons: Chaos Theory
Chapter 1: In Laymare's Terms
cha·os /ˈkāäs/
noun
“A situation in which a fully deterministic dynamical process can appear to be random and unpredictable due to the sensitive dependence of the process on its starting values...”
“Okay, what’s Discord done now?” Celestia asked, having repeated that very same question multiple times during a very long, stressful week.
“He’s making a commotion in the library this time,” the guard pony replied beside her, matching the princess’ brisk pace. “He’s kicked everyone out and is asking for you.”
“Ugh... why could I not have found him a hobby of some sort?” Celestia asked herself, her hooves marching along with dread in each of her steps.
It was the first week since Discord’s reformation, and things haven’t taken off as well as she had hoped. He was still adjusting to not using his powers for evil, though his definition of evil fluctuates more than the weather. From pranks on the nobles to changing all the vanilla pudding in the castle into chocolate (the superior flavor race, as he called it), Celestia has had her hooves full just trying to keep him in check.
At least he’s finally trying to put his magic to a more productive routine. Though this has proved to be disastrous as well. His attempt at gardening ended in enormous plant monsters invading Canterlot. Then there was try on feeding the homeless, which resulted in a zombie invasion. And, of course, there was that cleaning the castle fiasco that brought upon an invasion of mutant dust bunnies.
In hindsight, she should prepare the guards for invasions more often. There seems to be one happening every other day.
Stopping at the library doors, she said to the guard, “You may leave now. I can handle it from here.”
Saluting, the guard departed, leaving Celestia alone to whatever Discord was doing inside the library. From the sound of it, she was expecting something really destructive and high in collateral damage. Eventually the castle treasury room was going to be emptied out at the rate of consumption its been had for repairs.
Knocking on the door, she called out, “Discord, cease this mindless racket and come out at once.” In a flash of light that momentarily blinded her, she was inside the library itself. “... Or you could do that.”
Looking across the room, she was surprised to see that it wasn’t in a state of disrepair as she guessed. It was as perfectly tidy and neat as ever, with all the walls covered in an ample amount of olden tomes and books aplenty. Though many of the shelves seemed sparse, and it was quickly apparent why.
“Did you just build an entire tower of books?” Celestia asked, arching her neck up to try and get a look at the top of the book stack. She knew the library couldn’t be more than three stories tall, but it looked like there was no end to how high the tower was.
Popping a head out over the edge of the top of the tower, Discord waved to Celestia below. “Hey there, Celly! Didn’t expect to see you here! What brings you to the library?”
“I was about to ask you the same thing,” Celestia replied, her serious expression counteracting Discord’s joyous face. “Now, can you please get down from there and put all these books back? Some other patrons of the library would like to continue their work in peace.”
“Oh, like those stuck-up scribes and scholars had anything good to do anyway.” Discord chuckled gleefully, jumping off the edge of the tower and sliding all the way down along the side. Jumping off right before he hit the ground, Discord did a triple front flip with a twirl, and stuck the landing. Anonymous shouts of approval and applause followed, quickly cut off when Discord waved his hand in the air. “Besides, I have some serious work to do here.”
“This type of foolery is exactly why no one takes you seriously, Discord,” Celestia grumbled, rubbing her temple with a hoof. “And what kind of work involves locking yourself in a library and building a tower of books?”
“Well, first off, everyone else was much too noisy. It’s a library, for Pete’s sake, and they couldn’t stop shouting just because a couple of books started floating in the air,” Discord said, rolling his eyes and making moving mouth motions with his hands in a mocking nature. “And secondly, I read the books before I made the tower. The tower was just for fun.”
“I was able to call upon a storm of chocolate rain on all of Equestria,” Discord began, looking at his claws in a nonchalant manner. “Reading all of this was child’s play compared to that.”
“So... why exactly did you read all these books?” Celestia asked, still amazed yet curious as to what he was going to answer with.
“Why, to share my knowledge with the world, of course!” Discord said, throwing his hands up high and striking a heroic yet ridiculous pose. “I shall teach the masses the education only a god of chaos will know!”
“But you’re a spirit of chaos,” Celestia interrupted, her earlier amazement replaced with annoyance when she realized this was just another of Discord’s games.
“Close enough!” Discord answered back. “Finally, ponies across Equestria will learn to respect and fear me when they hear about my teaching curriculum!”
“Um... how does teaching gain you respect and fear?”
Discord laughed, shaking his head at Celestia’s simple mindset. “Why, by my rigorous and rewarding teaching system. That’s the respect portion. The fear comes along with me being scrutinous with grading.”
Celestia arched an eyebrow. “Well, I can see all this reading has improved your vocabulary and garnered you more confidence in your teaching abilities.”
Discord snickered. “Vocabulary-falabulary. I just say the first thing that comes to mind.”
“Yeah, I noticed,” Celestia said, a deadpanned expression on her face.
Disregarding her snarky comment, he said, “Anyway, I plan to open up a school–no, university! Discord University! Where chaos comes to you!”
