#Common Logarithms

[rollercoastermalfunction]

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

[math-journal]

Common / Natural Log

[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.”

[medusagorgongirl1]

Picture this, Tim drake in his robin era. He's on the young justice team (he is their fantastic and mysterious leader thank you very much), he's batman's protege (and sure that began rocky but it's improving), and his parents are alive (he's gotta one up his predecessors in some way), and you know what, life is good.

Until of course his parents are coming planning to come to town, and he's looking at his grades because they're not that fantastic and everyone wants their parents to see good grades so he's (frantically) picking up the slack

And yeah he probably shouldn't be working on his math notes and homework in the common area, but, well tough shit, logarithmic aren't going to wait

And that's where kon find him, half bent over a notebook scribbling away with his nose inches from his laptop... this is typical Rob behavior in Kon's eyes, though a tad more stressed than usual

"What kinda report has the bat got you writing now" kon questions, looking at the bird who seems enraptured by the wonders of his laptop.

But Rob looks up blinks owlishly and states 'logarithmics'

'Is that a rouges name or some kinda gang, who the hell is logarithmics?' Kon replies mildly baffled cause whom the fuck is calling themselves logarithmics

Rob continues to state at kon, doing that whole analysis stare that makes kon question if he's the only one on the team with x ray vision. "It's 11th grade math" the bird finally states

Kon stares blankly at the Robin, because what?

"I'm doing my math homework... it's logarithmics" The bird clarifies

And that how Robin and Super boy end up smashed together in a chair debating over logarithmic, and maybe just maybe that's when Robin starts to realize that (even more maybes) maybe he likes to hear Kon talk and maybe logarithmics will not ever seem necessary, but hey at least they make him grin a bit

[vestaignis]

Наутилус (лат. Nautilus) — род головоногих моллюсков, которых относят к «живым ископаемым». Самый распространенный вид — Nautilus pompilius. Наутилусы относятся к единственному современному роду подкласса наутилоидей. Первые представители наутилоидей появились в кембрии, а его развитие пришлось на палеозой. Наутилиды почти вымерли на границе триаса и юры, но все же дожили до наших дней, в отличие от своих родственников аммонитов. Некоторые виды древних наутилусов достигали размера в 3,5 м. Представители самого к��упного вида современных наутилусов достигают максимального размера в 25 см.

Спиральный «домик» моллюска состоит из 38 камер и «построен» по сложному математическому принципу (закон логарифмической прогрессии). Все камеры, кроме последней и самой большой, где размещается тело наутилуса с девятью десятками «ног», соединяются через отверстия между собой сифоном.  Раковина наутилуса двухслойная: верхний (наружный) слой – фарфоровидный – действительно напоминает хрупкий фарфор, а внутренний, с перламутровым блеском – перламутровый. «Домик» наутилуса растет вместе с хозяином, который перемещается по мере роста раковины в камеру попросторней. Пустое жилище моллюска после его гибели можно встретить далеко от его места обитания – после гибели «хозяина» их раковины остаются на плаву и перемещаются по воле волн, ветров и течений.

Интересно, что двигается наутилус «в слепую», задом наперед, не видя и не представляя препятствий, которые могут оказаться на его пути.И еще одно удивительное качество этих древних обитателей Земли – у них потрясающая регенерация: буквально через несколько часов раны на их телах затягиваются, а в случае потери щупальца быстро отрастает новое.

Nautilus is a genus of cephalopods, which are classified as "living fossils". The most common species is Nautilus pompilius. Nautilus belong to the only modern genus of the Nautiloid subclass. The first representatives of the Nautiloids appeared in the Cambrian, and its development took place during the Paleozoic. The Nautilids almost died out on the border of the Triassic and Jurassic, but still survived to the present day, unlike their Ammonite relatives. Some species of ancient Nautilus reached a size of 3.5 m. Representatives of the largest species of modern nautilus reach a maximum size of 25 cm.

The spiral "house" of the mollusk consists of 38 chambers and is "built" according to a complex mathematical principle (the law of logarithmic progression). All chambers, except the last and largest, where the nautilus body with nine dozen "legs" is located, are connected through holes with a siphon. The nautilus shell is two–layered: the upper (outer) layer – porcelain–like - really resembles fragile porcelain, and the inner, with a mother-of-pearl luster - mother-of-pearl. The nautilus's "house" grows with its owner, who moves as the shell grows into a larger chamber. The empty dwelling of a mollusk after its death can be found far from its habitat – after the death of the "owner", their shells remain afloat and move at the will of waves, winds and currents.

Interestingly, the Nautilus moves "blindly", backwards, without seeing or imagining the obstacles that may be in its path.And another amazing quality of these ancient inhabitants of the Earth is that they have amazing regeneration: in just a few hours, the wounds on their bodies heal, and in case of loss of tentacles, a new one grows quickly.

