Pie. Or is it pi?
With a heavy sigh, Twilight looked away from the heavy calculus textbook at her hooves, directing her attention back at the blackboard. It looked like it was going to be one of those days.
Yawning, she picked up a stub of chalk with magic and went back to the equation on the board, struggling to make sense of it. To an untrained eye, it looked to be mostly composed of malevolent hieroglyphics. To a trained eye, it was a hideous mess of partial derivatives, trigonometric identities, and obscure integral applications.
In short, it was a mathematician’s worst nightmare. And it was crucial for the magical theorem Twilight was attempting to prove.
After a moment’s pause, she scrawled a few lines on the board, and erased them a moment later. She’d been repeating that exact process for what felt like months, even though it was only a few hours.
Shaking her head in resignation, Twilight dropped the chalk and sat down on the floor. “I don’t believe this,” she muttered to herself. “One equation. One stupid equation, and I can work out most of the kinks in elemental transmutation!”
She pounded a hoof on the floor in an ill-tempered fit, glaring at the blackboard. The derivatives were all correct. She couldn’t think of any other identities to break down. All the variables were there…
“Agh!” she snarled, throwing her hooves in the air and returning to the textbook. It was more force of habit than anything else; the textbook had ceased being useful almost three derivations before. After all, she was effectively in uncharted territory.
Twilight flipped through a few of the pages, naïvely hoping a solution would magically appear. Evidently, whatever unknowable being governed what appeared in books and what didn’t was content to let her suffer, and filled the pages with the same theorems and identities that she’d been going through for the last several hours.
She glared at the board, grabbing the piece of chalk again. “Maybe if I try…” she mumbled to herself, scribbling again. A minute later, it actually looked like she was getting somewhere. Fighting back a surge of elation, she started on another line of calculations – at which point the pathetic little stub of chalk gave up on existence and snapped.
Biting back a stream of obscenities, Twilight stomped to her desk and fished out a previously new package of chalk. Spike had just bought it that morning, and so she was quite surprised to find it empty. She glanced back to the blackboard, noticing for the first time the dozens of lumps of chalk scattered on the floor.
Maybe I should take a break, she thought numbly. Had Spike not been out picking up a book order, he probably would have been bugging her to take one hours ago.
Twilight glanced back at the board. Almost instantly, the numbers and letters began to swim in a hypnotizing dance. With an immense effort, she tore her eyes away and shook her head. Yeah. Definitely break time.
She had just settled down with a mug of tea and a watercress sandwich when a strident knock sounded at the door.
Twilight gave her sandwich a longing glance, but finally relented. If someone was knocking while the library was clearly marked “Closed”, it was either one of her friends, Spike, or somepony with something more important than a request for directions.
She made her way to the door, flattening her ears when the knock came again. “I’m coming!” she called.
She swung the door open, expecting to be greeted by Spike, a tower of books in his arms.
Instead, she got an empty street.
Twilight poked her head out the door and looked around, frowning. Probably some fillies playing “Ding dong dash”, she thought to herself as she swung the door closed. Now maybe she could get back to her –
“Boo!” Pinkie shouted as she turned around.
“Gah!” Twilight screamed, backpedaling furiously and slamming into the door.
Pinkie Pie fell backwards, kicking at the air, barely able to talk through her laughter. “You… you should’ve seen the look on your face, Twilight! I was all ‘booo!’ And you were all ‘Waah!’ Ha ha ha!”
“Har har,” Twilight replied sarcastically. A small part of her wondered how the pink pony had gotten in without her noticing, but then realized it was Pinkie Pie. Logic didn’t necessarily apply to her. “Did you need something, Pinkie? Or did you just want to scare me?”
Pinkie stood back up and pouted. “Now what’s gotten you so frowny-wowny? It’s a beautiful day outside! You should be happy!”
Twilight winced. I guess I was a little harsh there. “Sorry, Pinkie. It’s just that I’ve been working on something all day, and it’s not going well.”
Pinkie perked up. “You’re working on something? Where is it? Can I see? Maybe I can help!”
Twilight got a chuckle out of that. “Pinkie, I’m working on advanced magical theory. I don’t think you can be of much help.”