“... You’re actually going through with this, aren’t you?” Celestia asked, her stomach sinking.
“Yessiree! Plus, tax purposes!” Discord said, rubbing his hands together in greedy glee while doing a complimentary villain laugh.
Celestia facehoofed. “Let me get this straight. You’re starting your own university... just so you can make money off of the tax system?”
“And the eager students who will pay boatloads of bits to be taught by me,” Discord replied, basking Celestia in the glory that was himself. “The best part being the skills I teach them will have nothing to do with them getting a job. So guess who gets an tidy sum of cash from student loans? Also me!”
“That’s... that’s... despicable,” Celestia said, split between being sick at the utter evilness of his plan, or surprised he came up with something on a mad scientist level of craziness. “And extremely complicated, even for you.”
“Complication is how the world works, Celly,” Discord laughed, drifting on in the air and back-stroking in a circle around the disgruntled princess. “In fact, that’s my first lesson I’ll be teaching in my classroom.”
“The stupidity of ‘get rich quick’ schemes?”
Discord snapped his fingers, causing a chalkboard a story high to appear before the pair. Written in a flourish handwriting was the words ‘Chaos Theory: 101.’ Picking up a piece of chalk in his claw, Discord turned to Celestia and smiled deviously. “Nope! The stupidity of randomness of the universe that is Chaos Theory!”
“Wait? You’re trying to explain what randomness in the universe is?” Celestia asked, her head tilted to the side as she stared up at the board. “Isn’t that contradicting?”
“Not at all, my dear student,” Discord said, strutting into Celestia’s field of vision dressed in a professor's jacket with wire rim spectacles and a trimmed moustache. “For you see, without dissecting every possible topic with the scalpel of study, we may never truly understand the organ structure of what we want to know.”
“Wait, we’re doing–”
“It was a metaphor, my dear.” Discord turned to the board and tapped the chalk against it. “Now, my dear, can you be ever so eager to answer what exactly chaos theory is?”
“First off, stop calling me ‘my dear,’ and secondly, I have no idea,” Celestia began, turning back towards the library doors. “I do not want to be a part of another one of your ridiculous schemes, so kindly leave me out of it.”
“Oh, fine then...” Discord sighed, slumping her shoulders downward with a deep set frown on his face. “I guess I could give cooking a try instead as my new hobby. They have fire extinguishers in the kitchen, right? Along with harpoons?”
Quickly turning back, Celestia sat down in front of the chalkboard. “On second thought, how about we continue with this lesson? What exactly is chaos theory all about?” She was laying it pretty thick with the fake enthusiasm, but luckily, Discord didn’t seem to notice.
“Well, of course, chaos theory is a part of mathematics. It is actually an underlying principle of many aspects of it, along with physics as well,” Discord said, writing down each term on the board. “The gist of it is that we look at certain systems and observe their behavior with change. The more sensitive the system, the more the amount of change, even the smallest, can make a system behave completely differently.”
“So, this isn’t complete randomness, right?” Celestia asked, genuinely curious as to where this lesson will go.
“Nothing is completely random,” Discord explained, pacing before the board. “There is always a certain amount of predictability. Such as a coin toss.”
“Either heads or tails, right?”
“Indeed!” Discord said, drawing into his pocket and retrieving a bit. “The random part is that we know it can be either side, a fifty-fifty shot. But the predictable part is that we know it has to be one or the other. A head or tail. No matter the outcome, we can predict with certain clarity that it could be a head, or a tail. So even though which one the toss will end up on is random, we know what either end result can be.”
Discord flipped the coin up in the air, but instead of it spinning, the entire castle did. Celestia screamed and held on desperately to the carpet floor as the room spinning around the non-moving coin in the air, until it finally fell to the ground. The spinning finally stopped, and the nausea set in.
Picking the coin up, Discord chuckled and showed it to the nearly-puking-her-guts-out Celestia. “Unless you have a certain spirit of chaos as the flipper.” The image on the bit, on of himself–except for the fact his head was connected to his tail–winked at Celestia.
“Th-that wasn’t... f-funny, Discord!” Celestia hissed, barely able to hold back her lunch as she shakily back up on her hooves.
“Ah, but teaching is best lead through example,” Discord said, ignoring her condition and returning back to the chalkboard. “So, we got a rundown on randomness. Now for how that randomness places a factor in what chaos theory is all about.”
Drawing several clouds and a cartoon smiley sun on the board, Discord said, “Okay, we know about weather, right? We can properly control it through the use of pegasi, so there isn’t any point in predicting it.”
“Yeah, your point being?” Celestia said, her face no longer as green as it was a few seconds ago.
“Well, before you ponies decided to control Mother Nature, the weather was unpredictable. Oh sure, you can guess whether it would rain or not from recent weather patterns or clouds in the sky, but anything you predict farther into the future is less likely to actually be true. So a few days is the best you can do.”
“So randomness places a fact in the matter whether it would rain tomorrow or not?”
“No, a butterfly does,” Discord replied, drawing a cartoonish grinning butterfly on the chalkboard.
