#logarithms explained

[brandboosterx]

In this video, we delve into the art of solving logarithmic equations with different bases, demystifying the process for you step by step. Whether you're a student brushing up on logarithms or someone facing more complex problems, we've got you covered. Understanding how to work with different bases is crucial when faced with logarithmic equations. We break down the techniques, providing clear explanations using frequently used words to ensure that you grasp the concepts effortlessly. No more getting stuck on those seemingly perplexing logarithmic problems!

[rollercoastermalfunction]

any fun math facts? Any thought cheats I could use to help remember how stuff works?

[crumblingspine]

I hope whoever invented the properties of logarithms knows that hell is a very hot place.

[lucyandthepen]

get you alone | ljn ( m )

ideally, jeno should have his hands full with teaching. (un)fortunately, he only seems to have his head full of you.

pairing: tutor!jeno x reader verse: college au rating: r ( minors, do not interact! ) warnings & tags: jeno is a college algebra math tutor & reader is failing, written in lapslock, not beta’d in any shape or form so please excuse mistakes, unprotected sex (wrap it before you tap it, folks), piv, oral (f!receiving), use of pet names (kitten, angel, sweetheart), praise, reader calls jeno ‘sunbae’ until she doesn’t, size kink i guess if u squint! word count: 8.5k

a/n : actually this was written for a different fandom but i’ve decided to make it a jeno fic bc idk why not! first time writing in a different perspective so it’s a bit odd for me & i can't say i fw with this style nor am i particularly proud of this fic but she is ... sumn! also i fear i have a thing for the math tutor trope but that’s neither here nor there AHA enjoy !! 

if you liked it, please consider reblogging to support (especially because this may get flagged for mature content)!

there wasn’t anything special about your case; at least, that’s what jeno had thought when he picked up your request before he met you. before he met you, you were just another student trying to demystify the painfully enigmatic art of getting through college algebra. before he met you, he had already tagged this case as another charity stint — a good way to get brownie points with the dean’s office and the mathematics and natural sciences department. in fact, thinking of all his tutoring cases as community service made them somewhat palatable, if not a little forgettable. he was quite sure, at the time, that you’d be in and out — both of the tutoring center and his memory. such was the case with most of his other tutees, anyway. 

he hadn’t expected you to be… well, you — a pretty little thing, with your sweet smile and your wide doe eyes. on the first day, you’d stood out; you’d arrived at the tutoring center’s lobby in a short dress, knit cardigan, and coquettish makeup, as if every fiber of your being were bidding the spring a solid farewell. multiple heads had turned, including his, as you came up to the front desk and asked for one lee jeno for college algebra. you were eager for summer, jeno had learned as you broke the ice little by little, in part because you looked forward to visiting okinawa with your family, but also because you were eager to get your first semester out of the way. that much, you had in common with most of his other students — almost all of the ones seeking help in college algebra only took it as a depressing core requirement of whatever degree they were doing. you, specifically, were focusing on fashion design; that very vividly explained your attention to your looks. this mathematics class was a thorn in your side, a mandatory thing that was simply supposed to get you through later business-oriented classes in your degree program. for jeno, however, college algebra had become the perfect excuse from the moment he’d laid eyes on you. 

the more time he spends with you, the more he thinks you’re exactly his taste. it starts off with little things he finds attractive, things he picks up while he’s watching you fill out the practice sheets he’s prepared for you on quadratic equations or while trying to get you to understand logarithms — your neat, tiny handwriting, almost like print; your habit of boxing your final answers in firm strokes, even if they’re hopelessly wrong; your colored tabs, cascading down the page side of your textbook. but as the weeks wear on, he sees all the little things in between — the way your long eyelashes quiver when you stop and close your eyes as you think for the answer, the upturn of your plush lips when you have the same answer on the practice sheet as he does, the deepening of your artificial blush with a natural hue when you realize you don’t know the answers to his gentle questions. he notices that you refuse to wear anything longer than a knee-length skirt despite the still-strong winds, notices that your tiny palms are always smooth and pink, that your hair always smells of coconut milk. these are things he can’t help but jot down in his memory — that was exactly what you were, after all: memorable. 

and the more he remembers about you, the more jeno wants you. yet he’s never made a move, never given so much as a hint of his interest, not only because there are prying eyes all around the building but also because you have never so much as shown a smidge of desire back. in fact, he has to wonder if you’ve ever thought of him in a different capacity — not as a tutor, but as a man. if you have, you’ve never made that obvious; you always talk to him respectfully, the little wall you’ve erected between the both of you remaining steady, and you never let your eyes linger on his face for longer than it takes for him to explain what you don’t know. jeno has had his fair share of female students, and in all of them, he’s seen the same kind of hunger — to few, he’s catered to their whims, if only to pass the time, if only for his own benefit. but you, with your ribbons in your hair and your sweet, sweet mouth, have never once shown that same kind of desire. 

he doesn’t know if it frustrates him, but he does know one thing — it makes him want you all the more. 

he wants you even now, as you sit across from him, dolled up as usual. even now, as your eyes take on a glassy sheen of defeat, your cheeks puffing out in the way that tells him you’re admonishing yourself once again, he craves you — maddeningly so. and he realizes that it doesn’t really matter if you're not the one to fall first, as long as he can still have you. 

“time out,” you beg, your fingers meeting the palm of your hand to signal a break. “my brain feels like it’s going to explode.”

“you just had a break ten minutes ago,” jeno reminds you, though there’s a lighthearted amusement to his voice that makes you smile sheepishly. “at this rate, you’ll be on more breaks than you’ll be taking the time to actually learn.”

“i’m trying,” you groan, your fingers curling against your forehead as you bump your head against your fist. “i just don’t think i’m cut out for this polynomial whatever — trial and error bullshit.” 

“you’ll hate me for saying this — but you’ll never know unless you keep trying.” 

“funny.” your sigh rustles the papers in front of you gently. “how do you do it, sunbae?”

“hm?” 

“you’re not only good at this stuff, but you’re so good you’re able to take the time to teach people like me.” 

“strengths and weaknesses — it’s the natural way of the world.” jeno smiles gently at you, and he notes how his chest feels tighter when you return the sentiment shyly. “i could never do what you’re doing in your own degree, try as i might. anyway, you’ll get there. i won’t let you become my first ever failed project, you know.”

“i wouldn’t want to let you down either, sunbae, but—” the back end of your pencil taps lightly against the surface of the table. “it just feels hopeless. i can’t focus on anything. it’s so… so abstract, and everyone here is talking all at once, and i don’t even know what i’m ever going to get out of this class in the long run.” 

even when you’re dejected, you look pretty; your bottom lip juts out naturally when you whine like this, and for a moment, jeno can’t say anything in response. he’s too busy wondering what your mouth would feel like on his — on him. when he snaps himself out of his brief reverie, he notices you’re looking around at everyone else — and he has to agree that with the noise level in this whole building, it isn’t the most conducive site for learning, especially when the learner is already so averse to the subject matter.

“i can’t help much in the way of it being too abstract,” he says kindly. “but it’s not a requirement for us to have our sessions here. i know it can be quite distracting, all these voices flying around, so why don’t you look for a place that better suits you, and we can start meeting there instead? the more comfortable you are in your environment, the better you’ll be able to absorb the material, i’m sure.” 

“you think?” your pencil comes to a slow halt as you refocus on him, a thoughtful light glimmering behind your gaze. “yeah — yeah, i actually wouldn’t mind that. then, i’ll look for a different place for us to meet, and we can start there next week. how does that sound?”

“whatever suits you suits me,” he responds easily. 

he lowers his gaze immediately after you flash him a blinding grin; there are far too many people here, as you both very well know, and if he keeps looking at you and your pretty little expressions any longer, he might just give them something to actually look at. 

it had been your idea, not his, so why did jeno feel like he’d dragged you into a compromising situation?

you’d texted him over the weekend that your search for a new venue had been absolutely fruitless; every cafe and study space you’d been to was either too expensive or equally as packed with people, if not both. jeno had seen the preview to your message, but he hadn’t been prepared for what it read out in full when he’d actually opened it. 

sunbae, would it be too difficult to just meet at my apartment? i attached a map, so let me know!

it wouldn’t be too difficult; logistics-wise, it was walking distance from campus and almost directly across the train station he takes home. it also definitely promised an environment you were comfortable in, and you wouldn’t have to worry about excess noise from any other tutoring groups. no, the difficulty really only lied in himself — you two, all alone, would certainly mean his mind would be up to no good for the two hours every monday, wednesday, and thursday you would be together. 

but for your sake, he’d try to rein it in, with the operative word being try. 

your place is as neat and as pretty as you are; he doesn’t know if you’ve cleaned up for him, or if you’re naturally this organized, but he likes it all the same. it smells of toasted marshmallow and expensive perfume, and all your furniture matches. jeno supposes he likes that in a woman — someone able to care for herself, someone who cares about herself. and you’re always just as neat and pretty to match, with your hair always styled sweetly, your makeup always enhancing your features. 

the problem is that now that he’s in here, where you live, and where you spend most of your time, jeno’s mind seems to wander too much towards thoughts about what you do in private. he rejects studying on the couch, not just because it’s bad for posture and concentration but also because he can’t help but imagine you pressed into the cushions by his hand. he suggests the small dining table you have, but on the second meeting at your place, he starts thinking about what you might look like seated on the table, your ass hanging over the edge and his face buried between your thighs. whenever you look up to ask him something, he drinks in your lovely, made-up face again, and starts wondering what your makeup would look like ruined before he interrupts that trainwreck of a thought with the answer to your question. 

by the end of the week, jeno’s defenses are all but shot, and he realizes that this situation might be optimal for you, but it definitely isn’t doing him and his now constantly straining cock any great favors. 

he supposes that your performance has somewhat improved; you’re less likely to trail off when you’re thinking and can actually do practice sets for a lot longer without all the noise and hubbub around you. your only real hindrance is yourself and your frustration; you have a habit of giving into your carelessness that sends you spiraling into despair, and it doesn’t help that when you press your cheek against the surface of your dining table and whine, the comfort jeno offers is noticeably delayed because he’s too busy thinking about his cock between your lips. 

