#something like the euclidean circles

[giulliadella]

Speculative Biology of Euclydians (and Bill Cipher) part 1

Part 2, Part 3, Part 4, UPDATE, Part 5

We're doing this, babies!

This analysis is based on two assumptions:

Before Bill Cipher became a demigod, he was a biological, living organism and so were the rest of his species.

Even after Bill Cipher became a demigod, he still retained some physical characteristics of his biological form.

I will clearly specify which of his abilities are innate abilities of his species, which ones are definitely his divine abilities and which ones could be both.

SO, without further ado:

What is Euclydia and what are Euclydians?

I'm gonna drop a bomb first.

Euclydia IS NOT a flat two dimensional plane. Before you load your shotguns, let me explain!

There are many proofs both in the Gravity Falls show and The Book of Bill that Euclydia isn't a flat plane like the imaginary two dimensional world from Flatland by Edwin A. Abbot.

The first one is actually Bill himself. Bill's species has complex camera lens type of eyes. Such eyes are possible in 2D world, but not on the front, like Bill has. He was born like that, so that is proof that Euclydia isn't 2D.

Next, when Bill is talking about his home in Weirdmageddon part 3, he shows an image of his home planet:

This planet has RINGS. That is COMPLETELY impossible in 2D. Even if the planet was completely flat, the rings would go through it. They would never be able to actually encircle this planet. So, if Euclydia was two dimensional, Bill's home planet would not be able to exist.

In the Book of Bill, we see image of Bill as a baby. In that image he's standing on some kind of field with grass and you can clearly see that there's grass in front of him and behind him, and that's impossible in 2D:

(also sorry for the shit quality of this pic)

But the best proof is that image from thisisnotawebsitedotcom.com that you get when you type VALLIS CINERIS in the computer. It shows Bill Cipher as a child with his parents. The parents are holding him in a manner that is completely impossible in 2D:

The image quality sucks, but you can clearly see that his parent's hands are IN FRONT OF him and he is also IN FRONT OF his parents. The position of "in front of" isn't possible in two dimensions and yet on this image the overlap happens many times. (I circled his parents' hands in red where they overlap with Bill and I circled him in blue where he overlaps with his parents. Bill's bow tie is also in front of him.).

With all that being said, what is Euclydia?

Well, just like Bill said, it's a flat world. Not two dimensional, but flat. The third dimension of Euclydia is limited somehow. Basically, in 3D, creatures are defined by 3 axis:

x axis is left and right (width)

y axis is up and down (height)

z axis is towards and away from (depth)

All three dimensional objects have both width, height and depth. Two dimensional objects have just width and height, so just x and y axis. And Bill has depth. It's a very limited depth, but it is depth nonetheless. So he's not really a triangle, more like a very thin pyramid. This is his side profile lmao:

So Euclydeans have some depth, but for whatever reason, they can't move on z axis. They can only move left, right, up and down. They also can't turn around.

This is how thisisnotawebsitedotcom.com explains Euclydian movements:

Two dimension to and fro, you always know which way to go. If you're lost, don't be afraid, in Euclydia you've got it made. Run too far right to right of frame, you'll appear on left again. Jump too high don’t cry or fret, pop up from the ground I bet. In this place, there is no fear, loved ones will be ever near. Roles and rules always flea/clear. Euclydia, we hold you dear.

So, if they move too far left, they'll come from the other side. This is actually something that in possible ONLY in non-euclidean geometry, which means that Euclydia, ironically, is a non-euclidean place. It's actually a sphere (or a similar elliptical body).

In non-euclidean geometry of the sphere, there exists something that sounds paradoxical: a straight line is actually a circle. But it's actually very easy to understand with this example:

Imagine that you're flying a plane in a straight line. You feel like you're going in a straight line, but your plane is actually following the curvature of the Earth. If you manage to fly around the entire Earth, you will appear on the same spot where you started flying. You were flying in a straight line, but because Earth is a non-euclidean sphere, you were actually flying in a circle. And both of those are true!

The plane is very very small compared to the size of the Earth. So, to the plane, Earth's curvature is so negligent that we could say that in a small radius around it the Earth is actually a flat plane. So, for example, houses, neighborhoods, even cities are built relying only on euclidean geometry (the geometry of a flat plane) because the Earth is so goddamn big.

And Euclydia is actually a whole fucking dimension. Let's say that our dimension is our universe. Our universe is approximately 93 billion light-years wide. So let's say that that's the size of Euclydia. How tiny is Earth compared to the Universe? That's why planets and everything else in Euclydia can be treated as a flat plane: every object is so small compared to the size of this giant sphere that the curvature could be completely omitted from the equation.

Now this is my theory, but I imagine that Euclydia looks like a giant soap bubble. Soap bubbles are made when two thin layers of soap molecules trap a thin layer of water:

Euclydia is the water - that thin layer is where all the planets, stars and living beings on them are located. That's why movement on z axis is so limited. The soap molecules are membranes that separate Euclydia from the other dimensions, one inside the bubble and one outside.

Since Euclydians can't move across z axis, they have eyes on their sides that can see only left and right. Their vision is limited to one dimension. But Bill's eye is located in a spot that allows him to see both left and right, but also up and down. He can see two dimensions, just like us! Here's a diagram I made, so you can understand better:

(there are stars outside too, but I didn't want to clutter this image more)

So, now that I've spent SO MUCH TIME explaining what is Euclydia, let me tell you what are Euclydeans.

Euclideans are animals (or their equivalent in their dimension). Animals are defined as multicellular heterotrophic organisms with an internal digestive tract. This basically means multicellular organisms that eat.

Euclydeans have to be multicellular because they have extremely complex structures such as: camera lens eyes, teeth, fingerprints, exoskeleton and so on. These traits cannot be achieved by a unicellular organism. And they definitely eat their food, we've seen Bill do it. So they are (their dimension's equivalent of) animals.

And how they function? What type of animal are they? Well, see you at part two, if this didn't bore you to death already!

Thank you to @forseenconsequences @extremereader and @ok1237 for asking me to do this. Hope you like it, guys!

[ckret2]

I was asking because the remains of Steve's body exist and regardless of what they did with them, the 3D eye (depending on whether it formed before splitting) that would mean that there was something else in Euclydia that protruded outside of it. Or I just remembered that psychics (they are, as far as I understood, others who could see 3D, although I don't know if they also had body parts protruding outside of Euclydia), sorry for my bad writing, English is not my native language, GoogleTraslate

I tend to imagine it as similar to a muscle that can flex in a certain way to "bend" into the third dimension. when it's not flexed, there's no bend. So even if Steve did have the same anatomy, without being alive to flex that muscle, nothing would happen.

I don't see them as literally sticking out of Euclydia, like a solitary bump in a perfectly flat plane. I see it more like... causing a slight wrinkle in the surface of Euclydia, and being able to perceive/take advantage of that wrinkle in a way nobody else can.

Ironically, I headcanon that Euclydia operates on non-Euclidean geometry: the people living on it PERCEIVE a flat plane, but from the perspective of the third dimension it actually isn't flat.

As a whole, I think Euclydia probably operates on spherical geometry. The song about Euclydia on TINAWDC mentions that if you go too far to the top you'll appear on the bottom and too far on the left and you'll appear on the right—it sounds like circling a globe. Plus I headcanon there can be localized bumps/dips/waves/ripples in the plane, visible from the third dimension but not the second.

(Have you read A Wrinkle In Time? The surface of Euclydia can form tesseracts. If you haven't read AWIT, forget I said that, because AWIT's definition of tesseracts is different from the normal definition.)

Bill, and other people with that mutation, are little puckers in the surface of Euclydia: they're perceived as perfectly flat by other people on the second dimensional plane, but they, and the universe itself, bend slightly outward. They aren't the only places the universe bends; but the fact that they bend is what lets them see off the surface of the plane.

[dunmomee]

Coffee and Classicals

Synopsis: The banter between you and Levi shows no signs of slowing, especially now that he’s pressing you with the new book recommendation. Meanwhile, you’re starting to settle comfortably into the chaos of his friend group, with Hange and Erwin circling close.

a/n: I was tempted to add something spicy to this part, but I didn’t want to rush the pacing or let the chapter get too long. I’ve really been enjoying weaving the story around these two—and getting to play with Hange and Erwin’s dynamic too.

Thank you so much for all the comments; they truly reignite the fire in me every time. And to every pure math major out there—please forgive me! I usually just pick the first topics that come up in my search. I hope you enjoy reading this chapter as much as I loved writing it.

<<Previous ☕ Masterlist ☕| Next>>

Part seven: I Want You in My Art

It was overcast, cold enough to make you wish you’d layered up. The wind tugged at the hem of your coat as you matched pace with Levi, his hands buried deep in his pockets, his expression unreadable as always.

You glanced sideways. “You’ve been brooding for three blocks. Is this still about Anna Karenina?”

His silence said everything.

“I wasn’t saying what she did was smart,” you clarified. “Just… tragic love is still love. It was real for her.”

Levi finally spoke, voice clipped. “Love doesn’t excuse recklessness.”

You shrugged. “Maybe. But there’s something kind of admirable about wanting someone that much.”

He shot you a look—eyes narrowed, calculating. “Is that what you want? A train-track ending over some guy who looks good in a uniform?”

“God, no,” you laughed, half-sputtering. “I just meant… I don’t know. I’ve never been in love. Maybe I’m too delusional.”

“Too focused on becoming a smut valedictorian,” he muttered, the corner of his mouth twitching into a smirk.

You choked. “Excuse me?”

“You’ve read half the erotica in the café, and your bookshelf screams quantum equations. If that’s not academic contradiction…”

You elbowed him lightly. “At least I read. You just brood and critique everything I say.”

His jaw ticked. “That’s not true.”

You raised a brow. “Oh?”

But he didn’t take the bait. He went quiet again, eyes fixed forward like he was working through something heavier than philosophy midterms.

You studied him for a beat, then asked softly, “Have you ever been in love?”

The air shifted.

He didn’t answer right away. Just exhaled, slow and measured, like the question itself had weight.

“Once,” he said finally. “Didn’t end well.”

Your steps faltered. His voice hadn’t been bitter. Just hollow.

“Oh,” you murmured.

He glanced at you then, gaze unreadable. “Don’t waste your life chasing someone who doesn’t want to be caught.”

You stared at him, blinking. It was the most Levi thing you’d ever heard. Sharp. Guarded and quietly devastating.

You opened your mouth to ask something else—

“Y/N!”

Moblit’s voice cut across the quad like a pebble skipping through still water. You turned, startled, just as he jogged up, cheeks flushed from the cold.

He fell into step beside you, cheerfully animated. “Hey, did you see the new problem set? All non-Euclidean geometry. You’re gonna love it. Rico saved us seats.”

You lit up. “Seriously? That’s perfect……I was just reviewing hyperbolic planes last night.”

Levi didn’t say anything, but you felt his presence retreat, like a wave drawing back from shore.

“Morning, Levi,” Moblit added, oblivious.

Levi nodded, barely.

As you and Moblit veered toward the math building, your laugh echoed once, soft enough to escape Moblit’s notice, sharp enough to splinter inside Levi’s chest.

He didn’t move.

His jaw clenched.

He scowled harder, stuffing his hands deeper into his coat pockets.

“She has shit taste,” he muttered, this time to himself.

And yet, he stayed rooted on the path, watching until you disappeared through the doors.

––––

It was another Sunday.

The scent of brewed espresso lingered in the soft-lit corners of the café as the hour edged toward eight. You were curled into the corner booth, boots tucked beneath you, one hand supporting your chin, the other holding Levi’s latest recommendation: The Handmaid’s Tale.

You’d just finished chapter four, brow furrowed at the slow-burn unease threading through every page.

Behind the bar, Levi moved with his usual quiet precision—cleaning, rinsing mugs, rearranging the pastry display even though it had been sold out since six. The “CLOSED” sign hung in the window. The last customer had shuffled out ten minutes ago.

He didn’t speak until he caught you flipping a page too fast.

“You sure you’re actually reading it?” he said, low and dry.

You glanced up. “I’m on chapter five.”

