Chaos Theory is Magic

Twilight Sparkle looked away from her telescope in order to make an obscure note regarding the orbital patterns of moons around gaseous planets.  She had been up all night studying astronomy; it had been a clear night, perfect for stargazing, and the weather team said the whole week would be free of clouds.  Twilight was looking forward to an entire week of flawless night skies, and learning more about the cosmos.

Owlicious hooted and Twilight glanced at him.  He was perched atop the clock in the library.  4 o'clock in the morning.  Twilight sighed.  She always lost track of time when looking at the stars, but it didn't help that she had to wait until nightfall to be able to study them.  It was inevitable that she would have to cut into her sleeping time, but it was worth it.  Suddenly, she felt the fatigue creep in as her body realized how long it had been awake.

"I'll just finish up here before getting a little shut-eye." She said to Owlicious.

The owl just hooted and resumed his still position on his perch.  Meanwhile, Twilight was making her last few calculations about ellipses and packing up her materials.  Finally, the room was organized to her standards and she walked quietly past a sleeping Spike before wriggling into her own bed and passing into a peaceful sleep.

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A knock sounded at the door.

Twilight woke up.  The pounding continued.  Who could want to talk at such an early hour?  She glanced at the clock again. Oh, it was 10 o'clock.  Well into the morning, but she had only slept for five and a half hours.  She climbed out of bed and blearily tried to make herself presentable.  The knocking grew louder.

"On my way!" she called.  She trotted over to the door, a purple aura causing it to swing open.

Cider season is the reason I've come to you today!

The work is done, let's have some fun and give a hip-hooray!

The apples picked, the trees all kicked, I hope you won't be tardy!

Get excited, 'cause you're invited to the Apple Cider Party!

Pinkie Pie stood outside the door, dressed in what appeared to be an apple cider barrel with a basket full of letters on her head.  Twilight levitated one out of the basket.

"Pinkie, I thought you were done giving personal invitation songs."

"Oh!  When I did that for Gummy's birthday party, it was a really long song that I sang to five ponies!  So I said to myself 'Pinkie, you don't need to stop singing your invitations, you just need to make them shorter!'  So I did!  And now you can come to the After-Cider-Season-Party I'm throwing for Applejack!   She's been so busy, I just know she'll love a chance to calm down and relax after a busy week of bucking apples all day!"

"Well, that sounds like a great idea.  When is it?"

Pinkie looked at her strangely, "That's what the invitation's for, Silly!"  then she turned and hopped away, presumably to the next party guest.  Twilight opened the letter and read it:

You are invited to an After-Cider-Season-Party!

Who:  Twilight, Rarity, Applejack, Fluttershy, and Rainbow Dash

Where:  Sugarcube corner.

When:  Tonight at six o'clock

What:  A night of really, super-fun games and food and stuff and things to celebrate Cider Season!

Twilight shook her head and grinned.  Even in a letter, Pinkie Pie was just being Pinkie Pie.

She turned to go inside, making a note in her planner.  One thing about Pinkie Pie that annoyed Twilight was her tendency to be so spontaneous.  Whenever she told Twilight about a party, it usually took place that day, which didn't give her nearly enough time to properly plan a schedule around the event.  Luckily, she didn't have anything planned for tonight until sundown when she was going to be stargazing.  That meant she could spend about three hours at the party before it would be dark enough to do some more studying.

In the meantime, it couldn't hurt to review her notes from the night before.  She took out her notebook, double checking the calculations, diagrams, and speculations she had made the night before.  Suddenly, something caught her attention, and she went back over her logic, again and again.  She let out a despairing cry.

"This doesn't make any sense!  I did all the calculations correctly, but my results conclude that it would take 39.7 more days for the moon to fully orbit that planet than it really does!  Spike!  Spiiiiiike!"

The purple dragon came running into the room.

"What's wrong Twilight?"

"Spike!  I need you to get The Astronomical Almanac of Celestial Bodies!"

Spike gave a salute and jumped onto the ladder, looking for the book.  Finally, he came back down with a tome almost as tall as he was.  He walked over to the table, swaying under its weight before he was able to put it down with an audible groan.

Twilight rushed over to the table, not noticing that she knocked Spike out of the way.  She riffled through the pages until she landed on the page she was looking for.

"I was right!  My calculation was wrong!  How can this be happening to me?"  she buried her face in her hooves, "I'm a horrible student!  I can't even do math correctly!  If Princess Celestia finds out, she'll send me back to grade school!"