“my dad’s going to kill me if i fail this midterm,” you grumble, stabbing the practice sheet with your pencil; it skids sideways, and jeno robotically fixes it back into proper alignment for you, careful not to brush against the arm that’s folded inwards, supporting your chin. “he only agreed to let me take this degree because of the business aspect of it. as if i’ll need to know about—” you check the header of the worksheet. “domain and range when i’m doing actual design work.”

“you’ll never know what might be useful later on in life. i definitely thought this was nonsense back in high school — and then i got this job.” 

“and now you’re rolling in dough?” you smile slightly. jeno chuckles. 

“i’m a long way away from having myself a scrooge mcduck golden pool, but i make enough to get by very comfortably, thanks to this.” 

“thanks to me, you mean.”

“you’re not my only student,” he snorts, pinching your elbow; you cry out exaggeratedly. “focus up. the hour’s almost over, and you should have finished with this much earlier.”

“can you leave it as homework?”

“not a chance.”

you blow out a sharp puff of air. “my mom used to do this thing where she’d give me rewards if i did well with my homework. i wish i’d still get something out of this.” 

“what kind of rewards did she give you?” 

“chocolates — candy, or sometimes we’d go out for milk tea together, if i did a particularly good job.”

“this is math tutoring, not a trip to the dentist,” jeno says, amused. 

“a trip to the dentist would be more enjoyable,” you mutter under your breath, picking up your pencil and doodling an angry face next to the number you’re only halfway through solving. “this totally blows.” 

“try to finish this before the hour’s up, and i’ll see if i can get you something nice. out of my own paycheck,” he stresses, prodding at your cheek to shift your attention back to the paper. he doesn’t miss the fact that your eyes light up, childish as the promise is. 

he doesn’t know if that’s really what motivates you, but you do manage to finish the worksheet with a few minutes to spare before the clock hits seven, and that earns you some light, solo applause. it isn’t much by way of true praise, but you flush with pride all the same. jeno packs his things in silence as you get yourself a glass of water, and you see him to the door. only there does he notice your eager eyes, your expectant smile. 

“what’s going through that pretty little head of yours?”

“are you really going to give me a reward? i did great today, you know,” you respond bluntly. 

“you were serious about that?” he laughs. 

“absolutely. i earned it.” you raise a slim finger, wagging it in his face. he trails it with his gaze, no shortage of amusement in his eyes. “next monday, i want something sweet.”

jeno takes in the sight of you, keeping your door open with your hip; he wonders if you know what you’re doing to him, what you’re asking of him — if you even know there’s nothing that could possibly be sweeter than you at this very moment. he drinks in the sight of your feigned haughty expression on your pretty features, the unnervingly low dip of your tank top, the tempting hemline of your shorts, and feels like you must be aware of what he’s going to do next. 

“if it’s something sweet you want, you don’t have to wait until next week.” 

he does it before he can think it through — surely, there’s nothing too harmful about a quick kiss? he angles your chin upward with his thumb and forefinger before you can even react to his words, and he tastes you like that for the first time. you’re just as soft and as sweet as he’d imagined, if not more so. 

when jeno pulls away, you step back; there’s shock written all over your face, your mouth still hanging open slightly. your voice is gentle, shaky when you start speaking. 

“sunbae, wha—”

“see you next week. rest up over the weekend, or there’ll be consequences.” 

he finds it easy to joke with you now, even after what he’s done — finds it easy to wave goodbye with nonchalance as he walks to the elevator, now that he’s gotten one thing out of his system. the look on your face, the growing blush across the bridge of your nose and your temples is indication enough for jeno to feel confident — if you hadn’t thought about him that way before, you were sure to spend the next few days doing exactly that. 

it’s exactly a week before your midterm exam, and jeno notices you’re less than focused. 

he’d let you stew over the weekend, not expecting much by way of communication; indeed, his phone hadn’t once been jostled by your texts. he’d taken that silence to assume that you’d been wrapped up in thoughts of the kiss he’d left you with, and you did not disappoint on that front; the next monday saw you fidgety, flushed, and constantly faltering in your words. you asked less questions, which normally indicated a problem, but today, he’d let it slide; you definitely had a little too much on that pretty little brain of yours. 

he notices you’re still dolled up — your eyelids are shimmery, and your lips are glossy; you’re wearing a tennis skirt that hits all the right buttons for him, too. it’s true that you’re always pretty well-dressed and put together, but today somehow feels different. if before, jeno had always seen you dressed up simply to look good, today it feels a little more like you’re dressed up to look good for him. he knows it’s a little bit egotistical to assume as much, but he also doesn’t miss the side glances you throw at him when you think he’s not looking at you answering your textbook or the way your cheeks glow when you make the slightest bit of eye contact. 

still, you try to focus as much as you can; it’s adorable, in fact, to see all your valiant efforts to appear unperturbed. he figures he’ll play along for as long as you will — what matters to him, after all, is that you’re in the game to begin with. you complain less today, focus on your worksheets, and jeno even manages to witness the sight of your forehead creasing up as you concentrate on a particularly difficult item. you’re adorable, in the kind of way that makes him want to pin you down and have his way with you. 

you finish your work without a fuss today; you only actually asked for his help twice, which was a feat in and of itself. and again, when the session is over, you walk him to the door.

this time, when you linger, he waits; you’re clearly not good at hiding your true intentions, as it’s become clear you have something you want to say. as you try to piece your thoughts together, jeno reaches into his backpack’s front pocket and extracts today’s gift — an actual chocolate bar, albeit a rather run of the mill one. 

“what’s this?” you ask, your thought process clearly derailed as confusion takes over your features. 

“your reward. for a good job last week and today — you said you wanted one, didn’t you?” 

“but i thought—” you stop yourself, your mouth opening and closing, suddenly wordless. jeno grins. 

“not good enough? i picked that up from a convenience store on my way here, so it definitely isn’t anything special, but i thought it would at least be a good motivator.”

you’re turning red, and there’s turmoil in your eyes — he enjoys this, he realizes, the way he flusters you. if he had known this would be the result, he would have made a move much sooner. you shift your weight from one foot to the other, back and forth, obviously weighing out your options too. finally, you say, “alright.”

“you seem disappointed.”

“i’m not.”

“i’ll get you a better brand next time, if you really don’t like it.” 

“it’s not that.”

“so what is it?” he doesn’t expect you to say it, and you don’t defy expectations; your bottom lip just quivers, and jeno chuckles low under his breath, stepping forward just past your doorway, just a little bit closer to you. “don’t tell me you wanted something completely different?”

you don’t say so, but he knows; he can tell by the way you tilt your head back, the way your lips part slightly, the gloss still trailing along the seam. he can tell by the way your torso arches just a little bit closer, almost like an accident. he can tell by the way your eyes bore into his, almost pleading. 

“what you did last week…” you start, but your voice trails off into nothing soon after. he chuckles again.

“ah, that. i might have gotten ahead of myself.” 

“was that all?” you press.

“and what would you do, if it wasn’t?”

“well — do you always like to play games?”

“i have a penchant for playing with my food before i eat it, if that answers your question.” he smiles down at your still-reddening face. “i was giving you a reward, as you wanted. i came up short on options then and there. you’ll let it slide this once, won’t you?”

“you did that just because i did well last week?”

“of course.”

“well, i did well today, too.” 

“you did, and that’s why you have this.” he gestures to the chocolate bar in your hand. 

“i don’t want this.” your voice is stubborn now, heated and frustrated, and you stuff the chocolate back into his hand. you must not like having to ask for something so blatantly — it’s too bad jeno wants to hear it in those exact words. 

“tell me what you really want, then.” 

you’re still unable to find the words, but your hands do the talking for you; they press into his shoulders and give you leverage to tiptoe until you’re just close enough to his lips. but you don’t close that gap, your mouth quivering only inches away from his, and oh, jeno wants to toy with you, but you’re just too irresistible this close to him. his warm palms press against your jaw, keeping your face steady as he closes the gap, and this time, he doesn’t just get a brief taste of you — jeno claims your lips with the thirst of a man who’s stumbled upon an oasis in the desert. 

you must have thought about this moment long and hard over the weekend, because the nonchalant side of you that’s turned a blind eye to him is completely gone; he drinks in your soft noises and short, breathless gasps — all signs of your eagerness — until he’s drunk on the taste of you. the deeper the kiss gets, the less you can keep up, but you try, and jeno always likes rewarding your efforts, his wide tongue taut and flush against your tiny one in the sweet, warm cavern of your mouth. he licks every inch of it, leaves the mild nicotine taste of himself there, before he pulls away slowly. your eyes are still closed when he creates distance, fluttering open in a happy haze a few seconds later. 

“good enough for you?” he murmurs, tucking a soft lock of hair behind your ear. you hum in assent through your dazed smile, and jeno knows he won’t be the only one looking forward to this coming wednesday.

you’d done really well today.

jeno’s proud of you — prouder than he’s been of most of his students in his career here at the university, actually. you’d finally answered a worksheet almost perfectly, save for a couple of numbers where you’d forgotten to round up, and those things are absolutely negligible at this point (by his books, anyway). you’ve been on your best behavior yet, avoiding all forms of complaint, and he knows fully well why, but he won’t criticize you for your hard work all the same, no matter the motivation behind it. 

in fact, you’ve done so good that he doesn’t wait until he’s about to leave to give you your sweet reward — which is why, twenty minutes before he’s meant to go, he’s got you on your couch, your legs spread, each one hooked over his shoulders. 

truth be told, you’d been good way before the lesson had started; you’d answered the door in a crop top and the tiniest pair of shorts you’ve dared to wear yet — all clothes that you couldn’t yet wear outside yet, given the weather. selfishly, jeno is thankful for this fact, and if he had to list down other things he’s thankful for, just off the top of his head, it’s that you no longer meet in the tutoring center and that your apartment’s walls seem thick and well-reinforced. 