“Well, how do you know that?” Pinkie shot back. “I can be good at advancing theorial magic!”
“That’s not what I said,” Twilight replied lamely, but Pinkie had already darted into the library’s rotunda.
“Is this it?” she asked, peering at the blackboard.
Twilight let out a tired sigh. “Yes, that’s it. I’ve been working on it all day, but I just can’t get past this final – what are you doing?”
“Vuh fock’s muffed!” Pinkie mumbled around the stub of chalk in her mouth, continuing to write on the board.
“What?”
Pinkie dropped the chalk. “The chalk’s smudged! That ‘s’ looking thing was supposed to be an eight! That’s why you couldn’t get any further!”
Twilight gaped at the board. “Wha…I don’t…”
“See?” Pinkie said, picking up the chalk again and scribbling down a few more lines of calculations, finally arriving at a neat, simplified function. “Is that what you were trying to do?”
Twilight scanned the calculations. Every one of them was perfect. In fact, it looked like Pinkie had proved an entirely unrelated theorem in her solution! “How did… the… uwaa…” she sputtered.
Pinkie clapped her hooves together. “Whee! That was fun! Do you have any more?”
The unicorn finally found her voice. “Pinkie, how do you know this? I could barely even–”
“Muffin button,” Pinkie cut in.
Twilight blinked. A dull grinding sound could almost be heard from inside her head. “What?”
Pinkie turned away and began flipping through Twilight’s discarded calculus textbook. “Are there any more of those in here? I know! Maybe we can make a game out of it! Like Monopoly, or checkers!”
I don’t even want to know how that works, Twilight thought to herself. She turned back to the blackboard and used the temporary respite to examine Pinkie's solution. Everything checked out, but complex mathematics liked being deceiving. Twilight had lost count of the number of times she'd arrived at a solution that appeared to work out, but was actually meaningless. And now that she thought about it, there was something odd about the final few lines...
“What’s this?” Pinkie exclaimed.
Twilight blinked, her suspicions forgotten. "What's what?"
"This!" Pinkie said, slapping her hoof in the center of the page. “That squiggly thing!”
Letting out a heavy sigh, Twilight pushed her hoof aside and scanned the page, which was filled with trigonometric ratios in radian notation. Squiggly thing, squiggly thing… wait, does she mean the pi symbol?
“You mean this?” she asked, casting a simple Glow spell to illuminate the character in question.
“Yeah, that!” Pinkie said. “That looks like a table that someone drew wrong! I mean, it has to be drawn wrong, because who would build a table with a wobbly surface? Unless it was in a funhouse. But doesn’t that have mirrors? Maybe it’s a funhouse mirror tipped on its side!”
“I… what?” Twilight sputtered. “No! It’s not that at all. It’s pi.”
Pinkie gasped. “Pie? I love pie! There’s nothing I like better! I mean it’s even in my name! I’d eat it all day if I could. Cherry and blueberry and strawberry rhubarb… my favourite pie’s chocolate cream, because it’s so sweet, but Mrs. Cake doesn’t like it. She says it’s too sweet, and if I eat too much then I’ll get a toothache, but that's silly because I eat cake and cookies and things all the time when she's not looking, and I don't feel anything.”
Twilight blinked a couple times as her mind struggled to work through the jumble of words it had just been assailed with.
“No, Pinkie,” she finally managed. “It’s not the kind of pie you eat. It’s… it’s just pi! I don’t need to explain it!”
Pinkie cocked her head, confused. “Wait, so it’s pie, but it’s not the pie you eat? What kind of pie don’t you eat? Isn’t that what it’s for?”
“No! Not that kind of pie!” Twilight snapped. “It’s like… the area of a circle! You know that?”
The pink pony blinked, dumbfounded.
“Pi times the radius squared?” Twilight said weakly.
Understanding blossomed on Pinkie’s face. “Oh! Now it makes sense!”
Twilight sighed in relief. “Good. I’m glad you underst–”
“The book’s talking about square pies! That’s what you meant about it not being a pie! Because a square pie would just be a... what would that be? Not a cake, not brownies, either…”
“No! It’s not talking about pie! It’s not talking about baked goods at all!”
