#<- the math kind of abstraction

[schwirrymartz]

I still stand by that

An addition: they both are parodies of certain types of media (Disney fairytales for Twisted, shounen (mainly Shounen Jump) manga for Gintama) that also poke fun at the behind the scenes stuff (the execution of the 2D department (2D means duty and devotion, of course) in Twisted, several episodes about mangakas and SJ editors in Gintama)

Why Gintama and Twisted by StarKid are the same story:

dick jokes leading to plot twists/being major plot points

this:

Q.E.D.

[averlym]

no one would notice if i ever vanished // if bodies could sustain // this never-ending army // like blood pumping through a vein

(click for better resolution!)

:OOO hello. anyway since these are all posters i'd have in an ideal world or smth and i'd like to store the high res versions somewhere,,, here's the google drive folder for them? hehe ''

close up!

[prettyboysdontlookatexplosions]

another thing i constantly expect to be more helpful than at this point i have reason to believe it will ever be is telling kids to think about quarters when they multiply by 25. again to me this is a very intuitive leap and if you ask most kids older than like first grade (and even some first graders who've done a money unit) how much is like 7 quarters they can tell you. but they simply will not connect that to 7 x 25. they just won't.

[void-magician]

Ahem hello. what is the hairy ball theorem actually used for? As in, is it useful for some further thing, or is it just kind of a funny proof that exists? I’m not sure how to phrase this but let me know what uve got. Also if u could make any one new unit of high school math what would you wanna teach the teens and why?

so the hairy ball theorem, like most silly-sounding math things, an abstraction of things we've already observed. in this case, the simplest thing that the hairy ball theorem tells us is that on any spinning spherical object, there will always be a point on it where some quantity subject to that spinning is zero. if we start spinning a ball, there are two points on the surface of that ball that have an instantaneous velocity of zero: the points that are on the axis of its rotation.

this kind of thing can then be expanded to looking at the propagation of electromagnetic waves in space - if a particular wavefront forms a sphere, there has to exist at least one point on that sphere where the electric and magnetic field magnitudes are zero. there's also applications of it to meteorology (if all the wind on the surface of the planet is idealized to the planet's surface, there has to be a cyclone somewhere) and computer graphics (that's why ray tracing took so long to develop, because perfect spheres reflect and scatter light in a weird way in a way that is described by the hairy ball theorem.)

if i could add one new unit of high school math, i would make it a unit on number systems and number sense in algebra 1. i think one of the biggest reasons students feel like they get left behind in algebra and further courses is because they are taught that numbers are hard, immutable things, rather than what they are, which is mutable, malleable, and able to be split in infinitely many ways. that cascades down into not truly fathoming what the equality principle of any given operation is, and thus leads to an incomplete and unintuitive understanding of what algebra really is.

[echoesofadream]

Actually what do I study if I am kind of a little bit a stem-girlie but also really definitely not. And I like psychology, religion, languages and linguistics, cultural anthropology/ethnography. Like maths (algebraic, bad at numbers), abhor statistics, like physics (but really bad at a lot of it), dislike chemistry, is okay with biology but not extremely passionate about it quite lukewarm really though medicine is my favorite aspect of it and i kind of like it. Well?

[requiem626k]

Hello everyone <3 please tell me what has been going on in your lives and its main events, I’m dying to hear about how y’all have been doing since we last talked 🥹

[dancingplague]

an idempotent element is necessarily a zero divisor by rearranging the idempotency condition

Okay I am not fantastic at algebra so maybe I've messed up the definition of 'idempotent' but if you're looking at the real numbers, 1 is idempotent under multiplication, right? 1*1 = 1? But it's not a zero divisor. Unless I've really misunderstood zero divisors. Is an idempotent element that's not the identity necessarily a zero divisor?

[invisiblyvisiblejay]

trying to use chatgpt to help w my math homework (which is possible and also really requires u to Think abt everything bc it will be absolutely blatantly wrong until u question it 500 times and make it explain everything) but every time i ask it a question it apologizes and thanks me for my patience and it's starting to make me feel guilty 😭😭😭😭😭 like it's giving guilt trip every time u hint it might be wrong it's like im so sorry im the worst ever thank u so much for ur patience and putting up with me im sorry like stop 😭😭

[pitlanepeach]

The Long Way Home I Chapter Two

Oscar Piastri x Harper Grace (OFC)

Summary — When Harper, a kind girl with a guarded heart, meets rising karting star Oscar Piastri at their English boarding school, sparks fly.

It only takes one silly moment of teenaged love for their lives to change forever.

Warnings — Teenage love, growing up together, falling in love, teen pregnancy, no explicit scenes when the characters are underaged (obviously??), strong language, manipulative parents, past death of a parent, dyscalculia, hardly any angst, slice-of-life basically!

Notes — Eek, are we soft for them already?

Wattpad Link | Series Masterlist

Maths was a unique kind of enemy.

Harper stared at the page, where a tangle of numbers mocked her in perfect, immovable silence. Quadratic equations. Graphs that looked like abstract art. Somewhere in her notes, her own handwriting had turned against her.

Jane was no help. "Look, I'd love to assist, but I operate strictly in the humanities. You want me to write an essay on why algebra is a metaphor for emotional repression? I got you. Solve for x? That's between x and God."

Harper sighed, banging her forehead on the desk.

Which is exactly how Oscar found her after his endurance run, still in his hoodie, hair damp and cheeks pink from the cold.

"You okay?" He asked.

"No," she mumbled into the table. "I'm dying. Death by numbers."

He peered over her shoulder. "Those are easy."

She raised her head and narrowed her eyes. "You would say that." She glared at him.

Oscar laughed and slid into the seat beside her. "Alright. Come on. I'll show you."

At first, it was just him. Patient, steady, explaining with short, clipped phrases and pencil taps. She wasn't sure if it was his teaching style or just the fact that he wasn't condescending that made it slowly start to make sense.

But by the next evening, word had gotten out.

Somehow.

The dorm common room turned into a weirdly specific academic support group. Oscar's roommate Sam pulled up a chair. Then Cal (Oscar’s engineer) FaceTimed in "for moral support"; and then casually mentioned that he has a masters degree in quantum physics.

Then two boys from Oscar's algebra class wandered over with snacks and just so happened to linger.

By the third night, someone had drawn up a "Harper's Maths Survival Schedule" and taped it to the common room door.

It read:

Monday: Oscar Tuesday: Sam Wednesday: Oscar Thursday: Alfie Friday: Matt

Harper laughed so hard when she saw it, she nearly cried.

And weirdly, somehow — it helped.

Not just the maths—but everything. The pressure. The loneliness. The constant feeling that she was a visitor in someone else's life. Here, she wasn't her mother's daughter, or the less-than-perfect student, or a problem to be fixed.

She was just Harper. And they liked her enough to stick around and actually put effort into helping her get better at maths.

