The Love Postulate

by SirDucky70

Rating: teen
Tags: Sex, Slice of Life, Twilight Sparkle, Main 6, My Little Pony: Friendship is Magic, Rainbow Dash, Romance
Length: 4428

Twilight has always been an egghead. But now she’s an egghead who’s also the princess of friendship. What could go wrong if you mix the two together?

Twilight was always an egghead. But now she’s an egghead who is also the princess of friendship. This title always felt off putting to twilight, it felt like it was giving her power over something that she herself didn’t completely understand. And she hates that feeling. But what if there were a way to mathematically prove friendship? And what would happen if there’s a proof that lies beyond what friendship can harbor?

Published 2023-11-13 18:00:01 UTC
Last updated 2024-03-19 05:27:31 UTC

The Elements

Twilight was always a studious mare for better or for worse. She had well perfected the art of destroying her sleep schedule either for the sake of studying a new concept, getting caught in a loop of following up on the research that she’s already studied the n’th billionth time, or Continuing to organize and plan out every action she would take for the next month. She really had no shortage of things that could take her attention and run with it.

Or at least she used to.

After Twilight moved to Ponyville, her priorities began to slowly shift away from her studies of the sciences and into the studies of the new friendships she had made and how it had changed her.

Because Celestia, if it didn’t change her.
Twilight could feel her wings flutter slightly at the thought. That slight bit more of a reminder that she isn’t who’s she once was. Now looking back on it, her past actions are mostly laughable like when she tried to explain pinkies ‘pinkie sense’. She got hurt a lot from that endeavor. Kinda like when I went back in time just to try and tell myself not to worry about the future and only ended up making myself worry about the future.

Twilight continued to muse about her many misadventures. A good deal of which we’re caused by her own insatiable desire to analyze everything. Her eyes caught the clock at one point and noticed that it was already 11:00 PM. This caused her to give a light shake of her head as if to dispel her inner dwellings on past events. She had to stay focused on the present after all.

“If only the present were more interesting.”

Twilight put her cheek on her hoof before it wandered up to rub at her lightly aching temple. Meanwhile she reached out with her magic to the top of her ‘to read’ pile and levitated the next book down to her desk. She glanced absent mindedly at the significantly smaller stack of finished books next to her and her gaze, once again, was attracted to the clock. Yep, still moving. For a second Twilight felt irrationally irritated at the passage of time but decide to shake it off and start reading.

“Oh joy, Diacanterus’ Mathematica, nothing like ancient equirians and their affinity for convoluted equish.”

Twilight rolled her eyes and started to read the convoluted old equish, or at least try to. She didn’t even get one chapter in before a headache developed. She groaned and instinctively almost called out for Spike to take a note to order a translated version. The “s” slipped off of her tongue and she sighed, Spike was already in bed. And not only that, but she was in her personal study corner of the castle library. She could’ve screamed for him and he would have been none the wiser.

She looked up and around at the crystalline walls of the castle. Though her friends may have done their best to make the castle feel more of a home, it could never be the same as the golden oaks library. The constant lingering stuffy smell of old ink and parchment etched into the walls, the echoing silence gently pierced with pages turning and quills scratching on paper, and those times when the silence was shattered by one of her friends' shenanigans or spikes’ tomfoolery. A tear fell gently down twilight's cheek and she gulped trying to wash the memories back down.

“Well, what’s done is done.”

That statement made her scoff at herself, that’s the same thing she’s said over and over the past few months. Almost every day now that she thought about it. If only she could convince herself to listen. She sighed, closed Diacanterus’ works and shoved it away from her. She pushed a bit too hard and it fell onto the floor making a loud bang. The resulting echo bounced around the library and leaked into the long empty corridors of the castle. Twilight winced from both the sound and knowing that she disrespected a book. She levitated the book up off the floor, inspected it to be sure that it wasn’t damaged in any way, then floated it up to the top of her discard pile. She put her head in her hooves and looked up at the clock once again.

“11:30, ugh. At this rate, I won't have a clue on how to make a proof for anything better yet a proof on magical frequency synchronization.”

