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Dark Skies
Chapter 152: Math

Chapter 152: Math

"Alright, so this room has these things." I point out the huge pieces of glass with writing all over them. Reena hums a little at them while I walk up to the same one from last time, with the floor to ceiling math, starting with the equation 8•8•8•4/(3+(8•8•8•2)) and ending at the number 15639664.10692. "Fifteen million, six hundred thirty nine thousand, six hundred sixty four." I say the whole thing aloud, but it still doesn't mean anything to me. Reena doesn't say anything either. She probably knows, but can't tell me. So I turn my attention to the huge drawing next to it.

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It's enormous, covering the distance all the way from the ceiling, down to the floor, like a tower of little circles with webs of lines drawn between them. At first, it looks like a huge mess, but I try looking closer, searching for patterns instead of just staring at the whole thing. As soon as I do, looking at it in parts, one pattern becomes immediately obvious.

This huge picture, it's actually just the same picture over and over again. I count it and find twenty four repetitions, going from top to bottom. That draws my eye back over to the equation. After simplifying, just like Claire taught me for algebra, they got 1.9941577, and raised it to the twenty fourth power.

So, these repetitions on the board are like them raising something to a power? Raising to a power is equivalent to repeated multiplication, so each of the twenty four sections are being multiplied together.

"Good," Reena confirms, and I smile. Moving on, the next thing would be... If each section is multiplied together, then they should each somehow represent the number 1.9941577. But there aren't actually any numbers involved. Looking at the picture- "This would be called a diagram," Reena lightly interrupts my thoughts with the correct word.

"Ah, thanks," I mumble, my thoughts still moving forward. The diagram has a few parts. Circles and lines. The lines basically just connect all the circles, but there are three... no, four different types of circles. Each one has a symbol inside. Either a '+', '-', or the letter 'A.' However, a couple of the 'A' circles are larger than the others, with an extra line coming off to another section of the diagram off to the side. So there are two different kinds of 'A' circles.

"Hmm..." I look up and around, but there isn't any indication of what the symbols mean as far as I can tell. I look at some of the writing off to the side, little arrows pointing out specific parts. I have to squint a little, but there's one spot pretty high up pointing out one of the little offshoot parts of the diagram that says, 'remember to build correctly, then insert here.' Its arrow is pointing directly at one of the big 'A's.

"Build...?" I mutter. I look at a few more of the little side notes. "Base factors... Resolve here first... Add here?" I stop on that last one and look where it's pointing. It's up near the top, pointing to one of the offshoot parts. Turning my attention to that same part on the repetition closer to the ground, where I can see it better, I go up to it.

"This part?" I look closer, my hand resting on the glass beside the black markings, and see that this part of the diagram is sort of different than the rest. For the most part, it's in big horizontal lines with lots of the 'A' circles, but this specific part is the only line that doesn't have any. Instead, it's just a single '+' circle all on its own. Adding...? Why is that only noted on this part, none of the other '+'s? There are a whole bunch of them around, but they're mixed in with the 'A's everywhere else.

Staring hard, I know that the diagram is related to the math on the glass beside it, but how...? I know I should know enough. I can figure this out, I can tell. So I keep looking back and forth, until the patterns finally become clear. "There, it's the eights." There are eight 'A' circles in a number of parts of the diagram, and they match up with the eights in the first equation at the top of the board.

"So..." Working from there, I match up the plus and minus signs, until those make sense too. "They represent addition, multiplication, and division." I glance across, but there isn't actually any subtraction in the equation. But the patterns of how they work are pretty clear now. Addition if the plus comes between two lines of 'A's, multiplication if it's in the same line. The same goes for division, so subtraction should work the same too.

"Ok, I've got it," I sigh, grinning a little.

"Good job, Aria," Reena finally speaks up again. "You figured that out very quickly." That makes me smile even more, but...