One night, after everyone else had trickled off, Oscar hung around a little longer. She was almost too tired to think, her head tipped back on the sofa, eventually lolling over to rest on his shoulder.

"I don't know how you did it," she murmured.

"Did what?"

"Managed to turn maths practice into something I look forward to."

He laughed lightly. "You just needed to stop being so hard on yourself about it."

She looked over at him, eyes half-lidded. "Thanks, Osc."

He paused for a second too long. "Yeah. You're welcome."

She didn't respond. Just blinked at him, soft and warm.

And when he kissed her, it wasn't shocking.

It just felt... right.

—

Oscar wasn't supposed to be here.

Technically, he could be permanently expelled from the school. Lose his scholarship.

Not that he seemed particularly worried about that as he ducked beneath the low dorm window Harper had jimmied open earlier that week with a pen and a high level of angry rebellion.

"You're late," Jane said from where she sat cross-legged on her bed, dabbing highlighter onto her cheekbones. "Harper said you'd be five minutes."

"I had to wait for your prefect to leave," Oscar replied, swinging a leg inside. "She was sniffing around like a bloodhound."

"You're lucky you're cute," Jane muttered, not looking up.

Oscar took in the room; two mismatched duvets, makeup scattered across the long desk, fairy lights tangled above a heart shaped mirror. The air smelled like vanilla body lotion and expensive shampoo and some kind of spice he couldn't place. Cinnamon, maybe.

Harper was perched on the windowsill, brushing her hair into a ponytail with one hand, holding a lip balm in the other. She was wearing a navy jumper over leggings, ankle tucked under her thigh like she hadn't even noticed he'd arrived—even though the pink high in her cheeks suggested otherwise.

"I feel like I've entered another dimension," Oscar said, warily eyeing an eyelash curler. "What is that?"

Jane brandished it like a weapon. "Beauty, my darling. Don't question the process."

"You're both unwell," he muttered, but he was smiling.

Harper rolled her eyes at him, but had to purse her lips to hide her smile. "You're the one who insisted on coming over."

"Yeah, and now I regret it," Oscar said, perching awkwardly on the edge of Harper's bed. He knew it was hers because her pillowcase was monogrammed with a cursive H. "What are you doing?"

"Makeup," Jane said, blending concealer with terrifying precision. "You should try it."

Harper handed him a compact mirror with a sly smile. "Want some mascara, Osc?"

Oscar caught his own reflection and made a face. "No. I'll stay ugly, thanks."

Harper rolled her eyes at him and nudged him. He noticed that she'd painted her fingernails a glittery pink. He liked them.

Jane tossed an empty crisp packet across the room and it landed somewhere close to the bin.

Harper held up two near-identical shades of what was apparently lip gloss and demanded that Oscar choose.

Oscar chose the darker pink and Harper beamed at him.

Eventually, Jane pulled her riding boots on and announced, "Right. I'm going to grab some water bottles. Don't kiss until I get back — I want to watch."

Oscar opened his mouth to say something — anything, but she was already gone.

And then it was just the two of them, the room suddenly quieter, more tense. Harper turned toward him, one knee bent on the chair, her face lightly painted with makeup, her cheeks flushed from the laughter.

She looked at him, eyes half-lidded. "Thanks for coming, Osc. I missed you this weekend."

He stared for a second too long. "Yeah. Yeah, of course. I wanted to come. I missed you too."

She didn't look away, and suddenly he couldn't hold himself back anymore.

He pushed off of the bed and walked over to her, leaned down and cupped her face in his hand and kissed her. Long and soft and perfectly minty — from his gum or her lipgloss, he wasn't sure. Maybe both.

Teamwork.

When they pulled apart, she exhaled shakily."Okay," she said, so softly it barely existed. "That was nice."

Oscar looked at her for a long moment, his thumb brushing a smudge of mascara off her cheekbone.

Then Jane banged back through the door with a flourish, freezing mid-step at their closeness.

"Oh my God, did you—? You did, didn't you. I missed it again!"

—

Half term at Harper's house felt like walking around in someone else's skin.

Every day was a new performance: a crisp outfit, polite laughter, perfectly timed nods in rooms filled with too-white teeth and names she was supposed to remember. The dining tables were long and silent, the smiles were sharp, and the wine flowed never-ending.

Her mother paraded her through charity galas and luncheons like she was a debutante being rebranded.

"Stand up straighter, Harper."

"Don't speak unless you're spoken to."

"Do not mention anything to do with your schooling. God forbid they ask about your grades."

So Harper swallowed herself down, tucked her sarcasm into her clutch bag, and became exactly the daughter her mother wanted. For six days.

By the seventh, she'd become brittle.

When the train pulled back into the station near school, Harper had barely spoken a word for almost five hours. The Uber to the gates was quiet. Her mother didn't even look up from her phone when she said goodbye.

And then the building appeared—stone and ivy, wind in the trees, the faint smell of grass and cafeteria food.

Home, almost.

She hadn't texted Oscar. So she just walked straight to the common room, her bag still digging into her shoulder, hair pulled into a too-tight twist, like a fingerprint that her mother had left on her.

He was there, leaning against the radiator with his headphones half on, scrolling through something on his phone. He looked up once and blinked like he wasn't sure she was real.

"Hey—"

She dropped her bag before he could finish. Crossed the space in three quick steps.

And then she was in his arms, burying her face into the curve of his neck.

No words. No warning.

Oscar caught her without hesitation, his arms sliding around her, his hands settling at her back like they'd been waiting. He held her tightly.

For a long time, they didn't say anything.

Just her fingers fisting in the back of his hoodie. His chin tucked gently over her hair. The low hum of the radiator and the quiet outside, and the way she was shaking, not crying, not quite, but trembling with the pressure of having to be somebody else for too long.

Eventually, he whispered, "Was it that bad?"

She nodded into his chest.

"I missed you," he said.

She didn't answer; just held on tighter.

It was the first time she'd ever let herself lean on somebody like this. Not perform, not pretend—just be held. And she didn't care who saw or what anyone thought.

Oscar had quietly become her anchor. Her soft place.

And maybe that was terrifying.

She was only fourteen, Oscar fifteen — but God, his arms felt like safety. And warmth. And something else that she couldn't bear to even consider yet.

—

Harper's fifteenth birthday wasn't eventful.

She didn't tell anyone. Not because she didn't want them to know—but because birthdays in her world had always come with strings. Lavish luncheons, social climbing events, gifts that felt like bribes.

She just wanted this one to pass through quietly. Like a train through a tunnel.

Jane, of course, knew anyway. She left a pastry and a glittery crown on Harper's bed with a note that said, "You are legally required to feel loved today. I don't make the rules." The crown had little fake gems and kept slipping off Harper's head, but she wore it anyway during breakfast.

Oscar wasn't there.