Twilight had been studying one of Starswirl's famous conventions in magic. The magical frequency synchronization convention or MFSC. It was a very daunting task for any respective physicist and has remained unproven through the many decades since Starswirl's passing. Twilight, in particular, had tried to solve it five different times now but always came up empty hooved. Recently with the lack of projects from Princess Celeastia though, she had decided to try again. Only this time she had a theory that a better understanding of math would help her. In particular, proofs. Unfortunately for Twilight, complex math was not something she found particularly interesting to study. Twilight's wings twitched slightly and she spread them so she could see her feathers.

“I’m gonna have to preen tomorrow or Rainbows gonna kill me.”

She folded her wings back along her back but her gaze lingered on them. Her mind wandered to how different her life had become since she got them. She was suddenly thrust into the position of being a princess. Not just any princess though, the princess of friendship. It was a lot of pressure to say the least. Suddenly she was supposed to be the one that everyone came to for a friendship problem. Not that she didn’t love to help her friends, but she needed to have answers for them. In science and math answers are easy. Their black and white, night and day, yes or no, correct or incorrect. It’s simple. But with friendship? She had only known friendship for 2 years up until the point that she became the princess of it. How could she-

GONG!

Twilight yelped and snapped her neck around to search for the offending noise.

GONG!

Twilight's eyes settle on the antique grandfather clock that Applejack had given twilight a few days ago. She let go of a breath she didn’t know she was holding and started to grumble.

“Stupid clock, I need to give that thing back to applejack, I knew she didn’t wanna get rid of it anyway.”

Applebloom had managed to convince Applejack to have a barn sale a few days ago. Of course, anypony who was anypony knew that Applejack didn’t want to get rid of anything, but Twilight thought the clock would add a bit more of an antique feel to the library and maybe make it feel more like the golden oak library. Instead, all it does is jumpscare her every hour on the hour.
Twilight turned her gaze back to the less intrusive clock on her wall to see that it was, Indeed, midnight. She rubbed the side of her head with her hoof to try and push away the headache and decided she would only do one more book for the night. At that, she levitated down the next book in her pile. This one was a reduced version of Euclop’s Elements. She opened it to the first page and breathed a sigh of relief as this version was translated from old to modern equish. Twilight read through all of the basic obscure definitions of basic math principles that made up the first 6 pages. They were so basic that it was hard for twilight to see how they would be of any use. She was about to start skimming through to see if it had anything to do with proofs, when she found them. Except they weren't proofs, they were postulates.

Postulates are ideas that are assumed to be true so that other ideas can be built upon them. Twilight didn’t think too much about the ones she read, it was all just trivial geometric stuff somepony figured out and defined ages ago.
Twilight rolled her eyes,snapped the book shut, and put it on the discard pile. She got up from her chair and shivered as her hooves touched the cold crystalline floors. The winter months were rapidly approaching and that meant that the castle would start to feel colder than usual. She stretched a loud pop out of her neck and back.

“That’s enough for a night.” She said as she walked away from her desk and started down the labyrinth of crystal halls toward her distant and waiting bed.

“Maybe I should just start looking into more princessy subjects to study. Anything that doesn’t have to do with rigorous mathematical proofs.”

Twilight shut the door to her bedroom and sat on the foot of her bed. The sheets glow with the purple-lavender hue of her magic as she pulled them open for her. She yawned,

“Maybe I should focus on answering friendship problems,” twilight tucks herself under the downy soft sheets. “S,not like there's proof for friendship.”

At that she drifted off to sleep.

Or at least she should’ve. Her final sleep deprived statement made her mind start to piece together an idea.

“Why not make a proof about friendship? I mean, at the very least trying to make proofs about something I’m supposed to know very well will get me the experience I need with proofs to work on Starswirl's convention…”

After thirty minutes or so of mental back and forth over this idea, her eyes opened again and she reluctantly pulled herself out from under her warm bed, set her hooves back down upon the cold crystal floor, and trudged back to the library. The time it took to walk back to her desk only made her unwilling and tired body further cave into Twilight’s now buzzing and work ready mind. A look back to her nemesis of time told her it was two in the morning.

“It’s gonna be a long night.”

Author's Note

This chapter is old and will not be part of the finished story.

Thanks for giving a shit.