Источник:://t.me/+t0G9OYaBjn9kNTBi, /sevaquarium.ru/nautilus/, /habr.com/ru/articles/369547/, //wallpapers.com/nautilus, poknok.art/6613-nautilus-molljusk.html, //wildfauna.ru/nautilus-pompilius, /www.artfile.ru/i.php?i=536090.

[askagamedev]

What are common keywords any game design resume should include?

It depends on the kind of designer position you're aiming for. We want to see key words for common tasks that those kind of designers have done. Here are some examples:

Common

Experience, craft, create, live, season, update, content, schedule, create, design, team, player, UX.

Level Design

Layout, place, trigger, volume, spawn, point, reward, treasure, quest, lighting, light, dark, texture, object, obstacle, blocking, whitebox, direct, draw, through, inviting, space, place, multiplayer, competitive, cooperative, co-op, deathmatch, capture the flag, ctf, domination, asymmetric, symmetric.

Quest Design

Text, reward, spawn, balance, level, pace, pacing, word, budget, localization, loc, narrative, item, itemization, dialogue, branch, spawn, difficulty, player, multiplayer, encounter, placement, place, trigger, chain, pre req, pre-requisite, condition, scripting, faction, seasonal, event.

Cinematic Design

Narrative, camera, character, blocking, screen, position, ease-in, ease-out, pan, cut, smash, storyboard, frame, framing, beat, cue, pacing, feel, shot, zoom, sfx, vfx, mark, contextual, conditional, quick time, event, timing.

System Design

Balance, numbers, formula, spreadsheet, excel, curve, quadratic, linear, logarithmic, growth, plot, level, power, over, under, even, normal, distribution, player, total, analysis, scale, scaling, script, scripting, math.

If you're at all familiar with the regular kind of duties and tasks that any of these kind of designers do on a regular basis, you'll immediately start to see how these words fit into describing what we do day in and day out. These are going to be the kind of words we see used to describe the sort of experience we expect to see on a resume/CV from someone who has done this kind of work before. We won't expect all of them in every resume, but we expect a good many of these words on the resume/CV of a reasonable candidate.

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[shayoranwriting]

Calm Among the Stars

Fandom: Sanders Sides

Pairing: Analogical; can be read as platonic or romantic

Word count: 490

Summary: With Virgil feeling a little pensive, Logan decides to keep him company using stargazing.

-

"You've been out here a while," Logan said as he cautiously approached Virgil, who was currently sitting on the grass in the yard staring up at the night sky.

"Yeah," came the quiet reply.

"Aren't you cold?" he asked.

"...yeah."

With a sigh, Logan summoned a thick blanket and, sitting himself down beside Virgil, draped it around both of their shoulders.

Virgil looked at him with surprise.

"Would you like to hear about some constellations?" Logan said simply.

Virgil huffed a laugh.

"Sure thing, Teach."

Logan straightened to attention, eyes shining with delight.

"Alright. Do you see that star right there? The one that's brighter than all the others?"

Virgil nodded, humming in acknowledgement.

"Well, that is Sirius, or the dog star, which is the brightest star in the night sky and part of the constellation Canis Major. It is actually what is known as a binary star, where two stars orbit one another and they can appear as a single body at this great distance."

Virgil made an interested sound to show he was still listening. He shifted to lean against Logan slightly, causing him to pause, smiling softly at the other.

"Now, moving up from Sirius, do you see that line of three stars right there?"

"Mm-hmm."

"That's Orion's belt. See the shape of his body? And there's his sword, his shield, and his club. Orion is particularly easy to find because the constellation has a number of especially bright stars. For example, Rigel, there, and Betelgeuse, right there, are among the brightest stars in the night sky and Orion contains six more stars with a magnitude below than 3. Where stellar magnitude is concerned, the smaller the number, the brighter the object."

"That seems a little confusing."

"Not really. It's a reverse logarithmic scale that was adapted from the original system proposed by Hipparchus, who defined the brightest stars as the first magnitude, the next brightest as the second magnitude, and so on."

"That's less confusing," Virgil said genuinely.

"Indeed. And because Orion is so easy to find in the night sky, it can be a useful tool for locating other constellations. For example, you can follow Orion's belt in the opposite direction from Sirius to find the Taurus constellation."

Logan glanced at Virgil from the corner of his eye. "Just like you can use the Big Dipper and Polaris to find the tail end of Draco."

"Draco is my favourite constellation! Dragonheart was a good movie," Virgil said, now seeming more present.

A stretch of silence passed between them, though it was a comfortable silence.

Finally, Virgil looked away from the stars and turned to Logan.

"Thanks, Logan."

Logan's eyebrows raised in surprise.

"You're very welcome," he said in a bemused tone.

"I'm ready to head back inside now."

Logan smiled, "Alright."

He stood up, offering Virgil a hand to help him do the same, and, together, they headed for the familiar warmth of the commons living room.

