He’s walked through this door what feels like a million times already, but Akihiko finds himself hesitating outside of Shinji’s room today. He’s struck with the terrible, paralytic notion that yesterday was just a dream, and that when he walks into the room he’ll find Shinji unconscious and unresponsive again.
It’s an absurd idea to even entertain, let alone be so afraid of, but– he really doesn’t know what he’d do if that ended up being the case.
Akihiko’s wrestling match with his own irrationality is interrupted when he realizes he can hear voices coming from the other side of the door.
One of them belongs to the lead doctor for Shinji’s case, talking about– something. Akihiko can’t quite make out what he’s saying, but he definitely catches the response.
“No, nothin’ like that.” Akihiko would be able to recognize Shinji’s voice absolutely anywhere, in less than a heartbeat. He knows it every bit as surely as he knows his own.
He leans against the wall and finally lets go of the breath he’d started holding.
Shinji really is awake. Akihiko hadn’t imagined it out of pure desperation.
Now he has to actually work up the nerve to open the damn door. It’s been all he could think about from the moment he’d left the hospital last night until this exact moment, but now suddenly the idea of speaking to Shinji seems as daunting as a title match. It’s never felt that way before.
Yet another thing Shinji would laugh at him for. He’s amassing a collection.
Well, since Shinji’s doctor is here, Akihiko figures he ought to be polite and knocks instead of letting himself right in. When he does, the muted conversation on the other side of the door grinds to a halt.
“Who in the world could that be this early?”
“‘S probably Aki. Dunno anyone else who wakes up at the a– the crack of dawn like he does.”
He exhales, a small smile tugging at the corners of his mouth. Just hearing Shinji’s voice again smooths down some of the prickling edges of his nerves. This can still be salvaged.
Hopefully.
“You can come in, Sanada-kun.”
Akihiko steels himself before he opens the door, and he still feels nearly bowled over when Shinji’s eyes meet his. Seeing them open yesterday was emotional enough when Shinji could barely keep them focused. Now his gaze is alert and aware, fixing on Akihiko with the keen scrutiny that he’s come to find so familiar– it’s almost overwhelming. He very nearly chokes, though at least this time the universe shows him a little mercy and he doesn’t make any embarrassing noises.
“Uh–” God. He needs to get a hold of himself. “Sorry for coming by so early.” Akihiko shuffles inside and closes the door behind him.
Shinji snorts quietly and looks away.
“It’s no trouble,” The doctor replies mildly, though Akihiko has a feeling he’s a little annoyed at being interrupted. “We can continue this conversation later then, Aragaki-kun?”
“Sure,” Shinji shrugs lightly. Akihiko has no idea what they were talking about, and it’s really not any of his business to ask. He steps out of the way and takes a seat in a nearby chair, as the doctor takes his leave to give them some time alone. Akihiko appreciates it, even if it does feel a little awkward at first.
“Never known you to be so sheepish.” Shinji’s voice cuts through the silence.
“Never known you to censor yourself like that,” Akihiko shoots back immediately. Despite the circumstances, all he’s been through these past two weeks, all his apprehension and hope and the nausea-inducing slurry they’ve blended into– despite everything, it’s still as easy as breathing to slip right back into their familiar, bickering rhythm.
“Yeah well, the doc doesn’t appreciate ‘profanity’ in his hospital.” Shinji rolls his eyes. “His words, not mine.”
“When has that ever stopped you before?”
“When he’s got the same glare as Sawashiro-san.”
“He can’t be that bad,” Akihiko laughs. Out of all the matrons who’d been at the orphanage, Sawashiro-san had been the most intimidating by an oceanic margin. She’d practically been a boogeyman to the younger kids– and the older kids, however much they would have denied it. She had never been cruel, at least not in hindsight, just ruthlessly strict. And after all this time, even Shinji still can’t say her name without an honorific.
“Go ahead and try swearing around him then,” Shinji returns. “See for yourself.”
Akihiko folds his arms and scoffs amiably. He will not be doing that.
He feels so much more relaxed now than he did when he first walked into the room. He wishes he could keep things like this, continue to bask in the simple camaraderie of nostalgia.
He knows he can’t.
