“What? But I just said—” Scootaloo winced and threw up her forelegs. “How many times do I have to repeat myself!? How can you believe that I can fly? If I really could, then wouldn't I have figured it out by now!?”

Celestia rubbed at her chin. “Apparently not, but don't worry. I think I can get you pointed in the right direction.”

Scootaloo couldn't bear it. All this talk about hope was just going to bite her twice as hard when it inevitably fell flat again. As if to emphasize that point, a past version of herself struggled to get above the ground. In the image, she managed to hover for a few seconds before falling flat on her face. This past Scootaloo was discouraged, but she got up and tried again, only to suffer the same result. Present day Scootaloo just couldn't see the point.

In the starry realm, she scowled. “So are you going to tell me what I've been doing wrong?”

Celestia nodded. “Yes, two things: First of all, you keep tying something that doesn't work. Secondly, you're not approaching it from the right angle.”

“How else could I possibly do it?” Scootaloo scratched at her mane. “Isn't that the only way?”

“Why don't we leave that part of your past behind and look elsewhere?” Celestia ushered the reluctant filly further down the hall. They walked in silence as she scanned the floating images, looking for a specific one. Finally, she pointed across the isle. “There. We can find part of the answer in that one.”

Scootaloo did a double-take. “What? But I'm just sitting in Cheerilee's classroom. I'm not even trying to fly in that one.”

“Sometimes, it's not about brute force. Stopping to think about things can often lead to better results than just plugging away at them.”

Scootaloo scratched her head. What was there to think about? Cheerilee wasn't qualified to teach any sort of flying lessons. She held her tongue though, as the lesson plan started. Technically, she didn't have to worry about interrupting since the event had already taken place, but watching her teacher tap on the chalkboard had ingrained a sense of obedience in her that was hard to ignore.

“All right, class, who here remembers what we talked about yesterday?” Everypony's hoof went up (they'd be dumb not to). She pointed at one of them. “Yes, Twist.”

“We talked about velothity and motion.”

d = vt

Cheerilee nodded, and everypony's hooves went down. “Very good. Thank you, Twist.” Writing on the chalkboard, she wrote down the equation. “To summarize, the distance you travel is equal to your velocity times the time you spend traveling. Now today, we're going to further complicate things. What if your velocity is not constant, but changes steadily over time? We call that acceleration, and that's factored in like this.”

d = vt + ½at²

While Cheerilee was writing on the chalkboard, ghostly Scootaloo tugged at her mother's leg and whispered up to her, “Mom, do I have to sit through the whole lecture? Because I already saw it once.”

“Hmm, I suppose not.” Celestia paused the image and Scootaloo relaxed.

“What does this have to do with flying? Isn't this just basic physics? Equations can't tell me how I need to flap my wings.”

“Well, I suppose not, but you have to understand that us ponies invented concepts like math and physics to help us understand how the world works around us. They can't tell you how to fly, but they can describe some of the factors that go into it.”

“Like what?” Scootaloo pointed at Cheerilee's chalkboard. “Being able to calculate acceleration based on distance traveled and time taken isn't going to help me get off the ground.”

“And if it can?”

“Huh?”

“Why don't we skip ahead to the practical demonstration?” Celestia fast-forwarded the lecture until Cheerilee started dropping a ball multiple times with the students timing her. She wrote a lot of numbers on the chalkboard.

Cheerilee scratched at her chin. “Okay, class, you've each taken a shot at timing how long it took for the ball to fall one meter. So out of twelve measurements, we drop the two biggest outliers, average the rest, and...” Cheerilee made some notes as she did the calculations. “It looks like the average comes out to be point four six seconds. That's actually fairly close to the expected result. Why don't you split into groups and calculate the ball's acceleration due to gravity and see how well we did?”

Naturally, Apple Bloom, Sweetie Belle, and Scootaloo opted to work together.

Sweetie Belle copied the equation onto a piece of scrap paper. “Okay, so distance is equal to the initial velocity times time, plus half the acceleration times time squared. Since we know the other variables, we need to solve for acceleration if we want to calculate it.”

“Yeah, but the initial velocity is zero, so we don't have to worry about that part.” Past Scootaloo crossed it out.

“Hmm, times two... divide by time squared...” Sweetie Belle frowned. “Ew, we have to divide by time squared.”

Past Scootaloo winced. “I'll get the multiplication table.”