He didn’t smile, but you caught the flicker of interest. “What do you think?”

“It’s unsettling. Sparse. Kinda claustrophobic.” You tapped the page. “Like the narrator’s choking on her own thoughts.”

He nodded once. “Good.”

You raised a brow. “That’s a weird reaction.”

“It’s doing its job.”

You tilted your head. “Honestly, I expected something more dramatic. Probably because of the series.”

Levi’s face darkened like a thundercloud. “Ignore the series.”

“Wow, okay.” You laughed. “Did Hulu hurt you personally?”

“It butchered the tone. Turned nuance into spectacle.”

You held up your hands, grinning. “Alright, alright. I’ll pretend it doesn’t exist.”

Satisfied, Levi moved to the tables near your booth, wiping them down with a damp cloth. He glanced over his shoulder. “That beast of yours still alive?”

You blinked, thrown. Small talk. From Levi.

He nodded toward you. “Beethoven. Whatever.”

You narrowed your eyes. “His name is Bertholdt. And yes, he’s alive—and judging everything.”

“Figures. He nearly killed me last time.”

You tried not to smile at the image of Levi being bested by your peaceful, chronically unimpressed cat. “He did not. He’s a good boy. Maybe your dry personality triggered him.”

“He has the energy of an apathetic doorman.”

You laughed. “That’s rude.”

A beat of silence passed. You tucked a loose strand of hair behind your ear and looked back at the book, adjusting your cat-shaped glasses. Levi returned behind the bar. A few moments later, he spoke again.

“There’s an art show next Saturday. Miche’s exhibit.”

You looked up. “Miche? I think Hange mentioned he’s built like a linebacker? She said he once cracked a chair by sitting in it too fast.”

“He prefers ‘sculpted,’” Levi deadpanned. “It’s mostly atmospheric stuff. Textural. Erwin’s going. Hange too, obviously. Might be tolerable... with another person.”

You blinked. “Are you inviting me?”

He shrugged, too casual. “You read depressing literature about velvet rods and senseless sex, and named your cat after a war criminal. You’re qualified.”

“So romantic,” you snorted.

“It’s not a date.”

You grinned, sensing how hard he clung to that line. “Sure, Levi. Definitely not a date. And ‘velvet rod’ is oddly specific.”

“Shut up.”

He didn’t look at you directly, but the corner of his mouth twitched. “Hange said she’ll pick you up.”

You watched him head toward the back, his jacket catching the amber light as he passed beneath it. You looked down at The Handmaid’s Tale, the pages open in your lap.

But you weren’t really reading anymore.

––––

All week, you buzzed with anticipation for your not-a-date date. You and Hange had spent hours debating outfits like the fate of the free world depended on it—sorting through color palettes, arguing over boho versus minimalist like it was a thesis defense. You counted down the days, then the hours, then the minutes.

Finally, it was Saturday.

The gallery smelled faintly of paint and eucalyptus. White walls, moody lighting, and a soft indie playlist hummed through the space like emotion had a soundtrack. Hange had practically launched you through the entrance with the kind of zeal she usually reserved for successful experiments and government conspiracies.

“Look alive,” she whispered in a stage-hiss. “We’re here to support Miche, whether you get the art or think it’s just emotionally-charged finger painting.”

“I already feel like a fraud,” you muttered, eyeing a nearby painting full of jagged red brushstrokes. “Is that a volcano mid-eruption or... someone’s unresolved trauma?”

“Same thing,” Hange said brightly. “See? You do get it.”

Levi was already waiting inside, clad in a sharp black jacket that made him look like the lead detective in an indie noir film. Erwin stood beside him, calm as ever, like he’d already accepted the chaos that came with this friend group.

Levi gave you a slow once-over. “You look like a Tumblr goddess.”

You blinked. “Thanks—”

“If Tumblr had a nervous breakdown in a cottagecore aisle at Goodwill.”

“Oh,” you deadpanned. “So it’s a backhanded compliment.”

“It’s a sentence,” he said, flat.

Erwin chuckled. “Translation: he thinks you look nice, but he’s physically incapable of saying it without sounding like an existential crisis.”

“She said she wanted to connect with the art,” Hange added smugly, throwing air quotes like confetti.

Levi stared at you like you’d confessed to baptizing yourself in acrylic paint. “And you thought dressing like a patchouli-scented goddess would help?”

“I thought maybe if I looked the part, I’d feel something,” you said with a shrug. “So far, all I feel is broke and underqualified.”

“That’s because you and Blind Bartimaeus here thought you had to ‘connect’ to the art,” Levi muttered.

Hange gasped, scandalized. “Did you just call me Blind Bartimaeus?!”

“I’m very sure it was your idea, Four Eyes.”

“That’s blasphemous,” you said, nudging him with your elbow. “Aren’t you worried about divine retribution?”

Levi rolled his eyes like he’d been punished enough already. “Let it come.”

“It definitely will.” Erwin murmured. “You should stop calling Hange names”

“No,” Levi replied. “She should stop calling me Shorty.”

“Aren’t you short?” you said, feigning innocence.

Levi gave you the coldest glare.

“Accurate,” Erwin and Hange chorused.

You moved through the gallery as a unit, an increasingly chaotic one. You paused at each piece, trying your best to understand. One canvas looked like depression if it were a weather system, another resembled tax season. Hange narrated every piece like she was hosting a paranormal documentary. “This one? Definitely Levi’s repressed feelings.”

“Keep projecting,” Levi muttered, deadpan.

Eventually, he muttered something about “saving what’s left of his brain cells” and tugged you away by the wrist toward another hallway.

You blinked at him. “Scared I’ll start describing the next piece as ‘corporate angst in gouache’?”

“No,” he said. “Worried you’ll try to write a thesis about it and get a PhD in Aesthetic Delusion.”

But you didn’t get the chance to answer.

You turned a corner and both of you stopped.

The piece ahead was quiet. It wasn’t loud or tortured. It was a horizon of deep navy and midnight blue, flecked with pale silver and streaks of lavender. It shimmered under the gallery lights like a frozen lake reflecting the northern sky. The plaque read: Northern Peace.

Levi stilled beside you.

His hands, usually buried in pockets or crossed in suspicion, hung at his sides. His jaw was tense, but his eyes were soft. Locked on the painting.

You watched him, not the art. “What do you see?”

“It reminds me of the silence after a fight,” he said quietly. “The kind that leaves you sitting in a room alone. Just… listening to yourself breathe. Wondering what the hell it was all for.”

The words hung in the air, like dust in sunlight.

You glanced at him again. “That’s… oddly poetic.”

“I’m full of surprises,” he muttered.

“Is that what’s behind the grumpiness? Secret poetry?”

He didn’t answer. But he didn’t look away either.

Slowly, you reached out. Palm to palm, nothing more. His hand twitched under yours but didn’t move.

“If anyone asks,” he said, eyes still on the painting, “I’m only letting you do this because I’m avoiding smiting from Tumblr Gaia.”

You smiled, fingers brushing against his lightly.

“Sure, Short King.”

Levi gave you a long-suffering look, but didn’t move his hand.

“Cute,” came a new voice behind you. “Didn’t know I was hosting a live performance of emotional growth.”

You turned, startled. A tall man stood there with tousled blond hair and a calm, amused expression. His voice was low and dry, like he didn’t speak unless it mattered—and when it did, you listened. He wore a muted gray coat, hands tucked into the pockets like he had nothing to prove.

Levi sighed. “Speak of the devil.”

Miche.

“Oh!” you straightened up. “You must be Miche. I’m Y/N.”

He nodded, taking your outstretched hand in an easy shake. “I figured. Hange doesn’t shut up about you.”

“That’s deeply threatening,” you muttered.

“She meant it in a good way,” Miche said, a trace of amusement in his voice. “I think.”

“I wouldn’t be so sure,” Levi deadpanned.

“I wouldn’t either,” Hange chimed in, reappearing with Erwin and a half-eaten brownie from the refreshment table. “But it was affectionate slander!”

You laughed nervously, then glanced around. “So… confession time. I didn’t understand a single thing in there.”

You gestured back toward the previous exhibit.

Miche’s brow arched slightly. “Not even one piece?”

“I thought one looked like a tax audit,” you said honestly. “Another one gave me heartburn.”

Miche stared at you for a beat. Then, he grinned. “Perfect. That was the intended effect.”

You blinked. “Wait—really?”

“No,” he said, turning smoothly. “But I like the honesty.”

Levi snorted behind you. “You’re fueling the wrong fire.”

“She’s refreshing,” Miche said simply. “Everyone walks in pretending to get it. No one ever says it’s all nonsense.”

“I didn’t say it was nonsense!” you exclaimed. “I said I didn’t understand it.”

“Which is fair,” Miche said. “Not everything’s meant to be understood. Sometimes it’s just meant to be felt.”

Hange nodded enthusiastically. “Exactly! It’s the essence of art!”

“You called one of the paintings ‘Levi’s rage in acrylic,’” Erwin reminded her mildly.

“And I stand by that.”

Miche tilted his head at you. “But really, I’m glad you came. You look good in this kind of space. Like you belong here.”

You blinked. “That’s... actually really nice.”

“Don’t encourage her,” Levi muttered, voice acidic.

Miche looked at him and smirked. “Someone has to. Otherwise she’ll keep taking your feedback seriously.”

“His feedback was that I look like Tumblr had a breakdown in a thrift store.”

“Stylish breakdown,” Miche said. “Very on trend.”

You beamed. Levi looked like he was actively reconsidering his life choices.

“I should’ve just come alone,” he mumbled.

“And miss all this ego inflation?” you teased. “Never.”

“Regret,” Levi deadpanned. “Pure and immediate regret.”

You couldn’t stop smiling.

Whatever you didn’t understand about the art, you were beginning to understand this. The cadence of inside jokes, the brushstrokes of teasing and quiet loyalty.

It was a kind of art you couldn't analyze, only feel.

Nothing like the equations or smutty paperbacks you clung to for comfort.

Maybe this, too, was worth reveling in.

----

a/n: I fully leaned into the Bertholdt meme. How could I not? It was way too juicy to pass up. Honestly, I had the idea long before I even wrote this part. Hehehe.

Also, I had a bit of a brainwave, do you think the title should stay as it is, or does Erotica and Classicals sound better? Let me know what you think!

[warpedlegacywrites]

Eldritch Horror Prompts

Based on the list found here. Please like and reblog the original version.

Forbidden knowledge

Made of the Void

A strange and ancient statue

Something pretending to be human

Parasite and host, puppet and puppeteer

It watches from above

A glitch in reality

I've seen too much

Eldritch corruption: human

Eldritch corruption: animal

Eldritch corruption: environment

A creature from the deep

Eldritch circuitry, what lives in the wires

Maddening music

Humanity's smallness

Too many eyes

Too many teeth

Non-euclidean geometry (think M.C. Escher)

Swarm or hivemind

Something in the walls

Unearthly arthropod

Fungal/plant takeover

Mirrors, reflections, and doubling

Vampiric entity

Ritual circle

Anatomy/body horror

Eldritch and fey

Horse/farm animal horror

Something on an old VHS tape

Fear (based on a phobia of either the writer's or the asker's)

Okay, fine: Tentacles!

[taatsums]

Kafka Oguro Ward Mayor Novel - Mother's Code: Season 1, Track 1 - Happy Birthday

I insert the silver memory stick into the laptop and the laptop's LCD screen flickers off, giving way to a hologram. A three-dimensional torus starts to rotate slowly, mathematical formulas forming on top of it.

“Hmmm… I see,” I mutter, “so this is still just a trial run.”  I can't help the grin that tugs against the corner of my lips as I suddenly find myself enjoying this so much. It's not my birthday or anything— This is just a "birthday present" that's delivered to me out of the blue once a year.

Just like every other year, Sakujiro handed me another small, silver memory stick.

The name on the simple packaging was… Rinka Oguro. My mother.

I thanked Sakujiro as I received the package, and with his usual expression, he asked, "Are you planning to remain occupied for a while?" Well, I couldn’t possibly put off something this interesting.