[next =>]
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The Bill Cipher Geometry Shitpost: Part One
Disclaimer: None of this is to be taken seriously
edit: actually yknow what scratch that i worked real hard on this you should take it seriously
So, as we all know, Bill Cipher is equilateral. That's because of that one line "sixty degrees that come in threes" from that one book that you'll easily find by ctrl+f-ing "equilateral" on the Bill Cipher page on the Wiki. See, but what if that's wrong though?
To do geometric analysis on Bill Cipher, we need to find instances where Bill is facing directly forward (if he's rotated along one axis, we can compare two sides). This is kind of hard. Especially since Bill can, like, bend into hyperbolic geometry to express emotion? (maybe I should do a detailed analysis of the Gaussian curvature of Bill bending later but that seems exponentially harder). Since I'm too lazy to record episodes, I'll just use the ones from the gallery that the Wiki has so generously provided (https://gravityfalls.fandom.com/wiki/Bill_Cipher/Gallery). I found a few, so I'll work with that I have.
Yes, I will come up with incredible farfetched interpretations for each observation. No, they will not be remotely true.
Right, so for our first picture, we'll analyse the Bill Cipher zodiac shown in the intro. This link has the Geogebra file:
There's a lot going on here, but I'll try to break it down. One problem is that Bill's outline has nonzero thickness, so there's really two triangles we can look at: the inner triangle (labelled ABC) and the outer triangle. I've done most of my calculations based on the inner triangle, and my observations should still hold to within experimental error.
First, Bill is (obviously) not a perfect equilateral triangle, because that's how drawing works. AC and AB are both longer than BC. This is unexpected; we'd expect Bill to be isosceles, but for his base to be, well, his base. Instead, it's his right side (from an onlooker's perspective), for some reason. To check that this is within experimental error, I took the perpendicular bisectors of AB and JK, and both are slightly right of C as can be seen in the few vertical lines. This shows us that Bill's right side is slightly longer than his left, and that his base is around the same as his left side. We can't conclude anything from this yet, but we'll get more as we compare to later images. Also, it might be remedied by the fact that Bill's left edge is not perfectly straight.
Our main conclusion comes from looking at the important points in bill: his eye, his bowtie, etc. I drew the line from C to the midpoint of AB as an approximation of the altitude of Bill (assuming he's close enough to Equilateral for that to work). The centre of Bill's bowtie is almost EXACTLY a fourth of the way up, the point a fourth of the way from F to C being labelled as M in the diagram. If we look at the part where Bill's bricks start, which I've labelled N on the right side, then AN = ~8.14, so AN/AK = ~0.63. Note that N can be moved up and down since, again, Bill has non-trivial thickness, and I found that the error gives AN/AK = 0.63 +/- 0.01(3). Particularly, this does not include any fractions with denominators equal to small multiples of three. The closest simple fraction it includes is 3/8, so we can assume that Bill's bricks are most likely 3/8 of the way up.
We can also look at the circles. I've labelled two of the zodiac circles as (OPQ) and (UTS), and their centres are at V and R below. Notice that I is the midpoint of the altitude, so within experimental error we can say that Bill is positioned, most likely, so that the midpoint of his altitude is the centre of the zodiac.
We can look at Bill's eye as well. Seeing as the distance from I to the centre of Bill's eye is approximately the same as the distance to the top of the bricks, we can conclude that Bill's eye's centre is approximately 5/8 of the way from the altitude.
The distance from Bill's top to the top of his hat, which I've labelled W, is almost exactly the same as the distance from C to the midpoints of AC and BC. The intersections between the circle centred at C with radius CW with AC and BC are labelled Z and A_1. Particularly, the line ZA_1 almost perfectly passes through I.
So what can we conclude from all this? Well, we notice that Bill has focused his appearance on fractions such as 1/2, 1/4, 3/8, and 5/8. These all have denominators which are powers of two, which is extremely surprising. Since Bill is (close to) an equilateral triangle, we would expect Bill to have many 1/3 fractions, not only because triangles have three sides (obviously), but because the centre of Bill (or, technically, centroid, and where almost every important triangle centre degenerates to in an equilateral triangle) is one third of the way up each altitude. However, the centre, labelled F_1, seems to have no significant meaning at all. I've also labelled the point 2/3 of the way up as E_1, and while you could argue it's meant to be the eye, 5/8 is much closer and makes more sense due to the 3/8 that already appeared. The point 2/3 of the way up is also usually important in equilateral triangles, being some of the points that lie on the nine-point circle. The midpoint of the altitude in a triangle has almost ZERO nice properties, unless you want to argue that Bill is a fan of Schwatt lines.