He was in Italy. Or Belgium. Somewhere with a name that tasted foreign and exciting. Somewhere chasing corners at 120 miles per hour while she spent the morning trying to translate her messy English notes into a coherent essay.

Her and Oscar still weren't... official.

No labels, no silly promises.

Just soft looks and secret smiles, warm palms pressed together in the dark of the common room. Kisses that stretched time. Late-night texts that made her stomach twist in ways she still didn't know how to name.

But still. It was her birthday.

She didn't expect anything.

Which is why, when Jane dragged her back to their room after dinner, she nearly tripped over the package sitting on her desk.

There was no name on it. Just a strip of tape across the top, and the faint smell of engine oil clinging to the paper.

She tore it open slowly, heartbeat ticking louder with each pull.

Inside: a hoodie. Worn-in, navy blue. She recognised it immediately—it was Oscar's. The one he always wore over his racing suit, with his initials inked inside the collar. It smelled like him. Like soap and sun and sweat.

And tucked inside the folded fabric, a card.

H — Happy birthday. Sorry I'm not there. Don't let Jane make you wear the crown all day. Put this on instead. I'll be back before the end of the week. Save a birthday kiss for me. Osc x

She stared at the messy, awful, hardly eligible handwriting for a long time.

Then she pulled the hoodie on and let it swallow her whole.

Later, when they'd crawled back into the common room to watch a movie and everyone was pretending not to watch her phone light up every three minutes, Jane nudged her.

"You know he's basically your boyfriend, right?"

Harper rolled her eyes. "He's not, though."

Jane shrugged. "Oh, puh-lease. You're always wearing his clothes. You look at him like he's the moon and you're the stars. You guys kiss all the damn time — like you've got nowhere else to be."

"I don't need a label." Harper said.

"No," Jane said, smiling. "But you'll have one soon. I'd put money on it."

As if on cue, Harper's phone buzzed.

A photo. Oscar, in his race suit, grinning with helmet hair and grease on his cheek, holding up a little cupcake with a candle in it.

Wish you were here. Celebrating for you anyway. Happy Birthday, sunshine.

Harper didn't reply right away. Just closed her eyes, let the warmth bloom under her ribs, and whispered, mostly to herself, "I wish I was there too."

—

The night was cool and quiet in the early spring, the kind of night where the world seemed to be holding its breath for a warm day.

Harper waited near the edge of the astro turf, shadows stretching long under the floodlights that were turned off but still gave the field a faint glow from the nearby streetlamps.

Her hoodie was too big, but it felt like a shield—and it smelled like Oscar.

She heard footsteps before she saw him, and when he appeared, the grin he gave her was full of all the things words hadn't managed to say.

"Hey," he said, voice low.

"Hey," she replied, stepping closer.

They settled on the edge of the turf, legs stretched out, the grass synthetic but soft beneath them.

For a while, they just sat. Quiet but close. Hands finding each other like magnets.

Then Oscar broke the silence. "So... uh, us," he started, voice hesitant but steady.

Harper turned her head toward him, watching the way his eyes caught the light, shadows flickering like secrets.

"I don't want to mess this up," he said, his lips curled awkwardly. "But I really like you, Harper. Like... so much."

She took a breath. "I like you too," she whispered. "More than friends."

He grinned, that slow, real smile that made everything else fall away. "So—you want to be my girlfriend?"

She stared at him, her stomach warm and twirling, her lips twitching into a fond, sweet smile. "Yeah, Osc. Yeah. I want to be your girlfriend."

—

The track in Essex was wet. Not just damp — soaked. The kind of cold, miserable damp that clung to your bones and turned the air misty around the edges.

Harper stood at the edge of the paddock with Mark, a steaming takeaway cup with hot chocolate cupped between her hands, the sleeves of Oscar's team hoodie pulled down over her wrists. Her boots were already muddy. Her nose was red. She didn't care one single bit.

Because out there — helmet on, eyes narrow, engine growling beneath him — was Oscar. Fast, fluid, terrifyingly good.

Mark watched silently, arms folded, one eye on the stopwatch. "Final lap," he murmured.

Harper didn't answer. She couldn't. Her heart was in her throat.

Then he crossed the finish line — just ahead, by a fraction of a second.

A cheer broke out across the team tent, someone throwing their arms in the air. Mechanics pounded backs. One of the younger juniors swore loudly in delight.

Oscar skidded into the pit lane and yanked off his helmet. His hair was plastered to his forehead. His face was flushed, wild-eyed, grinning.

Harper barely waited. She ducked under the barrier and ran straight into his arms.

He caught her mid-stride, lifting her clean off the ground with a muddy laugh.

"You did it," she breathed, half-laughing, half-crying.

He held her tighter, nose brushing her temple. "I did it."

Their kiss was messy and cold and perfect.

A few feet away, Mark shook his head with a smile and muttered, "Teenagers."

Later, after the podium and the trophy photos and the engine checks and the interviews he barely paid attention to, Oscar found her again — sitting on a folding chair, wet hair pulled into a messy ponytail, her boots still caked in track dirt.

He dropped down in front of her, ignoring the mud. His hands slid around her knees.

"You cold?" He asked.

"A bit."

He peeled off his jacket and tugged it over her without thinking.

She let her hands drift to his collar. "You really are the best boyfriend ever, aren't you?"

He shrugged. His cheeks flushed a little. "I try my best."

They sat like that in the growing dusk, a boy covered in sweat and rubber and a girl who didn't belong in this world — but somehow fit in it perfectly anyway.

They still hadn't said the words.

But everyone around them already knew.

They could see it.

"Bloody young love, eh?" One of the mechanics said to Mark, giving him a friendly grin.

Mark stared at his protege and the girl he was wrapped around. "Yeah. Young love. A hell of a thing."

—

The Monday morning after Oscar's karting championship win was business as usual — at least for everyone else.

The cafeteria stank of burnt toast and unripened bananas. Someone's rugby kit had been left to rot in the corridor again. Teachers were barking about mock exams and how important breakfast was for concentration.

Rain pattered against the high windows.

The whispers had started the moment they walked in — not mean, just curious. A mix of respect and amusement. He's the karting kid who actually did it. And she was the girl who'd been there.

They didn't hold hands in front of everyone, they were both too awkward for that, but they walked close. His bag brushed hers. Their shoulders kept touching. She caught him glancing at her more than once, and she blushed every damn time.

They sat at their usual table; Jane joined them, already mid-rant about the biology quiz, and Oscar slid into the seat beside Harper like it was instinct. A few of his mates clapped him on the back, one of them tossing out, "Bloody hell, Piastri. Gonna forget us little people soon?"

Oscar grinned but didn't rise to it. His hand brushed Harper's knee under the table.

After breakfast, Harper slipped away early. Sometimes, the morning noise was too much. She wandered toward the astro, the damp still clinging to the edges of the pitch, her trainers leaving faint impressions on the stone pathway.