“sunbae, don’t tease me.” your silly little whining voice makes its first appearance of the day, but all jeno does is smile — it’s an almost wicked expression, set firmly between your thighs. “you said i did really well today. don’t tell me you’re backing out on rewarding me?”

“not at all, sweetheart,” he hums, pressing a small kiss to your inner thigh. he likes seeing you shiver at the contact, likes the way you’re chewing on your lip in what appears to be slight agitation. “just thinking of how much of a reward you deserve.” 

in all honesty, jeno would like to take every bit of you now; you’re already so ready for him, anyway. he can smell the faint perfume of your arousal, can see the way you’re anticipating the most from him, and a part of him doesn’t want to deny you of that. the larger part of him has dreamed of burying his cock into you, anyway, and why wouldn’t he do that? but something also tells him to wait — or, rather, to make you wait, to make you want him just a little more. 

and so, he decides.

his mouth finds your skin again, pressing kisses up your thigh; they get wetter, hotter as his mouth moves up, until his nose and lips are buried against your clothed core. you squirm in response, but his grip on your thighs keeps you relatively steady, even as his tongue presses against thin fabric. the wet muscle pushes sharp against your tiny entrance, the tip meeting slight resistance against your shorts and panties, but he finds a way, burying half his tongue in alongside damp cloth. 

you’re already wet like this, and so needy that it might be possible for jeno to get you off just like this, still clothed, but the hunger in him spikes once you call out to him. 

“sunbae, please…”

with a groan, his fingers yank the fabric aside, exposing your pussy to the warmth of his breathing. it’s as pink, as pretty, as tiny as the rest of you, as fuckable as he’d imagined it would be, and he wastes no time in pressing his tongue flat against your folds, dragging it up in a wide, messy stripe; the muscle only tenses when it bumps against your clit, his tongue flicking upwards to tease it. 

you’re so reactive, even at the slightest things — you whimper, you squeeze your eyes shut, you squirm. you’re begging to be fucked, and jeno’s cock is strained tight against his jeans, but your taste is so addicting that he can’t help but dive back in. his tongue eases between your folds now, spreading them apart until they’re lewd and sticky with his saliva, and the nub of your clit has grown so pronounced now — so pert and lovely that he can’t help but purse his lips around it and suck with excess force. 

“sunbae — f—fuck,” you mewl; you almost sound tearful. “f—feels so good…”

jeno wants to tell you how fucking good you taste, how beautiful the sounds you’re making are, but his mouth is too busy; his teeth rake down your cunt lightly, earning him a jerk of your hips, and he has to place pressure down on your thighs again to make sure you’re still enough for him to slip his tongue into your cunt. 

he can tell even just by that how tight you’d be around him; your walls are warm around his tongue, and there’s a pressure against the muscle that tells him how good it’d feel for his cock to take its place. as if to simulate his desires, he presses his tongue deeper in, fucks you shallowly with its wetness until your whimpers become little sobs, broken and choked back. his thumb drags across your slit then settles against your clit, and he can feel the thrum of your pulse against the pad of his finger, beckoning him. he complies, easily, thumb tracing circles around the nub that start off slow, only for him to ramp up the pace alongside his tongue. 

you’re easily at fault for that; the way you whine for him, call him sunbae, tell him how good it feels over and over — why wouldn’t he want more of you? 

he’s not sure which of you really earns the sweet reward today; you cum on his tongue, your cunt trembling against his mouth and your fingers threaded into his hair, but he’s the one who comes out licking his lips like he’s had the best treat of his damn life.

come the middle of next week, jeno finds himself face to face with a test paper — one already clearly marked, with a number circled on the top-right corner. ninety. a stellar grade for anyone, and especially for you. 

you know it, and you look absolutely triumphant; you’re practically shining as you perch on your little dining table, your perfectly manicured finger jabbing at the score in emphasis. 

“flying colors, wouldn’t you say?” 

“color me impressed,” jeno replies smoothly, a genuine smile of pride tugging at his lips; he turns the page over, scanning your responses. you still draw your parabolas a little on the small side, making them a bit difficult to discern, and you’ve still got the habit of not rounding your answers up, but this is tremendous work, and he’ll be the first to praise you for it. “your dad must be filled to the brim with joy now, right?”

“i haven’t told him yet. you were the first.”

“well, i’m proud of you, sweetheart.” 

“proud enough to give me a reward?” 

he looks down at you in feigned thoughtfulness. here you sit, back in your little tennis skirt, looking up at him with hopeful eyes under those long, curled lashes. for someone who spent the first half of this semester acting ostensibly nonchalant, you’d very easily shown your true colors soon after — not that he really minds. in fact, he’s taken a decided kind of liking to how eager and willing you’ve come to be. 

“we’ve only just started our session, though,” he hums out, an idle thumb grazing his chin as he watches your expression turn from bright to cloudy, the beginnings of strategy darkening your gaze. it’s not like he wants to say no; he has no real intention to. but seeing you squirm in want makes him feel good about his decision to hold out a little longer — never mind the ache in his cock even then. “don’t we usually leave the rewards for a later time?” 

“i was thinking — since it’s the start of a new lesson —” 

“we wouldn’t want you falling behind from the start, would we?”

“i promise i won’t,” you pout. “i promise i’ll put in my best effort next time.” 

“next time? sweetheart, don’t tell me you’re thinking to get off scot-free today…” jeno trails off, his hand falling to the nearest surface it can reach — which, logic seems to dictate, is your soft, milky thigh. he feels you tense under his palm, and he bites back a smile, keeping his expression level. “i just don’t know.”

your small hands grip at the front of his shirt, and he hears you, for the first time, doing something he’s always wanted to hear you do. 

“please, sunbae?”

how could he say no to you? he hadn’t really planned on it, had only wanted to see you do this, but it’s still too much and beyond his expectation — your misty gaze, your quivering lip. it’s almost laughable that you don’t think he’d notice the way you shift yourself so that his hand, still warm against your thigh, slides up your skin, the hem of your skirt bunched up in the junction between his thumb and forefinger.

jeno chuckles — isn’t this exactly where and how he’s always wanted you? “how could you ask me like that and expect me to refuse, angel? in that case, i have no real choice but to dedicate all our time today to your reward.” 

your breathing hitches — in anticipation, in desire, in excitement — as his hand continues its trail upward, deliberately now, fingers hooking into the waistband of your panties. his head dips down, rests into the crook of your neck, and he inhales the thick, sweet scent of your perfume, your shampoo, of you and all that he’ll take from you. 

“just remember, you asked for this,” he murmurs against your skin. “so i’m going to take every bit of you until there’s nothing left for anyone else.” 

you’re so willing, so ready even before he can get his full bearings; your hips are rising slightly off the table, and jeno feels like it’s you that’s telling him to move faster. he tugs down your panties, letting gravity take its course until they’re a tiny puddle of fabric on the floor, and he slots himself between your legs. like this, you have no choice but to spread, and you do so without hesitation, your knees locking against his sides as he pulls you in for a tight, hungry kiss. there’s that taste of you he loves, that clean, sweet buzz that draws him in, and his hands are bruisingly tight on your waist as he reclaims your lips. 

you already look dazed when he pulls away, which is always cute, but a little unfair — jeno wants you to be aware still when he takes you, and damn, if he doesn’t want to take you right fucking now. he kisses you again, harder and more demanding, as if willing your attention back to him, while his hands explore you — run up your thighs, fingers brushing against the plush curve of your ass. it’s not enough, not by a long shot, and he’s pushing the waistline of your skirt up your stomach with his hands, letting his warmth transfer onto your skin; he chuckles as your stomach sucks inward at his touch, just as you let out a gasp against his lips.

and he wants desperately to hear that noise again; in fact, he wants to know what you sound like in every capacity. his mouth works down your neck, pleased to find that suckling wet and languid on a spot just above your collarbone has you writhing and whimpering. are you sensitive or touch-starved? whatever the reason, he wants to draw all of that out of you, his hands drawing back down to hook under your thighs. jeno drags you to the edge of the table, until your bare cunt is flush against the front of his jeans, and he lets you feel him — a brief tease of what’s to come. 

“i’m s—so wet already,” you whisper, as if he doesn’t know — as if you know it’s exactly what he wants to hear anyway. “sunbae, please, i need you.”

“not that,” he murmurs, his teeth grazing your collarbone as he speaks. “not sunbae. jeno. call me jeno, angel.”

“jeno,” you exhale shakily, and it’s music to his ears — as if the last thing holding him back from you had shattered. 

“that’s it — what a good girl,” he purrs, his hips rocking forward against your pussy before they retract, leaving just enough space for his hand to slip between. slender fingers trail down your folds, sticky and slick. “you are all wet for me, aren’t you? ready to take me deep inside?” 

even the way you nod, a tiny movement of assent, drives him wild, yet a part of him still wants to test the limit of your patience, his middle finger stretching to circle your entrance. 

“wouldn’t want to shock your tiny little pussy, though, would i? will you let me stretch you out first, kitten?”

“yes,” you mewl, sounding almost tearful. “anything— anything, please.”

jeno drinks in the long, drawn-out keen you set free when his digit sinks into you; he’s already felt your walls against his tongue, but a small part of him is still surprised at just how tight you are. that same part nags that he might not fit easily into you, but whatever that voice is is easily drowned out by a more assertive promise — he’ll make it fit. 

“can’t tell you how much i’ve wanted to feel your pretty little hole around my cock,” he presses on, his finger pushing deeper in; he feels you tense a delicious kind of tightness, as if it’s almost too much for you. is it? “ever since that first day you came into the tutoring center, dressed up all cute — did you do that on purpose, sweetheart?”

“yes,” you admit, breathless; the syllable is lengthened into a weak moan as jeno pumps his finger into you, slow, deep strokes that tease your tacky walls open. “wanted — wanted to make a good impression…”

“and you did, didn’t you? kept looking so sweet for me, so pretty every single time — got me thinking about all the ways i wanted to have you. got me so fucking hard every time we’d meet — is that what you wanted?”

jeno doesn’t give you much room to respond, but he can make his own answers to appease himself anyway; he reclaims your lips, already eager for another taste of you, and you comply with the same amount of desire, your soft whimpers melting against his teeth. in the space of pseudo silence, wet, messy noises, he manages to tease another digit into you, and you cry out against his lips as it pushes in, joining the first in how deep it reaches. he absorbs that too, takes in every minute sound you make, relishes the way you pulse around his fingers. even without the noises, he can tell your pleasure’s heightening, with the way you clench around him, your hips rocking pitifully as you’re eager to rut against his palm. 