Obviously, Sakujiro is aware of the existence of the memory sticks that have been delivered to me annually for the past few years. However, I'm unsure of just how involved with them the capable butler is exactly. Up until now, there has been no need for me to know, so I’ve never tried to find out. Maybe he’s in charge of delivering this to me at my mother’s request, or he’s simply handing me a package that arrived. Or maybe, he’s aware of everything, even the intention behind this gift.

Regardless, what I have to do never changes. The memory stick contains numerous codes, and solving the riddles is something I look forward to every year.

In the midst of solving some of these mathematical formulas, my roommate Renga walks into the room. I don't have to turn around to know that he's startled by the countless complex mathematical formulas that have started appearing one after another on the unfolding hologram torus.

Wanting to crack the code as fast as possible, I pay him no mind, moving onto the next problem.

"W-What're you doing? Trying to find the area of a shape, or something?" "Close. These are topology problems."

He's nowhere near hitting the mark, but I tell him he is anyway.

Renga looks intimidated as he keeps his eyes on the floating formulas.

"Out of all these graphs, which one do you think is the closest to the shape of a human?" "Huh? One of them looks like a human!?"

When I turn to hear his answer, he flinches like a dog about to jump away.

Well, I can't say I blame him. In front of us are circles, squares, and two circles put together. From Renga's point of view, they're just simple shapes. None of them look anything like a human. But, this is actually one of the more basic and simple problems.

"It's this one. The two-dimensional torus." "… That’s a donut, no matter how you look at it. Saying that's a human is horrifying." "The specifics differ, but from a topological perspective, humans and donuts have approximately the same shape." "From a top… W-What?"

I ignore Renga, who seems to have countless question marks floating above his head, and continue onto the next problem. This year, the riddles seem to be nothing but math problems, but that's not always the case. Some years it's science trivia, and others, the questions are historical or political, even containing facts about everyday life.

… Mother is probably testing me. Even problems that only university mathematicians can solve are child's play for me. I'm sure that was the case for her as well. Eventually, the hologram changes shape, and eight different shapes materialize.

"A sphere in a Euclidean space… Is this… a geometrical conjecture? A continuation of the topology problem?"

I'll have to look at it for a while and think about how the formulas that have appeared thus far have gone.

"Ah, is this the Poincaré conjecture?"

It's simple once you understand what the columns are.

We've jumped straight from Thurston's geometric conjectures to Perelman's proof.

"Energy, entropy… And the proof I need is…"

I type non-stop without pausing to breathe, engrossed in solving all these equations. Before I know it, I've managed to solve the mathematical formula that countless mathematicians had taken three years to find a conclusion to. As I finish typing, the final code appears.

—— [M…]

The hologram instructs me to enter what comes after "M". Oh, and for the record, this is suddenly no longer a mathematical problem.

But my mother is being too easy on me. This is nothing for my 20 year old self. I can't hold back my smile as I close my laptop's lid.

I want to solve the final code next to a certain someone I treasure.

"A-Are you done?" Renga asks timidly.

Apparently, he has been watching from behind me this whole time. Well, given Renga's personality, he's probably worried about me. I think as much to myself as I take a sip of the black tea Sakujiro had prepared for me.

I was so focused on solving the problems that I didn't notice my tea had gone cold.

"You okay…? It looks like you had to think a lot…"

He's probably worried about me. He was more worried than anyone else the last time I collapsed, after all.

"I'm alright, I'm good at this kind of brain work. If anything, it was a pretty good distraction." "… What was that thing you were solving earlier? It was all numbers and symbols and stuff like that, and it was kinda scary… Uh, it wasn't some weird curse, was it?"

Did they seem like curses to Renga? I feel bad for saying this, but I understand why everyone treats Renga like a dog. He wears his heart on his sleeve.

That's a good thing, because a lot of us in the Morning Team aren't exactly easy to read— Well, Yukikaze is, but his indomitable spirit kind of offsets that. It's good to have all kinds of people in your group.

"It's a birthday present from my mother, actually. Or maybe I should call it a challenge? Every year, she sends me a code, and I have to solve its riddles to get to the real thing." "It's your birthday!?" Renga exclaims, and I don't have to turn to look at him to know that he's forgotten all about the curse he was so afraid of. He's probably thinking something like, oh no, we have to celebrate!

But after a few seconds, Renga's expression twists into one of confusion.

"… Wait, your birthday is on July 3rd, right? It's nowhere near that time of the year right now." "Aw, thanks for remembering ♪" "Of course I'd remember! You're our president, after all..."

Renga, you do understand that Ten and Liguang act like that around you exactly because you say such simple-minded things, don't you?

I wonder what kind of face he'd make if I asked him that? I think about it, but decide against it. I'm rather pleased with the current relationship between the Morning Team and Renga, after all.

"Also… Isn't your mother…" He probably said that without thinking, because I could tell from the way he got quiet that he's starting to regret it. Now that I think about it, I did tell him about my mother back in the hospital.

"You know, don't you? Actually, this present was delivered from Heaven." I say as I stroke the surface of my laptop.

Renga looks confused by what I said. It really was, though. The only difference was that my mother had given me the first one directly.

—— "I have a birthday present for you."

I can still remember. My mother's voice as she called out to me and gave me the first memory stick some years ago.

At the time, she was hospitalized in the same private room as me in Oguro Hospital. I tilted my head in confusion and said, "Today isn't my birthday, though."

"Isn’t getting your birthday presents only on the day of rather ordinary and boring? I think receiving one out of the blue is much more interesting."

All I could do was agree. My mother was a strange person, and she often came up with strange ways to explain her ideas.

"Handing it to you directly every year wouldn’t be any fun, either. So I'll find a more surprising way to give it to you next year. Okay, Kafka?" She said with a hint of pride as she patted my head.

Her hands were shakier than usual.

But back then, I simply ignored it and went along with what she told me.

My mother died soon after, and the birthday presents that were given to me on days other than my actual birthday were delivered from Heaven… In the form of small packages.

Track 1 | Track 2 | Track 3 | Track 4 | Track 5

[crowdsourcedgender]

hey so what about euclidean and noneuclidean genders? like euclideangender or whatever is when every time you question your gender you end up in the same place and noneuclidean gender is the opposite. so in a euclidean gender you think "hm maybe I'm not X after all." and then you come to the conclusion that you actually are still X. but in noneuclideangender you think "hm maybe im not X. i think im Y" and then identify as Y. don't have a good flag or name for these but something about euclidean or not would be cool. and maybe you could clean up the definition?

[Image ID: Two flags with five stripes and similar color schemes. The first has the design of a circle that connects to the middle stripe, revealing another stripe below. Its colors go purple, light blue, blueish white, greenish blue revealed stripe, light cyan, and dark green. The second has the middle stripe suddenly bend up at an angle, continuing off the flag and revealing another stripe below. The colors go pinkish purple, blueish purple, purplish white, light turquoise, dark mint. /End ID]

Name: genderlooped / genderaltered

Genderlooped: A gender where the user frequently questions their gender, but comes back to the same conclusion like a loop.

Genderaltered: A gender where the user frequently questions their gender, and comes to a new conclusion each time.

For day 5 of @ecstasyangel 's 150 follower coining event, prompt: free space -> request (blog theme lol)

[teaandinanity]

Unsure if any friends or followers are playing Project Zomboid but I'm having enough fun I may actually try multiplayer someday. Like, probably not, because the default settings which I'm assuming the servers also use are BRUTAL, but maybe I can find a more survival-sandbox-y one..?

One of my favorite things about my current run (I started over because construction in this game is a circle of hell and remodeling existing structures creates non-euclidean geometry that miraculously does not cause my little survivor to take psychic damage but was making Me The Player do so) is that she's currently in the stage where I'm like 'I know I quite urgently need food and am almost out of decent weapons and may shortly be reduced to the alarmingly close range of my crafting knife/scissors/screwdriver and/or knocking zombies over to stomp them to death but consider; what if I raid the not-a-Blockbuster and fill my Whole Entire Car with skill tapes and the books I stole from zombified survivors.'

I desperately need axes so I can expand the current offroading+deer trail access I'm using and make something resembling an actual road to my base - I decided to set up camp in the McCoy mansion this time around and the access I can actually use is egregiously terrible but worth it for effectively having a moat... and we will worry about being able to create better access at a later date, by which I mean 'I'm going to see if stone axes are as bad as everyone makes them sound and you actually need 2-3 to take down one (1) tree.'

If that does wind up being the case I'm not quite sure what I'm going to do but again; a problem for future me, when she needs to be able to get an animal trailer in here.

I DID at least acquire a shovel so I can bury the like 30 people who tried to eat me when I got to the estate and, bonus, they will probably all have produced fishing bait by the time I get back. I have to go the long way whether I like it or not on account of a 20-car pileup mess on the more direct route that would take me to what is theoretically The Actual Driveway, hence why I am currently driving on what I assume is an electrical easement and then a deer trail.

Anyway, the food situation is pressing but not dire. The beauty of starting out with a slow metabolism is that my character actually needs to drop some weight and I can feed her rabbit food (sometimes literally because they keep jumping in front of my car, oops) with impunity for a while, unlike all the youtubers who start underweight and then have to make their survivors cram entire sticks of butter in their mouths to not die. Every time I start out overweight in this game I think of that 'are we running from the English again, lass?' post and giggle. We are running from the zombies! Very slowly. And it will, in fact, be to my advantage in a few more weeks for her to be genetically inclined to remain plump as a partridge.

Now I just need to re-acquire livestock.

The only things I am legit sad about losing from my prior save; cows and sheep. When/if they add horses and dogs I'm going to be insane about them and it is entirely possible that I will get my survivor killed rather than letting the undead murk my pets.

[kadavernagh]

TIMING: Current LOCATION: Just Couches PARTIES: Regan and Jade SUMMARY: What comes first, the couch or the home? Jade says couch! So she and Regan are off to find the perfect one, which will be without a single weird feature.

The Kavanaghs had a couch. It was covered in dark brown leather, the kind that sucked your skin in when you sat on it wearing shorts. Regan used to like the feel of it against her arms and legs, though in hindsight, maybe there was a little death there, too. Sometimes she plopped herself across the whole couch when Al came into the living room, forcing him onto the armrest if he wanted to sit at all. She watched late-night unpermitted horror movies with Liam that her dad would have hated, had he known. Reilly once sat her down there to discuss how their parents had started sniping at each other more frequently (a rough patch that was mended, but had all four of them wondering about a particular d-word for a few months; Al said authoritatively that it was her fault). Couches see a lot. And they had a couch. 

Then Regan had a couch. She couldn’t remember the color and material. She couldn’t even remember where she purchased it. Only that… well, she must have, right? In that old Baltimore apartment she also barely recalled, all of it awash in medical text memorization and memories of her hands inside of cadavers – though most of that was gone, too. It would have traveled back to Augusta, that theoretical couch, in that moving truck she must have rented, that had been filled with possessions she must have kept. Regan must have had a couch. And then she forgot what they were for about eight years, because comfort, her grandmother often reminded her, could not taint her capabilities. An instrument sliced through fabric; to be disarmed by such distraction as comfort would cost control; Cliodhna’s hanging rabbits spilled their coiled innards on the floor.

“I don’t trust it.” Regan said, appraising a bright orange couch coated in velvet, one of far too many options crammed into a claustrophobic store. Her grandmother’s similarly-colored wings flashed a warning in her mind. She walked around it in a half-circle like it was a crime scene, not even considering sitting. She had warmed up to the idea of being a couch owner, but primarily for Jade’s benefit, because they had a yet-to-be-determined house that would “require” furnishing. (And maybe they should have reassessed that order of business, but it wouldn’t be Jade’s beautiful but non-euclidean mind to do that, and Regan was… distracted.) She did not have to like the couches. That would be asking too much. “Velvet is difficult to clean, don’t you think? And the color… I cannot even think of a fluid found in the human body that’s comparable in hue. It won’t do. It is not even fit for Emilio.” She had bought a better couch for him. Jade needed something one hundred times better than that.

