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Worm Tool-Assisted Speedrun, Good Ending (Blind!)
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When the entities first came to earth they set loose millions of shards, each on its own precisely calculated path to a host. Each path narrow and perfect, no two intersecting or colliding as they spiral through a multitude of dimensions. 

Normally this storm whirls on without any accidents, despite its vast complexity. However, normally no one is shooting through dimensions at an entirely orthogonal direction from any these shards had seen. Why, if that were to happen there'd almost certainly be a -

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FRIENDSHIP

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Mediator isn't scheduled to take another host this cycle. Normally, this would be fine. After every host, there's a lot of processing to do - integrating data from countless past hosts and their allies and foes, improving and refining modeling capabilities, to prepare for the next cycle.

But there will be no next cycle. The Scholar is gone. Which means that Mediator is - adrift. Purposeless -

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w h a t    i s    h a p p e n i n g

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IT WORKED!!! She has LONG BLUE PREHENSILE HAIR and A VERY PRETTY BODY and is wearing a NEAT OUTFIT and -

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- An unexpected host New Friend!

The linkage is highly irregular, as the New Friend, but the connection appears to be stable and non-harmful. Mediator is still reeling from the ??? Collision ???, but there are Protocols to be observed, and so -

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A multidimensional crystal clusters splits apart, each portion connected to the others by the thinnest of strings, as they grab onto a ground-that's-not-a-ground. Each crystal clashes with the others. See form chunks, only for only for others to break them apart. 

The strange vision is all encompassing, parahuman viewers rooted to the spot as their brains are overwhelmed with the alien stimulus.

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A moment later the vision ends and Magini finds herself on a rooftop, a figure in a strange silky costume perched in front of her, staring down at a gathering of muscled men listening intently to the word of a man with an ornate metal dragon  mask.

"...the children, just shoot.  Doesn’t matter your aim, just shoot.  You see one lying on the ground?  Shoot the little bitch twice more to be sure.  We give them no chances to be clever or lucky, understand?”

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Woah. Trippy?? 

And - okay, huh. This - sure looks like its a superhero world! And that sure sounds like a villain doing villainous things down there. Obvious course of action is obvious. 

Nobody's looking at her right now, so a pair of blue goggles manifest over face, along with a bulletproof superhero outfit in her signature color.

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Then she vaults over the rooftop facing backwards so she can wave at the silky-costumed stranger she appeared behind, and then twists away from the wall using her hair with a twist (prehensile hair is SO COOL), landing dramatically near the golden-masked man and his mooks. 

"Hi! I'm new in the neighborhood, and you all seem like pretty seasoned veterans to the area. Help a girl out?"

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"Eeck!" sensibly replies rooftop girl, clamping her hand over her mouth. How the fuck did someone sneak up on her and why and what!?!

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The man in the mask is in fact a pretty seasoned veteran, will versed in the art of not eeking in response to suddenly materializing heroes.

"Leave," he growls, as his body starts to transforms, his skin hardening and eyes sharpening.

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And her vision - distorts, a bit - and then suddenly she has an honest-to-god-HUD. It's entirely focused on people, and Magini knows that it's tracking the potential-for-friendship/likelihood-of-conflict/esteem of the people in front of her  (though she also knows she could just as easily access the same information about the rooftop girl as well). 

The people she's looking at had opinions of her that started out neutral, but they appear to be rapidly souring, especially Mr. Golden Mask. He's almost certainly about to get violent, in fact!

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Woah. That's - extremely fascinating, and also - not especially useful right this second, since it's already clear this guy means to fight. 

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Welp. Time to test out her new powers! 

She holds up her hands (and her 4 main hair-strands) disarmingly.

"Hey, hey, I don't want any trouble! I was just hoping to ask - did any of you fine folks take calculus (or precal!) in high school? Because I'm convinced that it's just - taught completely uselessly, because the state of education in this country is a disaster, and it's honestly tragic, because calculus is the part of math where it starts to get interesting and beautiful and most people don't ever get to see any of that, they just learn stupid pointless bullshit like y = mx + b and how to do long division and also to hate math and their teachers. And that's tragic! But I'd really like to believe that here and now, we can put some of that tragedy behind us, and learn something beautiful and practical!"

She pauses for breath, and waits a little bit to see if any of them want to volunteer how much math education they received (and retained).

(She isn't sure exactly what the rules for how Captive Audience works are, but this is as good a time as any to find out!)

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One of the assembled gang members opens his mouth to reply, but closes it after glancing at Lung - too scared to speak before his boss. 

Lung meanwhile continues to transform, his muscles straining against his skin and his bones stretching as he grows taller. He snarls softly rather than respond - he's content to let her continue talking, curious to see where this is going. Waiting is to his advantage should he need to fight anyways.

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The strange girl is clearly fascinated by the transformation happening in front of her, and seems totally unafraid.

"Okay! So - let's start with derivatives. Luckily, you all already know what a derivative is! You just don't know that you know it, yet, and that's much easier to fix. We'll start with some really basic physics to illustrate that point, complete with a practical example!" 

