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Entrapta The Library.

Specifically, the library in KiraKiraFantastica. That library? Yes, that library! Stop asking over and over!

Which, of course, means that Entrapta is a pony. She was invited, so she showed up EVENTUALLY, and given that she's a library junkie I would guess that the librarians were warned to alert people.

Didn't stop her from getting into the books though. She's been requesting 'friendship magic' tomes, and going through them as fast as the pages will turn. Which is to say, she's got a few piles and a harried library assistant.

"Do you have anything with statistics? No? The equations shown are very vague..." She may already be beyond what a temp assistant can help with.
Hinoiri Kirara Hinoiri had offered to let Entrapta come and read some of the books, if she liked... though... admtitedly she was a bit wary about the idea of someone from Obsidian learning too much about magic from her world. So wasn't let her near anything TOO advanced. And, unfortunately, the section on 'friendship magic' was still... fairly... in development, as it were. The elements themselves were fairly unknown and only recently more learned about.

There were a lot of books, though, about equations and the like, at least. Basic stuff. So those she was given fairly quickly. And Hinoiri was much better with. Friendship magic... definitely different.

Laughter. Kindness. Loyalty. Honesty. Generocity. Magic. She really didn't get any of the six, heck, the last one didn't even seem like 'magic'.

"Yeah... when it came to actual friendship magic... we were definitely more about equations. A shame that like... the world on the other side of the portal isn't much for those, right?" Hinoiri said with a bit of a teasing grin, smiling over at the other girl. She seemed to be adapting well enough to being a pony, at least. And Hinoiri made a mental note... bribe the librarians with a gift basket later....
Entrapta Oh! Hinori was there too! To be fair, when Entrapta gets into a topic she tends to forget about little things like 'other people' and 'necessary functions'. She hasn't eaten or taken a break since her arrival, for example.

"I can't write down things without hands, yet," she admits as she very awkwardly slips Hinoiri's presence into her thought patterns. "But I mean, I've got whiteboards filled with equations. There's some people who can handle advanced mathematics. For example, have you seen this pattern?"

She smiles, then clops to a pile of books she'd been through earlier. A recent scroll written by a pony mage, on how when more than one friend is present, magic seems to have been amplified. "This. It seems like a recurring motif, in a lot of the friendship magic texts. I've been theorizing on the math involved."

Then a pause, and she says, "I'm quite capable with equations. That's why I came here. Math IS magic, after all."
Hinoiri Kirara "Yeah, I actually did a lot of studies on it," Hinoiri said. "There really were a lot of weird patterns about it. I actually had a... really weird and... admittedly... silly uhhhh.... supposition caused by it, when I was Sunbreaker. I thought Naru could amplify powers because.... Sailor Moon kicked my butt. Turns out a lot of magical people tend to get bursts of power when their emotions are more... awakened, as it were," she said flatly. "Like attacking their friends."

"But yeah, there's a lot of math and memorizing complex theorms and the like in pony magic. You'll find a lot of that in those books. It doesn't... quite carry over to that world, mind," she said with a small smile. "Trust me, I know. Math is pretty great, though. Big fan, I take it?"

It was kind of nice, though. Most of the people she knew tended to HATE math... she always liked it. She'd always been pretty good at it. Memorize all the equations, then just go through them, one by one, do them piece by piece... She was just learning not everyone was as good at that recently.
Entrapta "Oh if only people knew how much they relied on it! There's math in everything we do, and if you can see the way it all equates you can see the systems functioning! It's like a huge all-encompassing machine!" She tries to spread her hands wide, but having no hands ends up stumbling.

She pauses, noticing reality for a moment. Then shrugs and moves forward. "If you have more of it, I'd love to see what there is to study though! The way the different magical systems interact is a completely new field of study, and I swear the math for it is just out of my reach for now. But each one I get time to dig into makes it just that much closer! Can I show you my equations?"

She had an idea, but dang this girl is so easy to get off topic. But hey, that's what makes it interesting!
Hinoiri Kirara "I know, right? You can't do ANY magic here without magic being involved," Hinoiri Kirara said with a light laugh. "And your world, with all its electronics and whatnot, isn't that much better. Sure, I may not understand how all of them work, but they're definitely a type of magic in their own right."

"... Sure, you can show me what you have. But, uhhhh... I'll be honest... so like... I'll be honest, I'm admittedly a little... wary of what I show you getting back to Obsidian. There are some terrible people there. Many of whom have tried to kill me. So like... if you want some of my stuff to see... I'd want some confirmation that it's not going to be used to help certain other people at Obsidian."

There were only a handful of people at that business she trusted... and even those, there were ones like Takashi she only trusted on his good days.

