#arithmetic progressions

[mathswithnarendrasir]

Arithmetic Progression #arithmeticprogression #ap #maths #mathswithnarendrasir

[this-barbie-is-the-problem]

does anyone have any interesting info abt geometric progression, arithmetic progression, or sequences and series?

[plasticclipboard]

Gotenks: Chok!

Chok: We are Sex Bob omb and we're here to watch Gotenks KICK YOUR TEETH IN! 1,2,3,4!!!!

[onlinecomputercourse]

Arithmetic Progression Chapter-5 Important Questions with Solutions | Term-2 | Day-2

[cxmp-writes]

“you said you liked my cobain shirt”

“cocaine-coloured wedding dress”

Calling it now: next 5sos song will have the word “codeine” in.

[wri0thesley]

let me see - arlecchino x fem!reader (3.8k)

you work as a tutor at the house of the hearth; but the father of the children you teach seems to haunt your thoughts.

cw: not sfw, fem reader. employer-employed dynamics, reader calls arlecchino 'sir', chubby reader, reader is inexperienced. arlecchino calls reader 'good girl' and 'darling'. guided masturbation.

You see your employer only rarely, but that does not mean that you do not think about her often. 

It’s in the way that the children - your students, the ones you have been engaged to teach basic arithmetic and reading and as much history as you can squeeze in - speak of their ‘Father’. The look of wonder and devotion and just a touch of intimidation that comes over them, even as they chatter to you about the next time she is coming home and what they plan to do to welcome her. It’s in your salaries; perfectly paid, on time, with extra money left in an envelope and a note in beautiful, sharp handwriting mentioning your students by name and how well they’re progressing.

And, of course, it is in the times you see her - for you do not think anybody could see Arlecchino and not think about her regularly for the rest of their life. 

She makes you nervous. There is something about her commanding presence; her lovely marble face, the strangely striking appearance of her eyes, the self-assured way that she stands. You think her beautiful, of course - but you have always had trouble around beautiful people, and so you find yourself stumbling over your words, your cheeks burning hot, coming far too close to making a fool out of yourself whilst she keeps a small, polite smile on her face as she watches you falter. 

You worry, sometimes, she knows that you find her at once intimidating and irresistible - that something about the way you hold yourself will give away that you have wondered what her nails would feel like, digging into the soft skin of your throat as she tipped your chin upwards - or that you have wondered what it would feel like to have her corner you like a trapped rabbit and have her way with you--

But they are just daydreams. The truth is that you are as green as they come; you had gone to Sumeru’s Akademiya, a child who could not stop devouring books, who was obsessed with learning - and you had returned back to your native Fontaine to teach, and had no time in between that to pursue romantic relationships. The sum total of your romantic experience is a hurried kiss with another student, another beautiful older woman, who had pulled back and laughed at you, touching your cheek gently. 

“Aren’t you adorable?” She’d asked you, in a low, sleepy voice with her eyes half-lidded. “Maybe a bit too adorable for just right now. Come find me again if you’re ever in Mondstadt.”

So . . . your fantasies about Arlecchino are just that. Simple fantasies. You have other things to attend to, after all! You care about the children whose education has been entrusted to you - even those who have now grown too old to need your guidance, who you watch flower and blossom and strike out from the House of the Hearth. Even if they stray beyond the nation you live in, though . . . they always seem to come back, to pay their respects to Father. 

But it doesn’t stop the fact that sometimes she looks at you, when your paths crossed, with her head tilted just slightly to one side, and you feel like she knows exactly what you’re thinking. She always makes you feel strangely exposed; you keep up with fashion, because you enjoy it, but something about the fripperies of your gowns and skirts and blouses and the ribbons and the carefully chosen accessories in front of Arlecchino make you feel as though she is stripping you down in her mind, so perfectly poised and tailored. So you drop books in front of her. Your sentences get tangled together. You go hot all over and look at the floor--

But still she employs you, and still you hurry home at night and try to ignore the pounding in your chest and the way your breath goes short at the sight of her. Your paths cross only occasionally, you tell yourself. Next time you will be prepared. 

But you are not prepared, the day that Arlecchino meets you in the hallway (your arms full of books and the work of the children that you intend to look over that night), running late with your hair ribbons askew and your dress crooked and she looks at you and says, in a voice that brokers no argument;

“Won’t you stay a little longer and have afternoon tea with me?” 

“Do I make you nervous?” The red crosses in her eyes bore into you as she pours you a steaming cup of tea into a delicate teacup. You sit primly, your hands folded in your lap, your feet together, feeling entirely too exposed alone in this room with her. “You shake like a leaf whenever I speak to you.” 

You wet your lips awkwardly, your throat dry, as you reach out for the teacup. You notice your hands are shaking and try to stop them, but she leans forward herself and places one of her hands over yours, steadying you. You stare up at her, eyes wide, whilst she looks down at you with something calculating and predatory in her gaze. 

“I’m sorry,” you whisper, your voice very soft. You can feel your cheeks going hot against your will, and you wonder what you must look like to her - because you feel like a rabbit who is about to be pounced on by a wolf. Arlecchino slowly and purposely guides your hand back down, to put the teacup back on the saucer, and you begin to get the strangest impression that her invitation for ‘afternoon tea’ was actually an invitation for something entirely different. Her hand comes back up, and one of your idle questions is given an answer as you feel her sharp nails dig into the soft skin under your chin, tipping it up as she leans in closer. Close enough that she could kiss you, if she wanted - close enough you can smell the scent of Rainbow Roses and smoke that lingers on her clothes. 

