Complex Equations

by Dr Blankflank

Rating: everyone
Tags: Twilight Sparkle, My Little Pony: Friendship is Magic, Comedy, Discord, Slice of Life
Length: 3393

Twilight and Discord discuss quantum entanglement in passing.

Sure, Twilight knows the science behind magic; it’s in her cutie mark. What she doesn’t know is that the very laws of Physics (and the professors who discovered them) are under attack by an implacable foe. But is Discord breaking the laws of Physics, or is he simply rising above all that? A crowd of academic onlookers will bear witness to the ultimate ordeal: Twilight’s presentation speech at a major awards ceremony.

Bonus thanks to Doggyshakespeare for his invaluable help with editing!

Published 2018-04-27 19:50:12 UTC
Last updated 2018-04-27 19:50:12 UTC

1: Time Flies Like an Arrow

The quiet of this early Canterlot morning was delicious, equalled only by the sumptuousness of the castle room where Twilight sat reading. She adored this time best of all, before the cock’s crow; the hurly burly of the day was still asleep in hoof’d pajamas, and Celestia herself was still blinking sleep from her eyes. The room was exactly what Twilight wanted in a space, and nothing extra. One elegant walnut table stood at attention in the center of the bay window. One high stool, supporting Twilight as she took stock, stood before it. A side table rested inside a nook to the right of the window; upon the table was a tea service with honey pot and milk pitcher, and five teacups rested upon a silver tray beside these.

Upon the desk: one cup of tea with bergamot (and nothing else). One scroll of crisp parchment. Six quills. One vial of ink. One back issue of The Journal of Mathematical Thaumaturgy, used. Well, more than used. Loved. The journal, if not pressed between its sister volumes on the shelf, would simply fall open to a single article: “Space-Time Approach to Quantum Thaumadynamics”, by Fine Mane.

Thinking is an act of rebellion, she thought, then mulled over that particular act of meta-rebellion. Perhaps rebellion was an iterative process. She made a mental note to investigate, but was forced to admit that anti-establishment sentiment was rare in Equestria. There was the option of fomenting her own, but she dropped that idea as unethical. Somepony could get hurt.

Once upon a time she lived the life of a unicorn librarian, and time was abundant. The day simply dripped with hours (sweet succulent time!) to spend reading, cleaning, organizing and just drifting from one idea to the next. No longer. A Princess is more than just a title, and her hours are no longer her own.

The worst part about being a Princess, Twilight mused, is all of the pageantry. Awards for this, banquets for that, and all of them absolutely required a Princess to open, close, introduce, or otherwise stand and look Important for the attendees. Celestia, in her Wisdom, had deemed it a duty of all Princesses to spend time in the company of their subjects, so the Princesses were given a list of necessary engagements. This list, compiled by the Equestrian civil service, was submitted to the Princesses every month.

Twilight giggled. Celestia and Luna use “nose goes” rules for assigning the more odious tasks, and Twilight had practiced touching her hoof to her nose for weeks once she found out how decisions were made.

Today was different; today was the Royal Academy of Equestria’s lifetime achievement award ceremony, and the honoree was none other than Professor Fine Mane. Twilight had studied under Fine Mane while at university, and she considered him as much a friend as a teacher. When Celestia read that line in the monthly engagement list, Twilight half-leapt, half-flew out of her seat, slammed her forehooves down onto the table and shouted “DIBS!”

Once the papers had been retrieved, (and the tea service righted, and the lake of tea mopped up) the real bargaining began. Twilight fought a defensive battle for the remaining meeting, and felt herself lucky to only receive a Equestrian Public Works (EPW - working for a better tomorrow!) aqueduct ribbon-cutting ceremony, opening ceremonies toastmaster for a cultural exhibition on early griffonian pottery, and a bruised snout.

The best part about being a Princess is that sometimes you get first dibs.

She sipped her tea, offered a silent thanks to Spike, and started jotting notes onto the fresh scroll with her quill.

The common problem with honoring Fine Mane, and those rare ponies like him, was that he didn’t give a fig for honors. Many times he had won one award or another, and his acceptance speech was always the same: “The reward comes from figuring things out. These honors are unreal to me. I don’t believe in honors.” Twilight rallied: most awards were given by people who neither really knew Fine Mane nor really understood his work. Twilight, on the other hand, was the student who sat in the first row of seats. She knew the pony, and his work, as only a colleague can.