Pinkie frowned. “But you keep talking about pie. Why would you talk about pie if it’s not?”
“Because it isn’t!” Twilight snapped. “Pi is a number! It’s an irrational constant equaling approximately three-point-one-four-one-five-nine-two-six-five-three-five-nine–”
“Silly Twilight!” Pinkie cut in. “Pie can’t be a number! Pie’s something you eat. Like cake. Or candy!”
Twilight blinked, dumbfounded. “How could you – you know – solve that…” She waved a hoof at the blackboard, “… Without even knowing what pi is?”
“I know what pie is!” Pinkie retorted. “Pie is a pastry dough that covers and/or completely contains some kind of filling!”
Twilight closed her eyes and took a deep, calming breath through her nose. Her entire being wanted to leap back with some sort of retort, but she knew that wasn’t going to go anywhere. It was time for a different approach. “Yes, Pinkie,” she said evenly. “It is. But this pie is different.”
Pinkie perked up. “A different kind of pie? Really? I thought there was just one kind!”
Nodding, Twilight continued. “For instance, this one isn’t spelled P – I – E. It’s just P – I.”
Pinkie frowned. “That’s a silly way to spell pie.”
“It is, isn’t it?” Twilight replied. “But that’s okay, because it’s from a different language. It just happens to be pronounced the same way as normal pie.”
Pinkie bounced on her hooves. “So what’s so different about this kind of pie?”
“Well, it’s not a baked good, for one thing,” Twilight continued in the same slow, even tone. Am I dreaming or something? This is actually working! “It’s a number. A very special number.”
The pink pony sucked in a lungful of air. “And it’s special because it’s the number that represents pie!” she blurted.
“Yes,” Twilight said, before her mind caught up. “Wait, what? No! It’s not–”
“I guessed it ri-ight!” Pinkie sang, bouncing around the stricken unicorn. “I guessed it ri-ight!”
Twilight ground her teeth together, fighting the red veil that seemed determined to creep over her vision.
“Do you have any other funny symbols?” Pinkie asked, flipping around in the textbook. “I mean, if I’d known pie was in math, I would’ve actually paid attention in that class!”
That did it. “Pie isn’t in math!” Twilight yelled. “It has nothing to do with math! Nothing!”
Pinkie frowned. “But you just said–”
“I know what I said!” Twilight snarled. “Forget that! Forget everything I told you today! It’s easier to show you, anyway.” She glanced around, searching for a scrap of parchment or something – and then her eyes alighted on the blackboard. Perfect.
“Twilight,” Pinkie asked as the unicorn grabbed an eraser with magic and began wiping the complex computations off the board. “What are you doing?”
“I’m showing you,” she growled, scribbling several lines of formulas of increasing complexity on the board. “See? Here’s the method that Archimaredes used to derive p… the number represented by that funny symbol you saw.”
“Uh, Twilight?”
“See, it all has to do with circles. You can represent the radius mathematically, using a simple function, but it’s difficult to represent the circumference. So what you have to do is–”
“Twilight?”
“What?” Twilight snapped, flinging down the chalk.
Pinkie flinched. “That stuff on the board. Wasn’t that… you know… important?”
Twilight blinked. “What stu–” Her eyes widened.
She spun back toward the board, gazing in horror at what she’d done. Every line of calculations had been erased to make room for that stupid, useless derivation of pi. Hours of research, headache and exhaustive computation had been reduced to a few smudges on the board.
“It’s gone,” she whispered. “It’s all gone. Everything.”
Pinkie shifted awkwardly. “Did you remember any of it?”
Twilight brightened. “Yes! I saw the final function! I should be able to…” She trailed off as she began scribbling at the bottom of the board. A moment later, the chalk’s frenzied movement slowed, and an expression of uncertainty crossed Twilight’s face. “Or was it… no, there could have been… was it that?”
Finally, she let out a defeated howl and sank back on her haunches. “I can’t remember it! I can’t remember the formula! I’m going to have to re-derive it from scratch! I’m going to…” She glanced toward the textbook, feeling faint. “I’m going to… have to do it all… all over again…”
Her eyes rolled up in her head, and she collapsed on the floor.