Spike looked over at the distraught pony cautiously.  He was never good at handling situations like this, but he always tried to make Twilight feel better during one of her academic meltdowns.

"Are you kidding me?  You're the smartest pony in Ponyville!  Equestria even!  I'm sure there's just one dumb, obvious mistake you made that screwed up everything you've been working on the last few days."  He cringed.  He wasn't the most eloquent dragon.

Twilight looked at him, "You're right, Spike!  It's probably so obvious even a foal could see it!  But I looked over it again and again and couldn't find out the problem!  I'm so awful!"  She started pacing back and forth.

Spike began to panic.  If this went on for much longer, it could spiral into a repeat of the Tardy Letter Incident.  He had to avoid that at all costs.  He looked around at the bookshelves.  Twilight was curled up, stroking her tail, when a book landed in front of her.  She looked up at Spike.

"It's called Mathematical Mysteries:  Minor Miscalculations or Methodical Maladies?  Maybe you'll be able to identify your mistake once you read that!"

Twilight looked back down to the book, flipped it open, and started reading.  Spike gave a sigh of relief.  Giving a book to Twilight was the only way to distract her.  Of course, the book might actually give her an answer, but his main goal was to stop her hysterics.

Twilight flipped through the passages in the book, trying to find a hint of some vague mistake she could have made that would have affected her calculation.  She stumbled upon one that caught her eye:

…In some instances, there is a carry-through effect regarding

calculations in which any given trivial oversight may compound

exponentially in order to affect further calculations in a dramatically

differing manner.  Such errors may be virtually imperceptible,

yet the effect on the result is not negligible.  For further information,

See Chaos Theory.

Twilight glanced around the bookshelves, looking for C.  "Virtually imperceptible" is exactly what she was having trouble with, and the passage seemed promising.  She finally found a book titled Introduction to Chaos Theory, and continued her reading:

Chaos Theory is a study in mathematics in which small

differences in initial conditions result in drastic

alterations, via the Butterfly Effect (see page 293).

This theory has further applications regarding biology,

economics, physics, and philosophy.

Twilight knew a little about the Butterfly Effect.  She had read a short story named "Confound the Blunder" in which a unicorn time-traveled to a time before ponies existed.  While in that time, he accidentally crushed a butterfly, and when he went back to the future, the world had changed drastically.  The moral was that even the most minor action can have unforeseen consequences down the road.

She turned to page 293 and saw it was, indeed, the short story.  She went back to the math section:

An elementary example of mathematical applications

of Chaos Theory are evident when using a round-down

function over a series of calculations as shown in Example 1.

Example 1:

Decimal is preserved -  8 * 5.9 = 47.2 ; 47.2 * 3.5 = 165.2 ; 165.2 * 3.8 = 627.76 ; 627.76 * 2.7 = 1694.952

Decimal is rounded-down -  8 * 5 = 40 ; 40 * 3 = 120 ;  120 * 3 = 360 ; 360 * 2 = 720

Percent error between first and second instances - -15.25% ; -27.36% ; -42.65% ; -57.52%

It is evident, therefore, that while all the

mathematical calculations are correct,

by negating the decimal places, the resultant

error compounds upon itself in each step,

until the observed result differs drastically from the expected.

It should be noted that this error compounded to a significant

degree in only four steps.  In more advanced mathematics, the cause

of errors is much less evident, and much more devastating.

Twilight squealed in delight.  That is exactly what she had done last night!  She had been trying to preserve significant figures with her calculations, but all that did was cut off the decimal points!  She ran back to her notebook and redid her calculations.  Half an hour later, she saw her result was the same as the literature value recorded in the almanac.

"See Spike!  My calculations were right all along!  It was just the numbers that were wrong!"

"Huh?  What does that even...you know what?  Nevermind."  he didn't want to get caught in one of those conversations where he didn't understand a word.

Twilight turned away and walked back toward the book she had been reading.  It really was a fascinating read.  Out of the corner of her eye, she caught a glimpse of the letter Pinkie Pie had given her that morning.  She had forgotten about the party completely, she had been so absorbed in finding a solution.  Fortunately, she still had two hours before it began, and she intended to do a little more reading.

She flipped to Applications in Philosophy.  How could philosophy be related to numbers?

Consequentialism is a normative theory in philosophy that states

morality is based upon the consequences of one's actions…

She read for over an hour straight.  This book really was interesting.  Twilight enjoyed books that evoked thought, and this Chaos Theory was truly fascinating.  Supposedly, anything anypony did could result in something else happening in the future.  Did that also mean that multiple futures could exist depending on what action was taken?  Maybe multiple timelines, or even universes, were made based upon what action occurred, or didn't occur in this one.