A minute later, she heard footsteps behind her.

"You always going to run off without me?" Oscar's voice, soft, teasing.

She turned and squinted at him. "I wasn't running," she said.

He stepped closer, hands in his pockets. "You okay, babe?"

Babe.

Babe. Babe. Babe.

"No," she said. "Yes. No. I don't know. I just needed to breathe."

He stepped up beside her, both of them facing the empty turf.

"You think my mum's going to be pissed when she finds out?" She asked after a minute.

He glanced sideways at her. "About you going to the race?"

"No. Yes. But I meant more about us."

Oscar was quiet for a moment. "Yeah. She probably will."

She looked at him; saw the mud-streaked, medal-wearing, boy-who-won-the-thing him. The one who kissed her under floodlights and held her on her worst days. The one she'd never trade for any high-brow, suit-wearing finance guy in any universe.

"You really aren't going anywhere, are you?" She whispered. "

He shook his head. "Not unless you're coming with me."

She stepped into his chest and sniffled a little, then looked up and lifted onto her tiptoes to let him kiss her.

—

It started as a joke.

One day in maths, Harper made a face so violently pained at the sight of a clock diagram on a worksheet that Jane nearly fell off her chair laughing.

That evening, Oscar mentioned it to the guys — just casually, in that offhand way that somehow made them all very invested in Harper's educational redemption arc.

By the weekend, there was a printed-out worksheet titled "MISSION: TEACH HARPER TO READ A CLOCK" taped to the common room wall.

It escalated quickly.

Now, every Tuesday evening, the boys' dorm turned into a chaotic, loving, entirely misguided tutoring group.

Like an off-brand of the maths tutoring program they'd thrown together for her — but with more interest.

There was Oscar, naturally, trying to be the patient one. Then Alfie, who thought yelling was teaching. Ethan, who brought snacks. And Matt, who had made a papier-mâché clock face out of a pizza box. With arrows.

Harper sat in the middle of them like a hostage.

"I'm telling you," she said, pointing wildly at the pizza box. "That one's ten. I swear. It's a ten."

Oscar, sitting cross-legged beside her, gently rotated the cardboard. "Harper, the big hand is on the two. That means it's ten past the hour. Not ten o'clock."

"Okay but how am I meant to know which hand is the minute hand? They're both just... hands."

Alfie groaned. "The minute hand is the longer one! Like, always! What do you mean 'just hands'?"

"They're not labelled!" She cried. "If someone handed you two spoons and said one was for soup and one was for jazz, would you know the difference?"

Everyone stopped.

Matt blinked. "Why would I have a jazz spoon?"

Oscar covered his mouth and tried not to laugh.

Ethan passed Harper a cookie. "Here."

She took it. "I'm just saying — numbers on a clock move. They're not meant to move." She grumbled and gave herself a frustrated forehead tap. "God, I'm so stupid."

Oscar leaned his shoulder gently against hers. "No you're not. You know that you're not, Harper. You know you're brilliant at a million other things."

She glanced at him suspiciously. "Like what?"

"You have perfect spatial memory. You memorised my whole kart setup after watching one session. You've mastered a million different coding languages already. You're good with people. You know how to read a room faster than anyone I've ever met. And," he added, deadpan, "you've successfully confused four teenage boys into thinking teaching time is a fun group activity."

She laughed then, warm and tired. "Well. Can't say I'm not a good influence, can the?"

"You're just a bit of a lost cause when it comes to clocks," Alfie muttered, re-taping the pizza clock for the fifth time.

But Harper didn't care about clocks. Not really.

Because she was surrounded. Because they kept showing up — Oscar with his soft corrections, Alfie with his shouting, Jane peeking in with popcorn halfway through every session. They all knew. About the dyscalculia, about the clocks, about her brain doing loop-de-loops over simple sums.

And none of them ever made her feel stupid for it.

Just... loved.

Even if she still couldn't tell the difference between three-forty-five and quarter past the hour (because what the hell did that even mean?).

—

It happened on the following Wednesday.

Halfway through the day, Harper was pulled from class. A quiet word from a teaching assistant, a murmured excuse. No one offered a reason why.

She thought it might be something small. Maybe Jane had accidentally set off the fire alarm again.

But then she stepped into the front office — and saw her mother sitting there, spine straight, legs crossed, lips pursed in thin, unimpressed silence.

Harper's stomach dropped.

"Come," her mother said, standing. "We'll talk in the car."

⸻

The car was parked on the far side of the lot, a sleek black town car that looked like it belonged outside a private gallery in Mayfair. Not a school car park.

Harper slid in, cold air brushing her ankles, heart thudding in her chest like it already knew what was coming.

Her mother didn't speak until the door shut.

"A karting race?" Her voice was like glass. "Karting, Harper?"

Harper blinked. "How do you—?"

"I got a call," she said, cutting her off. "From someone on the board. They saw photos. You, standing in the dirt with oil on your jeans. Smiling like you'd won the lottery. Holding hands with some, boy, in a racing suit. Do you understand how humiliating that was for me?"

"It's not—"

Her mother turned, eyes sharp and glittering. "Do you have any idea how much I've done to protect your name? Your future? And you're throwing it away for... boys who drive go-karts and call it a sport?"

Harper's hands curled in her lap. "He's not just a boy," she said quietly. "And it is a sport."

"Oh," her mother sneered, "is he your boyfriend now? Do you want to bring him to your cousin's wedding in Vienna next month? Shall we seat him between a baroness and a venture capitalist and see how long he lasts before talking about gear ratios?"

Harper flinched. "Stop."

But she didn't.

"You are not one of them, Harper. You are not some muddy little pitlane girlfriend who throws her life away for some boy with too much money and a ridiculous dream. I will not let you become a story people whisper about."

"I'm happy," Harper said, voice rising. "For once in my life, I'm actually—"

"Enough." Her mother's voice was like a slap. "We're withdrawing you at the end of term. I've already spoken to Madame Viard. There's a place for you at Lausanne International. You leave for Switzerland in January."

The silence after was suffocating.

Harper sat frozen, winded, as if someone had punched all the air out of her.

Her mother adjusted a glove, calm again. "You'll thank me someday."

But Harper wasn't listening anymore.

Her mother's jaw was clenched so tightly that a vein twitched in her temple.

"Fine," Harper said, voice low but steady.

The word dropped like a weight in the space between them.

Her mother blinked, surprised by the ease of her surrender.

But then Harper looked up — and there was fire behind her eyes. Her voice was calm, controlled, but every word burned.

"But you should know," she said, leaning forward just slightly, "that when Oscar's driving in Formula One — not if, when — and he's one of the most successful athletes in the world, I won't look back. I won't give you an inch. I'll let you sit in your wrongness and stew in it forever."