“look at you now.” he’s selfish, but he doesn’t care — he wants to ruin you, and if the telltale squelch of your cunt as he fucks his fingers into it isn’t indication enough, then the way your mouth hangs open as he pulls away, letting his name fall freely from your lips, definitely is. “legs spread, all desperate to feel good for me. what a needy little kitten you are. this good enough for you, angel?”

you shake your head, only to squeal as he pulls you closer, his fingers shoving deeper into you; your hips are re-angled, allowing him to brush the pads of his digits against the rough, sweet spot, and he feels triumph bloom in his chest as you throw your head back, teary eyes squeezed shut.

“no, no, no,” you babble, and he can see the bob of your throat as you swallow hard, clutching at sense to make words. “want — need your cock, want to cum on your cock so badly, jeno — want you to fuck me, stretch me open, please —”

“greedy, aren’t you?” he murmurs, leaning in to nip at the spot he’d left reddened above your collarbone. “go on then — show me how much you want it. show me what a good girl you are, and cum on my fingers.” 

“but—” 

“come on, angel,” he urges above the squelching noises, increasing surely in volume. his fingers meet resistance when they spread apart inside you, but all it does is create a delicious friction that has you squirming in his hold. “don’t hold back. let me see you fall apart.” 

and you do, so prettily, your eyes rolling back and your voice unrestrained. jeno’s fingers ride you through your orgasm, pumping deep and steady despite how slick you’ve gotten, your juices coating his hand and wrist. he watches the flush rise to your neck, stopping at your cheeks, watches the heaving of your chest, the shine of your skin from a thin sheen of sweat, and he doesn’t want to let you come down from this high, but his cock is aching — practically bursting from his jeans — and all he can do is make the silent vow that the next time you look like this, he’ll be balls deep in you. 

“that’s my girl,” he coos gently, watching the tension slip from your shoulders; his free hand is at the small of your back quickly, easing you down as your torso falls back, and you’re laying on the table. “pretty little thing, aren’t you? cumming so sweetly for me.” 

“jeno,” you groan out weakly, your tiny hand clasping around his wrist. “cock — i want your cock, please—” 

“can’t wait?” he’s indecent for sounding amused, but even that does nothing to stay his arousal; how eager you are simply makes him want you all the more. “okay, angel — since you asked so nicely.” 

a slight twinge of disappointment runs through him as he pulls his fingers out, but it’s quickly buried by the feeling he gets once he gives you a clear sweep of a once-over; how slutty you look, still half-dressed but already half-ruined, your thighs shaking in an effort to keep them open for him, the remnants of your last climax still leaking out of your hole. the sight of you has him so distracted that unbuttoning and unzipping his pants feels like a fever dream of an act; he barely notices what he’s doing until he’s already bare in front of you, and alertness has crawled halfway back into your consciousness as you push yourself up on your elbows to look at him.

“it’s so—” you have the decency to blush, though there’s a pleased look on your face that tells him you’re not really embarrassed. “i didn’t think you’d be this big.” 

“does that worry you?”

“i’ve never had anyone… this big.” pride blooms in his chest — good, he thinks, because if he can’t be as memorable as your first, then he’ll take being the most in something as a prize. “i don’t think — will it fit?”

“does it matter?” he chuckles, and your blush deepens. “no matter what — you’ll take all of me in, won’t you?”

you chew on your bottom lip, as if considering your options, but to jeno, there’s really only one choice — the correct one, and you make it when you nod your head. 

“it’ll feel good, though, you know,” he muses. his hand wrapped around his base, he lines himself up with you, the tip grazing against your folds. “even better than just now.”

with just a little more pressure, he has his shaft flush against you; his girth sits against your slit, the tip pressed against your clit, and he starts to rock his hips — into his fist, against your cunt. your hips quiver, and a shiver runs through you as your pleasure spikes again, but he can tell it isn’t enough. your bottom lip is back between your teeth, and your eyes are flitting between his face and his cock. jeno reaches out, eases your lip out from between your teeth, strokes it gently, almost tenderly. 

“say it,” he commands in a soft, silky voice. 

“fuck me, jeno,” you breathe out, barely missing a beat. “fuck me, fuck my pussy, please.”

and if you ask that desperately, he’ll waste no time; he draws his hips back, dragging his cock down until he’s aligned with your entrance. his eyes are trained on your face, even when he pushes in, so that he can take in your expression — the widening of your eyes as his tip breaches the first wave of resistance, the way your mouth falls agape as his fingers dig hard into your flesh. he’s never seen a prettier sight in his life.

“stretched you out already, but you’re still so fucking tight,” his voice is a soft, melodious croon, a stark contrast to the way he’s forcing past your tightness. “tight and wet, like a good girl.” 

“so big,” you whimper, your fingers stretched far enough to tickle the front of his shirt. “can’t — can’t take it.” 

“of course you can, angel.” jeno doesn’t give you the time to brace yourself fully before he’s rocking his hips in a little more sharply, his cock now halfway into you. your fingers curl into a little fist, immediately flying back to block the noise from your mouth. “ah ah. don’t get shy on me now; you’ve been so noisy for me all this time.”

but he doesn’t really mind the way you clap your palm over your mouth to muffle your high-pitched squeal as he thrusts in fully, the adjustment period after the last movement close to nothing; he’s too busy focusing on how good you feel around him, how warm and wet your insides are. this is heaven, easily, and jeno wants to stay here for as long as he can. 

“god, you’re fucking tight,” he repeats, an appreciatory gaze running over where you’re joined. his thumb stretches over your folds, rubbing them — something of an apology, perhaps, although all it does is stimulate you more, and you shiver at the extra contact. “how deep is it, baby?”

“can feel you here,” you mumble out, your small hand pressing just above your pelvis. he feels the tightness multiply as you place pressure, even just for a moment. “your cock’s so much deeper than anyone else.” 

your hand falls away, limp, as he draws his hips back; you inhale, long and deep, before letting it out as a broken moan when he pushes back in. it drives him crazy, to start off this slow, when all he wants is to find a pace that has you sobbing, but the resistance of your pussy against his length isn’t easy to ignore. jeno works you open, his jaw set and his grip tight against your frame, and it isn’t long before he’s picking up speed, the slap of his flesh against yours fueling him exponentially, mingling with your cries, steadily increasing in volume. 

“that’s it. let everyone hear you,” he eggs on, his thumb now circling tight around your clit; your legs are quivering, threatening to close, but he keeps you steady, one arm wrapped around your thigh. his thrusts grow rougher, more deliberate, and when he looks up from where you’re joined back to your face, he sees your expression as a mixture of incredulity and ecstasy. a thin line of drool hangs from the corner of your mouth, your pretty pink lip gloss smeared, and fuck if he doesn’t want to make sure you look like this every single time he comes over. “let them know who’s fucking you good, angel.”

“j— jeno!” your voice hitches, lilts up as he presses in at a different, deeper angle, and he almost cums right then and there from the way your walls pulse around him. “your cock feels so good, fucking me just right— more, god, more—” 

he complies without hesitation, gathering both your thighs and pushing them closer to your chest; you look even lewder like this, folded in half with your sopping cunt presented to him like it’s all his to take, and it is, isn’t it? there’s an increase in the intensity, the vigor in which he pumps his cock into you, and he knows he’s brushing repeatedly against your spot by the way you’re blubbering his name out in a way that suggests you sincerely think no one else in this building can hear you. 

“that’s my girl,” he hums approvingly, though there’s a thickness in his voice that has him sounding a little more strained. “such a good girl, with your cunt all nice and sloppy for me. do you like it when i go this deep? does it feel good when i fuck you where no one else can?” 

“yes!” you sob out, your hands crumpling the end of your skirt up into tight fists. “jeno, i— cum, i need to cum again, please—”

“i’ve got you, kitten,” his tone is reassuring, a stark contrast to the rigor of his hips. “don’t have to hang on for me, you know; always love seeing you fall apart.” 

“m’close, so close —” 

“let go, then,” he urges, his blunt nails digging into your flesh. “let me feel that sweet cunt cum on my cock.” 

you comply without hesitation, though if you’d done it willingly, he can’t really tell; he has to pin your hips down to stop you from bucking up and causing him to slip out, and you writhe against him as you sob in ecstasy, your walls fluttering before they clench. stray tears leak from your eyes, squeezed shut, and jeno wants nothing more than to eat you up like this — broken, fucked out. 

you’re not even fully down from your high when he feels it — that sudden wrenching in his gut that tells him he’s about to follow suit. with a low groan, he peels your thighs apart again, lets you watch him as he bullies straight into your leaking hole. your voice is a staccato, punctuating every deep, sharp thrust into you, and it’s exactly to that melody that he wants to get off. 

“tell me where you want it, angel.” he doesn’t trust his voice, sharp and short as it is now. “should i mark your pretty face? your stomach?”

“want it against my pussy,” you whisper out, and jeno almost loses his mind as he watches you spread your folds apart with your forefinger and middle finger, inviting him. “make a mess of it, sunbae.”

he’s barely able to pull out before he’s spilling against you; he ruts against your slit, coating your folds and the insides of your thighs in thick, creamy white. you hold your legs apart for as long as you can until they start to tremble, and he catches them and gently eases them down. 

when you sit up to kiss him, you’re still demanding; he feels your hips rock closer, your sticky cunt pressing against the underside of his cock.

“not enough,” you murmur against his lips, and jeno chuckles as you bind your hands around his neck. 

“don’t worry, kitten,” he hums back. “we’ve got all afternoon.”

[todays-xkcd]

Update: The physics department has recruited an astronomer who studies meteor fireballs.