"But... yeah... the whole magic stuff IS pretty amazing. I've got a lot of notes I can show you when I get back to the school, we could probably compare notes. Have you done much research on the magical singing? There's a whole bunch of it, Utau in Easter does some amazing stuff, the Black Beauty Sisters were absolutely exceptional as well, but they don't work there anymore," Hinoiri said with a small grin. "Have you seen any of Riventon's scans?"
Entrapta Entrapta the Pony sighs. "Nobody really shares their actual information with me, that's why I was so interested in coming here. You actually list real information, and share it with others! You have no idea how frustrating it is to have secrecy when it comes to information. I can't work with that!"

She pauses, then motions around with her muzzle. "I can work with this. I've done some work with magical singing, sure, but mostly the mermaid forms. I took readings of their magic and did experiments on the waveforms. Here, look at this."

She pauses, then picks up a piece of chalk with her mouth. Then drops it. She actually curses, an actual swear word, then tries to pick it up again. It's not going well, but as she does she says, "Left the Obsidian place anyway. They weren't ...very good about...can you hep me pick dis op?"
Hinoiri Kirara Hinoiri blinked and then suddenly her magic would grip Entrapta and turn her around to LOOK Hinoiri in the eye. "Wait, REPEAT that last bit."

"You LEFT Obsidian?" she asked. "As in NO LONGER WORK for Obsidian?" she asked again. "As in, quit? Do they know? You do realize that they tend to send hit squads after people once they leave, right? As in people try to MURDER people who leave, right? Does Riventon know? Are you safe?"

Buck. She needed to tell Rashmi. Ugh. "... And yeah, I'll copy my notes for you once we get back to Radiant Heart, okay?" she offered. Distract the girl with math.
Entrapta Entrapony pauses, then says, "I can't pick up the chalk. Oh, do you mean leaving Obsidian? They know, I told Hawkmoth before I left. He wanted me to stay, said that I could do more good with them than with you." She pokes at the floor chalk with a hoof, deciding that it can stay there until it learns its lesson.

"I mean, he does have a lot of resources available to do work with. But I don't think I like being lied to when I'm working. It keeps me from being able to figure out actual answers. I can't write stuff like this, need to learn how to get information across in a more efficient way." She seems to not be as worried, but then she has no idea how dangerous Obsidian is.

Then, she pauses. She looks at Hinoiri, straight on, and smiles. "You're a very good data point, did you know that?"
Hinoiri Kirara Hinoiri sighed and face hoofed. Oh, she swore she was going to... She then sighed and picked up the chalk in her magic, before putting the tip to Entrapta's hoof. "Here, just hold it in your hoof. Don't think about it, just do it. Like holding a door." Never mind the fact THAT didn't make any sense, either.

"And, uhhh. Yeah. Obsidian does a lot of that. Lying, I mean. But thank you, I think. I try to be a good data point. But seriously. We can protect you from Obsidian, but... if I give you information, you cannot give said information back to them. I kept a lot of information away from them, for good reason. There are people there who want to use this information to blow up the world..."

"... Rashmi is going to be so happy you left, though. She always worried about you. Right, so, how to start, uhhhh... but... yeah. I guess. Believe it or not? I used to not be so good at this. People here used to.... I used to not be good at working with others. Still kind of suck at it, honestly. Getting... better. But it's a process."
Entrapta The chalk, in her hoof. Entrapta frowns, but tries not to overthink it. It's a skill she has yet to master; not thinking. But she does manage, with some work, to draw some lines as Hinoiri is talking.

"Go on, this is helping," she says, as Hinoiri starts talking about Rashmi, and working with others. "Yes, that makes sense. Look, let me talk for a second, alright? You don't have to give me information, for a bit. Best if you don't yet, just in case. But I have something related to show you, that might help."

She pauses, then grins a pony grin. "It's math. You'll like it." Then she continues drawing groups. "Yeah don't tell me anything sensitive, it's okay. Wow I'm bad at this still." Pony legs weren't meant for graphing.
Hinoiri Kirara Hinoiri nodded, watching the other girl work, cocking her head to the side. Admittedly, she couldn't help but feel for the girl. Earth ponies were not exactly made for this kind of work. Telekinesis was great for writing... Hooves? Not so much. Heck, she STILL had issues with like... handwriting, let alone normal writing, so she couldn't talk.

But she did listen, at least.

So, for now, she just sat and listened to Entrapta, watching the other girl work.
Entrapta It's a simple graph, and an incomplete one. But she draws on it as she explains.

"Patterns in friendship form, and the data is clear. You, right now, are a data point of one." She jots it down, a point on the graph. "In what I've seen, this is how it seems to work. Additively, one friend is added to yourself. Their abilities are enhanced by one, what you have, you share with me." She marks another point, herself, on the graph.