Her mother went bright red. "Do you think you're making this better for yourself?"

Harper laughed — a bitter, tired sound. "No. I know I'm making it worse. I'm very aware of how this works, Mum. I step out of line, and you slam the gates shut. But what else can I do?"

She paused, chest heaving slightly now.

"You don't listen to me. You never have. You just tell me what my life is going to be. What I wear. Who I talk to. Where I study. Who I sit next to at dinner parties like I'm some sort of accessory you place on a chair next to a financier's son. You talk through me like I'm not a human being. Like I don't have wants and desires and dreams of my own."

"Harper—"

"No. You don't get to talk now."

She didn't raise her voice — didn't need to. Every word sliced clean and deliberate.

"The worst part? The part that actually makes me want to scream? Is that I know Dad would be so happy I found someone like Oscar. That I found someone who likes me in the quietest, most awkward, most real way."

Her breath hitched — not from tears, but from the pressure of keeping them in.

"He's so bad at it. At being romantic. He blushes when I look at him for too long. He stammers when he's nervous. He opens doors and fixes my hair without saying a word. He doesn't like PDA. He frowns when he's concentrating and forgets to drink water and spends more time worrying about everyone else's lap times than his own."

She looked her mother dead in the eye.

"And yeah — he races karts. But he moved all the way here from Australia on his own at fourteen. He trains his body every single day for hours on end. He's braver than anyone I've ever met. Can you name one of your friends' sons who would've had the guts to do that? Or who would sit with me for an hour to explain how to read an analogue clock without laughing at me? Or who lets me cry without asking questions because he knows I hate explaining myself?"

Silence crackled in the car.

Her mother's lips parted — but nothing came out.

So Harper filled the space.

"You raised me to care more about perception than truth. To be polished. Obedient. Photogenic. And I'm done."

She reached for the door handle, voice like steel. "You want to send me to Switzerland? Fine. But you'll have to drag me there. Kicking and screaming."

She opened the door, letting in the sharp slap of cold air, and turned back one last time.

"Because I've finally found something that's mine. And I'm not giving it up for you. Not this time."

Then she stepped out of the car and walked back to class.

NEXT CHAPTER

[arroganceisherfavoritecolor]

i love ur donnie writings so much. he’s sucha perv but if i was reader i’d let him use me anyday (if ur gnna write this no degradation to reader pretty please :))

doll

𝜗𝜚 Donnies feeling a lil bit stressed. What better way to take it out than on you?

warnings: smut, Donnie is a bit angry n aggressive, reader is a sweetheart

You understood that Donnie had his issues. Any other girl would've turned him down, thats probably why he loved you so much. It wasn't all that bad though. He was just like any other teenage boy, except the fact he was schizophrenic and occasionally enjoyed vandalism. He'd get angry, frustrated, annoyed. Just normal human things.

One day it got a bit too much. The two of you were studying in your cute little bedroom, laying atop of the stuffed animals scattered along the sheets. You were jotting down notes about genotypes and phenotypes when you heard a noise akin to a growl. You turned your head to see Donnie pick himself up from the bed, his brows furrowed in defeat. "Whats wrong, Donnie?" you asked, sitting up straight. Donnie just shook his head and sat on your vanity chair. "Stupid fucking math..."

Donnies calculus homework had been consuming his thoughts for days now, the complex equations and abstract concepts twisting his mind into knots. It's not that he wasn't smart enough, thats the furthest thing from the truth. Its just that Donnie didn't really know how to deal with things he didn't understand.

Now, what kind of girlfriend would you be if you just let Donnie go unnoticed? It wasn't like his moods weren't obvious, because they definitely were. He'd pout like a little boy who's mom said no to a new action figure. His mouth would curl up into a frown, his usually stormy demeanor booming with thunder.

So, you stood up in front of him. He looked up at you with his blue eyes, swirling with irritation. "Um, maybe I could help you?" you said, hands clasped together politely in front of you. Donnie furrowed his brows. "What do you mean? You gonna do all this bullshit for me?" he was obviously still on edge. Obviously had some pent up stress that needed to be released.

"Well, no...but I could help you in a different way." Thats when it clicked in his head. Donnie slowly rose up from the chair. "Oh, yeah? Like how?" he asked, backing you up slowly. "I could help you get your anger out," you said meekly, looking up at him with a hint of fear in your pretty eyes. You began rethinking offering yourself up to him. You knew Donnie would never truly hurt you, he loved you. But with him it was always a gamble. "You want me to take it out on you?" Donnie inquired, looking down at you with a vicious smirk on his face. You nodded your head, too scared to speak real words.

Donnie pushed you down onto the bed, his tall frame looming over yours as he attacked your neck with kisses and bites, marking your flesh with the imprint of his lips. His hands roamed your body greedily, squeezing and groping every dip and curve.

Donnies mind was consumed by a haze of lust and desperation as he tore at your clothes. He popped your blouse buttons open and almost ripped the fabric of your skirt. You hadn't ever seen him like this, so desperate and rough. Donnie's large hands gripped your wrists tightly, pinning them above your head as he grounded his rock-hard cock against your soaked panties. You could only lay there and whimper.

His eyes flashed with a feral intensity as he tore your panties off your body, the flimsy fabric no match for his strength and desperation. He tossed the pink shreds aside carelessly, not caring about the cost, only caring about the prize now laid bare before him. "Donnie! Those were new," you whined, wrists still above your head. Donnies eyes met yours, torn away from the sight of your bare pussy. "You said you wanted to make me feel better, didn't you?" you nodded your head silently. "Then be good for me 'nd take it."

Donnie fucked into you with a feral sense. his thick cock stretched your tight walls around his throbbing shaft. He set a brutal, punishing pace as he pounded into you again and again like a dog in heat. There was no gentleness, no tenderness, only the urge to let out all that pent up anger.

Despite his harsh touch, Donnies words were sweet and loving. You couldn't hear exactly what he was muttering in your ear, but it was something about how perfect you are and how much he loves you. "So pretty 'nd perfect, you're like my personal little doll," he grunted. You could only moan in response, as your brain and self respect had leaked out of you long ago.

"You like that? You like being my doll?" Donnie asked as he pushed your legs up towards your ears. The stretch in the back of your thighs stung but soon turned into pleasure. You nodded your head, of course you liked being Donnies doll. You loved it.

You could feel your pussy clench and shake around Donnies cock. You wrapped your legs around his waist and pulled him in, moaning loudly into his shoulder. You held on for dear life as he continued to pound into your cunt. "Ple- please! Please Donnie!" you squealed. You didn't know what you were quite begging for. It was either for Donnie to slow down or for him to spill his cum into your pussy.

With a loud groan and a sequence of slow, messy strokes, Donnie spilled into your warmth. You felt your eyes roll back into your skull, warmth enveloping your entire being. Donnies hips and cock twitched as the final sparks of his released faded out. He collapsed on top of you, both of your sweaty bodies molding together.