Water Balloons [Explained]

Transcript

[Graph with Y axis labeled "Mass" running from 10-30 kg to 1030 kg on a logarithmic scale and X axis labeled "Lifetime", also on a logarithmic scale, running from 10-20 to 1020 seconds.] [There are three elliptical blobs on the graph: one on the lower left corner labeled "Mesons", another on the upper right corner labeled "Planets", and another in the middle (1kg mass, 1s lifespan) labeled "Flying water balloons". There are two bidirectional arrows pointing from the center blob to the two other blobs.] [To the left of the chart are Cueball and Ponytail. Ponytail is throwing a water balloon, and Cueball is dodging from one. To the right are Megan and Hairy. Megan is preparing to throw a water balloon, and Hairy is slipping in a puddle of water, with a water balloon having landed near his foot with a "Sploosh!".]

[Caption below the panel:] In the annual interdepartmental water balloon fight, meson particle physicists and planetary scientists are usually evenly matched, since they're both equally far outside their areas of expertise.

[bobacupcake]

Can you do one about the Sea of Thieves water?

OK

so . there was a biiig long talk about this at siggraph one year!! you can watch that here if you'd like . in the time between me getting this ask and me fully recreating the water, acerola also released a great video about it . the biiig underlying thing they do and the reason why it looks so good is they are making a Really Detailed Ocean Mesh in realtime using something called an FFT (fast fourier transform) to simulate hundreds of thousands of waves, based on a paper by TESSENDORF

WHAT IS AN FFT - we'll get to that. first we have to talk about the DFT - the discreet fourier transform. let's say you have a SOUND. it is a c chord - a C, an E, and a G, being played at the same time. all sounds are waves!!! so when you play multiple sounds at the same time, those waves combine!!! like here: the top is all 3 notes playing together, so they form the waveform at the bottom!!

now if someone handed you the bottom wave, could you figure out each individual note that was being played? how about if someone handed you a wave of One Hundred Notes. you would think it would be very hard. and well, it would be, if not for the Discreet Fourier Transform.

essentially, there is a way to take a bunch of points on a waveform comprised of a bunch of different waves, add them all together, do some messed up stuff with imaginary numbers, that will spit back out at you what individual waves are present. i made a little test program at the start of all this: the left are the waves i am putting into my Big Waveform, the top right is what that ends up looking like, and all the little rainbow points on it are being sampled to spit out the graph at the bottom right: it shows which frequency bands the DFT is finding (here it is animated)

this has enormous use cases in anything that deals with audio and image processing, and also,

THE OCEAN

tessendorf is basically like, hey, People Who Are Good At The Ocean say that a buuuunch of sine waves do a pretty good job of approximating what it looks like. and by a bunch they mean like, hundreds of thousands to millions. oh no.... if only there was a way we could easily deal with millions of sine waves..........

well GREAT news. not only can you do the DFT in one direction, but you can also do it in REVERSE. if you were to be given the frequency graph of a noise for example, you could use an INVERSE DFT to calculate what the combined wave graph looks like at any given time. so if you were to have say, the frequency graph of an oceaaaan, for example, you could calculate what the Ocean wave looks like at any given time. and lucky for us, it works in two dimensions. and thats the foundation of the simulation !!!!!

BUT WAIT

as incredible as the DFT is, it doesn't scale very well. the more times you have to do it, the slower it gets, exponentially, and we are working with potentially millions of sine waves here

THE FAST FOURIER TRANSFORM here we are . the fast fourier transform is a way of doing the discreet fourier transform, except, well, fast. i am Not going to explain the intricacies of it because its very complex, but if you want to learn more there are a ton of good 30 minute long videos on youtube about it . but essentially, due to the nature of sine waves repeating, you can borrow values as you go, and make the calculation Much faster (from exponential growth to logarithmic growth which is much much slower, and scales very well at higher numbers). it's, complicated, but the important part is it's so much faster and the diagram kind of looks like the shadow the hedgehog story plot

so if we use the inverse FFT on a graph of a rough estimate of what frequency of waves in the ocean (called a spectrum, basically tells us things like how many small waves, how many big waves, how different waves follow the wind direction. sea of thieves uses one called the phillips spectrum but there are better ones out there!!) now we have our waves !!!!!!! we can also use another inverse FFT to get the normals of the waves, and horizontal displacement of the waves (sharpening peaks and broadening valleys) through some derivatives . yayy calculus

OK MATH IS OVER. WE HAVE OUR WAVES!!! they are solid pink and look like pepto bismol. WHAT NOW

i cheated a bit here they look better than not being shaded because i am using the normals to reflect a CUBEMAP to make it look shiny. i think sea of thieves does this too but they didnt mention it in their talk. they did mention a FEW THINGS THEY DID THOUGH

FIRST OFF - SUBSURFACE SCATTERING. this is where the sun pokes through since water is translucent. SSS IS REALLY EXPENSIVE !!!!!! so they just faked it. do you remember the wave sharpening displacement i mentioned earlier? they just take the value where the waves are being sharpened and this will pretty naturally show off the areas that should have subsurface scattering (the sides of waves). they make it shine through any time you are looking towards the sun. they also add a bit of specular ! sss here is that nice blue color, and specular is the shiny bits coming off the sun. the rest of the lighting is the cubemap i mentioned earlier, i dont know if thats what they use but it looks nice !!!!!

then the other big thing that they do is the FOAM !! sorry i lied. there's more math. last one. you remember the wave sharpening displacement i Just mentioned. well they used that to find something called the JACOBIAN and well im not even going to begin to try and explain what it means but functionally what it does, is when the jacobian is NEGATIVE it means waves are clipping into eachother. and that means we should draw some foam!!! we can also blur and fade out the foam texture over time and continuously write to it to give it some movement, and bias this value a bit to make more or less foam. they do both of these!!!

YAYYYYY !! OK !! THAT'S SEA OF THIEVES WATER!!!!! THANKS FOR WAITING ALL THIS TIME. you can see my journey here if you would like to i have tagged it all oceanquest2023

thank you everyone for joining me :) i had fun

[yesterdays-xkcd]

If you think this is too hard on literary criticism, read the Wikipedia article on deconstruction.

Imposter [Explained]

Transcript Under the Cut

[Caption above the panels:] My Hobby: Sitting down with grad students and timing how long it takes them to figure out that I'm not actually an expert in their field.

[For all four panels below, there are two frames crossing the border of each panel. The ones at the top left have a caption, and the one below right has the result of the timing.]

[Ponytail and Cueball are sitting across from each other in office chairs.] Engineering: Ponytail: Our big problem is heat dissipation Cueball: Have you tried logarithms? 48 seconds

[Cueball is sitting in a chair at the center of a table looking left at another Cueball-like guy. To the right is a long black-haired girl.] Linguistics: Cueball: Ah, so does this Finno-Ugric family include, say, Klingon 63 seconds

[Cueball is standing with his hands up talking to another Cueball-like guy and Megan who has lifted her arm to palm her face.] Sociology: Cueball: Yeah, my latest work is on ranking people from best to worst. 4 minutes

[Cueball is sitting in an armchair with another Cueball-like guy sitting attentively in front of him on the floor.] Literary Criticism: Cueball: You see, the deconstruction is inextricable from not only the text, but also the self. Eight papers and two books and they haven't caught on.

[perkypeony]

𝔽𝕀𝕊𝕋𝕊 𝔻𝕆𝕎ℕ, ℙ𝔼ℕ𝕊 𝕌ℙ!

It was a rare sight to see the rooftop being used as a study group spot. Umemiya, Tsubaki, Mizuki, and Momose were gathered around the picnic table, discussing something about plants—not the usual talk about how healthy Umemiya’s tomato plants were, but the actual plant anatomy. Sugishita had joined them as well, flipping through his textbook. He kept getting distracted whenever Umemiya spoke, prompting the Furin leader to remind him to focus every now and then.

Seated on the floor nearby were Hiragi and the second-years—Kaji, Enomoto, and Kusumi. Hiragi was patiently explaining some questions on logarithms, since the second-years were struggling with the topic. He wrote out the calculations on a mini whiteboard—God knows where he even got it—while the second-years nodded along and took as many notes as they could. They occasionally asked questions when they got confused, and each one seemed to add to Hiragi’s growing stomach ache.

Just then, Sakura, Nirei, and Suo came up to the rooftop, unaware that this was how things looked three days before an exam. They were surprised by the change in atmosphere. Instead of the usual loud laughter and bickering, the air was filled with quiet concentration and academic discussion.

They made their way over to Umemiya. Suo raised an eyebrow and asked, “Why is everyone suddenly studying today? Is it because of the upcoming exam?”

“Yeah, that’s right,” Umemiya replied. “Actually, you guys don’t need to report patrols when exams are around the corner. Focus on studying until they’re over.”

“I’m glad to know that Furin values academics too!” Nirei said, pulling out his notebook to jot something down.

“Of course,” Umemiya smiled. “We fight together, so we study together too. We’ve gotta show everyone that Furin isn’t just a school full of delinquents who only know how to brawl. I hope the three of you can guide your classmates and help them support one another.”

Sakura frowned slightly. “I’m not smart enough for this kind of stuff. Don’t expect any genius answers from me.”

“Don’t worry, Sakura. You can count on us. I’ve already started studying weeks ago, and I’m sure Suo did too,” Nirei said reassuringly.

Umemiya smiled proudly at his juniors. “That’s the spirit we want!”

a/n: if you have any thoughts on how academic works in furin, feel free to share with me!

[rd0265667]

Karina x Reader: Extra #2

Permanent Taglist: @cwpiqwon @justme-idle

You are not the main character, not even one of the smaller side characters

It's a blessing, to be frank. In a world where people get caught up in their main character syndrome, thinking that they, not others, are the center of the world and that others are inferior, knowing that you're not a main character is weirdly comforting. A side character who can just live in a small bubble and exists for that 5 seconds at the side of the screen. No cruel twists of fate for 'character development', no weird drama to 'push the plot'. What's worse was that some who think that they're the main character were, obnoxious and stubborn in their belief, hard to handle, but to be honest, there is one main character in your school. Yoo Jimin. Otherwise known as Karina.