What if, for example, Rainbow Dash never made that Sonic Rainboom during Twilight's examination?  Everything would be different.  Twilight would never have become Princess Celestia's student, never have met her friends, never have defeated Nightmare Moon, or Discord; an entirely different reality would exist if that one event in time never happened.  And, theoretically, an infinite amount of alternate realities were possible, each stemming from this reality, and those alternate realities could result in a infinite amount of other realities!

Twilight's head started to ache at the possibilities and she finally decided to give it a rest, for the time being.  Thought experiments were interesting, but this speculation was pointless.  Different realities were impossible to confirm, or experience.  Besides, she had a party to go to.

__________________________________

The party was fantastic, as they always were when hosted by Pinkie Pie.  There was food, punch, music, balloons, streamers, cake, everything a party needed, and more.  After they played Pin the Tail on the Pony, Twister, cards, and any other game the ponies could think of, they sat in a circle talking.  Applejack had been kind enough to bring a cask of cider, which Rainbow Dash was ecstatic about, and the six friends sipped their mugs while trying to think of another game to play.

"Ohohohohohoh!  I know!  Spin the Bottle!"  this came from Pinkie Pie.

Fluttershy blushed a deep crimson, "Um, Pinkie Pie, I don't think that…"

"What's Spin the Bottle?" Twilight asked, curious.

Pinkie Pie bounced over, "It's easy, like Truth or Dare!  All you do is spin the bottle and whatever pony it is pointing to, you have to kiss them, or you lose!"

"WHAT?!?  Why would we play a game like that?"

"'Cause you get to see who becomes too embarrassed first, Silly!"

Rarity spoke up, "Pinkie, I don't think it's proper to be playing such a…crude… game at this party!"

Pinkie Pie cocked her head, "Really?  Why?"  her expression lit up, and she laughed"Oh, I know!  You've never kissed anypony!"

Rarity's eyes widened, her mouth agape, but her face turned pink, "What?  Of course I have!  Just because I am a lady does not mean I haven't given gentlecolts in high society a grateful peck on the cheek after a delightful evening!"

"That's not a real kiss!  I mean one on the mouth!"

Rarity's voice trailed off, "Well, I've also done that too…"

"Ooooohhhhh,"  Pinkie Pie bounced around the room, "Whowasit? whowasit? whowasit? whowasit?"

"Enough o' this nonsense!" said Applejack "Why don't we pick a game that normal ponies would play at a party?"

Pinkie Pie stopped her dancing, her expression turning slightly downcast, "You don't want to play my games?"

Rainbow Dash's memory suddenly flashed back to Gummy's After-Birthday Party that Pinkie had thrown.  It was not a pleasant memory.  "Uh, no, of course not!  We can play that game for a little bit!" Rainbow Dash sounded a little panicked.

The other four looked at her in shock.

"Um, I mean, it is her party…"

"Yay, thanks Dashie!  I'll go get the bottle!"

Fluttershy looked as if she wanted to disappear.  Throughout the conversation, she kept shrinking into herself, hiding her face behind a curtain of pink mane.

"I really don't think this is a good idea"  she practically whimpered.

"Relax, Fluttershy," said Rainbow Dash, "It's all harmless fun.  Besides, we would never force you to do something you were so uncomfortable about."

Her face brightened slightly, "Well, okay then…"

Twilight, on the other hand, had been sitting in shock throughout the conversation; her heart had been beating louder and louder until it was a miracle that the others couldn't hear it.  She felt extremely nervous.

"Uh, Sugarcube, you don' look so good…"

Twilight turned to Applejack giving a crooked smile, "Oh, no I'm fine.  It's just… I've never kissed anypony before and…"

Pinkie Pie came back at that moment with an empty bottle of sarsaparilla and tossed it at Twilight.

"Really?  Well then you can go first and get it out of the way!"

Twilight swallowed hard and she looked at the bottle.  Then at her friends, her face burning, and her heart beating harder than ever.

Well, if she was going to kiss anypony for her first, it might as well be one of her best friends.  Right?

She voice was even quieter than Fluttershy's, "Okay…"

She took a deep breath and put her hoof on the bottle.  Her thoughts flashed back to the reading she'd done that afternoon.  This spin might result in different realities.  She laughed silently at herself.  What a nerdy thing to think at a time like this!

She spun the bottle…