“Oh,” says Arlecchino, and she smiles at you and something about the smile makes you go hot and cold all over all at once. “Don’t be. It’s terribly cute.”

You don’t know how you end up sprawled out over her lap, your thighs hooked over the arms of her chair, as she takes control of you - but before you know it, that is the position you have found yourself in. Her hands roam slowly all over you, savouring the feel of your skin - soft and warm, generously curved - beneath her long, elegant fingers. 

“These ribbons drove me to distraction today,” she murmurs against your ear, as you melt helplessly against her and she tugs at a brightly coloured red ribbon that trims your blouse. “I kept thinking about tying it around your pretty wrists instead.” 

“M-Miss Arlecchino--”

She clicks her tongue at you in admonishment, running her thumb over the seam of your lips. 

“Call me ‘Sir’, darling.” You practically fall over yourself to rectify your mistake, your tongue messy and heavy in your mouth, and you win a little chuckle from the woman who has you at her mercy. “You’re just so eager to please, aren’t you? What a good, obedient little thing.” 

“Please--” You whisper breathlessly, as she tugs at the ribbon completely and the throat of your blouse falls open. Her nails scratch a slow line over your neck, almost like a threat, and you shiver again helplessly under the touch. 

“Please what?” She murmurs against the shell of your ear. “You know, I did employ you as a tutor . . . for an academic, you’re rather inarticulate.” One button of your blouse, torturously slowly. The next, and she smiles against your bare skin to see the way your chest is rabbiting. “One would think you’d never been touched like this before.”

She knows.

There’s an edge to the way she says that, a note that’s teasing and suggestive, and it tears from your throat a little whimper of embarrassment that, in turn, makes her let out a sigh of satisfaction. 

“My, my,” Arlecchino says to you - two more buttons, and your blouse is barely fastened. You’re inordinately glad you wore pretty underwear today, though you suppose it must look rather fussy to Arlecchino. “Have you not, sweetheart?”

“Sir,” you whine out, feeling tears spring to your eyes at the humiliation of the whole thing. Despite the humiliation, though, heat spirals out from between your thighs - your matching fancy underwear, you know, is soaked through. “Please-- it’s embarrassing--”

The final button, and Arlecchino’s fingers are running over bare skin now. The pudge of your stomach, the curve of your chest through the ruched cups of your brassiere. 

“Say it,” she says to you, her voice sharp in the command. She circles a finger over your nipple through the lace and chiffon and you squirm in her lap at the sensation of the bud puckering and hardening. “If you want me to touch you, you understand, you have to at least have the confidence to tell me the truth. Or I’ll just send you home without your blouse and with your poor little aching cunt untouched, hmm?”

“Sir--!”

She grabs your cheeks between thumb and forefinger, squeezing the roundness of them roughly. The Father of the House of the Hearth, after all, is not one to be intimidated by whining or begging. She has plenty of experience dealing with brats. Her fingers still as she waits for you to do as she asks, and you squeeze your eyes shut and hiccup out a sob of longing. 

“I--I’ve never . . . had anyone else touch me . . . l-like this--”

She lets out a pleased purr in the back of her throat.

“There,” she soothes. “That wasn’t so hard, was it? Good girl.” She drops a kiss on the side of your forehead like a reward, her hands sliding over your body to find the catch of your brassiere. There’s a brief tussle of movement as she ensures you are shed of both your blouse and your underwear, and then you’re once more on her lap, your entire top half bared, only your skirts and stockings and underwear still on. “And if I’m honest . . .” She moves back to your ear, pressing a kiss on your jawline beneath the earlobe. “I rather like getting my claws in someone before they can learn any bad habits. I, too, am an excellent teacher.”

She takes a firm hold of you, pulling you even closer to her so that her hands can each take a palmful of your breasts. You feel exposed before her; the rolls of your stomach, the way that your chest sags into her grip, but Arlecchino does not seem to care about these things - instead she just sighs like you’re a fine wine she’s sampling, palming and squeezing the heavy weight of them. 

“You’re such a pretty thing beneath the flounces,” she says to you, plucking idly at your nipples between thumb and forefinger - the movement sends hot lightning flashes of pleasure right down to the space between your legs. “If I were in charge, I think I’d leave you naked in my bed. Much more practical like that, don’t you agree?” 

“I--” 

“What about kisses?” She asks you, not letting you say anything. Your head is spinning pleasantly, and you cannot say that you are annoyed she’s stopping you from making a fool of yourself. “Are you as unversed in those, too?”

“I--I’ve kissed . . . someone--”

“Just one?” She laughs, a not unkind noise. “Oh, just the one kiss, I see. Poor thing, your cheeks are like Pyro slimes. Come here. Let me show you how to kiss someone properly, hmm?” 

Arlecchino pulls you into a kiss that is so unlike the one you once had that to call them both by the same name seems a great disservice. There is no other way to describe it; she claims you, her mouth like a conquering king, your own the battlefield. Her teeth tug at your lower lip and you are helpless to do anything but open your mouth, let her tongue sweep over yours. She tastes like fire and tea, some of the little cakes she had offered to you - and you whine helplessly, clutching at her slacks because there’s nothing else you can reach in the position she has you in. 

She lets go of your face with a satisfied sigh, and your head lolls back against her shoulder as she delicately wipes a smudge of her lipstick from the corner of your mouth. 