You'd be lying if you said you didn't have a small crush on Karina. Small also isn't exactly an accurate descriptor at that too, but hey, she's perfect. The Top Scorer in almost every subject, talented and gorgeous, it wasn't out of the ordinary to see her locker stocked to the brim full of confession letters and flowers from her countless admirers. So, what business does extra #2 have with THE Karina. Well, remember how you said she was the top scorer in almost every subject? Yeh, she had a weakness, math. And as luck would have it, math was your forte. Through countless hours of tuition as a kid, math came relatively naturally to you. You had heard of Karina's ineptitude with mathematics, but you always assumed that she'd find tuition outside of school, or just keep doing it till she got it. So it shook you pretty hard when your mathematics teacher made you stay back to have a chat, as he explained how Karina was failing math and needed help. Desperately.

"No, Karina, you bring the exponent down here, not change it." You explained as you leaned over, using your pencil to trace the workings. Logarithms. The great joy to everyone who goes through it

"Oh right..." Karina softly groaned as she changed her workings, going back to trying the worksheet as you settled back to your resting position, assuming an upright and relatively awkward position.

Pulling out your phone, you looked through the chapters you had to cover with Karina, not going to be any fun, calculus and stats remained the hulking giants in the smoke that threatened to burn the bridge.

Suddenly, you felt a chill go down my spine, feeling eyes on your back. Turning, you saw 3 girls, hiding behind a column as they were seemingly monitoring you.

"Umm, Karina, do you know them?" you asked as you lightly nudged Karina, gesturing to the three girls who instantly tried to duck away

"Ning, Aeri, Min, stop being weird, you're scaring my friend!" She chided as she gestured them over, the three sheepishly walking over

"Sorry about that Ji, this one insisted we watch." Winter explained, gesturing to Giselle, who raised her hands to surrender.

"Y/N, I've got to go, I'll see you here tomorrow, same time?" She asked as she hurriedly shoved her stuff into the bag

"Sure thing Karina, see you!" You waved, smiling awkwardly

"Call me Jimin!" She said, before running off with the 3 other girls

"Jimin" You kept repeating, laying in bed

It's a known fact that Karina was gorgeous, drop dead gorgeous, but now, after seeing her up close, gorgeous was an understatement. No words could convey the true extent of her beauty, and through the entire tutoring session, you couldn't help but glance or even out right stare at her. It's a wonder she didn't think you were weird to be honest

As you laid in bed, your mind began to wander away, to the first time your not so small crush on Karina formed

At that time, she didn't know who you was, and you didn't know who she was. Just two rookies in the volleyball team. While with the knowledge you have now, with Karina being your school's ace spiker, while you left the team after sustaining a serious shoulder injury, you'd scoff at the notion of being better than Karina, you were, well, once was. Being the child of a volleyball player, you had spent hours after finishing homework playing volleyball with your mom, a fun way to bond with her, so you had learned and grown a solid bedrock of skills. Paired up with Karina, you taught her some basic skills, and Karina, the protege she was, picked it all up easily. During the training sessions with her, you found yourself falling for her, her beautiful smile, her laugh and playful nature. Stories don't go that well for side characters however, as the two of you were separated to two different teams, with limited interactions. In those limited interactions however, those slivers of light, you found yourself falling, and falling hard.

As time went on, you actually got closer to Jimin, instead of splitting apart like you did during your volleyball days. With your help, Jimin's math slowly improved, with her grades reflecting that change. Through that time however, your relationship with Jimin never grew greater than friends. Weirdly enough, you got closer to Minjeong than you did Jimin, only now noticing that you shared two classes, Psychology and Economics. Despite being an introvert, Minjeong grew to be good friends with you, showing you a different, more playful side.

Sat in the lecture hall, you tried your best to focus on your economics teacher, Mr Fai's class, as he went on and on about fiscal and monetary policies, pros and cons, such and such. Mr Fai was a great teacher, especially for a relatively dry subject like economics, and usually, you would be paying full attention to him. Well, usually. This time, your eyes were trained onto none other than the girl of your dreams, Jimin. The only one with a free period before a planned hang out, Jimin had opted to do some revision outside the lecture hall, much to the dismay of your grades. Suddenly, you felt a chill up your spine, feeling a presence close to your back.

"Keep looking at Ms Yoo over there instead of Mr Fai's lectures and he's gonna gouge your eyes out."

You quickly turned, seeing Minjeong looking at you with a smirk. Yeh, she knew about your little crush on Jimin too. Well, her and Aeri, the latter having been asleep near you two so long you forgot she was there.

"I'm his favourite student Min, I'm sure he'll let me slack once." You said, going back to admiring Jimin.

"Whatever." Winter said with a chuckle, playfully shoving you before turning back to the lecture, shrugging to Mr Fai who shook his head with a smirk, glancing at Jimin, before continuing his lecture

As time went on, you tried to spend more time with Karina, endear yourself to her, but it was tough. While you were her tutor, other than math, you couldn't really help her with any other subjects, and tended to leave her alone to allow her to study. Time flew in the final year of your schooling life, national exams rushing by too. Before any of you knew it, the National exams all of you had spent so long running towards was finally over, now, the last event of your school life. Grad Night. The piece de resistance of your school life, in your opinion, at least for you. Fidgeting in front of your mirror, you groan at your little sister as she adjusts your attire.

"Han, please, it's been half an hour, it's grad night, not nuclear physics." You exclaimed in frustration

"Well yeh, obviously. You could probably handle nuclear physics, but your fashion blind ass cannot handle grad night." Hanni quipped as you rolled your eyes, her tiny stature getting up on her step stool, then leaning toward your hair, styling it one last time, before letting out a satisfied sigh.

"Okay, all done! Oh, and Karina's been here for the last 10 minutes." Hanni said with a casual tone, but your eyes almost bolted out of your head, causing you to jump, and you ran out of the room, panting as you looked at the living room, then checking the road outside.

The moment your sister's laughter echoed in the small corridor was the moment you calmed down a little, though a little part of you wanted to strangle the little gremlin. You loved her, but boy did she know how to set you off.

"Pham Ngoc Han, I swear to god." You began to talk, but Hanni immediately bolted away.

"Get away from me with that Government name shiiiii!" Hanni shouted back, running as you chuckled.

"Good Luck with Karina! Don't come home if she isn't dating you!" She shouted once again, before locking her door.

"Pham Ngoc Han!" You shouted again, slamming the door before sighing, leaning back on the door.

"It's going to be fine, just go alright?" Hanni whispered through the door, causing you to smile a little. Gremlin she was, but to be fair to her, the little gremlin did love you.

Hearing honking from outside the house, you bid Hanni farewell, before rushing to the door, seeing Minjeong in a limousine she had booked for all of you.

Climbing into the vehicle, you said hello to Minjeong, but it was clearly not the matter on Minjeong's mind, as once the door closed, Minjeong began hurriedly asking you.

"So what's the plan! Today's kinda your last chance you know? To confess to Ji." Winter asked, though you were a little taken aback.

"I'm not going to confess Minjeong, you know just as well as I do that I stand no chance with Jimin. I'm not going to ruin our relationship just because I want to indulge in some stupid fantasy that I could ever be with her."

Immediately, Minjeong's face went a little more somber.

"Y/N, you have to have a little more confide-" Before Minjeong could complete her sentence, you quickly cut her off.

"Where's the rest of the girls?" You asked, avoiding eye contact with Minjeong. A little reluctantly, Minjeong nodded, though a hint of disapproval was apparent on her face.

"Aeri woke up late, Jimin and Yi Zhuo are at her place to help her get ready." Minjeong replied, to which you nodded, before turning to look out of the window, allowing silence to fill the void in the limousine.

After about a 10 minutes drive, You noticed Aeri's house around the bend, seeing the three girls adorned in their beautiful gowns waiting by the curb.

"Hey!" Yi Zhuo enthusiastically greeted you and Minjeong before climbing into the limousine, followed closely by Aeri and Jimin, who was wearing a surgical mask, causing your eyebrow to crease in slight worry.

"Sorry about being late, someone was up too late reading Fanfiction." Jimin jokingly said, throwing a playful glance at Aeri who raised her hand in defence.

"Let me guess, there was a meet cute in college, and after some drama, one misunderstanding, maybe a love triangle, maybe even parents disapproval, the two leads finally get together and share a kiss to cap the story. Did I miss anything?" Minjeong playfully asked, Jimin and Yi Zhuo suppressing a chuckle as Aeri's head lowered a little in embarrassment.

"Listen, it's cute alright? It may be cliche, but its nice to think about. That one day, at the end of the rainbow, there'll be someone who truly gets you, loves and accepts you for who you are." Aeri began to retort, causing you to raise an eyebrow.

"That's for the main characters only though..." You muttered, to which Aeri tilted her head in confusion.

"These kind of happy endings aren't for everyone, those are reserved for main characters only isn't it?" You questioned, maybe a little too passionately as all eyes in the limousine turned to you. You could even see the driver's eyebrow raise in the rear view mirror.

"That might be true, but everyone's a main character, be it in their own story or someone else's." Aeri replied, sharing a little glance with the other 3 girls in the limousine, a little worried by your statements.

Just as you were about to reply, Jimin spoke up, "You're a main character in my Story Y/N. All of you are. So don't lose hope alright? I'm sure you'll get together with the one right for you soon. Also, it's prom, lighten up!" Jimin said as she jokingly punched you in the shoulder, causing you to quickly quieten down, a small smile spreading across your face at Jimin's words. As you turned to the window, glancing out as endless scenarios played out in your head, you saw Aeri lean over to Minjeong, whispering something to her, the both of them laughing out as they both smirked at you. You didn't hear what they said, but you could more or less figure it out, proceeding to flip her off, an act she playfully returned.

After what felt like an oddly long time, the 5 of you were dropped off at the hotel where your prom was being held, the 3 girls scattering around to find some of their other friends for photos, though Jimin seemed weirdly reluctant to do so.

Seeing Sakura, a mutual friend, you quickly called her over, asking a favour of her.