Regan finished circling around the couch and ended up right next to Jade again, where the thought of couches didn’t bother her quite as much. She tapped Jade’s hand lightly before stealing it for herself. “Come on, there has to be something here you would rather sit on. Where is the stone section? Or… I will compromise. I am famously good at that. We could get something wooden. Cats like wood, right? For scratching?”

—

Truth be told, Jade had never put that much thought into couches before (a true shocker there, right?). So like, as long as they were comfy, that was it, she was set. And sometimes not even that! Who was she kidding? Cause Jade had spent a decent amount of time on Emilio’s couch, so her standards could mean anything, actually. Couch used to be whatever. But the past didn’t matter, anyway. The present mattered. As did the future. Her future, their future. Cause she was so excited to pick her very first couch. Like a real true adult. Nah, a real true adult in a committed relationship. It was a lot, which was probably the reason why her entire body seemed to be buzzing like she’d drank five shots of espresso. Or well, she imagined that’s what it felt like. (She never needed caffeine to be that energized, people envied her). Seeing the Just Couches logo as they entered the store filled her with an extra dose of warm and fuzzy feelings. This chain had kinda become a staple in their relationship, right? Cause she would always remember her first date with Regan at Just Coffee. (And the mint julep she had after in the place next door, Just Cocktails). And now their first couch would be Just too. 

They hadn’t walked around for two minutes when Regan found their first option. Sorta. They just stumbled upon it, so it was time to judge it. And judge they did. “Oh? How come, baby?” Jade prompted after the initial assessment on the bright orange sofa. Regan inspected the thing like she was choosing her torture device instead of the sweet spot where they would have their most entertaining movie nights. But knowing the why behind that stiff gait and those shifty eyes meant Jade didn’t treat it as an obstacle. It might look silly to outsiders, but she knew this was important. It was a bit of a milestone for Regan too. And she would not stand (or well, sit) for any couch that Regan couldn’t at least relate to some type of bodily fluid. That was just, pft… entry level. So Jade would totally commiserate with her on this. “Was it mean mugging you? I swear, I totally saw it do that when we came in. I like the color, but it needs a better attitude.” Regan was right though, velvet was difficult to clean, and they both knew she was a little sloppy with her food sometimes. So, that was like, just inviting mess. And not the fun kind. She followed Regan without a rebuttal when she decided to move on, cause they were on the same page. (Or, well, the endgame was the same… despite their different ways of looking at it, so, same thing).  

Jade squeezed Regan’s hand as she grabbed it, the action tugging a smug smile on her lips. One that turned into something sweet as she beamed at the other couple making the rounds. They looked like their names would be Doris and Bob. Yup, Doris and Bob. And they were a few years into retirement, looking for a couch for their third house on the beach so their grandkids could stain it with chocolate ice cream when they came over. Doris and Bob probably wouldn’t have it any other way. Daydreaming about a similar future, Jade played with Regan’s fingers, pushing on the pads lightly, like they were the keys to her sister’s old Casio keyboard, the one she’d lock away so Jade couldn't get her sticky hands on it. (Joke’s on her, cause Jasper knew where she hid it). 

And, did Regan really just ask her about what she’d rather sit on? She quickly glanced down at her shoes, biting down the dozens of dirty jokes rushing to come out. She cleared her throat. “Oh, there is,” said softly, cause Bob and Doris did not need to hear about Jade’s sitting preferences. She could spare them. Cause even if the innuendo flew right over Regan’s head, she’d show her later anyway. “Yup, I love it when you compromise…” Where was Regan going with this? Oh. Nowhere bad, actually. “The frame can be wood or stone, that sounds super cute. Except you were so not thinking about the frame though, were you?” she gave Regan a skeptical look. The cats were something Jade was taking into account for sure, though. “Back in the apartment, we put scratching posts and pads everywhere so they wouldn’t care about the couch. It mostly worked.. but maybe we can get some covers too?” Cause, she loved her children like the most devoted mother would (at least she thought that was what mothers did), but this was obviously like, an investment for the future, she didn’t want it to be ruined in the first week. She didn’t want Regan to think that she wasn’t two hundred percent invested in this.  

“I really like…” she drew the L shape in the air, then nodded to the sectional couch they were approaching. She leaned in and pressed her cheek against Regan’s shoulder, closing her eyes when she felt her scent drifting. She was a little weak in the knees. Regan’s neck was truly a menace to society, no wonder she kept it covered a lot of the time. “It just feels like the prime snuggling couch, don’t you think? For purposeful holding only. All the extra space. And the nice armrest,” she sighed, staring at the gray… what was it, linen? The color was kinda eh. Or like, really eh. Which reminded her, she should probably let her non-negotiables be known. “I insist on soft fluffy cushions, think of the glutes, babe. I can compromise on material and color and shape, but like… what kinda bisexuals are we if we don’t pick a green one?” 

—

“There was no mugging,” Regan reassured Jade, though she didn’t really understand the question, “couches are not known for committing crimes, but the… leisurely attitude they encourage could be considered an unofficial one.” Jade’s voice had jabbed her with playful concern, and it was sinking in that it had been a joke of some kind. It still eluded Regan. She chalked it up as a Jade-ism she would need to conduct further research on so she could add it to her ongoing dictionary. “Well… I guess spare change ends up between the cushions, doesn’t it? Mugging.” Maybe that was what Jade meant. But probably not. Her bone partner seemed to have her eyes elsewhere as she teased her fingers (which was unheard of, actually, her looking at anyone else, so it must have been important). Regan followed Jade’s line of sight to an older couple. She made a mental note to keep her distance in case one or both of them were close to death. When her eyes flicked back to Jade, she still seemed caught up in her thoughts. Something light bubbled in Regan’s chest (indigestion?) as she guessed what was going on. And Jade was right for thinking it: that lady did look a little like the dead squirrel from the night they met over ulcers, stiff and grey. “I know,” Regan said quietly but fondly, Jade’s attention re-tangling itself up in her veins and arteries. “I see it, too.”

Regan was not superstitious; for most of her life, she couldn’t have been any further from it. She always thought that way of thinking was for the weak-minded humans, even though she had come to doubt that anyone had true autonomy – it was better to simply call it Fate and accept that it did not show its cards in the shapes of clouds or constellations at night. But Regan did listen to death. And if that older woman reminded her of the most important dead squirrel in their relationship, then it meant something. It was a reminder of how far they had come, wasn’t it? So Regan tried to keep her mind partially open, which wasn’t nearly as interesting as having an open brain. 

“The frame? No, I wasn’t talking about that. I meant instead of extraneous cushions. It would be nice and cool, wouldn’t it? You like that. Oh, and better for your posture than some… sack of feathers. Besides, how often would you be directly on the couch, anyway?” She might have known the answer to her earlier question about places to sit. Jade didn’t seem swayed. “I am attempting to compromise. We are getting a couch in the first place.” Her hardened expression didn’t last long, washed away by a simple raised brow and the soggy tide of Jade’s eyes. Of course there were things Jade wouldn’t budge on, either. And the sand always shifted under Regan’s feet when Jade asked something impossible of her (strange how it became less impossible when she slid enough to gain a new perspective).

The couch Jade seemed to like was oversized and she could imagine the pillows expelling down. Soft, fluffy cushions. Despite her best efforts, the thought put a scowl on Regan’s lips. She was trying to be human, and humans indisputably liked comfort (too much of it). But it was still hard to come face to face with such a deviation, to ask for it. Somehow different than ending up on Jade’s couch that she already owned, or purchasing one for Emilio that was far more self-indulgent than she would have ever allowed hersel– than she would have ever been allowed. But, again, a couch wasn’t only about her. And Jade’s gluteus maximus (and medius and minimus) deserved the world. “I do know your glutes… but… I mean, the cushions, if they aren’t made of stone, what if they’re too… and we should be disciplined, shouldn’t we? We’ll grow idle.” She hesitated. “I like green.” Her attempt to say she wasn’t so sure about this ended up being a rare mumble. 

When Jade made up her mind, she made up her mind. And… when Jade made up her mind, Regan did, too, now. [insert whipped vanilla pic]

When she exhaled what remained of her willpower, Jade’s face felt heavy against her shoulder. Trading one for the other hadn’t left her with regrets so far. [insert whipped vanilla pic again]

“There is a lot of space there.” Regan glanced down at her shoulder, where Jade’s bright eyes looked up at her. They said this was important to her. How did she do that, speak so loudly with a look? Even when neither of them said a word, Jade was never silent. Regan exhaled again, and it became an obvious sigh. Her hand slid around Jade’s waist, and she tugged her closer in some vaguely hug-like gesture that obviously wasn’t a hug, because she didn’t do that (her ‘last night on earth’ hug at the hotel didn’t count). “Okay. We can find a sectional like that. But the cushions must be removable. That’s… practical, anyway.” 

The store was a maze of couches, and while Jade might have been content bouncing from option to option, Regan needed a more organized approach. She scoped out the couch to the immediate right of the too-big one Jade had pointed out. A body could sink between the cushions and be preserved like it had been sucked inside a bog. They were huge and plush, so it met Jade’s specifications in that regard. It was also green – a muted pastel, not nearly saturated enough to be comparable to undigested bile. Remarkably, it might have fit the bill. For Jade, anyway. Which meant it fit Regan’s, too. She made an uneasy circle around this one as well, not trusting it. Her skin prickled like it was a familiar threat. “If only it were more cramped,” Regan mused, wondering if that was a concession Jade was willing to make when she thought about the end result of being cramped. Sometimes not being comfortable was better.

She alighted on the next couch. It was small, drab like a dead field mouse with only patches of its coat remaining, and it had a huge tag hanging off it (weirdly, it said the price was FREE?). Regan studied the whole couch first as if it could snap over her like a trap, and when she deemed it safe enough, she waved Jade over and checked out the tag. “Look, Jade, look at the tag. It lists the features. This one comes in a ‘suffocation’ model with an iron maiden mode.”

—

“Mmm. Phew! We don’t have to worry about the couches then,” Jade quipped after Regan explained that couches couldn’t be criminals. Her smile grew fond, smitten cause… why did she have the cutest girlfriend (er...bone partner, her bad) in the world? She won so hard, it was still like, wild to believe it. Their story grew more epic with time. Jade had lost her, then she came back, then they decided there was no point in being apart. And now they were buying a couch. Pacing around the store just like Bob and Doris (just in a sexier way). They were ready for the movie! (She didn’t think there were many options available to play her though). Anyway, it made her feel super validated to know she was right about them from the start. (The biggest kind of satisfaction). And like, sure a couch wasn’t much, but it was symbolic. It made the relationship feel serious. Which, obviously, it wasn't how she liked things to be. But when it came to Regan? She’d be the most serious person in the world. And to go back to the second cutest couple in Just Couches, Regan had also taken interest in them. Was she also thinking about the future? Did she envision buying more furniture with her? Did she think about all the fun they could have painting the walls baby blue? Or like, all the friends they were gonna host? It would be like, so many pounds of banana bread to feed the guests! 

Regan’s eyes were sparkly as she spoke, and Jade thought all those cliches about getting lost in blue eyes like they were the ocean kinda came up short when Regan had that dreamy haze about her. I know. Her stomach fluttered, cause Regan said she saw it too, and… look, considering the recent mishaps in communication, there was a fair chance they were on like, totally different wavelengths. It could mean anything. But Regan’s gaze didn’t lie (it literally couldn’t since the moment they met), there was love swimming in it. And Jade drowned for a moment, not caring about whatever words were being exchanged. She squeezed Regan’s hand, resisting the urge to go full on PDA, cause… well, she didn’t care they were in public technically (and neither did Regan if her past record was any indication) (Like, the cemetery, really?), but maybe if they behaved now, they could misbehave later, in like, a more ideal situation.   

And see, look at how serious she was taking couch buying! Cause there was going to be so much negotiation involved in getting the perfect one. And Jade wanted the perfect one, the 8.2/8 on the Bloodworth scale. If Just Couches wasn’t the one to provide it, then they’d go elsewhere. (She really hoped it didn’t come to that, though. The Just brand had never failed her before). Regan talked about frames and extraneous (?) cushions, while Jade looked up at her, batting her eyelashes. It was innocent, but she did like seeing Regan try to dictate her terms only for her convection to deflate by the virtue of some consistent eye contact. She finally broke it, letting Regan muster up some new resolve. In the meantime, she pressed a kiss to her shoulder. (Clothed, sadly. But a good shoulder either way). 