“Ah hate all this math stuff,” Apple Bloom complained while Sweetie Belle and Scootaloo did all the work. “It makes me feel stupid.”

Celestia paused the image there. “Do you remember the result you got?”

“Uh, yeah, we got ten meters per second squared.”

Celestia raised an eyebrow.

“We... may have done some rounding to make the calculation easier.” Scootaloo grinned. Celestia rolled her eyes. “But, uh, what was the point of making me remember that? Wouldn't it be easier to just look that number up in a book? That's what we wound up doing, anyway.”

“It would, but I wanted that calculation fresh on your mind because I'd like you to do it again soon.”

“What? Why?” Where was she going with this? It sounded like she had a plan, but it didn't make sense. Why can't she just give a straight answer?

“In a minute. But first, I want you to tell me how gravity is related to flying.” Celestia nudged her daughter with a wing, encouraging her to leave that image and walk down the Hall of Ascension with her.

Scootaloo stared down at the milky walkway because she could. “Uh, gravity is what keeps us on the ground, so... If I want to fly, I have to move faster than gravity?”

Celestia nodded. “Yes, that's correct.” In the middle of the starry field, Celestia created a glowing white board with her magic. In the bottom left corner, she drew a stick figure that looked like Scootaloo. She pointed towards one of the floating images showing Scootaloo trying to fly. “Can you tell me what your upwards acceleration is? Keep in mind that you're acting directly against gravity.”

“Uh...” Scootaloo winced as her past self landed flat on her face. “None now, but uh, before I landed I was managing to hover, so, uh, about equal to gravity?”

Celestia drew a tiny arrow above Scootaloo's stick figure and wrote, 'a ≈ g.'

“That's not very encouraging.” Scootaloo flopped down and crossed her hooves in front of her and rested her head on them. Her ears drooped low.

“Don't give up. We're not finished.” Celestia walked over and nuzzled Scootaloo until she got up again. “Come over here. Look at this one.”

Scootaloo raised an eyebrow. She was on her scooter, which was tied to two ropes. Her friends were standing on skis. “That was back when we were trying out for the flag-carrying team at the Equestria Games. I, uh, missed the train so I get there on my own.” She scratched her head. “What's so important about this one?”

Celestia didn't say anything and instead let the scene unfold. Past Scootaloo and her friends donned their helmets. Apple Bloom and Sweetie Belle picked up the handles attached to the ropes in their mouths and pulled the lines taught. Past Scootaloo's wings blurred.

“There.” Celestia paused the image. “That is when you began moving.” She held onto the imperceptible edges of the window. “Now, let us advance the scene, say, half a second.” She tapped on the left side, and the image sprang into motion. Scootaloo and her friends left ghostly afterimages behind them. Celestia stopped it again and stepped aside. “There.” She pointed at it and gave the Scootaloo in the starry realm a measuring tape. “I want you to see how far you've moved in half a second.”

Holding the tape in her mouth, Scootaloo nodded. The image didn't have any corners to catch, so the first time she tried to stretch it out, the reel snapped back and slapped her in the face. “Ow.” She rubbed her nose. She might not be wholly present in this realm, but getting slapped still hurt. Her second attempt, she kept the reel from retracting with her hoof. “Uh, one point eight meters.” Scootaloo blinked. “Wait, that's further than the ball fell in about the same time.”

“I think you can see where I'm going with this.” Celestia put her hoof on Scootaloo's shoulder. “But I would like you to finish the calculation, all the same.” She twisted around and pulled out a pad of paper and a pencil.

Scootaloo accepted the items and stared at them. As she wrote down the equations and relevant numbers, she felt something strange. It wasn't a bad feeling; it kind of eased her soul, yet it also had an edge to it. Twice the distance traveled was three point six. Time squared was point two five. All she had to do was divide the former by the latter. Dare she...?

Hope.

That's what she was feeling. It had been gone from her life for so long that she didn't even recognize it. Ten years of failure had crushed her spirit. It had been okay at first because she had yet to grow up, but the others had grown up around her and flown off. Then the teasing started...