She draws a line between them. One line, two dots. "So far, this is simple. You can do things that I can't. When the records showed ponies making friends, it's always been the same. The first friend was great, they helped a lot. But it wasn't transformative. Now see what happens when you add a third ...pony...to the math."

She adds a third, then draws lines between them. There's THREE lines, the three dots have become much more complex. "The third pony, or friend, always adds layers of subtlety and complexity. The same with a fourth," She adds another dot and the lines between them. "Up to this point, the growth changes from additive to multiplicative. Friends strengthen each other on a level unexpected by only one or two."

Then she grins. "But, the records I've seen, and what I've observed, show something...astounding, comes next. I feel like there's going to be something explosive when we reach five friends. Exponential growth. I only ever have one friend at a time, and I feel like you do too."

She draws lines, between five, then six friends. It's a lot.

"If friendship is magic...this has to be important."
Hinoiri Kirara "More than the sum of their parts and all that? Magic being exponential and all that?" Hinoiri asked. "Yeah... back home it seems to be that way. I don't know if it works entirely that that here. I mean... it might? The whole... elements thing seems to have... something akin to that going on."

"... Like, I know when I was going all Sunset of Sora, at least, I had a dozen or so sparkles power inside me. Despite that, they took me down with only a handful of them. But... trust me..." She rubbed her chin. "Trust me. They get more 'exponentially' stronger before they hit five or so. There always seemed to be more of them and those girls just seemed to multiply and grow stronger no matter what I did. Sure, I could pull off some stuff and work to counteract them... but they still kept finding new ways to just overwhelm me by pulling something out of their flanks."

"... Lucky for me, I guess. I've really gotta show you my stuff back in Radiant heart. And about my 'New sparkle dropped' theory. And the whole 'ley lines being moved' theory. And the way the fade is pushing things back. And how there are so many more sparkles now than there were in prior generations. It's just..." She gave a light chuckle. "You know, Entrapta, you stay out of Obsidian, you and I might get along just great. Rashmi is going to be gleeful to know you're back amongst us now."
Entrapta She, Entrapta the pony, looks like she wants to tug on her hair. Which is, appropriately, still quite long even now. "I admit, everything that I know about friendship is based on theories. Well, not quite everything, I do have a couple of friends now. One, really. But I'm willing to accept the possibility of more."

She sounds detatched, but she'd hardly be the first girl from Radiant Heart who has problems recognizing affection. Or interacting with it.

"Perhaps my math is off. It's from a very limited data set, I can freely admit. Can you give me the basic theorem of your theory? And," she pauses to peer more closely. "I am assuming you are using the colloquial, and not the scientific Theory terminology. I'd be very closely reviewing your documentation if so."

Pause.

"...I mean, I intend to regardless, but there are some concepts that require restating. So what's this about ley lines?"

She's a scientist. Gotta science.
Hinoiri Kirara Hinoiri sighed and shook her head. "Oh, honey..." she said. It was REALLY hard for her to not cross her hooves and lean on the wall. She was too used to doing that pose as a human now when she talked like this, and it made her grin and chuckle a little, shaking her head. "You have more than one friend, trust me. I'd even go as far as to say you and I are probably friends. Or, at least, I like to think we are."

"So... the basics of it are experience. When I was Sunbreaker, I could take just about any of the girls, one on one, with ease. Like... it wasn't even hard. I was just... better than them. It wasn't until more of them got involved that things got... weird. And not just a little, either. They'd get a lot worse. No matter how far ahead I was, or how much stronger. Or how much I was winning by... more of them would just... always manage to get exponentially stronger. It was like they were magnifying their power."

".... I didn't realize why until I joined them. Dark energy.... hurts, a lot. It burns you up, on the inside. It feels wrong. It hurts. So the more of it you use, the more damage it does to you. The more you lose yourself. But on their side? It's not the same. The more of it you use? The better you feel. The lighter you feel. The more you, you feel. You feel warm and happy and free. You feel... like you're with your friends. Safe. Secure. You feel... happy. Excited. You feel giddy. Amazing. Excited. You feel alive. That's the big difference. It doesn't hurt. You feel refreshed."

"As for the leylines... well... they were moved. I'll need to show you my notes to get the more detailed overview, but there's three points where all the leylines of earth were moved. The biggest focal point is Tokyo. There's also a second in paris and a third in seattle. That's why almost all magic is on those three points."
Entrapta Entrapta sits on her pony butt on the floor as she listens. She has a book open, but only one so that counts as rapt focus for her. Seriously she and another pony we aren't going to mention would get along brilliantly. "You said excited twice," she critiques. Well, she is reviewing the data.