“Let’s get this off you,” she says, tugging at the frills of your skirt. “Let me see you, darling.” 

You’re only too eager to assist, embarrassed but needy, wanting but nervous. The fastenings at your waistband are unhooked, and then she is carelessly sliding it off of you until you are back before her in nothing but your underwear and your stockings, digging into the fullness of your thighs. For a moment, you are embarrassed again of your softness - but Arlecchino grabs your hips, pulling you back bodily onto her, and you realise from the possessiveness of her movements that she does not see it for a moment as something to be ashamed of. 

Arlecchino’s hands are hungry as she squeezes at the softness of your thighs, as her palms sear hot across your stomach, as her fingers drift towards the gusset of your underwear. Her touch is feather-light, there, but you keen even so - terribly aware of every movement, even the smallest brush of her fingers. Arlecchino clicks her tongue against your ear again. 

“So sensitive,” she whispers. “I’m afraid I might hurt you, and I’m afraid I’d very much like it. Why don’t you show me how you touch yourself?”

Your breath gets caught in your chest. Her suggestions so far have been, perhaps, embarrassing - have put you at a disadvantage due to your lack of experience. But nothing so far has been quite so brazen. You burn with the unease of it, but Arlecchino is already grabbing your hand, placing it over your soaked underwear. 

“Don’t worry about making a mess,” she murmurs into your ear. “I’m afraid it’s too late for that. My pants are soaking.”

She seems to enjoy watching you squirm as you whimper again, face hot. But her hand does not move, keeping your own anchored against your underwear until you do as she asks and shyly, nervously, rub at yourself through the sodden fabric just a little. 

“Oh, darling,” she breathes, condescension dripping off every syllable. “You’ll never get anywhere like that.” You are inarticulate with your touches, still trembling and shaking at the strangeness of all of this - and you have done this, of course, but never with an audience! Never spread out over someone’s lap as they critique your technique!

“Sir, please--”

“You’re supposed to be a teacher,” she admonishes you. “You’re supposed to know everything, are you not? Have I really got to help you with something so simple as touching yourself?” She’s enjoying it; the sight of you, normally so prim and shy, utterly undone by her every word and action. Her hand moves over yours, holding it, guiding you to press two of your fingers together and circle over your swollen clit through the underwear. 

It’s different, with her guiding you. You turn your head to try and bury it against her collar as she continues to mercilessly guide you into circles, sniffling pathetically - but she just coos, just nudges you back so you watch the visual of her hand over yours between your thighs. 

“Shall we get your underwear off too?” She phrases it as a question, but it’s not one - she is already peeling off the frilly cotton, inching it down your generous thighs. She laughs a little meanly when she sees just how large the damp, darker patch is, and you think you will cry. Every feeling you have ever had is magnified a thousand fold here, in this incredibly vulnerable position spread over the lap of your employer. 

(There are whispers that Arlecchino is even more than that; that there is a secret purpose behind the orphanage you have been employed by. But you do not put much stock in rumours, even when the children look at each other strangely and whisper when they think you cannot hear them. The thought of who you might really be letting touch you . . . You wish it did not stoke a fire in you even hotter and brighter than before). 

“There we are,” she murmurs. “Good girl. Look at you. Look how pretty you are.” She deals your sex a short, soft slap - her palm comes away sticky, the noise indecent in the little room she had brought you to for afternoon tea. “I wonder how much prettier you’ll look with three of your fingers stuffed inside of you?”

Another strangled noise from your throat at the easy way she says the filthy things, and Arlecchino merely makes a soft huff of laughter. 

“Carry on touching yourself for me,” she says to you. “Let me see.”

It’s an order, and you know that orders from Arlecchino are to be obeyed. Shyly and hesitantly again, you bring your fingers back to your sex. She rests her head against your shoulder, and moves her own hand; uses two of her fingers to make a ‘v’ shape and places them on your sex, using them to spread the plump outer lips aside so that you have better access to your clit and your entrance, still soaking and leaking slick out onto Arlecchino’s lap. 

You’re hot and awkward as you touch your clit; as you try and mimic the circles that she had drawn on you earlier - but you are not brave enough to keep at it, and before long you have returned to your own faithful back-and-forth motion on your clit, your hips moving in little thrusts to try and prolong the sensation. You can hear yourself in the charged air; the hot little pants, the whimpers of frustration that none of it feels as good as it did when she was in charge. Arlecchino, though, merely watches you struggle. 

You cannot see her face, but you can imagine the look upon it; the barest quirk of the lip, the single raised eyebrow. You carry on as best you can, trying to think of all the things you would usually think of - but it all spirals back to where you are, what is happening, and the fact no fantasy can truly compare. 

Her voice is a little thick when she speaks next, and you realise with a strange jolt of pleasure that your inarticulate touching is still having an effect on her. It’s almost unnoticeable - but Arlecchino’s normal tone is so very poised, even the smallest change feels like a blaring siren to you. 

“Put two of your fingers inside of you,” she says. And then, as you inexpertly slide two of your fingers inside your channel, she lets out a shuddering breath. You’re wet and tight around yourself, aware that you must look a mess - but Arlecchino’s fingers are sliding between your sex, moving to touch the space on your clit you just vacated, and your entire mind goes blank. “Don’t stop. Let me see you move them.”

You do your best, but Arlecchino’s own movements are just too much. The sensation of her dragging the pads of her fingers over your swollen clit; the way she circles and flourishes and swirls . . . you try, desperately, to keep your fingers in some kind of rhythm as they slide in and out of you, but before you know it you’re using your other hand to clutch at her arm and whimpering as you hump upwards into her touch. 