[wayti-blog]

"Beams of light that can be guided into corkscrew-like shapes called optical vortices are used today in a range of applications. Pushing the limits of structured light, Harvard applied physicists in the John A. Paulson School of Engineering and Applied Sciences (SEAS) report a new type of optical vortex beam that not only twists as it travels but also changes in different parts at different rates to create unique patterns. The way the light behaves resembles spiral shapes common in nature."

"In a peculiar twist, the researchers found that their orbital angular momentum-carrying beam of light grows in a mathematically recognizable pattern found all over the natural world. Mirroring the Fibonacci number sequence (made famous in The Da Vinci Code), their optical rotatum propagates in a logarithmic spiral that is seen in the shell of a nautilus, the seeds of a sunflower, and the branches of trees."

"The research builds on previous work in which the team used a metasurface, a thin lens etched with light-bending nanostructures, to create a light beam with controlled polarization and orbital angular momentum along its propagation path, converting any input of light into other structures that change as they move. Now, they've introduced another degree of freedom to their light, in which they can also change its spatial torque as it propagates."

continue reading article

[cobra-wives]

Sniffling, Sam frowns before wiping her eyes with the back of her sleeve. “Dad, you haven’t failed me at all. At least, not with logs,” she professes. “That’s on Common Core’s standards.”

Daniel laughs. “That, we can both agree on,” he says. “But blame gets us nowhere. Not blaming the system, not blaming the teachers…”

A look of recognition flashes across Sam’s face. “I have a feeling you’re not talking about Precalc.”

Mr. Miyagi teaches Daniel about logarithms. 36ish years later, Common Core screws him over when he tries to teach his own daughter.

—

guess who’s horrible at reteaching the unit logarithmic equations, but great at writing characters talking in nerdy jargon turned normalspeak! ME!!! enjoy (as much as you can without being re traumatized back to algebra ii/precalc) my stupid karate-math-emotions allegory — and criticism of the commoncore system, lol.

[ophizz]

Ramblings of a Lunatic - 3rd Quarter reflection🌝 🌸

⚠️W A R N I N G⚠️

Firstly sir, before you subject yourself to reading this reflection of my learning journey, I would like you to know that you may need to take some of the information with a grain of salt. I am an over dramatic person sir, and I may have over dramatised my experiences. I apologise in advance for whatever I am about to write. I was not built for pisay, nor did I actually ever want to go through this harsh academic plan (or however you call it. training??). Thank you for being our teacher sir, thank you for your patience, I hope mag skip ka through a lot of parts, FYI boring siya sir

a. How would you describe your Math 3 second quarter learning journey?

It could be easily described with 3 simple words. I Give Up. I have given up sir, I'm not smart, I'm not hardworking, I'm not good, so it was only natural for my course in life to give up. No matter how many times the topic was discussed, no matter how many times I tried and redo all the problems, my brain can't handle it. My brain is unable to physically store it within its cells. “Memory Full, only 0.2 megabytes left” type of situation if you get me sir, like when my phone can't open WuWa because it takes up too much space. That's me in math, my brain can't run the math application  because the memory is full, and math takes up too much space. Adding onto that, I'm not prepared for the LT, nor have I passed the graphing activity you gave us sir. Further proving my point of giving up entirely on Math 3. It's not you sir i promise, it's a me problem that I'm too lazy to fix. 

b. Which topic did you find most enjoyable? What made it enjoyable for you? Provide clear

The topic I found most enjoyable was the easy ones. I felt like I was going on the right track but apparently it's like a roller coaster. At first it was fine and dandy, but as time went on, you could slowly feel the dread as it builds up inside. Then boom you're going up, down, left, right, and side to side, while your brain tries to grasp onto something to stabilise itself but whoopsies, apparently the handlebars broke. When you get off the ride, you tell yourself at least you enjoyed the beginning. The easy, calming, joyful part of the ride. To me, that part of the Ride was us learning the basics, the exponential to logarithmic and vice versa, as well as the properties of logarithm. To me, those were the best times of the helling ride. 

c. What concepts did you find easy to learn? What do you think made them easy for you?

The topics are the same as the previous question. I think they were easy for me because it only involved common sense, minimal memorisation, and simple arithmetic. Honestly sir, that's all my brain could handle. My brain overheats when it has too many things to do, so when we went to the solving parts of the later topics... thats when my processor got weaker. So basically I found the topics, exponential to logarithmic (vice versa) and properties of logarithm easy topics.

🌸♥*♡∞:｡.｡ P h o t o s ｡.｡:∞♡*♥🌸

Sir! I didn't say that my answers are correct sir🥺..... sorry sa photo dump po hehehe

d. What concepts did you find most interesting/inspiring? Why do you think so?