"Hey, Sakura, could you help me take a picture with Jimin?" A request that she quickly agreed to, putting her bag down as you walked beside Jimin.

"Hey Ji, let's get a picture together." You asked, to which Jimin seemed a little nervous.

Using her hand to beckon you closer, she tiptoed, leaning towards your ear, whispering in your ear.

Turning to her, you reached your hand to her mask, watching her face be clouded by a veil of insecurity, a look not usual for Jimin.

"You'll look amazing Jimin, it's you, you're always stunning. Anyways, I'm sure it's not even that big anyways." You reassured her, causing her to nod, letting you take the mask off her.

"See, pretty as always." You smiled, causing a smile to spread across Jimin's face as she kept her mask in her bag.

Suddenly realising what you had done, you quickly withdrew away from her a little, confused as to what had possessed you to do something like that.

Turning to face the camera, Jimin looked at you confusedly as she turned to Sakura, who shrugged.

"Why so awkward Y/N, come on!" Jimin said, quickly wrapping her hand around your waist then pulling you closer to her, her other hand guiding you hand over her shoulder.

"I swear you've never taken one of these pictures." Jimin playfully jabbed, to which you wordlessly nodded and forcing a smile, unable to muster any words to be uttered.

After posing for the pictures, you heard the ushers announcing that the doors were open, just as the other girls had came back, now planning to enter the hall together. As Yi Zhuo pulled Jimin towards her, talking about some post she had seen on Instagram, you looked at Aeri and Minjeong, both of whom had seen what had happened between you and Jimin.

"Say, Aeri, in how many of your fanfictions have you read in the last month, did that scene happened, almost moment for moment." Minjeong asked, smirking at you

"Hmm, pretty much all of them." Aeri replied, both girls immediately giggling as you rolled your eyes, but curiously, you could not wipe the smile of your face

Sitting at the banquet tables, your group sat about, consuming fine dining that was not exactly worth the price tag, but hey, you came for the experience, not the food. With the student council's organised performances, many laughs were shared, applauses given, smuggled in whisky shared, though your group made it a point to drink in moderation thankfully. As the evening drew to a close, the event photographer made her way to your table, signalling for you to huddle together. The 5 of you huddled together, and Minjeong looked at Aeri with a playful glint in her eye.

"Get ready." Aeri whispered into your ear, but before you could question what was going on, Minjeong stumbled forward, acting sufficiently drunk to play it off, causing Jimin to tumble forward. Bolting forward, you grabbed Jimin by the hand, steadying her as the two of you shared prolonged eye contact, losing yourself into the galaxies behind her irises.

Proud of what they had done, Minjeong and Aeri high-fived, all smiles while Yi Zhuo went up to the two of you, worried at what had just happened.

Embarrassed, you let out a soft cough, clearing the awkward air that had filled the room, letting go of Karina's hand as she steadied herself, before turning to hide the blush on your face.

"Minjeong I'm going to kill you, I swear." You whispered to Minjeong, who rolled her eyes playfully, pointing to the camera as the group photos were snapped.

While the rest of the group interacted with the rest of their friends, you hung back a little, thinking back on the fall. Maybe you were just imagining things, but was there a spark there? Did Jimin feel the way you did? Could you...?

Trying to compose your thoughts, you heard Minjeong shouting your name, gesturing to the limousine outside the building. Seeing the other 3 girls already having entered the limousine, you walked there with Minjeong, who hurriedly grabbed you.

"Listen, I'm going to be the first to get dropped off later, so I won't be there to push you. This is your best chance to confess to Jimin alright? I don't think you would want to look back on today and regret not asking her. Do it alright?" Minjeong whispered, and by the end of it, the two of you were in the limousine.

Again, the 5 of you were back in the limousine, joking around and discussing how the prom went, slowly, the limousine had reached its destinations. First was Minjeong, who winked at you just before she left the van. Then, Yi Zhuo was dropped off, and finally, Aeri, who whispered a soft "good luck" to you before getting off the limousine.

Now, only two remained, you and Jimin. You knew this was Minjeong's work, but you didn't know whether to thank her or curse her. You and Jimin made small talk, something you both enjoyed, making the rather long ride feel like just another one of your hang out sessions waiting for the other 3 girls after tutoring sessions. Chatting about a possible internship Jimin was chasing, you couldn't help but admire her as she spoke, her elegance and poise amazing you, all that in her amazing dress, she was a Disney Princess, a perfect Princess at that. Eventually, it had to come to an end, as you saw your street approaching, you looked down, contemplating about what to do.

Could you really be a main character in Jimin's story? You thought if Minjeong could be right. Could you really live with yourself if you didn't at least try? Those magical moments at prom had to be a sign, didn't it? Seeing your building in the distance, you realised you didn't have much more time to hesitate.

It was now or never.

Nervously, you turned to Jimin, hesitating for a moment as you saw her beautiful face illuminated in the moonlight. It all seemed perfect, the final moments of a fairy tale.

"Hey, Jimin. Do you think we'll hang out in the future?" You asked, sucking in your breath as you nervously waited for her answer.

"Of course, Aeri's been thinking of getting us to get together to play badminton, and, we're all in the group chat, we ca organise meetups anytime, so yeh, I'm sure we'll hang out in the future." Replied Jimin, a little confused at the question.

"No, I mean, me and you." You replied resolutely, nerves gripping you even tighter.

"Hmm?" Jimin hummed in curiosity.

"What I'm saying is, do you want to grab dinner together some time soon?" You blurted out, trying your best to not turn your head away

Jimin's smile dropped a little, turning to an awkward smile.

"Oh my g-, Y/N. I'm sorry, but I'm not interested. It's not you, bu-" Jimin replied, and you felt your heart shatter.

Not wanting her to continue, you quickly cut her off, "Don't worry about it, it was a stupid question, and I knew what was going to happen anyways. I just didn't want to look back on tonight and regret not asking. "

Jimin smiled at you apologetically, but you couldn't look her in the eye, muttering soft denials under your breath.

"Let's just pretend this didn't happen alright? I don't want things to be awkward with the rest of the girls." Jimin asked, to which you wordlessly nodded.

As you saw your house around the corner, you hurriedly packed your belongings, catching the polaroid you had taken with her earlier, it's very presence seeming to taunt you

"Take care of yourself alright?" You quickly muttered under your breath, turning to the front to thank the taxi driver, then getting out of the taxi.

You heard Jimin mutter a goodbye, an air of tension obvious between you, but you didn't turn, not wanting to break.

Hearing the taxi's engine rev and drive off, you dragged your feet as you walked to your home, turning the lights on and closing the door as quietly as you could, careful not to wake your slumbering parents.

Opening the fridge, it's fluorescent lighting illuminated you in a harsh glow as you pulled out a bottle of corona beer. Popping it open, you took a big gulp before walking towards the balcony.

Taking a seat, you stared out of the house, reality hitting you, causing you to let out a loud and bitter chuckle

You had gotten too comfortable, too stupid.

Only main characters got their happy endings.

You're just extra #2.

[scotianostra]

April 25th 1710 saw the birth of James Ferguson at Rothiemay near Keith in Banffshire.

James Ferguson is almost forgotten about nowadays, yes he gets a mention from me a couple of times a year and a limited audince on my Facebook group and Tumblr page, but in the 18th century he was a phenomenon, a self-educated astronomer and philosopher whose books sold widely and whose lectures on various subjects were the equivalent of the Royal Institution Christmas Lectures today.

His father was a farm labourer, but Ferguson rose from abject poverty to become the greatest populariser of science of his day, and much of his success derived from the fact that he was able to explain complex matters such as Newton’s laws in language that was clear and easily understood, perhaps a legacy of his own self-taught, which is much more than me, I’ve said before much of Mathematics is way over my head, don’t even start me on algebra or logarithms!

Sometimes referred to as the “wheelwright of the heavens”, showing remarkable intelligence and keen interest in all things mechanical, his only formal education was at the age of seven for three months to the grammar school at Keith.

In 1734 he went to Edinburgh, where he began to make portraits in miniature, by which means, while engaged in his scientific studies, he supported himself and his family for many years. Subsequently, he settled at Inverness, where he drew up his Astronomical Rotula for showing the motions of the planets, and places of the sun and moon.

He went to London in 1743, making mechanical devices and publishing the odd paper in the Philosophical Transactions of the Royal Society , of which he became a Fellow in November 1763. Throughout his life, he devised astronomical and mechanical models. His breakthrough came with the publication of Astronomy explained upon Sir Isaac Newton’s Principles in 1756,, which was so popular it required a second edition a year later.

James Fergusson died aged 66 in London on 17th November 1776 and was buried in St Marylebone churchyard,London.

[imagineanime2022]

A True Friend

Caspian Keyes X GN!Reader

Word Count: 776

Requested: Anon @kalebell46

Request: On god please I need more Caspian Keyes fan fiction. This internet is so dry, there's like none out there. Could be of a him x reader while he's finding himself, the first real friend in his life that isn't there by the choice of someone else. And he'd be so paranoid about it too. Gooooodddddd please. AND I would love for a caspian fic please there are none

Caspian had been alone for so long, since he was young he had always been the outsider, the black sheep, the target and he thought that was how it was going to be for the rest of his school life. That is until he met (Y/N). Now (Y/N) for all intents and purposes probably wasn’t the best example for Caspian, they got into trouble, paid around and never listened to anyone who assumed that they knew better than them. Except when they were with Caspian, who they had only met because they needed tutoring.

(Y/N) wasn’t stupid though most people treated them that way, in fact they had a basic grasp on most things that were taught in class, they just didn’t seem to get it down on paper very well. Caspian was asked to tutor them and the rest followed with time, tutoring sessions turned into skateboard races and trips to the comic book store. Caspian learned quickly that his new companion was not stupid as he had heard a lot of the others in their year saying so he did make sure that some of their time was dedicated to bringing up his grades, in the end it didn’t matter though.