"I haven't found any books on ley lines yet, aside from a fantasy novel which had very unscientific grounding. I doubt it had any proper documentation or sources," she says, which in her terms means she's not seen the data. She glances around, then says, "I'll ask for a few resources. I have a fairly solid library on the wavelengths of a variety of magical types, and they all vary rather wildly. I hadn't considered comparing them to mental states. That's...that's actually quite fascinating as a field of study. Have you considered the possibility of altering the wavelength of a form of magic?"

She's on a tangent. But don't worry, it'll spiral around.

"There's some evidence to suggest that dark energy can be converted to other forms, which allows me to theorize that the concept could apply to other forms, and I could potentially allow not only interchange of energy in emergency states, but also storage of the same. Which would likely lead to a monetization of mahou, through their energy surplus, but that would not lead toward increased friendship levels and if we're friends I don't think that would be entirely a good goal to approach, but as a scientific endeavor I hate to ignore a field of study simply because of what it could do wrong."

Pause. "We're friends?" She seems surprised, suddenly.
Hinoiri Kirara Hinoiri flushed a little bit, giving a little squeak. "Well... okay, yeah. I guess I did, huh? Aaaaanyway, my point stands. It's a different type of magic and feels a lot different," Hinoiri said.

"... And... maybe? Depends what you mean by 'wavelength'," Hinoiri said. Because, well. Yeah. Of course she had. Or hadn't. Depending on what she meant by that. "Cause like... that can mean a lot of different things. But... be careful about that. I converted it to gem magic. And... it didn't do as much as you'd hope. Trust me. Dark energy.... even if you change it to another type of magic? It stays dark energy. Even if it's not 'dark energy' as its base form, it's still dark energy. It just looks different, but change only in look, not effect."

".... And of course we're friends. I wouldn't have brought you here if we weren't," Hinoiri said without hesitation.
Entrapta Entrapta pauses, not talking for a moment. She's clearly thinking this through, uncertain how to spew an automatic response in her normal style. She frowns, her pony face quite expressive and open with what she's thinking.

She isn't uncomfortable. No, not that. It's more a matter of a lot of thoughts going through her head at one time, and inside she's like, 'how do I friend?' So, after considering the playthrough of 'being a friend' based on the systems that she's studied, she shakes her head, hair into her face, and says:

"Do I bring you snacks? I'm not sure how this works."
Hinoiri Kirara Hinoiri watched her, unsure how to react, cocking her head to the side.... before, finally... Entrapta responded. And Hinoiri, for all she could do...

Barely managed to resist giggling. She shook her head, a hand moving up to her mouth and she giggled instead.

"Oh, oh you are wonderful. You just need to..." Then she stopped and paused.

.... Wait. Actually...

"... You should talk with Rashmi. Because trust me, she understands this WAY better than I do. And she's usually the one I go to when it comes to friendshipping. But the most important part of it? Just... try your best. And try to not hurt them. Try to not cause damage and once you realize what hurts people.... try to not do it anymore."
Entrapta Entrapta looks like she should be taking notes. She is, but they're in a mental file that's set as 'under review' in the access folder. "Well it would have been good if someone had said that a while ago," she says as she taps one hoof on the tile. "Don't do the things that hurt people. That limits my avenues, I'm going to have to go back into Obsidian later. I left a few things active."

If she's ..if that rule is the why of the trip back? What the...

"At the very least I should erase my whiteboard. They could use that stuff to really mess people up."
Hinoiri Kirara Hinoiri sighed and shook her head before, finally... she just reached out and patted her on the head. "Entrapta? I'm going to give you the best piece of advice I can give you in this situation. Before you do anything else. ESPECIALLY before you go back to Obsidian."

"First, find a way to erase the whiteboard remotely. Secondly, go talk to Rashmi. Please. Nobody can give you better advice than her. There isn't a sparkle in this city that sparkles half as sparkly as that sparkle sparkles, and trust me. I make it my duty to study sparkles. So find her, learn from her and, most importantly?"

"Trust and listen to her. She won't steer you wrong."
Entrapta Entrapta nods, then gets up. She starts closing her books, nosing them shut (still hasn't figured out the 'use hooves as hands' thing yet. To be fair, she's able to walk at least. Then she pauses. Considers.

"I should do that now, right?" Well. I mean. It is an option. And the library will still be here. I mean, any excuse to break the cycle of 'READ MORE BOOK'.

And besides, you should get up every once in a while and get in some light exercise. Hydrate. Connect with friends.

Even if you are happiest as a nerd.

...Shut up. XD