The Proof is…

Celestia’s sun broke the dawn and chased away the lingering shadows of Luna’s moon. A glorious vibrant iridescence settled all around the horizon making an unending belt of pinks, oranges, and light grays all below the ever-illuminating dark blue sky. Any pony up early enough to witness the birth of the day In all its glory could revel in the growing warmth of the light as it warms up their chilled shadows. Truly, the rising sun is something to treasure and witness.

Then there’s Spike.

The young drake started to stir from the confines of his subconscious as the growing daylight broke through a crack in his curtains and fell on his eyelids. Spike turned away in an attempt to get back to the dream which was now slipping through the claws of his mind. He returned to his dream, but everything was out of place and not as he remembered nor wished it to be. Spike let out a low grumble as he yielded to his stubborn dream and settled on trying to snooze away the approaching day and the work it held. The battle for Spike’s consciousness was eventually won out by both his empty stomach and fear of Twilight complaining about him oversleeping again.

Spike put what effort he could muster into getting out of his bed. Unfortunately for him, he was successful and slumped out of it. He wasted no time in trudging out of his room and down the cold empty halls of the castle. His drowsy mind already starting to run through a mental checklist of what he had to do that day. After being the glorified sidekick to a mad-mare who made checklists for everything she did his entire life, he couldn’t help but make checklists himself.

He of course had his daily chores which consisted of cleaning the library,
This kinda included the whole castle but Twilight rarely did anything outside the library,
buying necessary things,
mainly quills and ink because Twilight went through them by the bucket load.

At that thought Spike shuddered as he could only imagine the fate of the hundreds of quills that Twilight went through, not even he knew what happened to most of them. It was probably best not to think about it.

Anything else?

“GAGCTHmeee!”

Spike suddenly squealed and soon found himself on the ground nursing a stubbed claw. He bit his lip as he glared at the offender, which was the corner of a counter. It was only then that he realized he was in the kitchen. His feet were on autopilot while his mind was in la la land and carried him to their predetermined destination. Spike took in the kitchen for a second as if trying to remember why he was even there before his stomach reminded him with a short rumble.

Oh yeah, cooking.

Spike was the cook for both him and Twilight as you didn’t want to let her near the kitchen if you favored living. The last of her culinary creations had grown sentient and is now in E.M.P Everfree’s maximum security prison for assault and attempted murder.

…and it was supposed to be Jello.

Spike grew an amused smile as he recalled the memory and got up off the floor. He walked, or rather limped over to the counter and hopped up on top so he could start getting breakfast started. They had bacon and eggs yesterday so he decided some prench toast sticks would be good. The idea itself made his stomach voice its urgency and Spike got to work

———-————————-

Twilight’s dreams were plagued with a seemingly endless loop of impossibly large things falling inside of unfathomably small things. It was uncomfortable, to say the least. It felt like her entire body was falling along with the large masses of nothingness and into a singularity that would never come. The feeling was powerful enough to stay with her even as she stirred. She would have whimpered had her mouth not been so dry that she instinctively knew any use of it would do more harm than good. The horrible feeling subsided as her lucidity grew. She could already feel the slow burn of a growing aching in her temples as she cracked her eyes open.

“Big mistake”

Usually, the curtains in her lightly regal fit room would be enough to keep the light out unless otherwise warranted. A shield to allow for nice and easy adjustment to Celestia’s sun. Here she found no such comfort. Twilight fought through squinted eyes to reveal the vast crystalline library around her. The green light of the tinted windows reflected off of the purple walls in a shimmering spectacle that would be admired by anypony who got more than 4 hours of sleep. Twilight smooshed her face with her hooves with a begrudging hum as if trying to rub away the pain. She looked down at her desk which contained pages upon pages of notes, some of which had drool mixing with the ink; she could retake those later. Things had started to flow after Twilight’s futile attempt at having a healthy lifestyle. She was able to source multiple books that were more oriented on the subject matter of Proofs and studied them rigorously. After finishing just the first 3 books (a small task for an in-the-zone Twilight), her fascination skyrocketed. As it turns out, In mathematics, you cannot say that something is always true just because it works in a few cases, instead you have to develop rigorous logical arguments that lead from results that you already know to be true. That is, in essence, what a proof is. This all made Twilight speculate over previously solved friendship problems, and if their solutions could even be used to solve the same problem at all. This idea sent Twilight into a six-hour frenzy of thoughts, theories, and mathematical postulation. The same environment that Twilight used to live and thrive in for years. Until she passed out.