“I ought to stop you,” she tells you, but she doesn’t for a moment stop her ceaseless assault on your clit; the wet, sticky clicking noise of your slick between her fingers. “You’re being a brat.”

“Please, Sir,” you whisper, babbling, “I’m . . . it feels so good--”

“Flatterer,” she murmurs, in that low, hungry voice. “You’re lucky that you look so very pretty like this, and that I am perhaps more soft-hearted than I appear . . .” Tears are running down your cheeks, sniffling, whimpering, helplessly moving your hips in time with her touches. Nothing seems to exist but the feel of Arlecchino’s fingers on your clit and the firm, certain way she touches you. “Be a good girl and come for me.” 

The order tips you over the edge. The knot of heat in your belly comes undone and you whine helplessly as you buck into her touch, and you feel a gush of your own slick wet the fingers that are still stuffed inside of you. Your thighs try to clamp shut around the sensation, but the position that Arlecchino has you in with your thighs over the arms of her chair stop you from doing it - and so does she, still working her fingers over your clit through every trembling moment of your orgasm. 

You come back down, panting, aware of the wetness between your legs and your nakedness, the stiff points of your nipples and Arlecchino’s fingers on you and the fact that Arlecchino is still dressed exactly as she was when she caught you in the hallway. 

She moves her hand, and to your surprise she presses her fingers against your lips, forcing your mouth open. 

“Taste yourself,” she tells you, and you are still so in awe of her that you can do nothing but obey - the slightly tangy taste of you lingering on your lips. You’re even more surprised when she uses her other hand to pluck your hand from between your thighs and guides the two fingers that had been inside of you to her own mouth, her tongue hungrily drinking in the wet webs of your slick. “Well. Aren’t you sweet?”

The unprofessionalism of what you’ve just done begins to creep up on you, shame drenching your back. All of those talks about ethics that you’d had at the Akademiya - but Arlecchino takes your head and turns it and gives you another firm kiss, another bite to your lower lip, another conquering that makes you feel weak at the knees. Your own taste lingers in your mouth, but, too, it lingers on her lips, and she seems supremely satisfied as she pulls back. 

“I’ll be away on business for the next week,” she tells you. “In Snezhnaya. I’ll bring you something back.”

“Sir--”

“I’ve been meaning to ask you,” she continues. “That little apartment you live in - well, it seems a shame, when we have so many empty rooms, and a live-in tutor would be far more beneficial - don’t you think? The children do adore you, and it seems so very practical.”

It’s a bizarre time to be having a business meeting, with your slick staining her clothes, with your own clothes a crumpled pile, with your position so terribly open and exposed - but all you can do is blink at her, and she smiles at you like a cat who has gotten the cream. She pats your cheek. 

“Besides,” she says. “It will give us far more time together. And I do have so much more I’d like to teach you.”

[inky-duchess]

Fantasy Guide to Education

I'm always asked what sort of education different people recieve throughout different historical eras and since I'm heading back to college soon, I thought it was high time I made this guide.

Disparity

Education is viewed as a right by many but for some and thoughout history it was a privilege. For the wealthy and those of high status, education can be easily accessed. They can afford to tailor an education to fit their needs, they can hire tutors, and they can afford tuitions to top schools. For the poor, education was a luxury. However this doesn't mean that it was available. Some communities would fund a school or send their children to a local teacher - usually they had to pay a daily fee or at least bring kindling for the heating. Many poorer children also worked so they could not attend school consistently or were pulled out very early into their education. However, some poorer students could gain access to high level education if they were extremely bright or caught the attention of a wealthy benefactor who could fund their education.

Education as a Weapon

Education could also be banned for certain groups in society. It could be illegal to fund schools or host gatherings for students of a certain background, race, religion or gender. Education against the law could be punished by imprisonment, exile or execution. This is a measure usually taken by oppressive governments in order to follow a moral code or restrict the betterment of a certain group. An example would be the Irish Catholics under the Penal Laws.

On the otherhand, there is education that is influenced by the state to inject certain values, moralities and Opinions into a population. This is the intense restriction of reading material, removal of books that contest the teachings of the government or the kidnap of children from their culture, in order to forcibly educated them in alignment to their beliefs. An example would be the residental schools of North America and Canada and the AHS schools of Nazi Germany.

Content

As above, content of what children learn usually falls into a certain category. This is also true for the education offered to the wealthy and the poor. The poor would be offered a basic education, learning literacy and arithmetic, usually with an expectation that the children would not go on to any jobs that needs a broader education. Any higher education would be hard to obtain because of cost and the discriminatory view of the enrollment panels. The wealthy would have access to an array of different subjects including: The arts (drawing, music, painting, poetry, dancing), sports (riding, martial skills, rowing, hunting), arithmetic, geography, languages, geography and history. While progression to higher education will still be difficult, any affluent families are legacies of prestigious colleges or can make a donation to grease a few palms. These schools would be where the wealthy make lifelong connections and get springboarded toward opportunities.

Private Tutoring

Whilst some affluent, aristocratic and Royal families send their children to schools, private tutoring in the home was a popular choice. Children would be educated at home but tutors who either lived in the home or come to the house. The children would be educated alongside siblings or the children of courtiers or neighbours. Private tutoring sessions would often be the only education for upper class women recieved, taught by governesses and tutors.