The world crumbled around Caspian as he found out about the real reason behind his birth, with his father gone and his mother keeping more of a watchful eye on him then usual, the only place he thought he might even be a little bit safe was with (Y/N) but then the thought crossed his mind… What if you had something to do with Logarithm's little experiment. That was why he stood outside your door hand hovering to knock, he jumped when you opened it smiling at him “what are you doing?” They asked “thought you were going to knock but you seemed like you were thinking about something.” They stepped to the side giving him space to come in but he didn’t move. “What?” “Are you really my friend?” He asked. “Really your friend?” They asked “of course I am.” “Really because I just found out a lot about myself that doesn’t make sense.” He answered. “Okay talk me through it.” They prompted stepping out and closing the door behind them. “I found something on my computer, they’ve been watching me.” Caspian answered. “They’ve been watching you?” They asked frowning, you were either genuinely confused or very good at acting. “Logarithms!” He answered more frustrated at having to explain himself at all. “Logarithms? Caspian you're going to have to start from the beginning if you want me to understand, remember I’m the slow friend.” They reminded him as he looked at you, that seemed to calm him down as he spoke again. “Don’t call yourself slow.” He grumbled, they shrugged as they looked at him waiting for him to continue. He took a second to calm down and then explained everything that had happened over the past few days.

It was easy to prove that you weren’t a part of it when you looked back at Stephen Holstroms life and realised that he didn’t have a best friend or a friend of any kind at Caspian’s age. (Y/N) was the only person that Caspian could trust but that didn’t mean that he wanted to drag them into everything that was happening, he still didn’t understand how they ended up in the car with him and Cary going to meet Maddie. “I’ll find a way to get you back home after all of this.” He promised. “Home?” They asked. “Why would I go home, you need someone right? Someone to trust?” “Yeah but-” “And we’ve proven that I can be trusted?” They asked. “Yes but-” “Then I stay.” they leaned back in their chair as Caspian glanced at her through the rear view mirror. “Why?” He asked. “Because I'm your friend, this is how friends work… Real ones anyway.” You shrugged. “Real friends?” Caspian asked. “Alright, how about this, I promise to be the one person that you can trust, a true friend, pillar to lean on and person to talk to, if you promise to stop thinking that you don’t deserve it. You didn’t ask to be made this way and no matter how you were born you are no less human than anyone else I know.” You said. “Alright, fine, as long as you don’t keep calling yourself the slow friend.” He answered. “Alright deal.” And that was the first time that he felt like he could trust someone, accept someone, turn away and they would still be there, a true friend he liked that security.

Request Here!!

[the-garbanzo-annex-jr]

by Joshua Hoffman

The Torah isn’t a history book, a physics book, or a storybook.

It is torat chaim — literally “instructions for living” in Hebrew.

“The more Torah you know,” said the late, great Rabbi Noah Weinberg, “the more fulfilled you become. Every word, every phrase contains a message for how to maximize pleasure in life. Look for the deeper message — the wisdom within — and you will reap immense rewards.”1

In the Torah, the basics are laid out in writing, but the rest must be learned orally, know as the Mishnah.

“When an engineer has a problem, he looks up logarithm tables. A lawyer refers to case studies. A doctor has medical journals,” said Rabbi Weinberg. “A Jew has the Mishnah.”

The Mishnah refers to the later works of the rabbinic period — most prominently the Mishnah and the Gemara, jointly known as the Talmud — which explain and expound upon the statutes recorded in the Written Torah.

So, how much do you really know about the Torah?

Enjoy these five surprising facts:

1) Four Levels of Understanding

Rabbi Noah Weinberg once said that a single word in Torah can yield multi-layered understandings — “if you know how to apply the right tools.” This isn’t metaphor. It’s methodology.

The Torah is written in a code, not a secret one, but a multi-dimensional one. Jewish tradition teaches that the Torah operates on four primary interpretive levels:

P’shat (פשט): The simple, literal meaning of the text. What is the Torah saying at face value? This is the level explained by commentators like Rashi, who wrote in 12th-century France but saw his work as clarifying what the Torah meant all along.

Drush (דרש): The homiletic level, found in Midrash and Talmud. It explores how verses teach moral, ethical, or spiritual lessons — often reading between the lines to discover deeper patterns.

Remez (רמז): Literally “hint.” This level uncovers subtler meanings — using Hebrew wordplay, gematria (numerical values), or alternate pronunciations to surface ideas hidden in plain sight. One reason the Torah scroll has no vowels or punctuation is to make these alternate readings possible.

Sod (סוד): The secret, mystical level. This is the realm of Kabbalah, of the Zohar, of cosmic structures and divine energies encoded in the language of the Torah itself. It doesn’t contradict the other layers — it reveals what they were whispering all along.

Together, these four levels form the acronym PaRDeS (פרדס) — which means “orchard” in Hebrew.

It’s a stunning metaphor. The Torah is not a textbook. It’s an orchard, a place of sweetness, beauty, shade, and sustenance. But like any orchard, you don’t get the fruit unless you’re willing to walk through it, get your hands dirty, and reach.

“The Torah is filled with delicious spiritual fruits,” wrote Rabbi Weinberg, “just waiting to be plucked and savored.”

[todays-xkcd]

Baseballs do present a challenge to this theory, but I'm convinced we just haven't found the right seasoning.

Sphere Tastiness [Explained]

Transcript

[Graph with Y axis using and arrow indicating tastiness from "Not Tasty" to "Tasty" and X axis labeled "Sphere Diameter (meters)" with a logarithmic scale running from 10-4 to 108 (with 10-3, 100, 103 and 106 labeled).] [The graph contains two points points for "Grapes" and "Melons" at the "Tasty" end of the Y axis, between 10^-2 and 10^-1 meters, and two points for "The Earth" and "The Moon" at the "Not Tasty" end, both around 10^7 meters. A straight dashed line shows a linear interpolation between the points. There's a circle with a question mark about halfway between them.]

[Caption below the panel:] My research suggests the existence of an 800-meter sphere that tastes okay.

[otesunki]

where can i find information on {0|0}. on *. i'm obsessed

colossal infodump incoming

alright there's this Very Very Good Book called Winning Ways for Your Mathematical Plays which explains combinatorial game theory and how they link into surreal numbers in what can only be described as an Unreasonable level of detail, including how it ties into Surreal Numbers oh God surreal numbers is just as loaded of a term Okay let me take a brief detour into That

so surreal numbers are like. imagine defining every number as a pair of sets of other numbers. a set of numbers Less than it and a set of numbers Greater than it. and we write this as foo = {less than foo|greater than foo}. so like. 0 = {|}, 1 = {0|}, 2 = {1|}, 1/2 = {0|1}, -1 = {|0}, that type of thing

the reason why surreal numbers are mindmelting is the fact that they happen to be the Largest Totally Ordered Proper Class and they contain Literally Every Other Totally Ordered Number System inside of them. totally ordered here means that any two numbers are related by < > or =. so like. complex numbers and quaternions aren't included. surreal numbers also behave just like real numbers in that you can do arithmetic on them exactly how you'd do arithmetic with any other real number. and for the surreal numbers that are also real numbers the classic laws of commutativity and associativity hold.

however the surreal numbers are. a.

a bit bigger than just all the real numbers. because there are also numbers that are infinitely big or small and you can make infinitely-bigger-than-infinte numbers and the arithmetic operations still work and also have you ever wanted to take the logarithm base infinity of a number too bad that's defined now

games are what happens when you look at the surreal numbers and go that's for rookies and decide that actually yes {1|-2} makes sense what are you Talking about. why Can't on = {on|} that's a perfectly sane definition also over = {0|over} also Also actually you can define a number that's Even Closer To Zero than over is and if you churn through the calculations you can literally Prove that 0 < tiny < over Yes the number is called tiny

right okay so what is star? in fact if x = {A|B} then -x = {-B|-A} and because A and B are both just the set { 0 } and 0 is {|} you can trivially prove that negating star gives you back star, it's not greater than zero because it has zero in the right hand side, it's not less than zero because it has zero in the left hand side, and it's not Equal to zero because playing a game with a value of zero means that the first player Loses but a game with a value of Star means that the first player Wins which means neither player has an advantage but it's a balanced game in a different way to how 0 is balanced and this is reflected in the Thermograph of star which is a way to draw what star looks like when you Heat it up and Heating a number basically means moving its left and right hand sides closer together in value until eventually they meet up

so Zero because both of its sets are empty is just a vertical line at x=0 because it can't heat up nor cool down but Star on the other hand stays at 0 when it is cooled down but if you Heat it up (make t negative) then actually the two zeroes in it begin Diverging and going in opposite directions

but because the whole thing is Horizontally symmetric it means that the number is its own negative because negating a number is equivalent to a horizontal flip. also if you thought thermographs couldn't get more complicated and involved you're wrong

so. That's. what. star is.

so have you ever wondered what would happen if you had a bunch of numbers that are all mutually recursive and not defined in terms of anything el-

[linguisticillustrations]

Pitch trace of the utterance "it's not that I", showing a peak on the negation not. A funky way of illustrating pitch? Pitch before Praat?

Labov, William & David Fanshel. 1977. Therapeutic discourse: psychotherapy as conversation. New York: Academic Press. [Figure 3, page 45]

A footnote explains the visualization this way: "Spectral Dynamics Real-Time Analyzer 301C with output displayed on a Tektronix 611 storage oscilloscope. The analyzer synthesizes 500 filters every 50 milliseconds over a variety of frequency ranges; the analysis can be terminated after any given number of filters and a new sweep started immediately. The pitch contour display used throughout this volume is made with a frequ ency range of 5,000 Hz. Each filter has a nominal bandwidth of 10 Hz and an effective bandwidth of 15 Hz. The sweep is terminated after the first 110 filters, so that a spectrum is generated every 11 milliseconds. The display on the oscilloscope is logarithmic and cuts off at 54 db below maximum. High-pass filtering at 12 db per octave begins at 3,000 Hz, and, in addition, the roll-off of the Nagra IV-S tape recorder - LS + FA - is used. Volume is then adjusted so that only the peaks of the wave forms are visible, thus tracing the path of the fundamental frequency without the interference of other signals"