Had she not thanked Regan enough for fighting against herself just to please her? Welp, that had to change. “Thank you for doing this, babe. I so appreciate it, you know. I'll show you how much when we get home, maybe... You could even get to choose the how?” Another flutter of her eyelashes, this time less innocent. Watching the rise and fall of Regan’s chest pick up just a bit was totally worth it. It meant she was in the mood to be persuaded. “What if a couch’s purpose is literally to allow for idleness? We’re allowing it to fulfill it. We’re so responsible.” And who knew more than the two of them about the struggle to carry out one’s purpose? But this was always gonna be a fun game of thumb wrestling. At least Regan wasn’t opposed to the color of their couch being green. “Yup, I know you do, babe” the amount of green in Regan’s closet had totally skyrocketed since they got together. She was such a sap. The dampest of them all. (And she’d chosen to share her dampness with Jade. Which, again… felt like winning the lottery).  

But even if she liked green, Regan looked a little lukewarm about the particular couch they were judging. A little whelmed. Cause even if this one was the right color (so a total plus), it seemed to be too big according to Regan, which sounded like a bad thing. Jade let her go to examine the couch for other flaws, knowing soon enough Regan would need her pressed up against her again. And yup, sure enough, two beats later she felt Regan’s hand tugging her closer, reeling her in. Right. Too much space was a bad thing, how dare she forget. (She couldn’t question Regan’s methods here). 

Jade met Regan’s gaze again, checking in with her. She’d learned by now, what those eyes revealed about Regan. When she was asking for help, or when she was done listening for the time being. She knew when they hit a roadblock, when Regan was done expanding, when it was time to relent. Or when, despite everything, a last minute push was needed. It used to be a push and pull, but it was more of an ebb and flow these days. Right now, her eyes read open. Hesitant, but open. So a little more encouragement could still go a long way. "A sectional then. And we can totally get removable cushions. That’s like super smart, anyway. But smaller, yeah? Cause you'd miss me too much, hm?” she quirked an eyebrow, then shook her head, pretending to be offended. “You just want me on top of you," and there was nothing wrong with, like, a cozier couch, that was true. Maybe she was focusing too much on choosing something to show off, instead of finding something for them. 

Regan was fine with a sectional, which was a step closer to finding the one, even if it wasn’t the pastel green they were in front of. Jade didn’t like this shade of green, anyway, she could admit that, cause it wasn’t pastel-y enough to remind her of mint. So to recap, no velvet, not too spacious. And no fixed cushions. That didn’t sound too restrictive at all. 

And oooh! It seemed Regan had found the one, judging by her voice. Her eyes darted from the green couch they were leaving behind to the new contender and… huh. It sure was a couch. Or was it a giant mouse cosplaying as a couch? Hard to tell. It was exactly the type of couch white people would fall for in a movie, and then they’d be haunted forever. But like, the FREE tag was tempting, totes. Why exactly was Regan in favor of this? Oh… as if reading her mind, Regan read the couch’s attributes. Of course it had a suffocation model. Not exactly what Jade looked for in a couch. (But like, she made a mental note of stopping by a different store when they were done looking at couches, maybe Regan could find something that would suit her taste there). 

She rolled her eyes, an affectionate laughter bubbling softly. “Stop it.  I love you,” she whispered, light and easy. Four months ago she wouldn't have dared to say those words, even as she was choking on it. But now it was as easy as breathing. And she was tired of sideway glancing stuff, so she shifted until she was facing Regan. She rubbed along her bicep, loosening Regan some more. “I want you to have comfort, I want your back and your thighs to touch the softest surfaces. I want you to feel like you’re literally sitting on a cloud,” Regan’s right eyebrow twitched, and Jade was so charmed. “Figuratively, babe. I know we can’t sit on clouds and it would probably not be a super great experience. And hear this: You could still sit on the frame for a few days. Test it out,” her eyes twinkled playfully which should’ve warned Regan she was about to rile her up. “I get the vibe you’ll cave in a few hours… Once you realize what’s on the other, superior side, anyway,” she wiggled her eyebrows, reaching for Regan’s hand to coax her away from the weird mouse couch, trying not to look back in case she had that wistful look in her eyes or that pout on her lips that made Jade agree to silly things.  

A deep burgundy couch came next, which kinda remind her of wine. She liked wine! Plus she kinda liked the color too, even if it wasn’t bisexual green. “I have nothing to hate her for, actually. She’s innocent. But it’s not… it doesn’t feel like it, how about you?" Before Regan could share her take, Jade glanced to the side, to a striped black and white model. Ooooh, like a piano, obviously. Nothing else. It was weird that the tag advertised it as the ‘quietest couch in the world’, though. What did it mean? Why would a piano couch be quiet? Was it that the base didn’t squeak or screech if dragged across the floor? Actually… that might not be too bad of an idea for them. The concept was very confusing though, so she tugged on Regan. “She’s giving me mixed signals, which is only hot when you do it.” Skip! 

—

The longer they were there, and the more they “compromised” (Regan was persuaded), the more obvious it was that Jade’s heart swelled at the thought of the perfect couch. Regan’s fingers trailed up to Jade’s wrist, capturing some of her pulse for herself; she wished she could borrow some of Jade’s certainty, too. She thought, at least, that they understood each other in this. The couch was meaningful to Jade because it was the first staple in the weepy incision that was their future together (it was a good incision; a surgical one, a healing one, and it wept profusely). Couches were meaningful to humans, to families, to couples – like that squirrely pair now approaching the first overly-bloated couch she rejected. 

Regan saw understanding in Jade’s patience, too. Maybe she realized more about Regan’s trepidation than Regan even did. That often seemed to be the case. Did she know that when she’d kissed Regan’s shoulder, hours of tension drained out of it? (And went lower, actually.) For someone who was new to planning, Jade’s actions sure had some suspiciously desirable consequences at times. Could Regan counterstrike without getting the two of them banned from Just Couches? Probably not. Did she care at the moment? …Not enough, but her law-abiding sensibilities gave her just enough pause to think better of removing any clothes. They could stop by a cemetery after this. If they did, would they be able to write the couch off as a ‘business expense’ due to Jade’s slayer credentials? Okay, that was a stretch.

Even the word stretch had become problematic. And the thank you? The tantalizing form of said thank you? …In a couch store. “Why are you like this?” Regan breathed, one of those stupid, almost human smiles on her face. The most beautiful eyes beamed back at her. How could she not fall into them like the deepest of bogs? Jade’s whole face glowed with love and… couch. Right. This was improper conduct at a Just store. She gave Jade’s arm a small tug then released her hand, because she needed both of them to be able to focus again– this was a particularly laborious mission, wasn’t it? 

In any case, it sounds like they more or less agreed: a sectional with removable cushions. So Regan could remove the ones under her own butt, and Jade could slide it under hers to double up and feel taller. If they could stay off of each other, which they couldn’t. Fearg an chinniúint, it wasn’t even worth asking herself how this had happened, because she had her answer every time her eyes landed on Jade. I love you came so easily to Jade now, didn’t it? It did to Regan, too, even if it stumbled at her mouth or keyboard sometimes (a work in progress along with all other expressions of emotion). And so much for behaving, because Jade had a lock on her, straight into her eyes. They could have been in a store called Just Jade, for all Regan noticed.

She also couldn’t really argue against Jade wanting something for her. Regan huffed once, then twice as the cloud comment was clarified. They both knew this was a losing battle (for Regan, as always). “They already do touch the softest surface on a daily basis. I don’t need to be on a couch for that to happen. Siobhan wouldn’t sit on a couch.” Actually… “Or maybe she would, because she no longer has a need to avoid such things. But it’s a slippery slope. If I’m comfortable on a couch, what’s next? A mattress pad? Cashmere sweaters?” She was, unfortunately, completely serious. Persuasive as always, Jade was. Regan groaned at the word test, because Jade knew she had this by making it experimental. “Credit me with more than a few hours. My mind is not so easily changed unless in the face of compelling evidence.” She reached for Jade’s arm and leaned toward her, because she appreciated the sentiment she argued against. “I’ll last at least four just to be right. Have you ever tried not sitting on a cushion, hm?” They both knew the answer to that. “Hey. This isn’t a bog or a cemetery.” Regan breathed a shaky sigh, like that ever helped her release any tension. “I think we’re supposed to sit on the couches to try them out. Not what we’re both thinking. Mostly you. I behave.” 

If Jade had been trying to lead Regan to another option without having her think twice about the patchy mouse hair couch in the rearview, she succeeded. She noticed the new contender. The color was okay, though she found it wanting for more brown. Then it might evoke dried blood a little more. It was a dead ringer for zinfandel though, wasn’t it? Maybe that’s why Jade seemed to be admiring it (when not looking at her), despite it not being the green they had discussed. Also, were couches gendered now, or was this similar to when Jade spoke of other inanimate objects as being female? “It looks like an ordinary couch to me. How can you tell when one is it? Are there any actual criteria, or are you going to tell me it’s more of an intestinal feeling?” Regan considered her own question and glanced at the red couch again. No. Her intestines did nothing other than obediently digest lunch. “When I bought Emilio a new couch, I asked them to select it. I didn’t care. My goal was getting rid of the old one. They could pick for us, don’t you think? I expect only couch experts to work here.” 

Jade had spoken, though. Not this couch. Onto the next. Which was larger, with deep cushions that were almost dizzying to look at due to the black and white vertical striping. “I like the color, if not for the stripes.” So solid black, or white. “More of a flesh color would be better, actually. Solid. Maybe in leather?” Out of the corner of her eye… had the couch moved? It almost seemed to shrink away when she spoke. Regan shot a harsh glance at the couch, the very same kind Jade thought she might have been receiving from the couches earlier. Had Jade seen it? Or was this one of those things that only she was gifted to see? What did it have to do with death? Regan’s face scrunched up when she noticed the description on the tag. Quietest couch? Absolutely not. “I would sooner buy a screaming couch than an exceptionally quiet one.” Neither of them were good at silence, and Regan held disdain for it, seeing it as an insult. The idea of a screaming couch perked her up though. “Do you think there is a screaming couch here?” She motioned toward the next in the row, ever hopeful. 

Regan lifted a brow at Jade’s assessment. “My signals should inspire the utmost certainty. Like right now, you can tell you’re able to walk all over me. Not literally.” She twisted her lips. “That, too, though.” And… the couch? This one was completely flat. No cushions at all, other than outlined suggestions in chalk. It was more of a drawing of a couch on the ground than a real couch. Because that’s what it was. “This one! What do you think?” Once more, ever hopeful.

—

Her laugh returned as she watched in real time how easily Regan folded with a few suggestive words. Really! It was just called having manners, nothing more. Why wouldn’t Jade thank her all the time? (And well, especially if she got that reaction). Anyway, her laugh grew in volume, but not enough to sound like a hyena. Cause she didn’t wanna disturb the older couple. She squeezed Regan’s fingers, but the urge to draw closer and bury her face on the crook of her neck just to hold each other for a prolonged time (also known in some circles as hugging) was like, a true test. Why are you like this? Jade could barely think when she spotted the soft smile stretching on Regan’s face. If making her smile had been a duty, Jade would’ve been the GOAT, no doubt. (And she would’ve never ever questioned if she wanted to continue doing it) (Not that… anyway). “Mmm, I hear no complaints.” But Jade did use to wonder why she was like this. And not like her siblings. Or like her parents (cause if she were, then maybe they would’ve loved—) And actually, that same question had been making a real comeback recently. But when Regan said it, it felt like… it could maybe be a good thing. Being… Just Jade. 