Right, so TL;DR: lots of powers of two in the denominators, not many multiples of three. The most clear takeaway is that Bill has shape dysphoria. Bill would rather be a square or some other type of triangle than an equilateral triangle, which for some reason he is anyway. He would rather be able to move around freely like a jazzy triangle. I think this works very well with his feeling of being trapped in two dimensions (and thus his escape and whatnot), as well as being an allusion to the tight caste system in the book Flatland, in which Bill, being the power-hungry triangle he is, would probably want to rise the ranks. However, he is, for some reason, trapped as an equilateral triangle, and thus he rebels by using midpoints for his important features, like a square would do.
I think this adds a lot to his character and backstory, why he's so power-hungry and why he's so hellbent on gaining control of everything, and why he wanted to enter the third dimension - after all, it lets him bend, and thus fixes his problem of rigidity somewhat.
Here's another image
It wouldn't be a proper scientific theory without more images to back me up. Here's Bill's Dreamscaperers portal entrance (link if you want to check my methodology):
This is a great image, because it has very little details that we need to deal with. Instead, we can just directly see that Bill's ``base" (if we consider him isosceles) is mostly on his right edge, though that right edge is now shorter. This lets us compare him to his previous appearance: now, in rebellious nature, he is somewhat breaking rigidity (but just barely, so perhaps he's unable to do it too much without... breaking flatland anatomy? I'm not sure). Also, Bill making his right edge his base is also rebelling against the norms of an isosceles triangle. This could also be because Bill considers that edge more important than his bottom edge (which would intuitively be the base). From Bill's point of view, the right edge is actually his left edge, which could be a clever allusion to the general opinion in history of the left being seen as more "evil" (the Latin word even being "sinistra"). (He makes deals with his right hand, which is weird, but I think it's something about how the deal itself must actually be genuine, even if under sinister intentions).
And again, the centre of Bill's eye, the main feature in the image, is at the centre of the altitude. And so the theory holds! Many features change across depictions, but his eye is consistently the midpoint of his altitude.
But Bill can be a pyramid!
Right, but I have a few counterpoints. First, although he has a square base, his features are still embedded on one of the triangular faces, which are probably still equilateral triangles (though I have to measure to make sure). Second, he only does this (I think) in Weirdmageddon, where he's already gained a lot of power - again showing he'll rebel against the rigid equilateral triangle regime whenever he gets the chance!
Wait, Part 1?
Yep, this'll be a multi-parter! In the next part, I'll analyse Dreamscaperers Bill (or "Lanky Bill") more, and give a few more diagrams. I'm busy though and wanted to get something Gravity Falls-related for the twins' birthday. I'll also analyse the Book of Bill cover which is really weird.
Alright! Thanks for reading!
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tbh i can't really ever see yao as warm towards human strangers. I don't know what the current state of hetalia fandom headcanon pool is, but while i guess you could make an argument that some nations might be more invested in interacting with their populace and having proper conversations/deep connections to some ordinary civilians (even if they're undercover/have concealed identity etc) idt yao is that type of person (at least in modern day)
he goes to buy breakfast from the little stall downstairs 2 blocks away and might hang out for a smoke at the public playground/exercise installations with some old grandpas but generally he's just living among them, nothing special about it. like he'll laugh at memes/douyins and go through the motions of human life, if he's in a mall and something stupidly unfortunate happens to the person 5 before him in line, he laughs and also takes a video if it's actually ludicrous, but overall his attachment to normal citizens is the average human's attachment to a random stranger. 0/10 would not hold the door for a person just because they supposedly make up his existence—much more focused on arriving on time or acceptably late to his meeting to spare the 5 sec it would probably take.
generally tho i feel like it's mostly a result of complicated feelings on nationhood, maybe somewhat from apathy, but also like efficiency and prioritization of his r/ships with other nations over humans that most likely will not remember him or that he will need to care about in the future. this is also partly bc of his personality too I think he's warm to ppl on whims or if that hospitality is extended to him first (cannot imagine him being mean to any old grandmother selling snacks), but otherwise he's just passing through. their existence is separate from his and it's not that deep, compared to his neighbors and others who've spent centuries to millennia interacting with, being shaped by, and shaping him
ig all this is to say that i can't really see him making any kind of ""special"" bond with some human he just met on the street as sometimes happens in fic
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