Now Twilight got to feel the other side of the coin that she seemed to have flipped one too many times back in Canterlot. It was like meeting the old bully from grade school again, with the same pains in the head and a slight squishing feeling in her bagged eyes. Not unfamiliar, but a pain nonetheless. Twilight willed her body up off her pillow chair and started out of the library. She felt her hooves pop as she took her first step and prepared to get the rest of the kinks out of her neck…

GONG!

GON–

SMASH!

The dinging of the grandfather clock was interrupted by getting enveloped in lavender magic and slammed against the crystal pillar next to it. The wood splintered into the sensitive gears inside it and a low ringing of the bell inside it bounced all through the refractant castle walls.
Twilight’s outburst turned from annoyed anger to guilt as soon as she realized what she had just done. She cupped her muzzle with her hoof and looked down at the well-shattered corpse of the clock. Her ears flicked toward the light pitter-patter of claws contacting the smooth hallway floors as it grew louder.

“Twilight! Is everything ok? What happened?”

Spike called, worry was evident in his voice; till he turned the corner that is.

“Oh”

Spike looks from his sister/mother to the shattered clock and back. His face slowly contorted into a smirk as he tried and failed to hold back his mirth. His giggle turned into a cough then into straight laughter.

“Y-you sh see the look on your face.”

Spike said an octave higher than usual as he continued to laugh. All the while Twilight was red from embarrassment, shame, and a bit of anger towards Spike’s enjoyment of this.

“Ugh, this isn’t funny spike. This was Applejack’s clock and I know she didn’t want to get rid of it anyway. She’s gonna be so upset if she finds out I broke it.”

Twilight said with a few tears in her eyes.

“Well I told you you should have taken it out of the library in the first place, all it did was interrupt you and anyone else in the library every hour. Was only a matter of time anyway.” Spike said matter of factly. Twilight glared at him.

“No one likes an, I told you so spike.” Twilight knelt and pushed on the splintered wood as if trying to push it back together before sighing. “Can you at least help me clean this up please?”

“Sure.” Spike droned as he walked past Twilight to get the broom from the closet.

Twilight had gotten as far as levitating the large chunks of wood and metal out of the pile before the distinct smell of burnt hit her nose.

“Is something burning?” Twilight said with urgency in her voice.

Spike’s eyes narrow to pin-pricks. He dropped the broom and left a cartoonish cloud of dust behind him as he dashed out of the library to the smokier kitchen. Twilight released her hold on the bits of the clock and ran after Spike. She arrived just to see Spike put a pan full of what she was assuming was the cause of the now smoke-filled kitchen into the sink. He turned the tap on and groaned.

“Well, there goes breakfast I guess.” Spike turned away disappointment in his eyes. Twilight’s heart hurt seeing Spike’s face like that, especially since she knew it was her fault.

“It’s ok Spike, tell ya what, how about after we get this mess cleaned up and maybe open a few windows, we go to Sugar Cube Corner? I’ll get you anything you want.”

Spike lit up at the mention of Sugar Cube Corner. “That sounds great Twilight, Thanks!”

“It’s no problem spike.” Twilight reflected Spike’s smile.

“I’ll start getting things cleaned up and in the meantime, I think you might need a clean-up yourself Twi.”

Twilight blinks before realizing that she probably looks like an absolute train wreck and blushes. “Yeah, you’re probably right Spike.”

Twilight went to take a shower while Spike busied himself with opening as many windows as he could, cleaning up the kitchen, and hiding the corpse of the clock inside the closet for “Future Spike” to deal with. The not-so-shattered clock had just hit 1:30 as the pair left the library.

Author's Note

(Pending rewrite)

Axioms (Chapter 1 Rewrite)

The night was calm. The cool mist of the infant dew started to settle on the grass and empty streets of ponyville. The sky usually lit by the presence of Lina’s moon and stars was cloaked in the approaching rampant clouds from the everfree.
Every window was dark except one. The light was faint and only barely floated out of the intricate stained glass windows.