Regan’s apprehension didn’t simply melt away, but Jade could see the small progress she made beat by beat, with a healthy mix of sound logic and shameful flirting. (And wasn’t that the most fun way to get through Regan anyway?) Plus, adding the removable cushions meant she didn’t have to fully embrace all of the softness just yet. Only until Regan realized that there was a superior side to the couch. (She was a smart cookie, she would get it eventually). “Siobhan totally sits on a couch, I’ve been to her place like, once or twice” her comment wasn’t needed, as Regan herself realized the flaw in her argument. And look, Jade was understanding of her concern about a slippery slope. (She’d been thinking about slippery slopes a lot recently) “You don’t have to be comfy in any of those things yet, just a couch, for now.” Did she… hear a ‘Ta-da!’ ding as she finished her sentence? The Just chains were amazing, weren’t they? She hoped one day she’d get to meet Mr. Just (Or Mrs. This had all the makings of a woman’s idea). “I can’t believe you want me to act like you wouldn’t look hot with a Cashmere sweater,” she sighed dramatically, eyes twinkling as they flickered back to Regan. If she could pretend it was for her benefit, she could probably get Regan to buy one, right? 

It was pretty cute, the way Regan believed she’d last for hours away from her. Adorable. She wasn’t gonna burst that bubble yet. More gloating for later. “I am compelling evidence, though,” and by the way Regan leaned forward, Jade was inclined to think she agreed too. Yup. And maybe she did let her eyes wander to Regan’s lips, but in a totally chill way. Cause they were in Just Couches, looking for couches. A gal knew about time and place. (Wasn’t it nice that nobody could contradict the blatant lies she told herself?) Regan did look like she had a cemetery or a bog in her mind though, and sure enough. Focus. Just Couches! Another laugh bubbled, cause Regan was openly joking with her. And something about that dryness in her tone and the quick wit, made Jade feel a little funny. “Wow, I can’t believe you’d lie about behaving while looking at me like that in a couch store,” she tutted, letting herself be pulled along before either of them could misbehave. “We’ll sit when we think we have one. It feels a little rude to sit on every single one.” Cause if someone truly desired that mouse looking couch, they should be allowed to test their cold, fluffy cushions in full glory.  

In front of the burgundy couch, Regan popped the most important question yet. (Nope, not that one) (She was pretty sure they were past that one already. But she should like, confirm some day, shouldn’t she?). How could they tell when they had the right couch? Jade didn’t ponder on it long at all, it was super obvious to her. She glanced at Regan, eyes soft but certain, “the same way I knew you were it. And how you knew I was it. The vibes, not vibrations, will come to you,” it was how she also knew that this burgundy couch was sexy, but there was a better one waiting for them. “Some would say it’s an intestinal feeling, yup. Like butterflies. Not the real kind. Like the ones we talked about at the cemetery,” the ones she felt that same night, looking across the ground to find Regan picking up a floral arrangement. 

It went without saying that Jade was letting no ‘couch experts’ decide where she and Regan would rest their beautiful behinds for the next few years. So the only acknowledgement she gave to that idea was a head shake, then moved onto the striped couch. Which, Regan wasn’t sold on it either, but like… not exactly for the same reasons. She wasn’t sure how she felt about a flesh colored leather couch, even if the leather bit of it kinda sounded sexy. She wouldn’t hate a leather couch, but she did worry a little about the cats. And… hadn’t they already discussed what the plan was to keep them away from it as much as possible? So, yup. She was warming up to a leather couch for realsies. And wait, Regan wanted a screaming couch? How was she not supposed to crack a joke about that? She nibbled on her bottom lip, sensing Bob and Doris strolling somewhere behind them. Nope, she couldn’t make any kind of jokes. Behave, she reminded herself. 

Thankfully, Regan was dutifully guiding them around the store, and if she could sense Jade was about to lose it, she didn’t even show it. When she was finally able to get back in the conversation, Regan had some thoughts on her signals, it seemed. “Oh, they do inspire certainty now. During the snail saga? Not as much.” But honestly? Who was she kidding? Then too. Jade always liked Regan’s signals, even when they pissed her off a little bit. Why else would Jade have been so persistent that there was something beautiful to explore between them?

Not as beautiful as the growth in their relationship, was the model Regan was pointing at. It was a drawing on the floor of where a couch should’ve been. And ugh, the way Regan pointed at it, hope sparkling in her blue eyes. It was unfair, okay? How dare she be the most endearing person in the world? And now she felt horrible, that she had to let her down. But she wasn’t gonna make fun of it. Even if she sometimes suspected Regan did this sorta thing to see how much she could push. Classic baby sibling behavior. Jade took it seriously. She rubbed her chin, pretending to consider it. “Well it is sectional, which we agreed to… But it’s missing my side of the cushions, isn’t it?” She raised a pointed eyebrow, like she was making the most logical argument in the world. (Cause she was). “I don’t wanna have to buy them separately,” yup. That was it. That was the reason. 

She tugged on Regan’s hand, distracting her from her dream couch, and stood on her tiptoes, doing a quick sweep of the store. There were like, so many couches. (Of course there were, they were Just Couches), but she focused on spotting the green ones. “Come on, there’s one there!” And sure, when Jade picked up pace and brought Regan along with her it meant they were bypassing a bunch of (probably) decent models in the process. And they weren’t really following any kinda order but, green couch! She speedwalked, giggling all the way to their next destination. A second (or third?) green couch. The cushions were so, so big on this one. Her feet would probably dangle if she sat. But it wasn’t huge to the sides, so Regan could still snuggle as much as she wanted. Jade was obsessed. She could probably hide like, several blades underneath. For defense reasons. She looked back at Regan, who was too far away from her liking. She needed more of her, so she got it, pulling her to her side. Hazel eyes greeted her first, and then she spoke. “I like it.”

—

Regan was a little unclear on how picking a couch was similar to falling in love, but she admittedly wasn’t an expert on either (she hadn’t done so terribly with the latter though, right?). Vibrations she knew; vibes, not so much. That was all Jade. Was she about to say this couch’s vibes were bad? Regan’s stomach tightened, because she wanted to defend this choice but logic was no counter to Jade’s decisions, sometimes. But when Jade spoke, it wasn’t about feelings that had no rational origin – instead, her concern was practical and cushion-related. “Would it be so bad to buy them separately? It means you could choose the color.” Currently, the couch – a simple outline – was the color of the floor itself, which was grey cement. It reminded Regan of headstones. Tasteful. A true classic. “You could get green ones. Or baby blue. Or maybe a nice pattern, like herring bones.” Regan looked at the couch again, a little more critically this time. “I suppose it is a little low to the ground.” Closer to the buried dead, she thought, optimistically. She knew when things became a losing battle, though, and Jade’s glutes needed to be as comfortable as Regan’s were sore. 

Jade was on a mission, and Regan barely kept pace as Jade surged through the store with more grace than any human ought to have. Every once in a while she’d pause, do a quick scan as if she had something in mind but didn’t see it, and then take off into a dash again. It was usually Regan herself doing this, in hot pursuit of death she was trying to pinpoint. The role reversal brought a small smile to her lips even as she was being pulled along. Regan chose not to interrupt such a delicate process. It didn’t take Jade long to find what she had in mind, anyway – like an osprey diving for a fish, she careened them toward a luxurious – and green – couch. If Regan had to describe the exact color, it would probably be, well, jade.

It looked far too inviting. This was a couch that would destroy one’s posture, reduce the firmness of the buttocks, and, who knows, maybe murder your family. It looked like the kind of couch Regan might have needed to leverage up to rescue a flattened decedent who had died underneath. The kind of couch with pillows ideal for committing a homicide via obstructive asphyxiation. Regan didn’t trust it, even if the color did remind her of the precious ring on her finger and the woman next to her. Curiosity compelled her to check the tag, which showed a reasonable price and, like the other couches, listed some of its features. Regan raised a brow as she read them off. “One hundred knife storage pockets, a cup holder – singular, I don’t know where, vibration mode, night mode, couch mode, disco mode, flotation mode, and includes one year of membership into the Just Club.” At least the membership was nice. And Jade would appreciate all the knife pockets. Regan wasn’t yet convinced.

But when she looked into Jade’s eyes – okay, the comparison to love started to make sense. Jade might have simply said she liked the couch, but Regan recognized what want looked like on her face. Jade was probably picturing the couch in all kinds of homes, thinking up decorations, carpets (Regan was also opposed to carpets), a fireplace. And, what Regan was most certain about: she was thinking about both of them on it. Suddenly all of her distrust hardly registered. Just like Regan had come around to soggy fries and chocolate so bitter it made her mouth pucker for hours, she would also come around to this. Probably. Maybe.

“What have you done to me?” Regan said under her breath, unsure if it had been in English or Irish, but with some amusement either way. Regan leaned against Jade, her head rolling to the side to rest on Jade’s shoulder. “You can’t go around telling everyone that I never say no to you, even if it’s true, okay? But I think I could absorb the look on your face right now forever, like decompositional fluid on a white shirt. So if this couch makes it stick – again, like decompositional fluid on a white shirt – then we will get the couch.” And even if seeing that beautiful shine of desire on Jade’s face forever was unrealistic, Regan would keep it there for however long the two of them would have together. And then even after, could she conjure it back up if she brushed her fingers over Jade’s maxilla and mandible, hundreds of years from now?

“Not so fast, though. Can we get both?” Regan tilted her head, making sure the depressing fluorescent lighting of the store hit her eyes now. “This one, and the flat one. A couple of cushions and you wouldn’t mind, right?” Plus it seemed compact enough that both couches could fit both in a storage unit, should they choose to reside there. “I don’t know how you expect me to stay awake during an entire movie on this thing. Which, come to think of it, we should ask if there’s a matching mattress that comes with the other couch, just as firm.” Jade’s eyes were quick to call her out. “Fine. An ottoman?”

—

Jade was totally sure she didn’t want to buy separate cushions. Like, almost as sure as she was of the ring on her finger and the meaning behind it. (Almost. The idea of baby blue cushions did give her a small pause). Nope, no cushions for the imaginary couch. In the meantime, Regan had found another con, and Jade latched onto it. “Mmmm, it's so low. If I wanted to be that low I would get one of those puffy beanbag chairs…” She trailed off, cause actually! Her eyes lit up at the idea. Weren’t beanbag chairs so comfy and cute? The best part is that they wouldn’t be able to get up after, they would be stuck there till the end of times. Kinda like her bog. As much as she was vibrating in excitement, she decided to spare Regan of her new genius idea, though. On the account of her mourning her dream couch. This way, they both lost something, didn’t they? It was a super fair exchange.

Plus, they had found a real contender now in the green couch, so beanbags were forgotten. It was promising that Regan was examining this one without the same stiffness she had the others. Maybe she had been exposed to so many comfy couches already that she had warmed up to them. They weren’t just torture devices anymore. Jade got her hopes up, for real. And oh! She hadn’t even read the tag yet. “Knife pockets!?” Wasn’t that like, so convenient and perfect? How did Just Couches know? That was probably why the Just chains were so popular. They catered to every interest. But, forget about knives (you heard that right), what was that about different modes? She moved closer to read the tag too. (And to get a better look at that sexy eyebrow Regan was rising) (Mmm, the right one). Yup. Disco mode? Vibration mode? They had to try all of them. Her excitement skyrocketed. And at this point, she was bracing for like, major disappointment if Regan decided to pull the plug for any reason. “Do you think this is couch mode?” she mused. Maybe it was store mode. She dragged her eyes lower, finding out about the Just Club membership at the same time as Regan. “I wanna go there, we are gonna go there,” she let out a dreamy sigh.

Her hand found Regan’s waist, pulling her closer. Sparkling eyes darted between her dream couch and her dream woman. (Wasn’t it weird, to be so freaking blissful at a couch store?) She didn’t have to say it, Regan could read the pretty please all over her face. And she got to see in real time how Regan melted to her mushiest version. Ugh, adorable. She snickered and not satisfied with a head on her shoulder, she nudged Regan so they could see each other. “Never. It’ll be our little secret,” she whispered, face inching closer just cause being in Regan’s orbit did that to her. She wasn’t gonna bring up the fact that a lot of people could probably already tell anyway. Cause there was nothing wrong with a small dose of delusion. Regan said yes to the couch, and Jade gifted her one of those smiles the other loved so much. It was a fair deal. In fact, she wanted to make it an even better one. Cause Regan was setting aside her own doubts and fighting her demons to find a comfy couch for her. It meant like, so much. She leaned in, for the faintest brush of their lips. And when Regan needed a little more than that, she gave in too. Cause Jade aimed to please, always. But she kept it sweet and gentle, okay? So nobody could come and yell at them to ‘get a room’ (which, knowing them, would've been more of an encouragement than anything else).