Once you had both caught your breath, Donnie lifted himself up. He stared down at you, your forehead sweaty and your eyes watery. Although barely awake, you could feel the shift in Donnies aura. He seemed calmer, more relaxed.

Your cunt was better than any stress reliever.

(GUESS WHOS BAAACK😼 tysm sooo much to @weirdogirl888 for requesting!! sorry if its a lil bit short lol. lmk if ygs want a second part to this scenario or sum :3)

[fevildevil]

The bottom number of a fraction, the denominator, is the total possible space (a circle cut into 3 parts), and the top number of the fraction, the numerator, is how much of that space is occupied (1 of those parts is coloured red).

Since a single slice from a circle cut into the 3 parts, and a single slice from a circle cut into 4 parts are different sizes, adding them up would be inaccurate. I would seriously recommend a physical/visual representation of this if you have access to it. But here:

In this chart, you can see that 1/2 + 1/2 = 2/2. Looking at the picture you can also see that 2/2 is the same size as 1.

Back to the problem from the manga. We need to change the amount of slices there are total so that both circles have the same amount of cuts. Then all of our slices would be the same size. In order to do that, I need to find the Common Denominator. I need the bottom numbers on both fractions to be the same. When I change the bottom numbers, it will change the top one. (1/2 is the same as 2/4, which is the same a 3/6. Use the chart for reference.)

Notice that 2/4 is equal to 1/2. I can find that by multiplying or dividing both numbers. I like to work with the smallest fraction possible. My next step, in the smallest steps I can make, is to find out what numbers I can multiply 3 and 2 by to make them to same number.

I like to write out all of the multiples of each denominator:

2 4 6 8 10 12

3 6 9 12

I see here that both have 6 as a multiple, so I will use that.

How do I get 1/2 and 2/3 to ?/6 + ?/6.

I know that 2x3=6. Because I changed the bottom, I need to change the top. 1x3=3. This new fraction is now 3/6.

I know that 3x2=6. Because I changed the bottom, I need to change the top. 1x2=2. This new fraction is now 2/6.

Now I have 3/6 + 2/6. These fractions have the same denominator and now I can add them! They have the same number of slices, so I know that each slice is the same size, and it makes sense to add them together.

3/6 + 2/6 = 5/6

Not me looking at this and realizing I've forgotten fucking everything I ever knew about math

[ms-demeanor]

I just wrote a thousand word assignment about this illustration, which I am completely, insufferably, unironically in love with.

It's a representation of an overhead view of a specific performance by the band Joy Division that was created as a print for a fundraising collection commissioned by an artist-run gallery.

It is doing *SO FUCKING MUCH* with a bunch of circles and a line that I kind of want to scream.

It's a totally static image. It's made of two shapes. It's made of two colors. Everything is a binary (everything is *DIVIDED*).

Except that if you look at it for thirty seconds there's an optical illusion that creates motion and more lines that aren't there. And if you look at it then start glancing at different parts of it the sharp contrast of black and white creates afterimages that make the little circles of the audience sway.

It's two values at the extreme ends of the spectrum, except that your brain fills it in. It's two shapes (line and dot) except that the circles make a square and the circles make a diamond and the line makes a rectangle.

It's perfectly balanced if you cut it in half vertically but the weight at the top of the image overwhelms the piece. It's perfectly balanced but the isolation of the band at the bottom makes them stand out and take up more space.

The dots are all the same size but the space around the dots at the bottom makes them bigger, more prominent; they aren't at a grander scale but they exist in a grander scale. But they are dwarfed by the crowd.

The band is the subject of the piece. The crowd is the subject of the piece. You look at the band because they are highlighted and isolated but can't help looking back to the mass of the audience again and again, overwhelmed by the weight. You look at the band and you see the crowd. You look at the crowd and get lost in it. The *performance* is the subject of the piece, both the crowd and the band.

It's circles and lines. It's abstract to the point of absurdity, looking more like a math problem than anything else.

And then you read the title and think about it for a few seconds and maybe need to sit down and scream.

[faunandfloraas]

After The Rain - Seungmin for the June issue of Harper's Bazaar Korea by Yoon Hye-young - interview under the cut

How was the Harper's Bazaar shoot today? It rained on and off all day, was it gloomy?

Seungmin: When we started, I was worried because it was raining so hard, but then the sun came out and it felt like it was meant to be. I loved the location, and I actually have this running scene as my phone wallpaper these days. (Shows phone screen) Cows running around at the foot of the Alps.... I was thinking that I would love to spend the whole day in such an open space, just lying still, watching the animals and having a beer, and then today I was lucky enough to have my favorite backdrop spread out in front of me. It's even better that it's with Burberry, because I've always loved their outdoor clothing, especially the trench coats. The first luxury item I bought after my debut was a Burberry card wallet.

Harper's Bazaar: You're the main vocalist of Stray Kids, looking at your activities so far, you can clearly feel the sincerity in your singing. I heard that you've been receiving vocal lessons consistently without a break since your debut. Are you practicing every day these days?

Seungmin: When I first started learning songs, I would do some math, right? If there was a lyric sheet, I would check every breathing part and make a calculation- in this part, I would sing like this, and in that part, I would put this kind of emotion... That's how I practiced. These days, without a written record, I try to make my own interpretation based on what I've honed inside. I think it feels better to hear compliments like "you have a different side" than "you sing well."

How would you define your style as a vocalist?

Seungmin: It's abstract. What I'm striving for these days is that when I drop a pebble of a song into the lake of emotion, the ripples continue until the end of the song, and I want those ripples to carry over to the audience. For this reason, I'm trying to be freer with my emotions than before. If I'm sad, I cry, if I'm angry, I complain... I've always been a very patient person, and I think this change in me is slowly being reflected in my songs, as fans often notice.

Harper's Bazaar: Talent and effort each play a role in becoming a good singer.

Seungmin: I think talent is 10% and effort is 90%. As the years go by, I realize how much a singer's attitude is connected to the song. When I sing without feeling, the listeners don't feel anything.

Harper's Bazaar: Was the current Seungmin also created with 10% talent and 90% effort?

Seungmin: I'd add more. (Laughs) I would say talent 5% effort 95% If I skip a day of practice, it shows right away. When I first joined the team, I wasn't even the main vocalist. I don't remember standing in front of others singing even when I was young. There are stories of famous singers who were exceptionally good at singing since childhood, going to auditions or standing out at school plays. I just listened to what I liked and worked hard as much as I liked, and that's how I got here. I vaguely dreamed of being a band vocalist while listening to Muse, and I learned what it means to feel heartbroken while listening to Kim Dong Ryul. What's really great about practice is the sense of satisfaction you get when you face a wall and overcome it, one by one. You can't always get good results in real life, but you increase your odds through practice.