During Fine Mane’s lectures, he would insist that the students never take his word (or anypony’s word) on a particular value or formula; in place of homework, students were instructed to derive every equation that appeared in the lectures with their own hooves. The article played a prominent role in his lectures, and the margins in Twilight’s copy were the artifacts of her own struggles with the subject. One particular passage was rendered nearly illegible with the sheer density of quill scratches left in the margins, between paragraphs, and all along the header and footer. Most of these had been crossed out by the doodler.

In a moment of purest brilliance, happening as she was brushing her teeth that last night, it came to her. Sure it was going to be hard, but Fine Mane would appreciate the effort she was making in his name. She, the Princess of Friendship, was going to complete this one journey - this singular quest! - that eluded her for years: she was going to finish her homework.

To be fair, Fine Mane always assigned this particular equation only to his favorite students, and only as extra credit. It was an excruciating formula, passing a complex-plane vector through Shedding Hair’s equation (or the equation that describes the path of a thaumaton through potential quantum states). She sat, rereading the text and remembering all of the mathematical twists and turns she had taken back when she was a student. Jotting notes, figures, equations; inverting a particular derivation, solving for delta-t.

A knock on the door did not break her concentration beyond the flick of her right ear to solve for that change in value. Nopony plus knock on door equals company.

Discord squeezed his tail through the gap between door and jamb and opened the door with his tail, stepping backwards into the castle suite. He stood, dressed for all the world like he was the eminent scholar being honored by the Royal Academy, and he said, "No time for pleasantries; I have rather a lot to do today, so if you will permit me."

His voice was curt, almost offended. Twilight cringed internally; despite Luna’s best efforts, his voice was still played a terrible role in her dreamscape. There was still something in his tone that chilled her to the core.

She took a breath, but did not raise her head from the text. "Discord! I'm just catching up on a few papers in the Journal of Mathematical Thaumaturgy."

Taking off his mortarboard and scholar’s cloak with a flourish, he smiled his smug all-knowing smile. "How quaint."

Twilight's head jerked from her textbook, and glared at Discord. "What? What's quaint?"

Discord snapped up her teacup, recently emptied but still damp with the remains of her last cuppa. "For ponies, anyway."

Stay cool, Twilight. She stood up off the stool and casually stretched in a downward pony position (modified for the presence of the desk). It was best to expect and prepare for sudden vigorous activity when Discord was in one of his moods. She sighed. "You're talking in riddles again."

He recoiled, as if her words offended him. "That past is history, because time moves in a single direction." He raised the empty teacup to his mouth and brought it back down, full to the brim with piping hot tea.

"What?” Twilight stammered. Surely he isn’t...going rogue. Twilight racked her brain for any supporting evidence pointing towards his recidivism, but came up blank.

She said, “You have been officially pardoned for your earlier…” what word should I use? He looks angry! “...transgressions."

Seemingly mollified, he drew to the sideboard where a pitcher of milk and a pot of honey rested next to a silver tray holding five teacups. The teacups rested, inverted, waiting to be used.

"Be that as it may, Fine Mane's entire position rests upon a foundation that you yourself destroyed. Or has that escaped your notice?" Discord asked, and further punctuated his question with a brandishing of the honey-wand, damp and glistening. He stirred the honey briskly into his tea and withdrew the wand. It was thick with honey.

He’s jealous, she thought, and she felt a touch of collegial pride spark her courage. "Fine Mane is the preeminent theoretical physicist in Equestria! His lectures are legendary!"

"Well, Your own temporal excursions into your past, however useless they appear to you, serve to underscore my point.” He gestured, and an elegant royal kettle appeared in his claw.

He continued, “His proposed barrier between quantum and classical forces is an illusion. A numerical sleight-of-hoof."

He smiled, and unpoured a cup of tea, pulling tea from the cup in a single graceful arc.

She gestured at the tea kettle. "This, coming from the master of sleight-of..." she huffed. “Claw?

The teapot in his hand vanished once again and he smiled. "Thank you. Fine Mane's refusal to consider his thaumic diagrams as having any significance in the macrophysical plane is really just a hoof-wave of an answer. The fact is, he simply doesn't have the math."

Doesn’t have the math?! "Laboratory experiments have shown, time and again, that the thaumic waveform collapse is a real phenomenon. His grasp of the mathematics is unimpeachable. What, exactly, is there to object to?"

He replaced the now dry teacup upside-down on the silver tray on the sideboard. "Very well then: his mathematical model for photothaumic particle states is certainly...illuminating—” he laughed a quick haha at his own terrible pun, and then continued “—but I disagree with some of his more philosophical points. Can I make a cup of tea, or am I still banished from the kitchen?"