For me, the most interesting one was the compounded interest. I now know how to manage finances because of that topic as well as sir Mike's crash course on investing! In all honestly, it's because its the one with the closest correlation to real life use, unlike logarithms, or graphing. That's why I see it as the most interesting/inspiring. Especially when you want to invest in a Condo, or house for example, and you now know how to actually compute for the price and know how to compare to know where you save the most money in the long run. It prepares us for the future! :D

e. What concepts have you mastered most? Why do you think so?

I will mention again and again, exponential to logarithmic and vice versa. It is because it is the easiest, just simple arithmetic and you're done. I admit that my arithmetic may not be the best, but I think I can do the arithmetic for that specific topic sir.

˖ ᡣ𐭩 ⊹ ࣪ P H O T O S ౨ৎ ° ₊

f. What concepts have you mastered the least? Why do you think so?

Sir I have not mastered graphing. I am so sorry sir, but I did not understand your discussion sir... But I have an excuse! I was undergoing through the trials of satan. Pushed to my limits as a girl forced to face the consequences of not having a parasite growing inside my uterus. The burning pain of cramps and a migraine. Sir I'm so sorry I truly don't understand anything and I know there is no use for an excuse. That the excuse does not veil my stupidity for not listening and understanding the topic. Im sorry sir.

˖ ᡣ𐭩 ⊹ ࣪ P H O T O S ౨ৎ ° ₊

sir I actually have no photos to show you... I haven't even done the activity in google classroom. Im sorry sir... genuinely sir...

g. What quick notes do you have for:

i. your teacher;

Sir, Im sorry for not reading your messages properly and thoroughly...Sir especially when you asked about the competition sir... Sir I'm scared to apologise to you in person sir, but Im sorry for wasting your time po... Im sorry for all the things I have done that might have offended you sir, or annoyed you sir... Ill try my best to be a better person sir... Sir if I did anything mean or anything of that same nature sir, I promise it wasn't intentional sir... Im sorry sir....

ii. your classmates; and

I just now noticed that the water was boiling. Thankfully I got out immediately.

iii. yourself?

Maybe, I should give up. Sometimes it's okay to start all over again. Push your limits, but not too far. You could always work on yourself but you're just lazy. Thats all you are. Lazy. You will never amount to anything, humble yourself. No matter how hard you try, your work will never be appreciated. You will never shine in your family of stars. Know your place in life.

⚠️sir this is a joke⚠️

Maybe I should actually review for my subjects... maybe I don't try because Im scared that if I try nothing will improve. Im scared that if I try I would still amount to nothing.

I wish he was real and I could steal his black card. I could manage his finances with compound interest, trust! Sylus save me from Lucifer's infected urethra!

Sir, thank you for managing to read it all the way here if ever you did sir. Im sorry you had to read all of that. Sir, I hope you don't mind the fact that I am slowly going crazy over the length of this post. I hope you have a good day after looking at this submission sir... truly my sincerest apologies.

⋅˚₊‧ ୨Thank you for reading!୧ ‧₊˚ ⋅

ଘ(੭ˊᵕˋ)੭ ੈ♡‧₊˚

[scotianostra]

On April 4th 1617 John Napier, the mathematician, died.

I hated maths with a vengeance at school, I'm not talking about counting, I can hold my own with that, but real maths. algebra, geometry, topology and worst of all logarithms, which we have Robert Napier to "thank" for, he introduced them in the early 17th century as a means to simplify calculations, aye right!

If John Napier had been born a common man he would maybe have been burnt at the stake, nothing to do with him and his maths nonsense but because he dabbled in the occult at a time when we were routinely setting such people on fire!

James VI was on the throne and his obsession with devilry consigned hundreds of unfortunates to the flames. Unless you were born of a noble family of course. A wee bit background on the Napier's his father was Sir Archibald Napier of Merchiston Castle, and his mother was Janet Bothwell, daughter of the politician and judge Francis Bothwell, Lord of Session, and a sister of Adam Bothwell who became the Bishop of Orkney. Archibald Napier was 16 years old when John Napier was born. John, as was the common practice for members of the nobility at that time, he was privately tutored and did not have formal education until he was 13, when he was sent to St Salvator's College, St Andrews. He dropped out of Uni and toured Europe for a time before returning to Scotland aged 21.

Back to his links with sorcery, several members of John Napier’s family – respected and wealthy participants of Edinburgh society - were commonly known to be wizards or sorcerers. Their necromantic power was feared by nobles as well as peasants from far and wide.

The family wizardry started with Napier's father, Sir Archibald, seventh Laird of Merchiston, who successfully predicted when Mary, then the former Queen of Scotland, would leave Lochleven Castle, where she was imprisoned. The story goes: "Claude Nan, the Queen's secretary, wrote that 'the Laird of Markyston (Sir Archibald), who had the reputation of being a great wizard, made bets with several persons to the amount of five hundred crowns, that by the 5th of May Her Majesty would be out of Lochleven." Mary escaped on 2 May 1568 – and the senior Napier was presumably wealthier for his prediction.

