Complex Equations

by Dr Blankflank


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!”