//------------------------------// // 7: The Marvelous Magic of Mathematics // Story: The Student and the Sun // by Ponycletian //------------------------------//         Celestia found herself encountering no little resistance in her efforts to dislodge her faithful student from her back. Twilight’s eyes were clamped firmly shut, and her grip, while relaxed, tightened rapidly at the slightest hint of movement. Despite her present, admittedly unusual, circumstances, finding herself in Fluttershy’s cottage rather early in the morning with an insensate Twilight latched around her neck, she was enjoying enjoying herself.         She wore a bemused grin as she considered ways to bring Twilight from her stupor. Considering how well it had worked before, she decided to appeal to Twilight’s appetite for knowledge once more. “Twilight, my faithful student,” she said professorially. “I’m afraid that if you do not wake up now, then the lesson shall have to continue without you.”         She was rewarded with a quiet murmur of, “no Princess, I promise I’m awake.” Twilight, apparently believing herself to have been asleep, loosened her grip and tried to roll over. This she managed to do, and she had fortunately chosen to roll in the direction of the couch onto which Celestia had been trying to transfer her. She landed with a dull thud, which seemed to return her to her senses. She jumped shakily to her hooves and looked around quickly. “Are we in... Fluttershy’s house?” Her voice rose in surprise as she recognized her surroundings.         “Yes Twilight, we are.” Her voice was pleasant and carefree as she started to explain what had happened since they had arrived above the Everfree Forest roughly fifteen minutes before. To Celestia’s immense satisfaction, Twilight did not seem to be worried that Fluttershy had seen her being carried by Celestia. Instead, her focus was devoted solely to the magic that she had seen.         Celestia was delighted when Twilight began to ask questions about the trip. “Why did you have to make three jumps? Why did you have to teleport from the open sky? Why was the flash so large? Will you teach me how to teleport like that?”         Celestia assumed her familiar role of teacher, politely interrupting Twilight when she paused for breath. “Please, Twilight, slow down and allow me to answer.” Twilight was almost bouncing with excitement at the prospect of having her questions answered, and she nodded eagerly. “I’m afraid there are a few things that I need to explain for my answers to have any meaning.”         “The first thing you must understand is that the relation between distance traveled and the magic expended increases at a rate proportional to the distance traveled. To transport an region of some volume a distance of one meter will require one unit of magic. To go two meters requires two units. Three meters requires three units, and so on.” She could see Twilight struggling to suppress her impulse to take notes. “This is all theoretical, since the only time that this is actually true is, well... under very specific and hard to reproduce circumstances. What this means, however, is that there is something else that causes the amount of magic required to teleport long distances to begin to increase exponentially, despite this linear relation between distance and magic expended.”         She was interrupted in her explanation by the return of Fluttershy, who had been in the kitchen preparing tea. She placed down a lovely tea tray, and deftly poured three cups with her mouth. “I’m so sorry for interrupting,” she said quietly when Celestia stopped talking.         Twilight looked flustered by the interruption, but after a moment, she regained her composure. “Good morning Fluttershy,” she said cheerily. “Princess Celestia was just about to explain the cause for the exponential growth rate of magic use as a function of distance.” Twilight’s voice was brimming with enthusiasm, and she looked hurt when Fluttershy failed to demonstrate the same level of interest.         Quick to notice the effect her lackluster response had evoked in her friend, Fluttershy said in a supportive voice, “really? That sounds fascinating, Twilight.”         Celestia, by way of reminding Twilight that not everypony necessarily shared her interest in magical theory, flared her wings slightly. Twilight seemed to understand the meaning of her gesture, for she looked momentarily abashed for having made Fluttershy uncomfortable. She gave an apologetic, nervous chuckle, saying, “right... no magic.”         Neither pony seemed to know what to say, so an awkward silence hung over the group for several seconds before Celestia stepped in. “Fluttershy,” she started in a curious tone. “I can’t help but notice the number of animal homes that you have.” Fluttershy nodded meekly, as if being criticized. “Do you have them in case of an emergency where you need to take care of an animal, or are they regularly occupied?”         Still sounding unsure, Fluttershy replied, “a little bit of both, Princess.” Celestia looked at her questioningly, so Fluttershy started to explain. “Some critters do live here with me, like my friend Hummingway,” she said with a small smile. “This,” she said gesturing to a large, blanket lined basket, “is where Angel Bunny stays. And my home is always open to any critter who needs or wants a place to stay.”         Twilight decided to chip in here, saying, “Fluttershy is amazing with all types of animals, Princess. She managed to convince the dragon to leave Equestria, and she also freed me from a cokcatrice.”         “SHE DID WHAT?” Celestia almost gagged on a sip of tea. Both Fluttershy and Twilight recoiled from her sudden outburst. “When did you encounter a cokcatrice, and what do you mean when you say that she freed you?”         Celestia wasn’t relaxed anymore. Cockatrices had been created by Discord during their war specifically to kill magical ponies. They would petrify their victims, and then slowly leech off their magic until there was nothing left. She had herself been petrified once before, and it had nearly been the end of her. To hear that Twilight, her protégé, the Element of Magic, and her friend, had encountered, and possibly been imprisoned by, such a creature, both frightened and infuriated her. She knew that some danger was inescapable, since the Elements of Harmony were vital to the protection of Equestria against foes such as Discord, but it shook her to think that she might have lost Twilight through such random chance.         Fluttershy seemed to have lost her voice altogether and appeared to be trying to disappear into the floorboards. Twilight looked completely stunned by the Princess’ sudden fury.         “I- I- I had been... ,” she took a deep breath to steady herself. “... On my way home from Zecora’s house. She’s a zebra who lives just inside the Everfree Forest,” Twilight explained hastily. “And as I was returning, I saw what I mistook for a chicken, and thought it must have gotten lost. I went to check if there was anything to indicate where it came from, but it turned me to stone when I got close.”         Celestia’s heart was racing. This was the type of thing that she dreaded. She could personally control the Sun, and could, through her subjects, manipulate the weather, control the seasons, and direct the entire lifecycle of almost every living being within her Kingdom. Despite her immense influence, the pony closest to her was nearly taken from her while walking home from a casual visit with a friend. This thought made her feel something that she hadn’t felt since before Luna’s banishment.         For just a moment, she seriously considered the idea of incinerating the Everfree Forest. She didn’t intend to evacuate it, or relocate the creatures. She wanted, in that moment, to burn the entire forest to ash for nearly taking Twilight from her. She heard a squeak from Fluttershy which snapped her from her foalish fantasy. She took a deep breath, calming herself. She forced her ethereal mane and tail back into their regular, multi colored forms, since they had turned bright gold, like the noonday Sun. “I’m sorry, Twilight... Fluttershy.” She hesitated briefly, formulating a plausible explanation for her reaction. “It just worries me that such a creature is loose in the Everfree Forest, and that it would venture close enough to the edge for you to encounter it.” She looked down to find that the cup from which she had been drinking had been reduced to fine powder, crushed by her magic.         She frowned as she realized the degree to which she had overreacted. She restored the teacup to its normal, non-powder, state, and magically cleaned the tea that had poured onto the floor. Fluttershy recovered enough to stammer quietly, “o- of cou- course, your Hi- Highness. I wou- would have written t- to inform yo- you i- if I had known it was so important.”         Celestia felt extremely guilty for having allowed her temper to carry her away. In a gentle, reassuring voice, she said, “thank you Fluttershy. Loathe though I am to admit it, however, I don’t really believe that there is anything that your letter would have changed. The Everfree Forest has always been a dangerous place. It is one of the last refuges for Discord’s chaotic creations, and although they are dangerous, so long as they remain in the Everfree Forest, it isn’t worth spending pony lives to clear them out.” Fluttershy looked slightly relieved, rising to her full height again.         Celestia smiled at her warmly. “I think that you and I shall have to get together and talk at some later time. I would love to hear how you managed to defeat a cockatrice, especially since it sounds like I have you to thank for ensuring that I still have a faithful student.” Fluttershy didn’t look comfortable with the invitation, so Celestia considered a way to make it more appealing. “I believe that on the night of the Gala, you had a little difficulty introducing yourself to the creatures in my gardens.” Fluttershy blushed deeply and looked as if she would rather be anywhere else but there. “I hope that you didn’t take it too personally. The critters hate the Grand Galloping Gala because of the number of ponies who aren’t always very respectful of their homes. I’m sure that they would be delighted to meet you under different circumstances.”         Fluttershy’s shyness diminished greatly as jumped into the air, speaking hopefully. “Really Princess? I felt just awful for scaring them, but I just couldn’t understand why they were so afraid of me. Do you really think they will give me a second chance?”         Confidently, Celestia said, “I do, dear Fluttershy. I am certain that they will be happy to meet a pony who is as kind, and considerate of animals, as you are.”         Fluttershy was beaming as she said gratefully, “thank you Princess Celestia.”         Celestia smiled politely, saying, “you’re welcome, Fluttershy. My schedule is somewhat uncertain at the moment, but I think that we should be able to get together sometime soon. Once I return to Canterlot and have had an opportunity to speak with Princess Luna, I will send a letter with possible times for us to meet. Does that sound okay?”         “Yes Princess,” Fluttershy said happily.         Celestia nodded her understanding and turned to face Twilight. Twilight was regarding her curiously, confusion etched on her face. Twilight’s expression rapidly changed once she realized that Celestia was looking at her. Her curious look changed to one of polite interest, and she watched Celestia expectantly for directions.         “Are you feeling recovered enough to go to the library?” she asked politely.         Twilight nodded and rose from the couch. “Thank you Fluttershy for the tea, and for letting me use your couch,” she said gratefully.         Fluttershy smiled and said, “you’re very welcome, and it was my pleasure to help.”         “Farewell Fluttershy. I shall be in touch,” Celestia said mildly as she focused her magic and teleported herself and Twilight to the library.         They arrived with a small flash of golden light. Twilight looked disoriented for a moment, but quickly regained her bearings. “Spike,” she called loudly. When there was no response, she turned to Celestia and said, “I’m sorry Princess, but I should go check and see if Spike is still asleep.” Celestia smiled when Twilight blushed, and Twilight hurried off up the stairs towards her bedroom.         Celestia expected that Twilight blushed because she worried that Celestia might disapprove of Spike’s behavior, which she would--doubtless--blame herself for. Celestia wondered what Spike thought about his living arrangements, but since he had never complained to her, and his living with Twilight was extremely useful, she didn’t think that she would be the one to bring up the subject. She slowly made a circuit of the main room, investigating the carefully organized shelves of books. She noticed that there was almost no visible dust accumulation on any of the shelves, which made her suspect that Twilight, or Spike at Twilights behest, made a point to dust and reshelve every book. She chuckled at the notion, and briefly reconsidered her decision not to ask Spike how he felt about staying with Twilight.         It took Twilight a little while to make her way back downstairs, carrying a piece of parchment with her magic. Celestia cast a curious glance to the parchment before returning to her inspection of the shelves. “It’s from Spike,” she explained. “He left it to tell me, in case I came back early, that he is helping Rarity with some preparations for the Sisterhooves Social.”         Celestia looked back with a hint of surprise. “From the sound of it, that means that Rarity will be participating in the Social.”         “It doesn’t say that explicitly, but that was what I thought too,” Twilight said with a nod.         Celestia smiled, saying, “then let us hope that this means that her disagreement with Sweetie Belle has ended.”         Twilight nodded again, but hesitated before saying anything else. Celestia grinned, suspecting that she knew what Twilight wanted. “Very well,” she said with an overly dramatic sigh. “Fetch a quill and parchment, and I will continue explaining teleportation. Actually,” she said brightly, “I think it would be best if you brought several pieces of parchment. There are some graphs that might be helpful.” Twilight almost flew up the stairs in her eagerness.         Twilight returned with a enough parchment to write a book, half a dozen quills, and as many bottles of ink. She placed them on desk that occupied the center of the room and waited for Celestia to begin.         Celestia reprised her professorial role, and resumed her explanation. She explained that the reason for the observed exponential growth of used magic was that as distance increases, ponies have a harder time conceptualizing, and focusing on, the transition. The less focused they are, the greater the waste, and this wasted magic was what caused the ‘explosions’ around the points of arrival and departure.         Twilight was following with rapt attention, taking down everything she said with practised ease. When Celestia began to draw graphs demonstrating the interplay between distance and excess magic, Twilight was careful to reproduce her charts in exact detail. She watched as her student eagerly absorbed every piece of information that Celestia gave her, and tried to analyze every implication of what she was hearing. She asked questions as they occurred to her, and they were always thoughtful and incisive. Celestia found herself forgetting about the reason for her visit to Ponyville. She was simply having too much fun teaching Twilight.         Twilight, also, seemed to be completely engrossed in their discussion. Celestia smiled at the way she would scrunch up her face when she considered some of the more abstract implications of the lesson. She smiled when Twilight would clap her hooves together after having some new insight. She smiled when Twilight stuck out her tongue distractedly while formulating the relationships between the different factors that influenced teleportation. She smiled at the frustrated frown that would appear when Twilight found herself stymied by some detail, and she smiled when that frown was banished by an excited giggle that indicated that a solution had been found. In all, Celestia realized distantly, she was smiling far more than usual.         She was slightly disappointed, therefore, when there was a knocking on the library’s door. “Spike, Twilight, is anypony there?” Without waiting for a reply, the door swung open to reveal Rainbow Dash, whose gaze settled on Twilight, apparently missing Celestia who was partly obscured by the horse head bust at the center of the table. She stopped just after entering, visibly surprised.         “Heya Twilight. Aren’t you supposed to be in Canterlot until tonight or something?” Without giving Twilight time to reply, she continued, “anyway, I was just stopping by to pick up the next Daring Do novel, if you don’t mind.”         Twilight looked surprised by her request, and asked, “Have you already finished the second and third books? I only gave them to you last week.”         “Rainbow Dash’s smile held a hint of bitterness. “Yeah, and they were totally awesome, but I’m still not supposed to stress my wing too much, so I’ve had lots of time for reading.”         Celestia decided to reveal herself, not that she was exactly hiding. “I’m sorry to hear that, Rainbow Dash. I hope that nothing serious has happened to the most promising flyer in Equestria.” It pleased her to see the effect her words had on the young mare.         Rainbow Dash gasped in surprise and made a hasty bow. “Princess Celestia. I’m sorry I didn’t see you, but what are you doing here?”         Celestia liked the way that Rainbow Dash didn’t hesitate to speak her mind. “Twilight and I were planning on observing the Sisterhooves Social, since I happen to have today off, so to speak.”         “That’s cool,” Rainbow Dash replied casually. “I didn’t know that Princesses got days off, or at least, I’ve never heard of you having one.”         Celestia found Dash’s bluntness refreshing, and she chuckled lightly at her remark. “They didn’t when there was only one, but thanks to you, Twilight, and your friends, that is no longer the case.”         Dash nodded. “So does that mean that Princess Luna has learned not to yell at everypony all the time, and has stopped causing lightning whenever she speaks?”         “RAINBOW DASH!” Twilight shouted, mortified at her friend’s tactless comments. “It’s impolite to talk about Princess Luna like that, especially since it wasn’t even her fault that she thought that those were the right things to do.” Celestia was careful not to let the guilt that she felt at those words show.         Celestia chuckled again, nodding cheerfully. “Indeed it does, and speaking of my dear sister, there is something else that I wish to thank you for. You may not have intended it as a compliment, but your decision to dress as a Shadowbolt on Nightmare Night made a lasting impression. She was quite proud of the fact that somepony had chosen the Shadowbolts over the Wonderbolts for their costume.” Rainbow Dash looked vaguely uncomfortable, and Celestia smiled knowingly. “So if you are ever discussing it with her, I urge you to remember just how important it was to her that somepony chose to honor the Shadowbolts by dressing like one, since I am absolutely positive that such was your intent. I am certain that you would not have chosen the Shadowbolts because of their frightening association with Night Mare Moon, and would never think of even implying that possibility to my dearest sister.”         She decided to carry her joke just a little bit farther, saying in an unconvincingly non-threatening tone, “after all, it isn’t like she only knows how to conjure lightning to emphasize her speeches.”         Rainbow Dash looked at hesitantly at Twilight, and swallowed nervously. “Of course not Princess,” she said to the still grinning Celestia. “I wouldn’t even dream of doing any of that.”         Again, the setup was just too perfect to pass up. Celestia’s smile grew even wider as she said, “I’d hope not, my little pony. Princess Luna can see those too.”         Rainbow Dash looked thoroughly spooked now, and seemed on the verge on fleeing. Twilight also looked unnerved by Celestia’s joke. “Gotcha,” Celestia finally said jokingly. Both Rainbow Dash and Twilight gave sighs of relief, and laughed nervously as the tension broke.         Twilight took the opportunity afforded by this break in the conversation to retrieve the next two books in the Daring Do series. She levitated them to Rainbow Dash who tucked them carefully under her wing. “Hey, if you two are planning on attending the Sisterhooves Social, then don’t you think that you should maybe consider leaving?”         Twilight looked around in confusion before her eyes settled on a clock. “Oh my gosh, is it that late already!” It was nearly three in the afternoon, which meant that they had spent almost six hours studying. “If we leave now, then we should be able to get there at least fifteen minutes before the race. That should give us enough time to get something to eat.” Twilight made that last point sound no less important than not missing the race. Celestia smiled at Twilight’s priorities, although she was feeling slightly peckish herself.         “If you are hungry, Twilight, I could simply teleport us there. That would leave ample time to eat and socialize, should you so wish.,” Celestia suggested politely.         She was mildly surprised, however, when Rainbow Dash demurred. “Um... I’d really rather keep my hooves, not necessarily on the ground, but in their current condition, if you know what I mean.” She supposed it was natural for the exceptionally gifted flyer to mistrust magical transportation.         Rainbow Dash’s reluctance all but made Twilight’s decision for her. Without so much as a moment’s hesitation, Twilight levitated her saddlebags onto her back, deposited a bag of bits inside them, and headed for the door. “Of course, Rainbow Dash. And besides, we have plenty of time.”