Sir Archibald married Janet Bothwell, sister of Adam, Bishop of Orkney, who the paper said was "a notorious necromancer", so that their son, the future mathematician, inherited "a double inclination towards the magic arts". This might explain some of John's odd behaviour. A necromancer is a wizard or magician by the way, I had to google it!

Tenants who lived on the vast Merchiston estate south-west of Edinburgh thought John to be a bit mysterious at times, Napier would be seen many evenings wearing a long gown, pacing outside his tower chamber, a private work area where he often would pass many long hours alone.

Many people thought that his pet black cockerel was a familiar – a supernatural being which assisted witches and wizards in their magical practice. However, the Napier family held the hereditary role of King’s Poulterer and Napier may have kept the cockerel on a whim but I have read he travelled not only with the bird but also with a black spider in a small box, not normal behaviour.

The Scottish writer and translator Sir Thomas Urquhart, who, told of a demonstration of devastating artillery Napier devised against the threat of invasion by Spain.

"He gave proof upon a large plaine in Scotland to the destruction of a great many herds of cattel and flocks of sheep, whereof some were distant from other half a mile on all sides and some a whole mile,"

A well as being a wizard and mathematician Napier was also a fervent Protestant, much of his writing is vehemently anti-Catholic even by the standards of the time. He was a man of contradictions though, as he is said to have had friends who were Catholic, including Alexander Seton, the Earl of Dunfermline, although the vast majority Catholics back then had to hide their faith.

The last interesting, and worrying, fact I found out about John Napier is that his cause of death according to wiki he died "from the effects of gout" at home in Merchiston tower, now I suffer from gout and it is bloody painful but I didn't know it could kill you!

[formlines]

Seahorse

Dylan Thomas

from the website:

"This design developed while I was exploring the artistic possibilities of logarithmic spirals. Spirals have been fascinating humankind for most of recorded history. The Archimedean spiral - a spiral that maintains the same distance between each line after every rotation (imagine a tightly coiled fiddlehead) was named after the Greek mathematician Archimedes, one of the earliest people to formally study the spiral in the third century B.C., but it wasn't until the sixteenth century that Rene Descartes became one of the first people to write about the logarithmic spiral: a spiral which widens as it circles outward. This type of fractal spiral - which is much more complex mathematically - is actually much more common in nature: snail shells, hurricanes, certain flower petals, draining water, and the tails of certain animals (such as the seahorse), all spiral following a logarithmic pattern.

After experimenting with the spiral, I decided to use the opportunity to create a seahorse - an animal not found in the Pacific Northwest (and thus not found in traditional Coast Salish art). I adjusted some of the designing techniques from my more traditional art to create the head and body - then attached it to the logarithmic spiral to create the tail. In the end, I had a design that combined some of my favourite elements of Coast Salish design with the elegant beauty of geometric balance." - Dylan Thomas

[whenthewindhasblown]

random doodles i found in my math notes

how I think Mary I would look in a SIX modern setting, plus a stick figure doodle of her saying "it's common knowledge that I popped out of the womb in an emo phase that never left" (quote from SmokeeBee on YT, thought it fit Mary quite well)

anne boleyn + jane seymour modern AU fanart that took me like 4 math classes to finish. i'm not even that proud of it at the end of the day but the concept is still funny

modern anne boleyn as a cafe worker. i actually don't like the art at all but the concept is still really funny to me (again)

drew my friend wearing anne boleyn and kat howard's SIX costumes but i never finished the k howard one for reasons unbeknownst to me

girl with a burn scar, a burn scar study, and a literal hand for some reason? i remember tracing my own hand for that shit

yet another anne boleyn, this time partially based off a girl in my math class. i actually really like this one and couldn't get a very good photo of it :(

taken from a page of random doodles i did one day. there are a lot more but i don't feel like discussing all of them atm; this one is my favourite (no i don't remember what it means)

unfinished human person thing (i think it was going to be eponine from les mis but i gave up)

another unfinished les mis. it was either going to be javert or enjolras but i didn't finish the hair so i don't remember which

shitty stick figure designs for all of les amis de l'abc (all super cute if you ignore bahorel)

my math teacher lmao (he would say this like every two days during our logarithms unit so i decided to draw him. no he doesn't know, yes he'd find it funny)

another modern jane seymour, the most recent actual drawing. i am very proud of my decision to give her mom jeans

a (really bad) mashup of on my own and beauty and the beast, featuring shitty treble clefs everywhere you look. my favourite part is where i tried to solve a quadratic in the middle there, gave up, and continued writing the music

[oliviabutsmart]

Physics "Friday" #9 [OPINION]: Is Fahrenheit the better temperature scale?

So as the title suggests, this post is a lot less facts and logic, and a lot more opinionated. It is still physics-y I just believe it's an interesting way to delve into a subject by turning it into an opinionated peice.