Premises and Equipment

As mentioned above, wealthy and aristocratic families would usually attend established schools or attend school at home. They would be provided any equipment they needed. If they attend school, they would often wear a uniform. Some schools had multiple variations of the uniform for different activities. Many of the schools attended would be boarding schools. Boarding schools offered education to those who boarded and day students, however day students were often looked down upon as lesser than.

Poorer schools would be relient on donations and fees paid by students. As mentioned above, there may be a building reserved for classes - sometimes an designated schoolhouse or a teacher's home or a public building such as a gathering house or sometimes even outside - hedge schools. Equipment would be provided by the school. Uniforms at poorer schools were not a thing but students were expected to show up neat and tidy.

Corporal Punishment

Corporal punishment at schools was the go to punishment for students. Teachers had free rein to strike children for mistakes and bad behaviour. Punishments include insolation, physical stress positions such as standing on a chair all day, getting objects thrown at them, being slapped on the back of the legs with a cane, being rapped on the palms or knuckles with a crop or ruler. Students may also be humiliated by teachers through the use of dunce hats, encouraging other children to bully them or by the use of verbal abuse. Corporal punishment did extend to all classes except for royal children since that was either taken by proxy by whipping boys or left up to parents.

[studyyblur]

day 33/100

oh god i began my menstrual cycle today and it took up my whole dau, i almost died due to cramps, don't question me ♡

so the entire day, i did nothing but sat with a heating belt bawling my eyes out, but we're good now, i was able to complete the redox lecture and its problem sheet, but i wasn't in the condition to do math at all, but I did do a few questions and i really need to get them done before tomorrow evening anyhow, so the to do for tomorrow goes like this:

lecture 1 on sequence series (arithmetic progression + geometric progression)

solve the rest of previous year problems on complex numbers

solve previous year problems on redox reaction

attend live lecture on complex numbers

[thisisnotthenerd]

for those of you who like spreadsheets as much as i do:

xp leveling chart:

the bad kids' xp progression in spreadsheet form:

freshman year:

oneshots:

sophomore year:

night yorb quest:

bad kids' overall totals:

the rat grinders' xp progression in spreadsheet form:

all of the arithmetic has been standardized; any errors from the original post have been corrected.

i hope this is useful.

[megumi-fm]

👾 megumi.fm ▸ hello may <3

—🎓 a c a d e m i c 🎓—

⭐ Level: bi in biotechnology Challenge 1: undergrad course completion ✅ [2/2] prep and complete last set of final exams ✅ internship presentation ✅ internship report 🔓 Achievement Unlocked >> amateur scribe — completed all written and typed documents for uni Challenge 2: graduate matriculation 📩 you've got mail >> next tasks and deadlines in June Challenge 3: GRE prep ✅ text completion section [Ptr + 5lb] 🔄 vocab 🔄 arithmetic section

—💻 w o r k 💻—

🎯 bi-weekly challenge complete! ✅ run alignment against self ✅ chose high degree nodes to run alignment against temp 📌next week’s task: binding site domain annotation [💬 view all phase2 challenges?] 8 weeks of remaining internship to unlock achievement —⚗️ sorcerer’s apprentice

—📢 s t a t s & u p d a t e s 📢—

🍶 2L+ water [◆◆◆◆◆◆◆◆◆◆◆◆] 👟 movement [◇◇◆◇◆◇◇◆◆◆◇◆] ⭐ Level UP >> de-lalali-nquent — learnt the chorus of SVT's LALALI

📅 ↪ moving future stats to daily tracker posts [💬 view progress?]

[1st - 12th May; week 19+20/52 || last weekly post in this game format xD I'll probably shift to a timeloop theme from next week to match my tatami galaxy challenge posts xD this is a super late update bc i literally forgot about it T-T from next week I'll keep these a lot shorter bc my daily's are already pretty extensive]

[forevergulag]

Bourgeois economists try to justify the existence of unemployment under capitalism by references to eternal laws of nature. This was the aim served by the pseudo-scientific fabrications of Malthus a reactionary British economist who flourished at the end of the eighteenth century and the beginning ‘of the nineteenth century. According to the “law of population” invented by Malthus, the population, from the very beginning of human society has increased in geometrical progression (as 1, 2, 4, 8, etc). but the means of subsistence, owing to the limitations of natural resources, have grown only in arithmetical progression (as 1, 2, 3, 4, etc.) This, said Malthus, was the fundamental cause of the existence of surplus-population and of starvation and want among the masses of the people. The proletariat, in Malthus’s opinion; can free itself from poverty and hunger not by abolishing the capitalist system but by abstaining from marriage and artificially restricting childbearing. Malthus considered wars and epidemics beneficial, since they cut down the working population. The theory of Malthus is profoundly reactionary. It is a means whereby the bourgeoisie justifies the incurable taints of capitalism. Malthus’s fabrications have nothing in common with reality. The mighty technique which mankind has at its disposal is capable of increasing the amount of means of life at rates which cannot be overtaken by even the fastest growth of population, But this is prevented by the capitalist system, which is the real Cause of the poverty of the masses.

political economy, part two: the capitalist mode of production, chapter IX: accumulation of capital and the impoverishment of the proketariat; the industrial reserve army. 1954

[gallifreyinstituteforlearning]

How complicated is it to get a degree(s) in temporal engineering?

How complicated is it to get a degree(s) in temporal engineering?

🔍 The Basics: Enrolling

First off, you don't just stroll into Gallifrey's prestigious Time Academy and sign up for Temporal Engineering 101. You have to pass the entrance exam, and that's not just a spelling test.