Scootaloo shook her head. There was a chance here, hidden in the numbers. All she had to do was–

“Dividing by point two five is the same as multiplying by four.”

d = vt + ½at²

a = 2(d-vt)/t² = 2d/t²

t = 0.5s

t² = 0.25s²

d = 1.8m

2d = 3.6m

3.6m / 0.25s² = ?

times four

3.6 * 4 = 2.4+12 = 14.4 m/s²

Scootaloo shot a glace at her mother. Way to ruin the moment. Well, the answer was, er, carry the two... She scratched on the paper. “Fourteen point four meters per second squared.”

Celestia smiled slyly, as if she were sharing a great secret. “Well there you go. That's clearly higher than gravity. You can fly.”

“But, um...” That couldn't be right, could it? Scootaloo knew she couldn't fly. Something had to be wrong. “Wait, what if the time was off? What if the acceleration wasn't constant? Wouldn't that throw things off?”

f = ma

Celestia kept her eyes fixed on her daughter's. Her smile didn't fade; it grew. “It's good to see that you were paying attention during Cheerilee's lecture, but you actually have less to worry about than you think. I don't know if you've discussed this yet, but there's another equation that's relevant here, and that's this one:” Celestia wrote it on her glowing white board. “Force is equal to mass times acceleration.”

“Force? But isn't gravity a force?”

“Well, technically yes, but we measure it based on the acceleration it causes because that's the part that's constant. Nopony really knows why that is, or how or why it came to be the value of nine point eight one meters per second squared, but when magic's not involved, everything always goes back to falling at the same speed.”

“Huh, that is weird.” Scootaloo scratched her chin then shrugged and turned back to the frozen image of herself pulling her friends. “But you were saying?”

“What I was saying is that in this particular moment, the force that you're exerting from your wings is being split amongst the three of you. By yourself, you'd have only a third of the mass to move, and, with the force remaining the same, your acceleration would triple.”

“Triple?” Scootaloo's jaw dropped.

Celestia nodded. “Yes, that is how it works.” On the glowing board, she drew a larger arrow in front of the Scootaloo stick-figure pointing forward parallel to the ground. “Hmm, since we like rounding to make the math easier...” She wrote, 'a ≈ 4g.'

Scootaloo stared blankly at Celestia's magical blackboard. She pulled her jaw shut and pinched her lips together. “But, that's still no good is it? Going fast along the ground is great and all, but that doesn't get me up.”

Celestia drew a quarter-circular arc in front of her drawing of Scootaloo. Above it, she curved an arrow until it was pointing straight up. “That's the easy part. All you have to do is ramp things up until you get pointed in the right angle.”

“Augh, puns.” Scootaloo winced.

Celestia giggled. “Sorry, I couldn't resist.” Scootaloo recovered, but still stared blankly at the board. Celestia's smile faded. “Are you okay, dear? I thought you'd be happier to see this.”

“It's—well...” Scootaloo fidgeted uneasily. “You make it sound like it's so easy.”

“It's not meant to be difficult, Scootaloo. Most pegasai can still fly even while carrying others.” Celestia unfolded a wing and pointed at the image of Scootaloo pulling her friends, but when Scootaloo looked even more apprehensive, she opted to say nothing further. {perspective error}

“I-I can see the numbers. What you say makes sense, but–” Scootaloo clenched her eyes shut, but she couldn't stop herself from tearing up. “–I've been trying and trying and trying and–”

“Ssh, it's okay, my baby.” The motherly alicorn picked up her filly and held her close to her heart. “I know how much you're been trying for this–” she peered down the hall of floating images “–well, I know now how much you've been trying for this. I admire your persistence, I really do, but the end is finally in sight. You know now what you must do. All you have to do is try one last time.”

“One last time...” Scootaloo looked up at her mother with wide eyes.

“Yes.” Celestia nodded firmly, as if she were the one who was struggling and not Scootaloo. “But we can't do that here. Come on, let's get you home.” Celestia lingered a moment longer, simply cuddling her filly before she added magic to her embrace. The warm flow washed over Scootaloo, who couldn't help but feel content.

...

Scootaloo, or rather her awareness, found herself alone again within the dazzling rainbow cavern. The sun must have been lower on the horizon because the colors cascaded through the cavern in fluctuating dance. The sparking spires that lined the cavern's maw radiated their hues out in competing patterns along the cavern's walls. Even after spending so much time here, the sheer dazzling beauty left her breathless. Scootaloo's awareness wished that her friends could see this place, but the raging colorfall that washed over the entrance was just as hostile as it was beautiful. Next Chapter: Wayward Sun Estimated time remaining: 50 Minutes