dy/dx = 1xy, f(1) = 3
“I’m just not getting it! Spike, do you know how frustrating this is?” Twilight asked with a hair out of place.
Spike moaned, rolling his eyes. “Is it any more frustrating than listening to someone repeat ‘Spike, do you know how frustrating this is?’ thirty-six consecutive times?”
Twilight crooked her head in confusion. “Well, I guess it depends how often it’s repeated.”
“How long have we been here?”
“Uhm, I don’t know, about three hours.”
“Then about once every five minutes.”
Twilight rolled her eyes back at Spike in realization. “Wow, Spike, you’re really good at math. It’s a shame you’re not using your skills to help.”
“...Touche.”
Twilight sighed. “I just wish I had someone here that was better at this than me….”
“Twilight, I think you’re stressing out over this way too much. I mean, just take a break.”
“But, if I take a break, then I’ll have to come back to it and figure out where I left off! That just wastes time.”
Spike shrugged. “Ask Starlight or something.”
“I can’t ask Starlight!”
“Why?”
“Because... Spike, she’s the student. I have the keep the dynamic.”
“What? Dynamic? You mean the ‘student-teacher’ dynamic? Why?”
“Well… uh…. It’s just… something that is.”
“Twilight, can you describe this dynamic?”
Twilight snorted. “Well, I would think from the name it’s pretty self evident.”
“Please, humor me.”
“Ah, well, it’s… hard to put a hoof on, you see. You need to… look at many examples, before you can understand it….” Twilight meandered. “I mean, well, I teach, and she learns.”
“So teachers can’t learn from students?”
“No… I mean…. Yes? No, they can learn from students. That’s what I mean.”
“...Right. So then this is just about you not wanting Starlight to know more than you, isn’t it?”
Twilight grimaced in disgust. “No! That would be shallow! And, Spike, I’m the opposite of shallow.”
“You mean deep?”
Twilight smiled condescendingly and looked away.
“I’ll go get Starlight.”
“No, don’t!”
“Twilight, do you want help on this problem or not? After all, you could just say this is a ‘very simple test’ and pretend you told her to study for it. It’s not like she’s listening to you at dinner.”
“I gue—wait, no, that’s not why I don’t want her here!”
“Then what is the reason?”
“Th—the dynamic! The one with the teacher and the student!”
“I’ll go get her. I’d use the ‘test’ plan.”
Twilight made strange noises as Spike walked away.
Spike opened the door to Starlight’s room.
Starlight was sitting on her bed with a distinctly lewd book hovering in front of her, mouth agape. Her eye’s opened wide and she quickly tried hiding it beneath the disarrayed covers. “Ah S-Spike, I didn’t expect you to come barging into my room unannounced! What a surprise!” Starlight said with a pained smile.
“Uh, yeah, whatever,” Spike said dismissively. “Twilight needs you in the library, by the back.”
“Y-yeah, of course, just, uhm, one moment.”
“Okay. I’ll just wait.”
Starlight trotted out of the room a moment later. “Uh-uh, Spike, don’t look under my bed, by the—” realizing what she was doing, Starlight tried stopping herself. “J-just kidding! You can look under my bed any time you want… But don’t! I mean, uhm, my… diary is there,” she said with a profuse blush.
“Is that where you keep your stallion magazine too?”
“NO!” she shrieked. “I don’t keep those there! I-I mean, I don’t know what you’re talking about!” Please, somepony, kill me.
“Starlight, I’m thirteen, I think I’d know by now what mares do in their spare time.”
“But I don’t do that!”
“As you wish, Ms. Sparkle.”
Starlight stopped her trot, trying to figure out what he meant. She shuddered at the possibilities.
The two reached to library a short time later, and found Twilight waiting patiently, smiling ominously.
“Starlight, Spike! I’m glad you could make it.”
“Well, it’s not like I was doing anything else!” Starlight said frantically.
“...Right. Starlight, here’s the test I told you about at dinner. It’s just a simple test, as you can see.”
Starlight started panicking. “O-oh, test? Yes! Of course. I uh…. Right.”
Twilight turned toward the board. “As you can see, this is a very important problem in friendship that models… uh….”
Starlight looked at the problem with wide eyes and turned back to Spike—who was possibly enjoying this a bit too much—and mouthed “HELP ME”.
Spike rolled his eyes and mouthed “FINE”.
“...What it models isn’t important, of course! We’ll learn that at a later date!”
“Twilight, don’t you think this is a bit much? You never told her to study for that type of problem.”