🧠 Intermediate Steps: Becoming a Junior Time Lord

Once in the Time Academy, your learning includes:

Temporal Physics: Understanding the fabric of time itself. Expect lots of quantum mechanics, chronon theory, and paradoxes.

History of the Universe: You need to know what happened, what’s happening, what could have happened, and what did happen but then didn't in the future and past.

Practical TARDIS Mechanics: It's not just theory; you need to know how to pilot and maintain a TARDIS.

Temporal Dynamics: In-depth study of how time flows and can be manipulated. This includes advanced mathematics that make calculus look like basic arithmetic.

Paradox Management: Learn how to handle, prevent, and sometimes even create paradoxes without tearing the fabric of reality apart.

Chrono-Spatial Navigation: Mastering the art of navigating through time and space.

Final Temporal Engineering Examination: An oral test where the Education Committee grills you on everything you've learned, from Time Lord Law to advanced temporal theory.

+ more (see related)

🏫 So…

It's probably not for you.

Related:

What are young Gallifreyans/Time Tots taught?: Detailing what the kids of Gallifrey are taught.

How do grade levels work in Gallifreyan schooling?: How the Gallifreyan education system works.

How long until the Earth might reach the technological age of Gallifrey?: Handy guide for humans wishing to progress.

Hope that helped! 😃

Any purple text is educated guesswork or theoretical. More content ... →📫Got a question? | 📚Complete list of Q+A and factoids →😆Jokes |🩻Biology |🗨️Language |🕰️Throwbacks |🤓Facts →🫀Gallifreyan Anatomy and Physiology Guide (pending) →⚕️Gallifreyan Emergency Medicine Guides →📝Source list (WIP) →📜Masterpost If you're finding your happy place in this part of the internet, feel free to buy a coffee to help keep our exhausted human conscious. She works full-time in medicine and is so very tired 😴

[f4iry-bell]

guys, how is the answer to the new riddle is 71???? 😭😭 there is no direct arithmetic progression where you'd get 71 (i think. i tried okay)

[wheels-of-despair]

Always Worth It | Ralph Penbury x You | Series Masterlist

The Most Amazing Wife in the World Summary: Ralph is having a rough day, but his amazing wife knows exactly how to turn things around. Words: 900ish

You hear a groan of frustration as you pass through the hallway outside Ralph's study.

You peek your head inside and see your usually-happy husband red-faced and angry at a desk full of papers. He glares at the page in front of him and holds a pen in his hand like he's ready to stab someone with it.

On another man, this sort of rage might be terrifying. But on your Ralphie, it feels about as threatening as an angry kitten.

"You're looking awfully grumpy in there, pup," you tease from the doorway. He looks up, and his face softens immediately. "Is everything alright?"

"Not really," he sighs, setting his pen aside. He rubs his eyes.

"Can I help you with anything?"

"Yes."

You step into the room and await instruction.

"A kiss, if you please."

You smile and approach his desk. Ralph pushes his chair back to make room for you, and you settle on his lap. He closes his eyes and tilts his head up, lips puckered and ready for his kiss.

You give him several, for being such an amazing husband.

Eventually, he rests his head in the crook of your neck and wraps his arms around you.

"What are you working on, love?" you ask, reaching for a piece of paper and trying to make sense of the figures that had been causing him so much grief.

"Boring financial things, mostly. I've been struggling with the arithmetic for so long, my fingers are starting to cramp."

You put down the paper and reach for his hand, bringing it to your lips and kissing each of his ink-smudged fingertips. Managing your own finances is hard work, but Ralph had decided that it was something he wanted to try, and you'd support him however you could. Even if it just meant distracting him when he needed it.

"How long 'til you're ready to stop for the day?"

Ralph looks at the grandfather clock and sucks air through his teeth.

"How about this," you suggest, placing a finger beneath his chin and guiding his gaze to yours. "You give this one more chance, and if you can't make sense of it in the next half-hour, you'll take it to a professional tomorrow."

"Alright," he smiles.

"Come to the garden when you've finished."

"Isn't it chilly out today?"

"Wear a jacket," you tease with a tug on his lapel.

Half an hour later, Ralph traipsed into the garden, bringing a blanket in case it was chillier than he thought.

But you'd already brought one.

A picnic blanket was spread on the ground beneath his favorite tree. On it were his smiling wife, a bottle of wine, and a basket that likely contained food.

Ralph's face split into a grin. This is exactly what he needed.

"Come on, pup, I have a surprise for you."

Ralph bounds over to the blanket, bubbling with excitement. TWO surprises? Mrs. Ralph Penbury is the most amazing wife in the world.

You hold up a pair of mittens. You're still new at knitting, and often laugh at your own attempts, but Ralph is so proud of your progress. Each new project is more beautiful than the last!

"They're lovely, darling!"

"I made them just for you," you smile, offering him the mittens. He takes them and turns them over in his hands, admiring the work and care and love you'd put into these. The finest, most expensive store-bought garments couldn't hold a candle to the things his wife made in their very own home. To think, a person could create something so thoughtful and personal with only a bit of string! He puts his mittens on, and his hands are soon as warm as his heart.

He grins at you and holds up his hands to show off his lovely gift, and you smile proudly.

"Are you ready for refreshments?" you ask, opening the basket you'd brought into the back yard. Ralph nods and scoots closer.

He moves to take his new mittens off, but your hand stops him. He looks up in confusion.