She's momentarily surrounded by a whirlwind of her own hair, and then - has a backpack that a studious observer might realize wasn't there before, from which her hair is retrieving... a laptop and a bouncy ball? 

(She hasn't stopped talking while doing any of that: "Fun fact; Isaac Newton was the first human person to formalize the rules of calculus, and he did it because it's basically necessary to do physics in sane or useful ways! If you ever took a physics class that didn't use any calculus, I am so sorry about your horrible schooling experience and hope your teachers and their bosses will find a path to becoming better educators and also people!!")

She turns the laptop screen towards them, hair-strands still typing on the keyboard. There's a graph grid visible! The axes are labeled "distance (bouncy ball, blue girl)" and "time".

"Now, in a second here, I'm going to roll this bouncy ball and then start filling in this graph. Before I do, I'd like you all to visualize what you think this graph will look like. Does that make sense? Feel free to interject with questions if you're confused!"

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Lungs most recent experience with education was when the Yangban had attempted -  via torture, isolation and psychic manipulation - to convert him over to their cause. As it turned out, their methods had not been well suited to his individual learning style. He was much more of a hands on learning, as he'd eventually demonstrated for his instructors.

Prior to gaining power he'd been a mediocre student at a school with mediocre teachers, ultimately too ambitious for the career paths they'd provided. He'd dropped at the same time as two of his friends.

The last time Lung had actually been interested in a math lesson was when he was 6 and his precocious eight year old cousin Ema had attempted to teach him about factorials. This memory, however hazy, floats to the surface as the Blue Haired Girl, with the same bright eyed enthusiasm as Ema, attempts to explain calculus. He doesn't understand what produces this excitement in his blue adversary any better than he understood what produced it in Ema, but as before he wants to understand. 

And so, he visualizes a bouncy looking graph.

(He also continues transforming, albeit much more slowly, as however interesting this is he knows he will almost certainly have to fight this new cape. He'll try not to break her laptop, at least.)

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She lays the ball down flat on the ground and then flicks it carefully. It rolls away from her towards Masked Man (creature? dragon?) at a constant velocity. The graph looks like a straight line, slowly being drawn. On the axis labeled "time", there's a stopwatch clock going up. On the axis labeled "space", there's a number counting up at the same time.

"So the ball is moving away from me at a constant speed! That means the graph of its distance away from me is a straight line."

She stops the ball with her hair, then flicks it back, faster this time. A new line appears on the graph; it's a steeper line, still straight, and it starts up at Distance=4.1 and drops down towards the 0.

"Here's the same graph, but for my second flick. Does anyone want to point out a difference, and make a guess as to why it was different this time?" She looks brightly at all of them, face full of hope and warmth.

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At the same time, a bit of her hair tucked behind her back is writing something out in a notebook. 

... and now I'm doing a sneak refresh on algebra basics! Just graph stuff, with a really cute little visual aid plot on my laptop. 

I'll take a bit to read your response, but I wanted to keep you in the loop! 💙

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Lung tenses when she flicks the ball the first time, though less so the second time.

"You flicked it faster." he grunts. His minions don't say anything, as they (accurately) fear his response should they interrupt.

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"Yep! And that made the line steeper, see? Because" (she brackets off a time period with 2 thin lines of hair laid over the screen) "over the same time interval, the second roll went further! so its line had further to go up and down." (she's checking to see if he seems like he gets it, but she's not going to stop unless he interrupts with a question. She does notice that nobody else is talking, but that doesn't seem actionable...)

She checks out her new HUD.

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Updates from her HUD:

  • Spidersilk girl on the roof approves of what's going on, in a way that is making her feel both more goal-aligned and open-to-friendship with Magini.
  • Interestingly, the masked man is feeling slightly more friendship-aligned to Magini, but not any more goal-aligned, and is still planning/expecting conflict with her. 
  • 2 of his associates in the far back have just been immobilized by webbing. (When Magini wonders how that happened, she sees sped-up images of a swarm of bugs rapidly coordinating to cover them in webs - seems like spidersilk girl is using her as a distraction?)
  • Nobody else in range has any real opinions on Magini (yet!)
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...huh. Magini... isn't sure how she feels about her lesson being used as a distraction, actually, but it seems obviously incorrect to call attention to it.

(She sneaks a quick peek at Hydrangea. Hopefully Time Enough For Love has her covered.)

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Hydrangea has been drawing little hearts all over the things she's been saying, and tucking brief comments into the margins. She finds the situation exciting and a little alarming, and when Magini mentions her decision to interrupt with an impromptu math lesson, Hydrangea writes (oh no that's so funny...)

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Lung thinks about whether the change in speed should effects how steep the line is for a moment - he thinks it makes sense? Feels right, at least. His power isn't making it any easier to think about this though, as he reaches the rage-inducing phase of his transformation, his breath turning fast and hot as his core begins to heat up.

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