Preamble: A summary of Metric vs. Imperial arguments

Education level: Primary (Y3/4)

Topic: Measuring Systems (Metrology)

Now before you throw your hands up at the title and your silly little internet brain is like "this silly impericuck is fahrenpilled!" ... I'm an astronomy student living in Australia - I use SI units (and other unit systems) on the daily.

Though ... it is pretty notorious in astronomy to use like 17 different unit systems. Here's a list of examples:

My beloved SI units

CGS Units

Whatever the fuck a Jansky is

Don't even start with natural units I can't live without big G

"Ampere in CGS units is g1/2 cm3/2 s−2"

Solar Luminosity/Mass of Sun

Angstroms (like please can we just use nanometers?)

How many Jupiters or Earths fit into this cloud of gas?

The vomit of parallax units i.e. AU, pc, Mpc, arcseconds, radians

Steradians (Solid angles can be finicky)

Logarithms, logarithms everywhere!

Hubble's constant being in km/s/Mpc but then having to turn that into Hz or per year - like can someone please acknowledged how cursed this is?

When you do Kepler's 3rd law on Mercury and realise it doesn't work (because you forgot Einstein existed) ... so no units end up working

ADUs and/or whatever you get when you deal with telescope outputs

And as an Australian, I use SI units very regularly. Only measurements of human height and cooking weights are really imperial. And I can express all of them in metric units.

Now generally, the Metric (or SI) units are better than the imperial (or USC) units. The main points in favour of SI are:

(Almost) Everybody uses it

It's basically universal in science (see exceptions above)

It fits well with our base 10 counting system, easy scaling (e.g. 1 kg = 1 000 g = 1 000 000 mg)

It's directly pinned to many natural constants and unchanging laws

Different units interact with eachother much better

Now, generally, the main arguments for imperial units involve a bunch of patriots™ screaming about how "THIS IS THE CoUNTRY OF FREEDOM AND GOD!! AND I AIN'T USING NO CHINESE UNITS!!!1!".

That, or how metrification is hard. Which, well, metrification can occur over the course of decades, literally teaching your kids metric helps the country adjust to a metric system.

The best arguments I've found for imperial units is as follows:

Numbers like 6, 12, 60 etc. - i.e. units based on highly composite numbers - are very easily divisible by 2, 3, and 4

Units like feet, inches, pounds, stone, etc. are of a much more human-friendly scale. Because these units are based on bodily proportions or common objects

Generally, the arguments for metric vastly outweigh the arguments for imperial. And the main reason why is that the two arguments for imperial conflict with eachother. You cannot easily subdivide your units neatly and have human units.

For example, the Roman mile is a unit that measures the usual amount of distance a footsoldier can cover before needing a short stop. An acre is the amount of land that a manual-labour farmer can cover in a day's work. An inch is about the size of your thumb.

The problem is that all three of these units, based on length, are completely off kilter. 1 acre = 43,650 square feet, 1 Roman mile = 58260 in, etc.

The only cases where I would say the human-ness and divisibility of units actually becomes a stronger argument than decimalised units are, time and temperature.

Time is obvious. 1 hour = 60 minutes = 3600 seconds. It's nice, clean and simple. And an hour or half-hour is a very human unit, the same as a second or a minute. We often operate on hour and minute schedules, and that's not just because of capitalism. 30 minutes just appears to be the amount of time we like to work before taking a short rest.

Temperature is a bit more nebulous however ...

Where (I think) Celsius fails

Of course, celsius is an understandable scale. 0 C = Water Freezes, 100 C = water boils. Pinning your scale on water makes life easy for you as you know what the bounds are.

The problem is that there are temperatures that exist outside of the 0-100 scale. And this kinda breaks the neat decimalisation of a scale.

A cold winter's day in Tasmania could drop into the negatives. And just because your in the negatives doesn't mean ocean water or rain will freeze. Temperatures below 0 C doesn't guarantee snowfall.

Similarly, say you are in a desert during the day. The temperature can get as high as 50 C - it's reasonable to say that you're unlikely to see temperatures above 50 C outside of your oven or kettle.

Do you normally see temperatures between 70 - 90 C? Unless if you're pasteurising milk, distilling alcohol, or doing chemistry, you are not going to encounter these temperatures. And do you really need your temperature numbers to be below 100 to do chemistry?

This is the downside of Celsius. Because temperature is a scale, and operates differently to other units, it doesn't really matter where you set the zero point. A boiling point of ethanol at "78" is no better than one at "173".

Celsius also doesn't account for temperatures that are very well below the freezing point of water, temperatures which are very common to experience.

So is Fahrenheit Better?

Fahrenheit solves this problem, partially. It's a more human friendly scale. 0 F is a very very cold day whereas 100 F is a very very hot day. Things beyond both numbers are relegated to the scientists, chefs, and extremophiles of the world.

If we were to completely remove all requirements of not pissing off a bunch of people, we could even create our own temperature scale to make things even better: 0 X = -50 C and 100 X = 50 C.