“Well… this is an honors course, and she should be able to figure it out! Right, Starlight?”
“Come on, Twilight, that’s a bit mean spirited.”
Twilight bit her lip, her eyes conveying a frown. After a few moments of contemplation, she gave. “Okay, okay, Starlight. You can go. I’m sorry.”
“I-it’s okay!”
“But, uh, make sure you’ve studied for this type of problem for next time!”
“Right. Will do.”
Some time passed before Twilight complained again.
“Ugh, Spike, I still don’t don’t know how to do this problem.”
“You could ask Cadance when she comes over.”
Spike and Twilight both shared a hearty laugh.
“Why do I have the strange feeling that someone is insulting my mathematics skills?” Cadence put a hoof under her chin.
Shining armor laughed.
“What?” Cadance asked.
“...Uh, well, I’m sure it’s nothing.”
The couple finally arrived in Ponyville, greeting Twilight gleefully at the station. “Cadance! It’s so nice to see you!” Twilight exclaimed. “And Shining, you too!” She took turns hugging them both.
“You too, Twilight,” they both answered.
Twilight and the couple wandered back to the castle, making sure to take in all the sights and sounds of Ponyville.
“I’ve been cooped up in my castle working on this crazy differential equation. I just don’t know how to solve it!” Twilight said, expecting a dismissive response.
“Oh? I could have a go at it,” Cadance said, intrigued.
Twilight and Shining Armor both laughed.
“What?”
Twilight laughed again. Shining Armor, noticing his wife’s sincerity, stopped.
“What’s so funny?”
“Uhm…. nothing…” Twilight wandered.
“No, I think I understand.”
“I uh….”
“You think that I can’t do math.”
“I—I never said that! You have me all wrong!”
“You’re thinking it.”
“Well….”
“Well, you’re not really the math type, in Twilight’s defense…” Spike chimed in. Twilight nodded.
“It’s the coat, isn’t it? I get it, pink isn’t a math color.”
“No, it’s more… the Princess of Love thing,” Spike helpfully answered.
Twilight hesitantly nodded, looking away.
“Okay.... But, I would like to point out that, first of all, I’m the Princess of the Crystal Heart.” Twilight was about to say something, before Cadance continued. “Second, I’m not exactly sure how the Princess of Friendship is any more suited.”
“Well, the Princess of the Crystal Heart is basically the Princess of Love, let’s be honest. Also, Twilight is practically the Princess of Magic,” Spike helpfully replied.
“Spike!” Twilight interjected.
“Well,” Cadance continued, “Just because I’m the ‘Princess of Love’ doesn’t mean that I can’t enjoy math.”
“I mean….” Twilight trailed off.
“You mean what?”
“Nothing. Nothing. You like math, that’s fine.”
“Thank you, Twilight.”
“You’re still not very good at it…”
“What was that?”
“Nothing! Just talking to myself.”
The three finally made it back to castle, and Twilight showed Cadance and Shining to their room.
“So, Twilight, where’s that problem you were talking about?”
“Oh, uh, don’t worry about it.”
“No, no, please, I want to see it.”
“Well… I… solved it. Already, in my head. It was just some variable switching or something.”
Cadance rolled her eyes. “Well, I still want to see if I can do it.”
Twilight cringed, holding a hoof up in retort. “Well….”
“Just show me the problem.”
“Please, don’t embarrass yourself, Cadance.”
“What?!”
“Cadance, I hate to break it to you, but you’re not good at math.”
“I… can do math just fine!”
“Cadance, you never even studied math. Seriously.”
Cadance looked back at Shining Armor with a pleading expression, but he simply looked away. “Just show me the problem.”
Twilight sighed. “Okay, Cadance.”
The two stood in front of the chalkboard, Twilight being embarrassed for Cadance.
The pink mare stood in front of the problem, contemplation plain on her face.
“So…” Twilight smoothly said.
Cadance simply ignored her, staring deeply at the problem. Then she grabbed chalk and began writing.
“I don’t understand what’s going on at all,” Spike added helpfully.
Lines and lines appeared beneath her chalk, and finally, she circled her answer, a simple solution point.
Twilight checked the answer. And then she checked it again. And again. And again. And she checked it one more time just to be sure. Then she checked her check. And she checked the check of her check, and checked that too, but wasn’t confident so she checked—
“You can stop checking it!”
“But—what? How? This—when? Why? Where? Who?”
“Now you're just asking nothings.”
“But… this is—I—how—wha—”
“I’ll stop you right there,” Cadance said with a thoroughly satisfied smile. “Now you can’t call me an airhead.”