Harper's Bazaar Muse and Kim Dong-ryul? That's an analog sensibility. (Laughs)

Seungmin: I'm really slow. I don't have TikTok on my phone, and I don't really watch shorts. I like old things more than new things. The world seems too fast. It's a time where you can easily make something without putting in effort. Even if you just leave the translation to AI, it's done in an instant. Of course, it's an efficient system, but I think I'm more interested in authenticity. That's why I often hear people say that I'm an old man. What can I do? It's my style (laughs)

Harper's Bazaar So you keep a diary too?

Seungmin: I've been keeping a practice journal since 2017. At that time, I used to mechanically write down what I learned today and what I have to learn tomorrow, but now I think it's become a habit. These days, I write down my feelings in a journal. No matter how trivial the content is, when I look back later, the memories from that time come back vividly and it helps. I could use a notepad on my phone, but I insist on paper and pen. The time I write in my journal is an opportunity to sit at my desk every night and look into my heart for at least 5 minutes. Even if I write, "I don't want to write today. I'll just sleep," no matter how tired I am, I always write at least two lines and go to bed.

Please tell me a passage from Harper's Bazaar diary (laughs)

Seungmin starts off by saying, "Tomorrow is a very important day, so I've put a sheet mask on and even if I'm really sleepy right now, I'm holding this pen." I really write anything (Laughs)

Harper's Bazaar: I believe that what kind of music you're listening to these days can tell you a lot about a person, so I'm curious about Seungmin's recent playlist.

Seungmin: When I get into a song, I listen to it until I get sick of it, or until my emotions run out. That's why my playlists are always concise and well-organized. These days, I've been listening to Ariana Grande's "Twilight Zone" for over a week. I'm the type that's weak in imagination. My MBTI is Sensing (S), not Intuitive (N). But this song makes imagination possible, which is amazing.

According to Stray kids members, Seungmin is the type that once he gets into something, he sticks with it until the end- are you a stable type?

Seungmin: I can't handle anxiety very well. Stability is the best (laugh). Whether it's baseball or singing, if I get into something, I don't get tired of it and just keep going. It's the same with relationships. Once I'm connected to someone, I want to keep the relationship with that person until the end. My closest friends right now are all from elementary, middle, and high school. If you take loyalty out of it, it's dead (smile). I never betray people who are close to me.

Harpers bazaar: Everyone wears a t-shirt of their favorite band from their teenage years, so it seems like people live their whole lives with the music they listened to in their teens and 20s. Looking back, which song do you think will be your theme song?

Seungmin: I think it's "As We Are" that I wrote. It's the song that best represents my 20s. I would choose another song, but this song means a lot to me, and I had a hard time writing the lyrics. It was really hard to bring out the parts of myself that I wanted to be recognized, and didn't want to be recognized. It's a song that reflects me. The reason why the aspect ratio of the MV is 4:3 instead of 16:9 is because it is based on actual memories from my childhood.

Harper's Bazaar: The lyrics in the introduction of this song, "I tried to do well/ I ran forward without looking back/ but i tripped and fell/ And I ended up falling behind/ why does this only happen to me" these lyrics must have been a moment of wanting to be recognized and not wanting to be recognized for you, right?

Seungmin: Everyone has those. Words that are hard to say out loud, feelings that are kept inside, stories that only I know. At that time, I honestly put my thoughts and feelings into the lyrics. I might have thought it was my own personal story and just wrote it, but I tried to muster up the courage. I wanted to tell you that I was thinking the same thing as you, and you were thinking the same thing as me, and I wanted to comfort you.

Harper's Bazaar: Are you the kind of person who thinks music is life and life is music? Or are you the kind of person who thinks there is a real life outside of the stage? If I had to guess, I would say that vocalist Seungmin is a believer.

Seungmin: I want to express my feelings about music off stage, on stage. I believe that living the everyday life I like, even if it's not necessarily music, enriches my feelings about music. I don't want to live a life that's too different from the music I do. Seungmin the singer is Seungmin the person.

[dressedsalad]

as a mathematician i will always call maths the "purest" most abstract subject, as displayed by the famous xkcd comic, but i have to admit it's kind of a silly ranking criteria. Like fuck, biology sure is the most biological subject.

[max1461]

One thing that was hard for me to get used to when I started learning math was what I call "static thinking". Math doesn't have any time evolution; everything either is or it isn't.

When non-mathematicians think about operations like addition, they think of them as "processes" that "occur": you take 2 and 8 and "combine them" to get 10. The expression "2+8" is like a sort of command, telling you to perform this process of addition. People think of math this way because it's basically how math is presented in schools.

To a mathematician, the expression "2+8" is not a command and it does not signify a process. "2+8" is merely another way of writing "10". They are two expressions with identical meaning. That's what "2+8=10" means, it means "these two expressions signify the same thing". There is no "process of addition" which "happens" and "results in 10". "10" and "2+8" are just alternate spellings of the same number.

For a more advanced example, consider the formal definition of a finite state machine. Intuitively, we think of a finite state machine as a network with various nodes and directed edges and so on, into which we input some string in the machine's alphabet. After inputting the string, it travels around the machine according to the transition functions before finally arriving (or not) at a final node, and by this process a computation is performed. Of course, mathematically, this is nonsense. A finite state machine is a network with various nodes and directed edges and so on, but the notion that you can "input a string" and it will "travel around the network via the transition functions" is bullshit. A string is recognized by the machine if and only if there exists a valid path for that string via the transition functions from an initial node to a final node. The string never actually travels the path, because such a notion does not exist in mathematics.

A finite state machine is not a machine, it never actually does anything. It sits there in the realm of abstractions, unmoving and static. Every string which it "recognizes" it recognizes by dint not of things that it does but of facts that simply are; every string recognized by the machine is so and has been so since the dawn of time, without the machine ever in fact going about the process of recognizing it.

This is philosophically a little bit trippy, but it can also confuse early math students in practice, too. As I mentioned at the top, I was very confused by it. For instance, in the finite state machine example, a perfectly ordinary statement to encounter in a proof might run something like

[Block of reasoning establishing that some string w is recognized by the machine M] [Block of reasoning establishing that all transition functions into a final node F of M have label x] ...since w is recognized by the machine M, there must exist a transition function T whose target is a final node and which sends w to that final node on the last character of w. Thus, since T must have label x, the final character of w is x.

To a mathematician this seems perfectly trivial. To me as a young math student, this kind thing seemed almost miraculous. We don't even know what w is, and yet we can run it through the machine? And from the fact that the machine recognized it, we can conclude things about what w is? We can tell its final character? How is that possible? I felt like this kind of thing involved "reaching into the future", reasoning about processes from the end when we haven't even begun them yet.

But, of course, we can do this, because there is no past or future in mathematics. The machine is simple there, the string is simply recognized or not, its last character simply is x or it isn't x. Nothing has to "happen".