Even better because now the 0 and 100 of this scale becomes the absolute limit of what we could normally experience on earth, the hottest desert and the coldest tundra. It even comes with the benefit that 50 X = the freezing point of water and 150 X = the boiling point of water - it preserves our common "anchors" of the phases of water.

The problem is that there's a second hidden benefit of Fahrenheit: it's specificity. What do I mean by that?

Well, for every 1 C increase in temperature, the Fahrenheit scale increases by 1.8 F. This means that a temperature of 20 C could mean 68 F or 69 F.

For a lot of normal/casual processes, the Celsius scale may require us get past the decimal point, to express minor changes in temperature, whereas Fahrenheit would not.

For chemistry and physics, our significant figure requirements immediately become extra precise. 58.8 F is a more accurate measurement than 14.9 C, without requiring any more decimal places.

You may say "well why not we use a deci-Celsius scale where 1000 dC = boiling point of water". The issue is that too much precision may be putting it over the top. We don't measure the size of cities in centimetres.

But then what about Kelvin

Of course, the main SI unit for temperature, and the unit physicists and chemists use is the Kelvin. The reason for this is of course:

It is tied to absolute zero by setting it to 0 K

Because of this, we can apply SI order of magnitude quantifiers like milli-Kelvin, kilo-Kelvin, Giga-Kelvin without upsetting the position of our anchor points

It covers and measures cleanly low-K processes

Very hot processes end up having Celsius be approximately equal to Kelvin

It would be difficult to use Fahrenheit because 0 F ~ the freezing point of saltwater.

But let me introduce you to the Rankine Scale. What Kelvin is to Celsius is what Rankine is to Fahrenheit.

Rankine takes all of the benefits of Fahrenheit with it (aside from the human-ness of the scale - but that's not the purpose of the Rankine and Fahrenheit scales), but it also takes the benefits that Kelvin gets.

We can too, have milli-Rankine and Giga-Rankine. And the best part is that it is twice as precise as Fahrenheit.

Even better is that the Rankine Scale is very easily convertible to the Kelvin Scale. 1 K = 1.8 R; 1 K⁻¹ = 0.556 R⁻¹. This means I can very easily re-formulate some fundamental constants:

Boltzmann constant = 1.381 × 10⁻²³ J K⁻¹ = 7.672 × 10⁻²⁴ J R⁻¹

Stefan-Boltzmann c. = 5.67 × 10⁻⁸ W m⁻² K⁻⁴ = 5.40 × 10⁻⁹ W m⁻² R⁻⁴

Ideal gas constant = 8.315 J mol⁻¹ K⁻¹ = 4.619 J mol⁻¹ R⁻¹

Wein's constant = 2.898 × 10⁻³ m K = 5.216 × 10⁻³ m R

Let's hope I converted it correctly, idk my Saturday brain no thinky.

Conclusion: So is it actually better?

Short Answer: In my opinion, yes. But I'm not switching to it.

Of course, when talking about subjective opinions, people can point out the flaws in each others' opinions. I've made it clear that the imperial vs. metric debate very solidly falls to the metric side with only a few exceptions.

Temperature is one of those scales that are more up-to-debate over the usefulness of certain units of choice. Especially because the alternative unit system is still commonly used.

I could've made the same arguments about the meter, and said that we should use a decimalised inch or foot with kilofeet or millifeet. Or invent a completely new unit system that is technically "superior". But that's obviously much more ambitious.

Of course, the likelihood of the global Fahrenheit revolution is almost non-existent, and this is more of a series of "well, technically speaking" arguments that are more for the point of exploring an idea than implementing one.

Regardless I'd like to hear YOUR arguments over why I'm a stupid poo poo head or I'm actually the mother of the next great napoleonic French empire.

I tried to add a bit of colour in this post, specifically with the quotes. I just didn't want it to be a bland wall of text.

Again, feedback that may be unrelated to the specific "you're right/you're wrong" debate like my writing style etc. is also appreciated.

I don't really know what I will do next week. Because technically I was supposed to do philosophy and ethics in science ... but I might not have that time given my university study.

Currently I'm doing three courses in QFT, GR, and Cosmology. And they are all very big and hefty. Thankfully, I think there's a bit of a break period coming as we're now moving to canonical quantisation (which I've found easier than Feynman diagrams), and the measurement of gravitational waves.

Now don't worry that last paragraph is not a flex, it's more an indication that I'm learning a lot of this stuff as I make these posts. More an excuse as to why I might in the future delay posts and such. Like I mentioned the Higgs mechanism in the last post at the same time I was actually learning about the Higgs mechanism.

Anyways, I'm going to go and scarf down some chocolate now.

[chaoticbuggybitchboy]

random fact, please?

*mind immediately blanks on everything I’ve known, ever*

The pH scale is logarithmic, meaning that something that’s a 6 is ten times more acidic than a 7, and a 0 is I think 10000000 (? I’m dyscalculic and so bad at zeroes) times more acidic than water (7) is. Another common example of a logarithmic scale is the Richter scale for earthquakes.