"Well, I figured out their strange diagram, but what does it actually mean?" I question aloud. As far as I can tell, it looks like a significantly more difficult way of expressing math than just using numbers. Why would they do that? "The notes said it was for building something. What are they building that has a structure li-"

A structure.

"Oh."

"Hehe, smart girl," Reena chuckles in my head.

Part of me doesn't want to jump to conclusions and make assumptions like that, but since Reena's basically confirmed my guess... "It represents a mana structure," I make my conclusion. "When they have specific forms, it works for math." I don't know what the math is for yet, but it must be important for something. There must be a very good reason for them to put so much work into coming up with such an incredibly complex mana structure to calculate that specific number.

"Fifteen million, six hundred thirty nine thousand, six hundred sixty four." I say it again, doing my best to memorize it. I have no idea what it means yet, but it must be important. I'll have to work on matching it up with other things when I can.

For now, I check the time, finding that I've been away from the other rail units for about eighty ticks now, so I should probably head back soon. In the time I have left, I look across the other two big pieces of glass in the room, standing near each of the other two walls.

The diagrams on these are much more simple, but don't have any math beside them, with only a few little notes that don't give me much to go on. I look up at one, and it looks like it's split into a few different pieces. There are more more letters inside the circles instead of just 'A's here. 'F', 'E', and 'L' show up too. Besides that, there are more '-' signs, but no '+'s.

"I can assume they stand for the elements," I nod to myself when I see that specific mix of letters. That means that other big one, all of those 'A's must stand for air. On this glass, rather than one diagram, it looks more like a few smaller ones all placed side by side. They follow the same form too. The element, followed by two '-'s in a row. Air, fire, earth, and lightning are included. But not water?

Immediately, I'm struck with a sense of familiarity. I know this. Why do I know this? I squeeze my eyes shut, trying to remember, then it comes to me.

This is exactly like Effy! Err, her manastone, I mean. It definitely had these mana structures inside! I grin as I figure it out. I'm making progress. These diagrams are of parts of our manastones. Looking over the notes once more, I try and apply the context.

I go over a few, sounding out the words, then catch on one of them. "Exclude water, detri... de-tri-men-tal..." I sound out the unfamiliar word slowly.

"That means it is bad for something," Reena explains and I nod, grateful for the help.

"So they didn't do water because it was bad somehow? But none of the other elements?" I wonder aloud, and she returns an awkward, guilty feeling. "Oh no, don't worry about it," I assure her. "I know you aren't allowed to explain, I'm just talking to myself." That makes her giggle, but she definitely still feels a bit guilty.

Since none of the other notes seem helpful right now, I turn my attention to the last glass, this one only holding a single, somewhat simple diagram.

Just as I'm starting to look it over, Reena hisses angrily. My eyes go wide in an instant. "R-Reena?" I question timidly.

"Sorry, don't worry about it, Aria. You might want to head back though, you've been away for a while."

"Sure, that's fine," I agree immediately. "Thanks for helping me look around."

"You're welcome. Now, get going." I nod and finally stop channeling my mark.

It's only after that, when my thoughts are my own, that I wonder, what on Loqa was that? I shake myself, trying to get rid of that creepy, worried feeling from her suddenly doing that out of nowhere.

"Right right, have to get back," I mumble, and turn away from the last glass. I'll study it some other time.

It's a quick trip back through the spiral room, then I get back to the tiny room that will lead me back to the entrance. Once I'm there, I glance up at the light on the wall, pouting because I forgot to examine those. One more thing to put off until next time, I guess...

Straightening back up, I listen closely behind the hidden door to the entrance. It's pretty thick stone, but even that can't block my ears entirely right now. For the most part, there are just small thumps and scuffing sounds, probably rail units walking around. Then there's a voice. A man's voice, it must be a handler. I can't make out the words, but he sounds commanding. Are we being called into formation?