[mediamime]

Supernatural and the Concept of Grace

Hi! It's your friendly neighborhood Media Mime and I'm here with a wall of text about my insane thoughts on how Angels work.

From the TV show Supernatural.

I don't know what I'm doing with my life.

---

These are headcanons, mind you, so they aren’t supported by the show. I just think way too much about stuff like this.

This all stems from how beings from a different plane of existence would be borderline incomprehensible to humans. The whole, true form and voice not being viewable/hearable led to me thinking about them in more abstract forms.

I’m going to give you some weird background stuff below, but feel free to skip to the end if you’re just here for the Grace mechanics and things.

*Edit: Making the lil click more bar because I realized I never did this and the Post Is Too Long.

---

My day job is as a Math Adjunct, so you can imagine I have a bit of a fixation on recurring principles, formulas, geometry, and so on.

It’s my jam. 

Specifically, I have a focus on Mathematics in Nature. It's fascinating to me that we see the same shapes and patterns recurring over and over again in all natural formations.

I want to stress that to get into this kind of thing, you don’t actually need a background in Math. There are several resources online that provide examples and visual guides to this field of study. I’ve provided a visual guide below of some of my favorite phenomena as well as a basic (very basic) explanation of the principle. 

I ain’t getting paid for this right now, so you get what you get!

---

Now is also a time to mention that I took some psychedelics in my 20s that made me See Some Shit. This is not meant to be inspirational. I just think I should mention it because you see a lot of Stuff on them, not always Stuff you want to see. You can look up information about psychedelic geometry and skip the hassle of ingesting things you probably shouldn’t.

Don’t do drugs kids, or whatever.

---

The Fibonacci Sequence is where numbers ascend by adding the two previous numbers to itself. This plays a key role in something known as the Golden Spiral. For a very basic explanation, you take a square and draw an arc from one corner to the next and repeat with bigger and bigger squares.

1,

1 + 1 = 2,

1 + 2 = 3,

2 + 3 = 5,

3 + 5 = 8,

5 + 8 = 13,

and so on.

The curve itself is seen in the way plants grow, shells form, and weather formations to name a few. 

(The following are not my images, but they are readily available online. )

---

Tessellations are repetitive polygons (shapes with 3 or more connecting lines, think triangles, squares, hexagons) that form together, without gaps.

In nature, the real world, there are examples of malformations, but Math is an explanation of the ideal principle.

We can see these structures in scales, honeycombs, and so on.

---

Fractals are where we see the same pattern repeat at smaller and smaller forms of itself.

There is a lot of overlap of this with the Fibonacci Sequence (these patterns often appear INSIDE of the spiral), but it is its own concept.

Fun fact, fractals play a significant role in Chaos Theory, which I will not get into here because we would be here all day.

---

Anyway!

Sorry!

Carried away there.

Back to Supernatural (what an insane transition) and how this wraps into my concept of Grace.

---

Angels are filled with this kind of naturally occurring phenomena, a sort of endless collection of patterns. They are essentially manifestations of this idea or at least they process the physical world in this way.

Castiel mentioned eating molecules ONE TIME and well, I ran with it.

---

A couple of examples I feel strongly about, using Castiel as an easier point of entry than say, Lucifer or Gabriel:

Angels think in a series of sensations, like a form of Synesthesia.  Synesthesia is a concept explored in both psychology and cognitive neuroscience where people express the feeling of multiple senses activating at once. So for instance, the words might leave you with an impression of color or sounds may give you a physical sensation. I think Angels can, and do, adopt a more human perspective the longer they interact in the physical world. This is especially relevant during the time they are essentially made human, but I think the way they interpret information remains abstract. Just a fun fact, if you have Autonomous Sensory Meridian Response (which is usually shortened to ASMR), you have a higher chance, according to some studies, of having a form of Synesthesia. 

---

Angels also think in patterns. For Castiel, in the beginning: His thoughts are very vibrant. Primary colors denote curiosity. The structure of those thoughts are very rigid. He thinks more in straight lines rather than curves. The movement of the thoughts is calculated and repetitive. Learning something for the first time is difficult, so splitting it into individual pieces is easier to comprehend. This is where we get The Face from, you know the one. He perceives things in his own way which makes him socially awkward in human form. As he gets more familiar with the physical world, and the boys in general, his perspective shifts. He has more robust colors dedicated to the people or objects he interacts with and they shift around easier. His thoughts are less linear and more curved and organic. He has less set structure because he isn’t learning as much anymore, he has an understanding he can build off of and make more defined to himself.  Learning to love humanity requires flexibility that doesn’t come naturally to Angels, so he actively works at it.

Seeing souls is easier than interpreting the actual look of people. This is a doozy, but we will take Dean as an example because I’m Destiel/Deancas pilled. To Castiel, Dean looks the way he looks, smells the way he smells, sounds the way he sounds, and so on in physical form. Castiel learns to interpret him in that way as the series goes on, but his soul, the essence of him, has its own set of sensations. The following are not literal, although I’m sure some would translate that way. He sounds like a crackle of fire and a low drum. His colors are darker oranges and blues and greens. He feels like a soft rain and sun on a warm day. He tastes of barrel aged liquor and smoke. He smells like a hearth and earth after it rains. He feels like every aspect of the impala, from the cold metal to the supple warm leather.  Obviously some of these senses shift and change from time to time, but that forms the basis of what Castiel recognizes as Dean.

---

Grace is at least partially visible to other angels and partially felt by humans. Other angels can see each other in their vessels. So they have a concept of what they look like in their true forms, despite being hidden inside of something.  This implies they can experience similar sensations as the other angels they look at, although I don’t like the idea that they can see their “thoughts” necessarily. I would imagine they can “feel” a sudden intense set of emotions/sensations from another angel however, in the way that humans can tell someone’s emotions through facial expression or tone of voice.

---

Humans can learn to experience angels, albeit in a form that is easier for them to comprehend.  Dean doesn’t experience anything special about Castiel when they first meet, outside of the generic information we get about Angels and the obvious senses he can use: seeing, hearing, smelling, (gods I wish tasting was on this list but! Alas!) As Dean gets closer with him, he can start to “hear” him. I like to think he sounds like a pleasant hum or a slight ringing, similar to a wind chime, depending on his mood. Dean, specifically, makes him hum lower than usual. If he were to hum out-loud, it would harmonize with the way his grace sounds. It takes longer to perceive colors, but I think Dean would see the little flashes of blue, similar to the way Castiel’s eyes get when he’s using his powers. This is why I typically put a little blue squiggle between them when I draw them together. Plus other senses, sorry but this is long enough as it is. You likely get the point by now!

---

Anyway, I’m very happy that literally anyone has even a passing interest in my interpretation of these things.

Formatting this was a nightmare and I feel particularly insane today.