The source was of a single lit candle, despite its lack of luminosity it was able to reflect off of the crystalline walls of the castle library and illuminate just enough for Twilight to cast a fire spell onto the fire pit and brighten up the room.
She rubbed at her temple as the bright light seemed to awaken the headache caused by her grotesque sleep schedule.

Sleep has always been Twilight's worst enemy. She has been defying her body's natural circadian rhythm ever since her parents stopped making her have a bedtime. Why would she sleep when she could spend time studying for another exam? Why sleep when she’s this close to a major breakthrough in magical physics?

Every time the headaches and eyebags tell her why.

She suppressed an offending yawn and plopped down on the pillow next to her many towers of books. It’s a wonder why they even have shelves in the library when Twilight is usually using half of them anyway. Without a word her horn lit up and pulled the next of many books in front of her.

The sound of scribbles on parchment was endless as Twilight studied for hours farther into the night. The clouds had overtaken the sky, the dew started to frost, yet the light in the library remained.

Her research was on a topic that was by no means new. It was in one of Starswirl’s final manuscripts “Magimanus Mundi” and in it lies a dilemma that has stood for hundreds of years. He had it organized as any other self respecting physicist at the time.

You first had your established facts. These were called axioms and otherwise known as postulates. Statements that were considered to be fundamental truths the rest of the manuscript can build off of.

After establishing these truths you can start developing your proofs. These are the bulk of the manuscript, yet these were mostly sound, sans some discrepancies found years later. The thing that has perturbed magical physicists for years is at the end.

The final parts of the manuscript were unusual. They were not a summary as is customary, but multiple stipulations proposed by starswirl over many seemingly outlandish ideas. At the time, many thought that his final stipulations were just the ramblings of an old stallion, yet later as Starswirl's legacy grew, physicists started to look into them. They were surprised to find that all of these stipulations were proved to be true. Except one.

Magical Resonance Synchronization or MRS.

Given how much of a Starswirl fangirl Twilight was, it’s no surprise that she would be transfixed on trying to find the proof for this. Nor would it be surprising that this would be the seventh time she’s tried to prove it. Yet still, it eludes her.

Her eyes burned and her resolve for fighting her need for sleep started dwindling. The candle had been burned down nearly to the base.

“Just one more book, please?” Twilight said as if she was pleading to sleep itself.

She tried to pick up the next book in her horn but the headache made her attempt only reward a groan. It took everything in her to not just face-desk and pass out. She reached over to her book pile and was surprised that there were only a few left.

She looked at her discard pile but saw past the books. All she could see were dead ends and loose trails that just led off the inevitable cliff of another failed attempt at proving the final ideas of a silly old man.

It doesn’t make any sense. Every other final idea was correct and if she of all ponies couldn’t figure out whether this one was then what kind of princess of magic even is she?

Wait, she’s not the princess of magic, she’s the princess of friendship.

At this thought, Twilight sighed and could feel her wings ruffle as she became conscious of their existence. Conscious of her position. Her obligation to be the knowing and deciding factor for something that she herself hardly knew anything about just two years ago.

And yet, this is who she is. The princess of friendship.

“Whole lotta good I am at it, s’not like I can prove friendship like a buckin physics paper.” She grumbles before pulling the next book off of her pile and starts reading.

It’s “Diacanterus’ Mathematica” a legendary manuscript over the founding ideas of mathematics. It was a translated version to modern equish that Twilight had ordered more recently since her old copy was destroyed along with the golden oak library. It would be a great read for an aspiring mathematician, yet Twilights aching eyes stay transfixed on the postulates.

What if there are proofs of friendship?

This thought rang in her head and the more she thought about it, the more sure she became, and the less tired she felt. Her headache replaced with determination and her horn sprung to life.

A new candle with a fresh wick, a new pile of books, fresh ink and parchment, the chirping of birds outside, clouds pushed away, frost melts into dew.

Author's Note

This is finally the rewrite of chapter one. It’s a lot cleaner than the original and I can take this story in the direction I want to now.

I made a few edits since I first published it, nothing major.

Expect more. And a complete rewrite of chapter 2.