Pinkie froze, hooves still outstretched. “Twilight?” she asked, her voice shrill with panic.
No response.
The pink pony swallowed. “Okay. Don’t worry, Twilight! I know CPR! Just stay calm, and I’ll–”
One of Twilight’s bloodshot eyes snapped open and focused on Pinkie. “Get out,” she growled.
Pinkie cocked her head to the side. “No, you’re doing it wrong! See, I’m supposed to save you!”
“GET OUT!” Twilight screamed, thrusting a hoof toward the door.
The pink pony took a step back, uncertainty flashing across her face. “What do you mean?” she asked, her voice quavering.
“It means I want you out of my library!” Twilight snarled.
The wounded expression that appeared on Pinkie’s face could have reduced a statue to tears. “Nopony’s ever told me to leave before,” she choked. Without waiting for a response, she turned and ran out the door, sobbing.
“Pinkie…” Twilight said halfheartedly, reaching out with a hoof, her rage vanishing as quickly as it had come. Great. Not only had she just lost an entire day’s work, she’d just driven away one of her best friends.
Muttering a couple choice obscenities, she kicked the door closed and glared at her chalkboard, now cluttered with a derivation of pi. Stupid pi, she thought ill-temperedly. Why the hay do you have to sound so much like pie?
Twilight let out a heavy sigh and stepped toward the blackboard, picking up the eraser with magic. After erasing the first line of calculations, she suddenly stopped and frowned at the blackboard. I wonder if…
An instant later, her nose was buried in the textbook, and a fresh piece of chalk was scribbling wildly on the board. No wonder she couldn’t make the calculation work! The fact that Pinkie managed it was irrelevant; it was Pinkie, after all. She’d been using the “golden ratio”, phi, as her exponential base. If she replaced it with pi instead…
Twilight dropped the chalk, dumbfounded. It all worked. It worked out perfectly. The original equation that she’d erased appeared to work, but the constants were all wrong! That equation was useless!
I don’t believe it, she thought. If Pinkie hadn’t made me erase it… I would’ve made a complete fool out of myself! I’d be a laughingstock!
With shaking hooves, she pulled out a fresh sheet of parchment and copied the calculations down. As soon as the ink had dried, she jammed it into a filing cabinet and raced out the door.
She had a friend to win back.
----------
The bell over the door let out a quiet tinkle as Twilight raced into Sugarcube Corner. “Is Pinkie here?” she asked breathlessly.
Mrs. Cake jumped and glanced up from her newspaper. “Oh, hello Twilight!” she said a moment later, smiling warmly. She glanced upstairs, her expression becoming more somber. “Pinkie’s here, but… well, maybe now’s not the best time. She ran in just bawling her eyes out, and locked herself in her room. Now she’s refusing to talk to anyone.”
Twilight swallowed hard. “Oh,” she said quietly, glancing around the store. Luckily, it was near the end of the day, and they were the only ponies in there.
“Tell you what,” Mrs. Cake replied. “Why don’t you just wait here for a bit? I’ll see if I can’t coax her down. In the meantime, why don’t you have a slice of pie?”
Twilight blinked. “Mrs. Cake, that’s really not necessary.”
“Oh, no, I insist,” the earth pony replied, trotting over to an empty table with a plate balanced on her back. “Between you and me, it’s a new recipe, and none of us have tasted it yet. Usually, we have Pinkie do it, but…” She shrugged and deposited the plate on the table.
Twilight glanced down at the slice of pie before her. Pie, she thought bemusedly. That’s what got me into this whole mess.
Well, there was no point turning down free pie. She picked up a fork and took a bite. To be honest, it wasn’t bad. Some sort of tart flavor that she couldn’t identify… gooseberry, perhaps? Whatever it was, she was sure Pinkie would hate it.
With that thought came another stab of guilt. What am I doing? she thought. I just threw my best friend out of the library, and now I’m just sitting here eating pie? What’s wrong with me?
Twilight slammed down the fork and strode purposefully toward the stairs. “Mrs. Cake?” she called. “Don’t worry about Pinkie. I’ll talk to her myse…”
Her voice trailed off as she saw Pinkie appear from around the corner. More alarmingly, her hair seemed to have lost most of its puffiness. “Oh.”