“I-I never called you an airhead!”
“Really?”
Twilight’s eyes darted around the room.
“Twilight.”
“No, not really….”
“Well, take it back.”
“I take it back….”
“Well, now that that’s solved, let’s go get some lunch.”
“But… but I have so many questions! Like… what—I mean, how—where—whe—”
“Ah ah! Twilight, breathe.”
“Y-you’re right. I just… when did you learn to solve differential equations?!”
Cadance blushed, looking wistfully off into the distance. “...Ah, that’s a long story. I don’t want to get into it.”
“What are you looking at?” Spike asked.
“Wistfully off into the distance,” Cadance replied.
“But… Cadance! I have to know! How did you know how to solve that?”
“Well first I used polynomial long div—”
“You know what I mean!”
“Well… like I said, it’s a long story and I’m not too fond of telling it.”
“Cadance… Please? For me? I mean, you didn’t murder anypony or something, right?”
Cadance’s eyes splayed in horror. “How did you know?!”
Twilight stepped back. “What?!”
“I’m just kidding, Twilight.”
“Well it’s kind of hard to tell now!”
“Hey, guys, I’m going to do something else for a while. See ya’,” Spike said as he sauntered off.
“Well… I… did some things that I’m not too proud of.”
“Like… dark magic?”
“No?” Cadance looked at her with befuddlement.
“...I was just asking…” Twilight shrugged.
“What made you think that I had to use dark magic to be good at math?”
“...I didn’t say that. That was never said.”
“Well... if I tell you, Twilight, you have to promise to never tell anypony ever. I mean, you can still tell them that I’m good at math, but leave out the back story. I don’t want them to know. Plus it might be amusing.”
“I promise. My lips are sealed.”
Cadance sighed. “Hm… where to start?”
“From the beginning?”
“Okay. In the beginning, there was nothing. Then, in an fraction of a fraction of a fraction of second, everything you see around you was created in an expansion so intense and so forceful the very laws—”
“Too early.”
“You’re right. Okay,” She cleared her throat. “Call me Ishmael.”
“Ishmael?”
“Some years ago—never mind how long precisely—having little—” she stopped herself. “Oh, sorry wrong story.”
“In my younger and more vulnerable years my father gave me some advice that I've been turning over in my mind ever since. ‘Whenever you feel like criticizing any—’”
“Cadance.”
“I’m sorry, I got confused.”
“How did you get the Big Bang mixed up with Pony Dick with The Great Gelding with your own life?”
“They’re all pretty similar, in my defense.”
“You never even had a father!”
“That hurt.”
“I’m sorry. But, just tell the real story. Please?”
“Fine.”
“Oh, hey Starlight—”
“FOR CELESTIA’S SAKE, SPIKE, JUST FLIPPING KNOCK!” Starlight screamed, scrambling to cover her periodical.
“Oh, you’re getting all soft with the language? Besides, Starlight, it’s nothing I haven’t seen before.”
“What does that even mean?!”
“Oh….”
“Scratch that, I don’t want to know!”
“Well, anyway, I was seeing if you wanted to go get some ice cream.”
“Ah—I—uh…” Starlight said, shaking her head, “I guess so.”
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wow the few first fanfics i read fully
Well, obviously. Math and crystals have so much in common, after all. It's only logical.
Apparently, Princess Cadance is also more well-read than anyone would have reasonably given her credit for. Just an all-around intellectual, that horse. A real Renneighsance pone.
y=c*exp(0.5x²)
Also, assuming f(x)=y, c=sqrt(9/e), which is approximately 1.819592.
You're welcome.
Please. Everyone knows that from some point on, higher mathematics entail dark magic. In other words, once you're good enough at math, dark magic comes naturally. Not the other way round.
Edit:
Rereading that sentence just made me cringe so hard in so many ways that I accidentally intersected myself.
7278342 Oh, so someone else did solve this. I'd prefer to write it as: y = 3*e^((1/2)(x^2 - 1)). Personally I find it a little clearer, but it's a matter of taste. Feel like this should be in the main story page's comments, too...
To the edit, eh, I've seen worse descriptions of the Big Bang, I'm pretty sure. I can't think of one right now, but it's a pretty good bet that I have. XP
Everyone who has a tween/teen niece or daughter, get them to check out Danica McKellar's books and maybe study the Polgar Sisters or Ada Lovelace.
Also, screw Barbies or brushie horse toys. Get them an abacus.
7278342 7288910
So how would you describe the Big Bang in 1-2 sentences? Use whatever jargon words you like.