Immediately, I jab my thumb into the little indent in the wall, pushing a bit of mana through, and dash through the opening as soon as the door slides away. There's just an instant, looking around, to see everyone else in the middle of turning away from me, perfect timing as they're looking toward the other side of the room, and then the door closes behind me.

The rail units are just starting to move, and I go quickly to join them. As I thought, they're all beginning to get into formation, so I go too, sliding between them until I find my way to the center of the group. From there, I just stand and wait, letting out a shallow, relieved breath.

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The trip out of the city is just like last time, from the head handler instructing us, to the speech in the church, and my being completely blind, buried in the center of our formation. It's only after we make it out of the city and we're dismissed from the formation, that I can get enough space to see anything. It's really relieving, not being surrounded on all sides by big adult rail units...

We walk for a while, the head handler leading our whole group. Hmm, if he's in charge, does that make him Quint Varish, the head of the rail unit program? No, those handlers said that even if he's in charge, it was Kurt Ordlyn who did all the work. So is he Kurt then? Or someone else under him? I wonder...

While my mind is wandering idly, Effy pulls away from the other rail units to walk at the back of the group with me. "I didn't see you earlier," she says quietly, not looking at me. For a moment, I consider using telepathy so we don't need to worry about being overheard, but I can't actually do that with a rail unit, can I? Her manastone basically protects her soul from magic...

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Well, being seen touching, like if we held hands or something would obviously be out of place now anyway, so I forget that idea and respond in a quiet voice myself. "I was looking around. There are some really interesting things in that building."

"Oh." She goes quiet for a while before adding, "Tell me about it later?"

"Sure." Our short, seemingly flat conversation hangs silent. It's surprisingly comfortable, just being with Effy. I don't know why, whether it's part of her familiarity as a rail unit, or because she's not like the others. It's hard to say. Either way, we cross the northern bridge before the head handler calls everyone to stop. With a few words, he hands command over to a scout, then heads back to town. I'm still standing at the back with Effy, so I turn a little to watch him walking off.

Then the scout has us start, and I can tell by his voice that it's a different person than last time, so I don't go up to talk to him. I just trot along to keep up with the others. We don't walk for long before I turn my attention back to the forest. "Alright, it's time. Hilde, Avara, can you start heading north?"

"Sure," Avara responds, while Hilde agrees wordlessly.

"Everyone else, keep an eye on the town, please. I really hope the guards don't get overwhelmed."

"They can handle themselves for a couple days," Myra tries to laugh it off, but I'm still worried about them, so she just sighs and lets it go.

Then we walk. On and on through the fields of grass and flowers that spring up here and there. I stare off at the bits growth, random lone trees, little leafy bushes clinging low to the ground, hardly tall enough to show up above the grass. Sometimes I gaze up at the sky, the fluffy white clouds drifting lazily despite the strong, freezing winds way up there where they float. Distant sections of darker gray clouds, with some far off rainclouds to the east.

I wish things could just be peaceful and beautiful like this...

A hand taps on my shoulder, and I turn my attention to Effy. Instead of saying anything, she touches my cheek. The wet feeling makes me jolt a little, realizing I was crying. Covering my face with the sleeve of my robe, I wipe away the tears while throwing my water mana into my well. I completely forgot I made a lot of that earlier when I was listening to those handers.

With it gone, the strange, aching sadness eases a lot, but not completely. I try to ignore it and finish wiping my face, glad we're at the back where none of the other rail units would see that. I have to swallow roughly, before I can speak to Effy quietly. "Thanks."

She hesitates, the faint twitch of her eyebrows showing she's thinking. "You're welcome," she answers with a tiny, pleased smile. I guess she's still working on learning expressions like that.

However... It's been a while already, why are her expressions still so... small? It doesn't look like she's stiff, still working on getting used to physically making the expressions... Maybe her manastone is still suppressing her emotions some? I can't think of any other reason at least...

I wonder about that for a bit, but eventually push the thought away. Even if her emotions are partially suppressed, she still feels them, and that's good enough for me to care about her.