Parting was always the worst part, but she stayed close, enjoying the softness of Regan’s skin against the tip of her nose. No one ever warned Jade about how addicting that softness would be, but she had zero complaints. “You’re gonna love it too, I just know,” and when had she ever been wrong when it came to Regan? Reluctantly, she put more distance between them, cause they had a store clerk to call and like, sort out the purchase. She reached for Regan’s hand when her words stopped her. “Hm?” Both… what? Oh. Nope, actually, she was back to blanking on what Regan was trying to communicate, her two brain cells short-circuiting a little bit when she saw the fluorescent light reflect on Regan’s eyes. She could stare at her all day, and that was not a hyperbole. She had to restrain herself from going for another kiss. And shoot, right, Regan was talking. “I don’t see why not,” and maybe, that was her gayness talking, what about it? She knew Regan would ditch the outlined couch the second she saw Jade sprawled on their fancy green couch, ready to be snuggled (those back examinations were gonna hit so hard). She let out a cackle. “A matching mattress?” so, like… made of air? Those were a real thing. Except Regan probably meant another rectangle taped on the ground. Her eyebrows pinched together, and Regan came in hot with a correction. She laughed again, feeling extremely waterlogged. Regan was so sure it was her who never said no to Jade’s whims, but did she know how hard it was for her to not go along with every silly idea that popped into Regan’s head? Especially when there was a smile that reached her eyes? Hardest thing she’d ever done. Forget about hunter training. “Yup. We can get you an outlined ottoman, baby.” So really, why say no? Her hand reached down, giving her a love pat. “Come on, let’s find someone, before we end up agreeing on the free mouse couch too”.

[canmom]

No, this is not non-Euclidean geometry. Euclid was perfectly au fait with curved lines, the Greeks used them all the fucking time (think of all those ruler-and-compass constructions), and more to the point, constructing a circle is literally the third Euclidean postulate. You can construct this shape perfectly well within a Euclidean plane, such as your computer screen. Non-Euclidean geometry is generally speaking something subtler: a space where parallel lines can meet or diverge.

For a super basic example, here's a triangle with three right angles constructed on the surface of a sphere:

You cannot construct a triangle with three right angles in a flat plane, so this is non-Euclidean geometry (to be specific, the surface of a sphere does not obey Euclid's parallel postulate). On a sphere, the 'straight line' (which we generalise with the notion of the geodesic) is a great circle, so you can construct 'polygons' using great circles. The interior angles of a triangle constructed on the surface of a sphere will in general add up to more than 180 degrees.

The 2D surface of a sphere is not all that weird to us 3D creatures, since it can be easily embedded in a 3D Euclidean space... but there are many more, much stranger curved spaces in mathematics than this, particularly when you start considering higher-dimensional curved spaces. There are a few games out there which are all about playing with non-Euclidean spaces, such as Antichamber or HyperRogue. There are also some great visualisations of curved space on ZenoRogue's channel, such as this one:

As much as Lovecraft could get freaked out by some pretty innocuous shit (e.g. penguins), there are some pretty damn weird spaces in mathematics, and I think if you found yourself in one you'd be less than chill about it. (I mean, if physics even worked there.)

That said, our universe is actually a 4D curved spacetime, so you are in a non-Euclidean space right now. That's what gives us gravity! The geometry on the universe is on very large scales, and in deep space, approximately Minkowski space, which is sort of like Euclidean space but the time dimension works a bit differently. Close to a massive object, it gets more complicated - some structures like a spinning black hole (Kerr metric) even permit you to go in a time loop if you're on the right trajectory.

I love seeing a meme and being like oh, tumblrs going to love this one

[edgythoughts]

Why are irrational numbers non-repeating decimals?

You’re here — which means you already know that irrational numbers are decimals that go on forever and never repeat… but your brain’s like, “Okay but… WHY though?” 😩 Let’s skip the mathy snooze-fest and get into this like two friends trying to figure it out while doodling on a notebook margin in class. Grab your brain snacks — we’re diving in. —

Why Are Irrational Numbers Non-Repeating Decimals?

Alright, first things first: Let’s break down what the heck irrational numbers even are. 🧠 Irrational numbers are numbers that: - Go on forever (infinite decimals), - Don’t ever repeat in a predictable pattern, - And most importantly: can’t be written as a neat little fraction like a/b. Now let’s get into why their decimals are so dang wild. — 🥧 The PI-cture of Irrational Numbers (Yes, like π) Take Pi (π) as the poster child of irrational numbers. It’s 3.14159265358979… and it just keeps going. Forever. No pattern. No rhythm. No way to “guess” what comes next. It’s the math version of a chaotic playlist on shuffle. If Pi repeated like 3.1415926535—6535—6535… then it wouldn’t be irrational anymore. It’d be a repeating decimal. And repeating decimals are always rational (which means you could write them as fractions — we’ll explain that in a sec). So basically, irrational = the opposite of neat and tidy. —

🧮 But Why Don’t They Repeat? Okay, imagine this: - Rational numbers (like 1/2 or 5/6) can be written as fractions. - Every fraction, when you divide it out, either ends (like 0.25) or starts repeating (like 0.333…). That’s because fractions are built from whole numbers. There’s only so many possible ways to divide whole numbers — it’s a limited toolbox. But irrational numbers? They’re not born from neat divisions. You can’t make them from a/b, no matter how fancy the numbers get. So their decimal form? Totally unpredictable. Think of it like someone drawing forever with no pattern. They don’t circle back. Ever. No loops, no echo. And since there's no underlying "division story" holding them together, the digits never settle into a repeat. — 🔢 Real-World Example: √2 Let’s look at the square root of 2. It’s about 1.4142135… Try squaring a few random fractions like 3/2 or 7/5 — you’ll get close, but never exactly √2. Why? Because √2 isn’t the result of any a/b fraction. Its decimal never ends and never repeats. It’s like the universe is teasing you with “almost” — but never “exact.” That’s the flavor of irrational numbers. — 🪄 So... Can a Decimal Repeat and Still Be Irrational? Nope. As soon as it repeats, it's like “Tag! You’re rational!” 🎯 Even something like 0.121212... is rational — because it follows a pattern, and you can turn it into a fraction (fun fact: 0.121212… = 12/99). Irrational numbers are that extra level of wild — not just infinite, but unpredictably infinite. — 🧁 Quick Recap (aka snack-size version): - Rational = fraction = decimal ends or repeats - Irrational = not a fraction = decimal never ends or repeats - Repeating = predictable = rational - Non-repeating = chaotic = irrational - So irrational numbers are non-repeating because they don’t come from neat, closed divisions like fractions do. That’s the tea. — 📌 Disclaimer: This easy version is meant to help you understand the concept better. If your exam or teacher expects a textbook explanation and you write this one instead, we’re not responsible if it affects your marks. Use this for understanding, not copy-pasting. — 🔗 Related Articles from EdgyThoughts.com: What Makes Non-Euclidean Geometry So Different 2025 https://edgythoughts.com/what-makes-non-euclidean-geometry-so-different-2025 Why Does Time Move Slower Near Massive Objects 2025 https://edgythoughts.com/why-does-time-move-slower-near-massive-objects-2025 🌐 External Resource: Wanna dive into the full mathy universe of irrational numbers? https://en.wikipedia.org/wiki/Irrational_number Read the full article

[omegaphilosophia]

The Philosophy of the Circle

The philosophy of the circle examines the symbolic, metaphysical, and mathematical significance of the circle as a fundamental shape, reflecting ideas about unity, infinity, perfection, and cyclicality. The circle holds deep philosophical meaning in various traditions, from ancient cosmology to modern geometry, and is often associated with wholeness and the eternal.

Key Concepts:

Mathematical Foundation:

Geometric Perfection: The circle is considered a perfect shape in geometry due to its symmetry. Every point on the circumference is equidistant from the center, embodying the concept of equality and balance. Mathematically, it is a key figure in Euclidean geometry and serves as a foundational shape in trigonometry and calculus.

Pi (π): The relationship between the circumference and the diameter of a circle is defined by the constant π, an irrational number. The infinite, non-repeating nature of π has intrigued mathematicians and philosophers, symbolizing the complexity and mystery of the universe.

Symbol of Unity and Wholeness:

Wholeness and Completeness: The circle, having no beginning or end, symbolizes completeness and unity. In many philosophical and religious traditions, the circle is a metaphor for the universe, eternity, and the interconnectedness of all things. It represents an ideal form in which all parts are equally connected to the center, embodying balance and harmony.

The Ouroboros: The ancient symbol of the serpent eating its own tail, the Ouroboros, is often depicted as a circle and represents the eternal cycle of life, death, and rebirth. It conveys the idea of cyclical time, self-sufficiency, and regeneration.

Metaphysical and Cosmological Interpretations:

Circular Time: Many ancient cultures, such as the Greeks, Hindus, and Native Americans, viewed time as cyclical rather than linear. The circle symbolizes recurring patterns, cycles of nature, and the eternal return. Philosophers like Nietzsche also explored the idea of eternal recurrence, suggesting that time may repeat infinitely in a circular fashion.

Sacred Geometry: In various religious and mystical traditions, the circle is central to sacred geometry, representing the perfection of divine creation. It is used in mandalas, which are circular designs symbolizing the universe, and in architectural forms like domes and labyrinths, which reflect cosmic order.

Philosophical Symbolism:

Infinity and Eternity: Since a circle has no beginning or end, it symbolizes infinity and eternity. Philosophically, it challenges the finite nature of human existence by representing something boundless. In this context, the circle also becomes a symbol of the divine or the absolute, as seen in concepts of God, the universe, and the soul.

Unity of Opposites: The circle can represent the reconciliation of opposites, as seen in the yin-yang symbol, where dualities (e.g., light and dark, male and female) are unified within a circular form. This notion aligns with philosophical concepts like the dialectic, where opposing forces or ideas interact to create a higher synthesis.

The Circle in Ethics and Society:

Social Equality: The circle has been used as a metaphor for equality and fairness in social and ethical philosophy. In a circle, no point is privileged over another, symbolizing egalitarian relationships where everyone is equidistant from the center of power or decision-making.

Circular Economy: In modern economic thought, the concept of a "circular economy" is gaining prominence. This philosophy emphasizes sustainability, where resources are reused and recycled in a closed-loop system, much like the circular flow of energy in nature.

Platonic and Aristotelian Views:

Platonic Forms: Plato viewed geometric shapes, especially circles, as representations of perfect, unchanging forms that exist beyond the material world. In his view, the material world is an imperfect reflection of these ideal forms, and the circle represents the purest kind of form, embodying perfection.

Aristotle’s Cosmology: In Aristotelian philosophy, the heavens were believed to move in perfect circular orbits, reflecting the idea that celestial bodies are part of an unchanging, divine realm. The circle’s eternal, unbroken nature was associated with the divine and the unchanging aspects of the cosmos.

Psychological and Spiritual Dimensions:

Mandala and Inner Wholeness: In Jungian psychology, the circle, often in the form of a mandala, symbolizes the self and the process of individuation—achieving a harmonious balance between the conscious and unconscious mind. The mandala represents inner wholeness, healing, and the integration of the different aspects of the psyche.

Meditation and Focus: Circular shapes are used in meditation practices to promote concentration and mindfulness. The practice of focusing on a circular object, such as a Zen circle (ensō), represents the simplicity, beauty, and wholeness of the present moment.

Challenges to Linear Thought:

Circular Reasoning: In logic and philosophy, circular reasoning is considered a fallacy, where the conclusion of an argument is presupposed in its premises. Despite this, the structure of circular arguments has been explored in fields like hermeneutics, where understanding is seen as a circular process—interpreting the parts in light of the whole and vice versa.