Pinkie glared at her with bloodshot eyes. “What do you want?” she grumbled.
Mrs. Cake glanced worriedly between the two. “Well, um… I’ll just leave you two alone.”
Pinkie said nothing until the earth pony had retreated down the stairs. “You’ve got a lot of nerve, coming back here,” she finally snarled.
Twilight winced. She’d had an apology prepared, but now that it was time to deliver it, her tongue had frozen. “Pinkie, I…”
“You what? Did you just come here to throw me out again? Is kicking me out of your library not enough?”
“The equation!” Twilight blurted. “The one I erased! It was useless anyway!”
“Why should I care?” Pinkie snapped, closing the distance between them. “It’s your stupid equation.”
Twilight took a step back, feeling her rump impact the wall. “Well… uh…”
Pinkie turned away. “If you’re going to apologize, don’t bother. I don’t want to hear it.”
“Pinkie…”
“La la la la la! Can’t hear you!”
Twilight hung her head. “I know you’re upset. You have every right to be. I had no right to throw you out like that. But I don’t want to lose a friendship over something as silly as a math equation!”
Pinkie said nothing.
Twilight bit her lip. “I guess all I can say now is… I’m sorry. I really am.”
Immediately, Pinkie’s mane inflated back to its usual mess. “Well, why didn’t you say so?” she said, spinning to meet
Twilight’s shocked gaze.
“Wait, what? You forgive me?” Twilight stammered. “Just like that?”
“Well, duh, Pinkie replied. “I mean, you came over to apologize! If you’d really meant what you said earlier, you wouldn’t have done that!”
Twilight blinked. “I… well, I guess that makes sense.”
“Of course it makes sense. I said it, didn’t I?”
Before Twilight could respond, Pinkie had grabbed her in a crushing hug. “Friends?” Pinkie asked.
“Friends,” Twilight gasped. “Now can you please… let go?”
Pinkie laughed. “Aw, come on. You don’t need to breathe. Well, I guess you do. This one time, I tried to hold my breath for as long as I could, but I passed out after about ten minutes and when I woke up there were all these bright lights and wires and machines and ponies in masks…”
“Pinkie…”
“Oh. Sorry.” The pink pony released her friend and stepped back, beaming. “I’m just happy we got this all fixed up! And after something as silly as a constant mathy thing!”
Twilight frowned. "A constant... what?"
Pinkie cocked her head. “That pi thing you were talking about! You know what that gave me an idea for? I’m going to bake a pie, then cut every slice at an angle of exactly one radian! Then I can have pi pieces of pie!” She licked her lips. “I can almost taste the math!”
For an instant, Twilight's brain started to go through the suicidal motions of deciphering Pinkie's statement, but wisely decided against it a moment later. "You do that," she finally said.
Dear Princess Celestia,
There are times when you think that you have to do something yourself, just because nopony else understands what you're doing. But sometimes, you can get help from somepony who... well, who doesn't even know what pi is. Even though she somehow managed to solve an advanced quantum equation.
You know, I'm not even sure that Pinkie didn't understand what I was talking about. I'm almost convinced she was just messing with me. Trying to make me arrive at the proper solution myself... ah, what am I talking about? I'm sure it's just Pinkie being Pinkie.
Your faithful student,
Twilight Sparkle
Spike frowned, looking up from the letter. "I don't know, Twilight. Are you sure you want me to send this? It seems really..."
"Confused?" Twilight cut in.
"Yeah," Spike replied cautiously.
Sighing, Twilight plucked the parchment from his claw with magic. "That's what I thought, too." Her magic quickly tore the parchment into pieces and flicked them into the wastebasket.
'What was all this about, anyway?" Spike asked. "I mean... you really haven't told me anything."
"Oh, it was nothing. Pinkie barged in while I was working on that derivation, and I ended up trying to teach her what pi was."
Spike frowned. "Isn't it like a pastry thing with fruit filling?"
Twilight quickly faced away, in order to hide her rapidly twitching eye. "Yes, Spike. Yes it is."