Then she speaks up again, asking, "What was that?" I'm not sure what she's asking at first, and have to ask her to clarify, before she says, "How your eyes and face got wet." Hearing her say it like that makes me want to cringe, but I resist the urge and explain instead.

"I was crying." I admit. It feels kind of awkward explaining this, but I do my best, for her sake. "It's a thing that happens sometimes. Usually when you feel really sad, but sometimes it will happen when you're happy, or nervous, or from other feelings too. I still don't understand it completely."

"Were you sad?" The question is simple, but that hint of a frown makes my heart squeeze painfully.

"No." I know that's not completely true. "I mean, well, not exactly. It was actually something related to my mana."

"Oh, ok. That's good, I don't like it when you're sad." When she puts it bluntly like that, my cheeks heat up a little. She doesn't understand being embarrassed by things like that yet, does she?

"Thanks..." I respond, glancing away and mumbling a little.

She doesn't hesitate this time. "You're welcome." The note of pride finally makes me smile, just a little. I have to remind myself not to be too obvious in case one of the other rail units look back at us.

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From there on, we eventually fall into a comfortable silence, walking on and on as the sun slowly crawls its way across the sky. There isn't much to say, but we exchange a few words here and there, some comments on how things have been after the attack on the city, a couple bits about the fields of flowers we walk through.

But for the most part, it's nice just walking together. Even if we haven't spoken all that much and we're about to go into battle, I feel strangely safe with her. I guess because I know how hard she'll fight to protect me... right? A number of times, I glance up at her as we walk, wondering if I can ask. The handlers said she's supposed to defend me again, so of course she'll do it, right?

But that would be because she was ordered to. Last time, both her and 8C defended me with their lives even though they weren't commanded to. Will she do the same this time?

As the sun is beginning to fall closer to the mountains in the west, I finally swallow down my worry. Quietly, I move a little closer and ask, "Hey..." She turns her attention on me, and staying careful to keep my expression blank, I say it. "You'll protect me this time too... right?"

I'm surprised when she doesn't hesitate, not for an instant. "Of course, with my life."

I blink a few times. "R-really?" Why is she so determined? "Why?"

Effy looks right down at me. "Working together is our best chance at living as long as possible."

Oh.

Wait, I mean, it is? But I see Effy hesitating, just a faint flicker of her eyebrows giving her away. "Also... I like you."

I stammer for a moment, before I get out, "O-oh... thanks..." Why does she like me? I mean, I've tried to be nice to her, and I taught her about her feelings so she didn't have to suffer through everything on her own, and I'm the only one in the whole world she can can really talk to...

Right, that's why... Shaking myself a little, I look back up at her, actually feeling a little guilty now that I know I'm her only frie-

Oh, I'm Effy's only friend. Because we're friends, aren't we?

I... really don't think these things through enough, do I...?

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Eventually, I manage to recover and try to get back to our conversation. I clear my throat softly. "So, you said we'll survive longest together? Why is that?" She used almost all of her mana last time, just to protect me. Won't I just keep dragging her down?

"Because you have a lot of mana."

"Huh?" Well, I guess. The handlers did say I have about thirty thousand which is a lot compared to normal. I can't use it, but if I give it to her like I was thinking...

"You gave me forty one thousand mana last time, and you already have another thirty four thousand."

"..." My mouth falls open.

Forty...

...thousand...?

For some time, I can't really wrap my head around that.

I gave her that much? All at once? No wonder why I wrecked myself for three weeks, that's like nine thousand times what I should be able to hold at once.

But- but how? Immediately, I flail my mana toward my mark to contact Reena. Since I can't channel it here, I use telepathy instead.

"R-Reena!" She jolts at the sudden shout, but I barrel on. "Why do I have so much mana?!"

My question immediately makes her smile coyly. "So, you finally noticed?" When I can't manage to respond, she goes on. "Remember, I told you that you have incredible potential."