He just...it’s a trick. "Don't try to distract me! Time travel is the most complicated magic in existence. There are only a handful of ponies who could even attempt such a casting. Fine Mane's conjecture factors in the exponential power required to quantize..."

Discord smiled, his face an essay on insincere incredulity. "Quantum. Plural: quanta. Oh, it's a perfectly valid opinion for a pony with no concept of physical reality, but it clearly lacks scientific rigor. If you get my meaning."

Pedantry and insults; I’ve had enough. "I have some reading that I'd like to return to."

Discord peered at her journal, lying open on the desk. He mocked her with a cheery tone, "You're reading Fine Mane's text on quantum thaumic entanglement." He gathered his ludicrous (and likely unearned) scholar's robe and mortarboard.

Twilight sat firmly upon the stool, and turned her back to Discord. "Perhaps you would like to check on Fluttershy. She's toucan-watching in the garden."

The door flew open, and Discord backed slowly out of the room. His voice seemed delighted by the change in subject. "Ah, just the pony I came to see."

Twilight fumed, silently playing with the quills on the desk.

Discord closed the door with a corny fanfare. The room was silent once more, but the taste of it had soured for Twilight.

She stared at the jornal for five solid minutes, not reading a single word. Occasionally she would mutter under her breath, then lapse back into thought.

A growing feeling came over her, that she was missing something important. She looked down at the desk, at the leftover tea ring slowly soaking into the oak desk and ruining the finish. I should get a coaster for my teacup...well, it’s not my teacup anymore, is it?

She looked over at the sideboard, where six unused teacups sat, waiting to be used.

She looked back at her half-baked equations, balanced like an inverted pyramid of teacups on a single precarious assumption. She mentally removed the assumption, and the pyramid collapsed...but not completely. It reformed into a ring of bidirectional equations.

That’s impossible…

She looked back at the sideboard. The impossible teacup was still there, still waiting.

Discord’s laughter rang in her ears, “Ah, just the pony I came to see…”

He wasn’t talking about Fluttershy!

Five minutes later, she hastily packed her saddlebags with scrolls, the Journal of Mathematical Thaumaturgy, and a tray of teacups; she ran from the room shouting “SPIKE! I’m heading to the High Energy Thaumaturgy Building! Meet me at the ceremony!”

2: Fruit Flies Like a Banana

The quadrangle at the Royal Academy of Equestria sat between the building complex for the College of Arts and Letters, and the College of Science and Engineering. Surrounded by magnificent marble buildings and old and well-groomed cherry trees, it was the centerpiece of a venerable and handsome campus. Today, an outdoor stage occupied the northernmost end of the quad, and the blossoms on the cherry trees framed the stage in an exultation of pink and white petals.

The crowd, and a substantial crowd it was, was uncomfortably seated in row after row of small wooden folding chairs. Their discomfort was threefold: first, the chairs were always at risk of simply resuming their folded state; second, the Professors in the audience were forced into close proximity, and there is nothing a Professor dislikes more than others of their own kind; and lastly, it was becoming evident that the ceremony was not going according to plan.

Five minutes into the ceremony, the Dean of the Royal Academy of Arts and Letters (professor Great Books, a stoic and heavyset bay stallion) was stalling. He had recounted the list of Fine Mane’s achievements to the audience, and the audience generally regarded it as a good and thorough list. He had told the “worthwhile problems” anecdote, and received the usual amount of polite laughter. But now, he was harrumphing through a brief aside about funding and facilities in the Physics buildings, and looked certain to founder completely when his salvation came to him from above.

Using the Royal Canterlot Voice, Twilight bellowed, “Clear the stage! I’m coming in hot!”

She slammed into the recently vacated space behind the lectern, bounced, did a complete somersault in mid-air, and landed again on all four hooves. She held that pose for a moment, checking all four hooves for confirmation of her upright position. Her face blossomed with unexpected joy as she turned, breathless, to the lectern. She stood, grasping the lectern for support as she drew a scroll from her rumpled saddlebags with her horn.

The crowd was silent.

She panted. “One...moment…”

She took three slow, deep breaths. She looked like she had been dragged across campus by a manticore. She wasn’t simply dirty, no; she was entirely out of sorts. Every part of her coat had been rubbed against the nap. Her mane was standing straight up at the roots, as if they were trying to escape from her scalp by the most direct route. She had apparently engaged in a game of kicky-hoofsies with a bottle of ink, winner to be decided once cooler heads could prevail upon the combatants.

“Fillies and gentlecolts,” she said. She was still breathing hard, and her brain hadn’t really switched gears yet. She paused, and smiled. The silence was deafening.