"You said your fingers were cramping from all the work you've done today. Give them a rest. Let me feed you."

Ralph nearly chokes on his own saliva.

While he sits there in stunned silence, you pull out finger sandwiches, fruit, and little treats to nibble on. When everything is out of the basket and on the blanket, you pour two glasses of wine and hand him one. He reaches out with his mittened hand and takes it with a smile that's starting to hurt his cheeks in the very best way.

"What looks good, pup?"

"Everything," he beams.

You smile, pick up a strawberry, and bring it to his lips. He leans forward just a little bit to take a bite of the sweetest, juiciest berry he's ever tasted. He feels the juice drip from his mouth, but doesn't dare dab at it with his new mittens. He reaches for a napkin, but--

"You've got a little something..." you whisper, leaning in close. Ralph freezes. Your tongue meets the trail of juice dripping to his chin and drags upwards until you meet his lips in a strawberry-flavored kiss.

You pull away with a warm smile, but Ralph needs more.

"You missed a spot," he breathes, as soon as he remembers how.

You laugh and give him another kiss, longer this time.

Is this really his life? Unscheduled picnics with a perfect wife who loves him and surprises him and makes him things and feeds him treats when his hands hurt and never gets tired of kissing him?

You've made Ralph Penbury the happiest husband in the world.

[kaywavy]

transforming soffits reorganizing keys formalizing immersion joints justifying kick extractors advising aggregates managing elbows recasting connectors achieving aluminum trowels officiating disks exhibiting absolute spigots progressing coil hydrants jerry-building reflectors informing casters inventing rubber hoists performing wrenches judging chalk adapters upgrading ignition paths

regrowing flashing recommending ratchets approving barriers sweeping impact fillers sewing mirrors detailing collectors enforcing measures distributing systems presenting plugs interwinding registers piloting ash diffusers gathering cranks supplying eave pockets undertaking scroll stops accelerating straps designing fittings protecting diamond boilers logging downspouts correlating shingles uniting mallets qualifying electrostatic lifts sharing clamps obtaining circular fluids ranking foundation gauges sensing miter brackets originating space networks translating drills regulating guards selecting gable padding utilizing pellet dowels reconciling artifacts altering pulleys shedding space filters determining vents representing mortar remaking flash rakers supporting funnels typecasting rotary chocks expressing junctures resetting auxiliary vises professing strip treads inlaying matter trowels questioning drivers forming edge fittings sketching blanks overshooting spark breakers rewriting controls playing tunnels inventorying buttons enduring joint handles effecting ratchet bibbs unwinding couplings forsaking vapor conduits defining sockets calculating heaters raising grids administering tiles measuring resources installing ignition remotes extracting corners manufacturing ventilators delegating consoles treating mounting stones enacting jig deflectors intensifying alleys improvising cargo pinpointing bobs prescribing arc masonry structuring metal chucks symbolizing lathes activating plumb kits adapting coatings fixing channels expediting cordage planning compressors enlisting hangers restructuring keyhole augers shearing ridge hardware collecting reciprocating bolts maintaining corrugated dimmers whetting hole collars conducting mandrels comparing assets compiling sealants completing paths composing equivocation wheels computing dampers conceiving electrostatic treatment ordering cotter grates organizing ties orienting ladders exceeding materials targeting thermocouples demonstrating emery stock expanding latch bases training wardrobe adhesives overcomming[sic] fasteners streamlining storm anchors navigating springs perfecting turnbuckles verifying gate pegs arbitrating arithmetic lifts negotiating outlets normalizing strips building surface foggers checking key torches knitting grinders mowing planers offsetting stencils acquiring bulbs adopting rivets observing avenues ascertaining coaxial grommets slinging wing winches instituting circuit generators instructing wicks integrating pry shutters interpreting immersion lumber clarifying coils classifying wood bits closing cogs cataloging matter strips charting holders conceptualizing push terminals stimulating supports overthrowing shaft spacers quick-freezing connectors unbinding ground hooks analyzing eyes anticipating gateways controlling proposition rollers converting power angles coordinating staples correcting benders counseling joist gaskets recording gutter pipes recruiting drains rehabilitating rafter tubes reinforcing washers reporting guard valves naming freize sprues nominating rings noting straps doubling nailers drafting circuit hoses dramatizing flanges splitting framing compounds refitting stems interweaving patch unions placing sillcocks sorting slot threads securing mode cutters diverting catharsis plates procuring load thresholds transferring syllogism twine directing switch nuts referring time spools diagnosing knobs discovering locks dispensing hinges displaying hasps resending arc binders retreading grooves retrofitting aesthetics portals seeking stocks shrinking wormholes assembling blocks assessing divers attaining lug boxes auditing nescience passages conserving strikes constructing braces contracting saw catches serving installation irons recognizing fluxes consolidating fuse calipers mapping shims reviewing chop groovers scheduling lag drives simplifying hoists engineering levels enhancing tack hollows establishing finishing blocks

[mariacallous]

In late 2017, Ashwin Sah and Mehtaab Sawhney met as undergraduates at the Massachusetts Institute of Technology. Since then, the pair have written a mind-boggling 57 math proofs together, many of them profound advances in various fields.

In February, Sah and Sawhney announced yet another joint accomplishment. With James Leng, a graduate student at UCLA, they obtained a long-sought improvement on an estimate of how big sets of integers can get before they must contain sequences of evenly spaced numbers, like {9, 19, 29, 39, 49} or {30, 60, 90, 120}. The proof joins a long line of work on the mathematical impossibility of complete disorder. It also marks the first progress in decades on one of the biggest unsolved problems in the field of combinatorics.