"I... I thought you meant in the future, why do I have so much already? I can only hold four point seven five, but my well's like two or three hundred thousand?" My head is spinning, but she just assures me quietly that it's alright.

"Don't worry. I can't explain how it works exactly, but you're developing just like you should."

I have to keep breathing for a bit, trying to calm down, before my heart stops hammering so hard in my chest that I can focus on Effy again. "Alright..." I say silently to Reena, then thank her for assuring me everything is alright. She just offers another happy smile, and I break off my connection. I cough a bit, clearing my throat once more, and try talking to Effy again. "Ok, so I have a ton of mana. We can use it to survive, together."

"Yes," she agrees, bobbing her head ever so slightly.

"Actually, how much mana do you want? I really hurt myself giving you so much so fast last time, so I should probably start soon, now that I think about it. How much do you have left? You know, after the attack?" I ask, a bit nervous talking about that when I remember her facing all of those enemies, all alone.

"I used a few thousand, I have about forty thousand left. We used about thirty six thousand in the last battle, so I might have enough, but..." she pauses, thinking for a while. "Since 8C is gone, I'll probably need to use more powerful armaments to make up for it. That will cost more mana, so... Can I have fifteen thousand?" She actually sounds a bit worried as she asks.

"Of course," I assure her immediately. "You're protecting me, you can have as much as you want."

That eases her worry, the tiny pinches around her mouth smoothing as she lets out a quiet breath. "Thanks."

"Here, I'll give it to you, this will take a while." Glancing once more at the rail units ahead of us, I touch Effy's wrist. It's a little awkward, staying in contact while maintaining a jogging pace to keep up with the adult rail units, and also focusing on my mana.

Since she doesn't have her divine gear lit up, I can't gauge exactly how much mana I'm giving her, so I just aim for about half of the mana in my well right now. If I keep emptying almost all the mana I can hold before pulling more, it should take... three thousand one hundred fifty seven times, I think.

I'm counting off repetitions one after another until we're called to stop by the scout. I pause while he gives instructions similar to last time, basically just telling us to go fight when we hear the whistle. Without thinking, I turn my attention to the mountains, far to the west and down to the south, around the area I remember hearing the whistle last time.

Then my attention shifts again, to the magical creatures making their way north, not far from that section of mountains. I watch the scout walk off in that direction briefly, before continuing to work with Effy.

"Can I see your mana?" I ask when I get to three thousand times, thinking I should be close.

"Ok. Release." Her gear flares to life, drawing some attention from the other rail units before they lose interest. I have to squint into the light for a bit to read the number floating between the round, floating, slowly spinning gear. "Fifty four thousand, eight hundred eighty three," I read out. Just two hundred short.

Wait, that can't be right, I haven't given her that much yet. Maybe she already had a few hundred more than forty thousand when I started?

Thinking that, I keep giving her more, watching the number increase, but no, it definitely isn't the same as before. Her gear doesn't go up by five three times, then four once. The pattern is different now. It's five almost every time.

...Four, five, six, seven, eight, nine... and four this time? I keep working, and accidentally go over fifteen thousand a little, but I nail down the change.

I can hold four point nine mana now.

"That... that can't be right." I mumble. That's point one five more than just a month ago. I thought I gained about two thirds of a unit per year, but at this rate I'm looking at now, it should be more like one point six per year.

I try thinking of other possibilities. What if my mana growth isn't based on physical age? Like how Emily mentioned what Francis thought about the blight? If I use five years instead of seven... no, then my growth rate would be about one unit per year, still too low.

After considering it for a little longer, staring silently into the grass at my feet, I see it. There's only one possibility I can think of, but it's... sort of terrifying...

Since my current rate of growth is higher than it could possibly be based on what I have so far, my only guess is that the rate isn't set, it changes over time.

And if it's higher than it was before, it's increasing over time...

Could it be exponential?