“I’m sure you are all familiar with Fine Mane’s groundbreaking work, ‘Space-Time Approach to Quantum Thaumadynamics’, published by this very institution.”

The crowd made general noises of assent.

“Well, I have just come from the high-energy thaumaturgy buildings, and I can tell you now that his published quantum equations are incorrect!”

With this, the crowd broke completely. Several ponies elected to take it upon themselves to manage the defense of their colleague, who was clearly being oppressed by an uncaring and out of touch royal. Others took the opportunity to attack the honoree for having the impertinence of being right all the time. A dozen verbal skirmishes broke out.

Fine Mane stood directly in front of the stage, and with a mad grin he said, “Surely you’re joking, Ms Sparkle!”

“Oh, Fine Mane! You wouldn’t believe the day I’m having!”

Fine Mane looked around at the bickering ponies, and back to Twilight. “Something like this, I imagine?”

Twilight laughed. “Yes, okay. I see your point. But look here: you assume that delta-t is a positive value. If you remove that assumption, look at these results here…”

Twilight got down from the stage and they conferred for a few moments. Soon enough, the crowd conversations died down and began to pay closer attention.

Fine Mane’s voice peaked, “That’s good, but for macroeffects to be seen, it would generate massive numbers of anti-thaums. We’ve never seen a physical specimen that comes close…”

Twilight interrupted with a raised hoof. “I have a present for you in the high-energy lab.”

“A present?” Fine Mane smiled.

“A teacup, actually. It’s impossible!” Twilight laughed and the scroll trembled in her hooves.

“In the lab? You’re using the Cloud Chamber?” His voice was charged with wonderment.

“The measurements are off the charts! It’s incredible!” Twilight’s voice was squeaky like a whistling teapot.

Fine Mane popped his head up, looked to Great Books and said, “Someone get us a couple of chalkboards!”

Great Books harrumphed again, and found a few students to browbeat into the job. Once the chalkboards had appeared, Twilight and Fine Mane began to fill them with equations. Ten tense minutes passed. They were oblivious to the crowd, checking each other’s work, commenting on techniques, and finally settling on a single equation set that satisfied both ponies.

Twilight looked a bit dazed, but she radiated pure joy. “We need to preserve this work.”

Fine Mane turned to Twilight and said, “Let me show you the most powerful magic spell I know.”

He went up to the chalkboard, and wrote “DO NOT ERASE” in the top-right corner of the board. Below that, he wrote his initials, “FM”.

He threw the chalk over his shoulder. “There. Safe as houses.”

Twilight snort-laughed.

Fine Mane was looking directly at her now, thinking silently to himself. Finally, he said, “Shedding Hair famously described his own process as ‘10% inspiration, 90% depilation.’ He’s not...a distant relative of yours?”

Twilight grinned., “I’m going to pretend I don’t know what you are talking about.”

“Still, that was a pretty good entrance. Here’s my turn.”

With that, Fine Mane turned to the audience. “Fillies and gentlecolts, allow me to introduce you to your Princess, Twilight Sparkle. Not only has she saved Equestria countless times, she is one heck of a scientist.”

The crowd applauded, and Twilight curtsied in response.

He turned back. “There’s your honors, right there.“

“I could never have done it without you.” She gazed at the chalkboard. “What do you think it will mean, in five or ten years?”

“No idea. That’s for the next generation to figure out. Now, I expect your preliminary write-up of these findings on my desk first thing Monday morning.”

“First thing?”

“Oh, the hard part is already done; you’ll find the thing writes itself. Say, what are you going to call this?” He waved a hoof at the chalkboards, now being carefully wheeled back to the lab.

Twilight beamed. “I call it ‘The Discord Exception’.”

Just then, a tan unicorn mare with a cap and steno pad walked up. “Wow! I’m Hot Scoop, with the Canterlot Herald. Pleased to meetcha!”

Twilight goggled for a split second, but recovered her smile. “Yes! We are always happy to meet with the press,” she lied.

“Great. I have to say, I could smell a story here from halfway across town. Can we get a picture of the two of you?” She gestured to a nondescript gray stallion with a stony face and carrying a massive camera bag.

“Of course we can!” Twilight scooped Fine Mane under her wing and pulled him in before he could escape. She grinned her best camera smile, which only gave her the look of a pony possibly turning carnivorous.

The bulb flashed with no warning.

The picture was printed in full color, across the whole of the front page: Twilight and Fine Mane, several ponies arguing wildly around them, a chalkboard being wheeled into a nearby building. And, if you looked closely, you could just see a strange professor in robe and mortarboard, walking his pet goldfish.