And back to the pH scale, there are super acids and super bases!! Technically because the technical definition of the pH scale you can’t actually have a pH less than zero but the chemists figured that out (I don’t remember exactly how) but there are acids with negative pH values and based with pH over 14. There’s not a lot of practical uses for that stuff since they’re so corrosive but hey, chemists.

[gayarograce]

🌻

(Oh man, the mortifying ordeal of actually having to pick something to talk about when I have so many ideas...)

Uh, OK, I'm talking about galactic algorithms, I've decided! Also, there are some links peppered throughout this post with some extra reading, if any of my simplifications are confusing or you want to learn more. Finally, all logarithms in this post are base-2.

So, just to start from the basics, an algorithm is simply a set of instructions to follow in order to perform a larger task. For example, if you wanted to sort an array of numbers, one potential way of doing this would be to run through the entire list in order to find the largest element, swap it with the last element, and then run though again searching for the second-largest element, and swapping that with the second-to-last element, and so on until you eventually search for and find the smallest element. This is a pretty simplified explanation of the selection sort algorithm, as an example.

A common metric for measuring how well an algorithm performs is to measure how the time it takes to run changes with respect to the size of the input. This is called runtime. Runtime is reported using asymptotic notation; basically, a program's runtime is reported as the "simplest" function which is asymptotically equivalent. This usually involves taking the highest-ordered term and dropping its coefficient, and then reporting that. Again, as a basic example, suppose we have an algorithm which, for an input of size n, performs 7n³ + 9n² operations. Its runtime would be reported as Θ(n³). (Don't worry too much about the theta, anyone who's never seen this before. It has a specific meaning, but it's not important here.)

One notable flaw with asymptotic notation is that two different functions which have the same asymptotic runtime can (and do) have two different actual runtimes. For an example of this, let's look at merge sort and quick sort. Merge sort sorts an array of numbers by splitting the array into two, recursively sorting each half, and then merging the two sub-halves together. Merge sort has a runtime of Θ(nlogn). Quick sort picks a random pivot and then partitions the array such that items to the left of the pivot are smaller than it, and items to the right are greater than or equal to it. It then recursively does this same set of operations on each of the two "halves" (the sub-arrays are seldom of equal size). Quick sort has an average runtime of O(nlogn). (It also has a quadratic worst-case runtime, but don't worry about that.) On average, the two are asymptotically equivalent, but in practice, quick sort tends to sort faster than merge sort because merge sort has a higher hidden coefficient.

Lastly (before finally talking about galactic algorithms), it's also possible to have an algorithm with an asymptotically larger runtime than a second algorithm which still has a quicker actual runtime that the asymptotically faster one. Again, this comes down to the hidden coefficients. In practice, this usually means that the asymptotically greater algorithms perform better on smaller input sizes, and vice versa.

Now, ready to see this at its most extreme?

A galactic algorithm is an algorithm with a better asymptotic runtime than the commonly used algorithm, but is in practice never used because it doesn't achieve a faster actual runtime until the input size is so galactic in scale that humans have no such use for them. Here are a few examples:

Matrix multiplication. A matrix multiplication algorithm simply multiplies two matrices together and returns the result. The naive algorithm, which just follows the standard matrix multiplication formula you'd encounter in a linear algebra class, has a runtime of O(n³). In the 1960s, German mathematician Volker Strassen did some algebra (that I don't entirely understand) and found an algorithm with a runtime of O(n^(log7)), or roughly O(n^2.7). Strassen's algorithm is now the standard matrix multiplication algorithm which is used nowadays. Since then, the best discovered runtime (access to paper requires university subscription) of matrix multiplication is now down to about O(n^2.3) (which is a larger improvement than it looks! -- note that the absolute lowest possible bound is O(n²), which is theorized in the current literature to be possible), but such algorithms have such large coefficients that they're not practical.

Integer multiplication. For processors without a built-in multiplication algorithm, integer multiplication has a quadratic runtime. The best runtime which has been achieved by an algorithm for integer multiplication is O(nlogn) (I think access to this article is free for anyone, regardless of academic affiliation or lack thereof?). However, as noted in the linked paper, this algorithm is slower than the classical multiplication algorithm for input sizes less than n^(1729^12). Yeah.

Despite their impracticality, galactic algorithms are still useful within theoretical computer science, and could potentially one day have some pretty massive implications. P=NP is perhaps the largest unsolved problem in computer science, and it's one of the seven millennium problems. For reasons I won't get into right now (because it's getting late and I'm getting tired), a polynomial-time algorithm to solve the satisfiability problem, even if its power is absurdly large, would still solve P=NP by proving that the sets P and NP are equivalent.

Alright, I think that's enough for now. It has probably taken me over an hour to write this post lol.