“It’s phenomenally impressive that they managed to do this,” said Ben Green, a mathematician at the University of Oxford. At the time the work was released, the trio were all still in graduate school.

Sequences of regularly spaced numbers are called arithmetic progressions. Though they’re simple patterns, they hide astounding mathematical complexity. And they’re difficult, often impossible, to avoid, no matter how hard you might try.

In 1936, the mathematicians Paul Erdős and Pál Turán conjectured that if a set consists of a nonzero fraction of the whole numbers—even if it’s just 0.00000001 percent—then it must contain arbitrarily long arithmetic progressions. The only sets that can avoid arithmetic progressions are those that comprise a “negligible” portion of the whole numbers. For example, the set {2, 4, 8, 16, …}, in which each number doubles the one before it, is so spread out along the number line that it’s said to make up 0 percent of the whole numbers. This set has no progressions.

Forty years later, in 1975, a mathematician named Endre Szemerédi proved the conjecture. His work spawned multiple lines of research that mathematicians are still exploring today. “Many of the ideas from his proof grew into worlds of their own,” said Yufei Zhao, Sah and Sawhney’s doctoral adviser at MIT.

Mathematicians have built on Szemerédi’s result in the context of finite sets of numbers. In this case, you start with a limited pool—every integer between 1 and some number N. What’s the largest fraction of the starting pool you can use in your set before you inevitably include a forbidden progression? And how does that fraction change as N changes?

For example, let N be 20. How many of these 20 numbers can you write down while still avoiding progressions that are, say, five or more numbers long? The answer, it turns out, is 16—80 percent of the starting pool.

Now let N be 1,000,000. If you use 80 percent of this new pool, you’re looking at sets that contain 800,000 numbers. It’s impossible for such large sets to avoid five-term progressions. You’ll have to use a smaller fraction of the pool.

Szemerédi was the first to prove that this fraction must shrink to zero as N grows. Since then, mathematicians have tried to quantify exactly how quickly that happens. Last year, breakthrough work by two computer scientists nearly solved this question for three-term progressions, like {6, 11, 16}.

But when you’re instead trying to avoid arithmetic progressions with four or more terms, the problem becomes tougher. “The thing I love about this problem is it just sounds so innocent, and it’s not. It really bites,” Sawhney said.

That’s because longer progressions reflect an underlying structure that is difficult for classical mathematical techniques to uncover. The numbers x, y and z in a three-term arithmetic progression always satisfy the simple equation x – 2y + z = 0. (Take the progression {10, 20, 30}, for instance: 10 – 2(20) + 30 = 0.) It’s relatively easy to prove whether or not a set contains numbers that satisfy this kind of condition. But the numbers in a four-term progression have to additionally satisfy the more complicated equation x2 – 3y2 + 3z2 – w2 = 0. Progressions with five or more terms must satisfy equations that are even more elaborate. This means that sets containing such progressions exhibit subtler patterns. It’s harder for mathematicians to show whether such patterns exist.

In the late 1990s, Timothy Gowers, a mathematician now at the Collège de France, developed a theory to overcome this obstacle. He was later awarded the Fields Medal, math’s highest honor, in part for that work. In 2001, he applied his techniques to Szemerédi’s theorem, proving a better bound on the size of the largest sets that avoid arithmetic progressions of any given length. While mathematicians used Gowers’ framework to tackle other problems over the next two decades, his 2001 record remained steadfast.

In 2022, Leng—then in his second year of graduate school at UCLA—set out to understand Gowers’ theory. He didn’t have Szemerédi’s theorem in mind; rather, he hoped to answer a technical question related to the techniques Gowers had developed. Other mathematicians, fearing that the effort needed to solve the problem would eclipse the result, tried to dissuade him. “For good reason,” Leng later said.

For more than a year, he didn’t get anywhere. But eventually, he started making progress. Sah and Sawhney, who had been thinking about related questions, learned about his work. They were intrigued. “I was amazed it’s even possible to think like this,” Sawhney said.

They realized that Leng’s research might help them make further progress on Szemerédi’s theorem. Within a few months, the three young mathematicians figured out how to get a better upper bound on the size of sets with no five-term progressions. They then extended their work to progressions of any length, marking the first advance on the problem in the 23 years since Gowers’ proof. Gowers had shown that, as your starting pool of numbers gets bigger, the progression-avoiding sets you can make get relatively smaller at a certain rate. Leng, Sah and Sawhney proved that this happens at a rate that’s exponentially faster.

“It’s a huge achievement,” Zhao said. “This is the kind of problem that I really would not suggest to any student because it is so incredibly hard.”

Mathematicians are even more excited by the method the trio used to get their new bound. For everything to work, they first had to strengthen an older, more technical result by Green, Terence Tao of UCLA and Tamar Ziegler of Hebrew University. Mathematicians feel that this result—a sort of elaboration of Gowers’ theory—can be improved even further. “It feels like we have an imperfect understanding of the theory,” Green said. “We’re just seeing a few shadows of it.”

Since completing the proof in February, Sah and Sawhney have both graduated. But the pair’s collaboration has not yet slowed down. “Their incredible strength is taking something that is extremely technically demanding and understanding it and improving upon it,” said Zhao. “It’s difficult to overstate the level of their overall accomplishments.”