Critique of Progress: Linear progress is often contrasted with circular notions of time and development. Philosophers who critique modern ideas of progress, such as those influenced by environmentalism or postmodernism, may invoke the circle to suggest that development is not always forward-moving but involves cycles of repetition, reflection, and renewal.

The circle is a rich philosophical symbol that encompasses ideas of unity, infinity, balance, and cyclical time. It serves as a bridge between the finite and the infinite, the material and the immaterial, and the individual and the universal. Whether in mathematics, metaphysics, ethics, or psychology, the circle represents completeness, harmony, and the interconnectedness of all things. Its use in both ancient cosmologies and modern systems of thought reflects its enduring power as a symbol of the eternal and the ideal.

[delphiniumarchangelmoon]

Had a weird ass dream last night, guest starring Schlatt

So it was one of those all-nighter type dreams, the ones that really feel like it took 8 hours to get through it, so bear with me.

For context, if you look out my kitchen window you can see an empty lot diagonal to my back yard, and beyond it the street is split around a retention pond so the street behind mine kind of has a knockoff roundabout in the middle of it.

Anyway the dream starts with a bunch of dogs out on the sidewalk between the circle and the empty lot and I want to go give them treats, so I root around in the cupboard for for treats.

But when I stand back up all but one dog has been replaced with a cross???

And the last dog stands up and oh shit, it’s not a dog, it’s a person wearing a dogs head as a mask! What the fuck?

And somewhere in the middle of this sequence of looking away from the window and back (it’s like, five seperate instances of looking out the window) I see an orange jeep driving down the street behind my house and somehow I just know this car belongs to Schlatt, who is apparently my neighbor and I’m far too shy to talk to

I go out to the front of the house to tell my neighbors to get the fuck inside there’s a maniac on the loose, and I’m also dead set on fighting the guy for some reason idk I always turn into a goddamn action movie protag in my dreams I’m always ready to throw down.

But, I can’t because between me and the fence lead g to the empty lot there is, I shit you not, an angry water buffalo.

So I scream for everyone to get inside because now there’s a maniac and a water buffalo on the loose. And they do. And we have a moment if “well wtf do we do now?”

I don’t remember how we all got to this decision but everyone went to the other end of the street and all gathered in a specific house. And some of my cousins were there, and the kids all left to go practice shooting (we all apparently just. Accepted that there was an apocalypse I guess? So the kids were shooting guns idk)

But after a minute I’ve of the kids comes back and screams that my younger cousin (wheelchair bound, this is notable) has also lost his mind and gone rogue.

So I take the girl and run back to my house and ask her to explain what was going on. But her story doesn’t line up, she says he attacked her and his sister but it shouldn’t be possible given how easy he is to outrun or subdue with his specific medical conditions.

I realize this about the time she does, and she attacks. I parkour around my garage like gravity doesn’t exist because it’s a dream and I can, and escape out the back door and hop the fence.

I then see the orange jeep driving fine the road again, so I wave it fine and ask the driver (literally just done dude) if he’s with Schlatt. He says he is and tells me to get in when I say I’m being chased.

While he’s driving us back to their house (which takes way longer than it should and we are definitely not going the correct direction but my dreams are rarely Euclidean so I’m not surprised) I explain what I’ve discovered about this seemingly contagious madness

We get back to the house and I am face to face with Schlatt and desperately trying to play it cool, but I hardly get a chance to say hello before the guy who drove me in says something about “releasing a prototype”

Schlatt freaks out—apparently this was not a good idea—and tells me to hide.

I run through the house and start locking doors behind me, I find a (badly) hidden door that leads to a bedroom with a back door, I lock it behind me and run, internally monologuing about how I can’t trust anyone, I have no idea who’s been infected.

I get ahold of a phone and somehow log in to a chat room with Schlatt and his friends, they tell me to come back to the house, it’s safe now, but I don’t listen. Instead I break into a random house and hidden under a mattress on the floor

and then, just as it was getting good…

…my alarm goes off and I wake up.

Tl;dr imagine a zombie plague but they retain all their intelligence and have no visible sign of infection until they’re trying to kill you and also Schlatt is there for some reason

[the-city-in-mind]

The Aesthetic City looks at the new Cayala district of Guatemala City, designed from the ground up by Estudio Urbano with Léon Krier.

It’s a human-scaled, mixed-use, moderate density development using traditional town planning principles, incorporating a mix of Spanish colonial, classical, and indigenous Mayan architecture; it’s designed for the local climate, and is a carfree / autoluw environment.

People flock to it. They spend money there. It’s such a success, new developments nearby advertise how close they are to it.

I don’t want to say “see, this isn’t hard,” because in our current car-centric, Euclidean-zoned planning environment, with every type of NIMBY group waiting to complain about the nerve of other humans to exist within their field of view, it’s very hard to build something like this.

Cayala succeeded because it was an entirely private real estate development on privately owned land, whose owners could have built a cluster of generic five-over-ones that would degrade in a tropical environment, but chose instead to allow themselves to be won over to this kind of vision.

If I were king of Chicago I would insist that this be the norm, and that when parts of land are up for redevelopment or expansion, this kind of process and insistence on high-quality, detailed building be mandatory.

Thinking again of the area around the UIC Circle Campus, the weird dead zone in the Motor Row District / South Commons hospital campus, or any of the clusters of office parks out towards the airport or Schaumburg, there has to be a strategy to rehabilitate these non-places into real places.

[taperwolf]

There's many things that could be upgraded in my Eurorack case, but its biggest actual failing is that out of 16 modules, only four of them have any kind of blinkenlights.

(Those are the two Sigma function generators, the Within the Scope oscilloscope module, and the DSPFX effects box — and of the latter two, the first uses an OLED screen and the second just LED 7-segment displays, so they're kind of borderline.)

[happi-tree]

Terrow and/or oakworthy?

Hey, Rae! Hope you're having a beautiful day 💜💜💜

First up: Terrow!

While they're not my absolute favorite of the kiddad ships, I love them and also their potential dynamic! I diiiiiid have a fic idea lined up for them at one point that is still very dear to me so mayhaps. Eventually. I'll give it a shot sbdfakbffs. I think they'd be SO cute together and... I don't want to necessarily say good for each other bc like there still would definitely be issues but maybe the two of them would actually be one of the pairs to talk out their issues. I really think Terry and Sparrow have such an interesting dynamic to explore - they're both such observant people and kind of the therapist friends of the group by default (Sparrow as the lovewolf, Terry as the son of a therapist). I'd love to see how they'd navigate a relationship together - it's something that holds a lot of potential to me!

Up next: Oakworthy!

THEY ARE. SOOOOOOOOOOOO GOOD I NEED THEM TO KISS I NEED THEM TO KISS PLEASE FOR ALL THE GROSS TEENAGERS OUT THERE!!! Okay now that that's covered I think Oakworthy actually has so much depth to it beyond them being gross weirdo overdramatic rival(!!!) silly guys in love (though that very much is an important and vital part of their appeal). Normal and Hermie are both struggling so much with their identities this season and kind of. Foil each other in that respect. And what is SO interesting to me in the aftermath of episode 31 is where it all goes from here (obviously). Like, Normal's entire life has been turned upside down with the revelations about his family, the discovery of his powers and his attunement to the Doodler, and he threw off the identity he so desperately clung to in order to help his friends fight for a better world and save his family and fix this catastrophic mess. And now, with Teeny stolen, there's a very real chance that Normal can never get that part of himself back, creating even MORE identity issues and problems in the process (Normal is a cleric and Teeny is his idol, and having that taken from him is devastating on so, so many levels as both the source of his power and of his personal beliefs and ideals). On the flip side, Hermie ALSO had no idea what the fuck he was getting into - he just wanted the costume, but he just had to commit himself to the performance and in the process he learned that (1) something is inherently fucked up with these teenagers and also they're probably the only ones who can stop,,, whatever happened to Tony Pepperoni at the dance, (2) the world is ending apparently? has been ending???, (3) he's adopted, and (4) he's never been human because he's actually half non-euclidean trickster and half demon. Like, the "I'm either disassociating or this is who I am" line is SO MUCH to me actually. He just wanted to do something for his school and then he ended up with his entire identity stripped away from him! Who is Hermie? How is he supposed to know? And then, after everything, he goes and circles back and steals the mascot outfit - and, I might be eating my words with this one come Tuesday, so take this with a grain of salt - he steals Teeny, and this reads to me like he's doubling down on the person he used to be and reprising that role in an attempt to mentally push down those feelings of not knowing who the fuck he is anymore. Which, you know, valid! But his actions are stripping away a huge piece of Normal's identity in the process, therefore rendering Normal incapable of doing the very thing that Hermie is attempting to do - use his previous persona as a sort of safety net, a safer place to return to from a bygone era when things were simpler and he was just a regular kid, more or less. And I think that there's something pretty poetic about that.

Oh my god, that got long. Um, yeah, anyway, I think the world needs more representation of disgusting weirdo-for-weirdo teenagers being in love and I think Oakworthy should be that representation. Please I need them to kiss. Like. Pretty please I'm begging.

[ckret2]

(Just realized that I accidentally put the above reblog on the original post instead of on the reblog it was actually replying to... oops.)

@anisecandy said: Homebrew flatland gender discourse to drive Bill mad: "can a LINE identify as a rectangle"

Now, something like "can a line identify as a rectangle" or "can an octagon identify as a triangle" or anything else about shapes identifying with different sides is loosely equivalent to "can someone who's AFAB identify as male." Your answer to that question determines whether or not you're on board with trans issues at all, and probably correlates with a lot of your other opinions on flatland politics.

"Can a trapezoid identify as a rectangle" is more like "can a guy identify as a butch." It's a niche question that you only hear if you're neck deep in the queer community and/or if you know somebody personally affected, but it addresses a facet of genderqueerness and gender nonconformity that only partially overlaps with mainstream trans issues.

Bill was born with a rare genetic condition that put him in contact from a young age with people who look like lines in Euclidean geometry but who are biangles in spherical geometry and want to be acknowledged as such; and his dad was a trapezoid who usually called himself a rectangle because people knew how to handle rectangles more easily and he has a more rectangular sounding name and honestly his dad didn't think there was any real difference between an isosceles trapezoid and a rectangle besides furniture sometimes not fitting; and meanwhile all this is a game of checkers compared to the seething 4D gender chess match that's been playing in Bill's head since he was like ten but didn't talk to anybody about because he grew up in a cult.

And so very early on Bill "I'm Just A Triangle Trying To Save You From The Delusions Society Gave You" Cipher latched on hard to "I think anyone can do anything they want forever and who are you to tell them otherwise." Lines can be rectangles, trapezoids can be rectangles, rectangles can be circles, circles can be trees, hexagons can be prisms, octagons can kin dragons, whatever, be weird, get weirder. He's willing to get into fights over it, but he doesn't have to, because anyone who would've disagreed with him is long extinct.

Now Mr. Gender-Anarchist is one of the only beings left in the multiverse who remembers what his dead society's gender roles were like, and he gets aliens asking him questions like "what shape would I be?" "I dunno, you've got a pentagonal name I guess."

A conversation after the Pines find out about Bill's 2D home dimension like,

Mabel: "So what kind of a shape would I be in your dimension?"

Bill: "Easy. Pentagon."

Dipper: "What about me?"

Bill: "Another pentagon."

Mabel: "What about Grunkle Stan?"

Bill: "Heptagon. Seven sides."

Dipper: "So, is Grunkle Ford a heptagon too?"

Bill: "Nope, octagon."

Dipper and Mabel privately debate what this means. Do sides decrease with each generation in his dimension? So the grandparents & great-aunts/uncles generation has 7 sides, the parents/aunts/uncles have 6 sides, and the kids have 5 sides, and when Dipper or Mabel becomes a parent the kid will have 4 sides? Does Ford have one extra side because he has one extra finger, is that like a mutation? How can Bill tell which generation they're on, though?

Bill doesn't tell them that he just counted the number of letters in their real first names and assigned sides based on that.