“Um... you lost me,” Celestia said.
“Chaos theory works on the principle that even the smallest change or error can make the entire system change completely. Like how a drop of water could make an entire damn burst. A change that you think is insignificant can completely differentiate a system if it’s sensitive enough.”
“Wait, wait, hold up here,” Celestia interrupted, waving her hoof in the air to catch Discord’s attention. “So you’re saying a butterfly can make the weather change? How?”
“By flapping its wings, of course,” Discord said, drawing gusts of wind coming out of the butterfly’s wings. “Since even a butterfly can make enough wind with its wings to change the system, the weather can completely change whether a butterfly flapped its wings or not.”
“That’s ridiculous. That means a fly farting could make it cloudy tomorrow,” Celestia rebutted.
Discord giggled, holding back a laugh with a claw covering his face. “Pfft, you said farted! Hehehehehe.”
“Oh, grow up,” Celestia muttered, rolling her eyes as his childishness.
“Hey, I haven’t even gone through puberty yet. Give me a break.” Discord drew a fly, who was indeed farting and looked quite happy about it. Moving to the corner of the board, Discord drew a swirling pattern over and over again. “Anyways, either from a butterfly’s wings flapping or a fly farting, the weather can drastically change according to how the system works. Heck, a tornado could appear in Canterlot if a butterfly flaps its wings in Ponyville.”
“There is no way that could happen,” Celestia said.
Finished with his masterful drawing of a tornado, Discord moved to the windows and opened them up. “Oh really? Then what’s that?”
Going to Discord’s side, Celestia looked out the window to discover a massive tornado throwing off gale-force winds fastly approaching Canterlot mountain.
Looking back to Discord, she scowled at him. “Cut that out.”
“Hey, don’t blame me. Blame the butterfly.” Seeing that his words of protest were having no effect, Discord sighed and snapped his fingers, the tornado stopping in an instant and fading away.
“Okay, so, was there any point in this endeavor?” Celestia asked, tired already of Discord’s obnoxious behavior. “I got the basic gist that even the smallest change can lead to big shifts in how a system can work. Anything else?”
“And what do you think is the point in understanding chaos theory?” Discord asked, an ever annoying, smug grin on his face.
Celestia shrugged, the best guess to his answer.
Tutting under his breath, Discord tapped a claw to her forehead. “And here I thought you were the smart one. It’s to observe patterns in random systems.”
“But I thought you said prediction was pointless,” Celestia said, waving off his hand.
“No, I merely said prediction wouldn’t accurately work all the time,” Discord explained. “Some systems may appear random at first, but with the use of chaos theory we can point out the patterns in these systems. If you got your head out of the gutter, even you may notice these chaotic patterns. By noticing the chaotic change that causes a system to be different than what we predicted, we’ll be able to incorporate this pattern into our prediction to be more accurate. Not completely, but closer to right.”
“So chaos theory is actually just studying how these changes work in making systems appear random?” Celestia guessed.
“I’d say more along the lines that a minor difference at the start of a system can cause a major change in how it continues as time progresses. So basically, chaos theory can apply to any aspect of mathematics or physics to correctly observe the chaos of a system and how it makes it act random.”
“Wow, that’s pretty... knowledgeable,” Celestia said, surprised she even admitted that. “I did not expect for you to actually teach me something.”
Removing his glasses and huffing on them, Discord cleaned them with a handkerchief with a rubber ducky design. “We all change one time or another, Celestia. Plus, I have to apply my own theory to myself. The change of being reformed caused the handsome system we know as Discord the Magnificent to become a college grade professor. Neat, huh?”
“I suppose so.” Turning back around to the doors of the library, Celestia made her way there and called over her shoulder, “Well, continue what you’re doing then. I can’t really stop you if you just want to teach, and if ponies are willing to shell out bits for that teaching, more power to you. Just please let ponies back into the library and we’ll be just fine.”
Celestia was suddenly stopped in her path by the random appearance of a desk. Grunting in pain at the soreness of her chest when it impacted with the desk, Celestia glanced back up at Discord.
“Ah, ah, ah. Not so fast,” he said, wagging his finger. Snapping his fingers, a test paper and a number two pencil appeared on the desk. “Now’s the time for the test. No notes, and forty-five minutes to complete it.”
“What? I am not taking a test!” Celestia argued, glaring right at Discord’s smug face. “I am a princess, not a student!”
Discord turned his back on her. “Fine, I guess I’ll just be making my way to the kitchens now. It’s Casserole Tuesday, correct? I always wanted to try my hand/claw/paw at that.”
Sighing, Celestia sat down at her seat, already scribbling down her name as fast as she could. “Do I get a bathroom break?”
“No. Hold it in.”
“Damn,” Celestia muttered under her breath, looking over the first question and biting the eraser end of her pencil.
Discord chuckled lightly, looking down at his student to make sure no cheating was underhoof during test time. “Even the most minor of differences can make a big change. Quite a big one indeed.”
