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omegaphilosophia · 5 months ago

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The Philosophy of Calculus

The philosophy of calculus explores the foundational, conceptual, and metaphysical questions surrounding calculus as a branch of mathematics. It delves into the nature of continuity, infinity, limits, and the relationship between mathematics and the real world. Since calculus involves concepts such as infinitesimally small quantities, rates of change, and accumulation, philosophers have long debated its implications for our understanding of space, time, and motion.

Key Concepts:

Continuity and Change

Foundational Questions: Calculus, by its very nature, addresses the study of continuous change. Philosophers explore how calculus formalizes change, especially how it captures instantaneous rates of change (derivatives) and accumulations (integrals). The question of how change can be captured mathematically while still being grounded in reality is a central issue.

Zeno's Paradoxes: The ancient Greek philosopher Zeno posed paradoxes, such as the paradox of Achilles and the tortoise, that question how motion and continuity can exist if space and time can be infinitely divided. Calculus provides a mathematical resolution to these paradoxes by showing how infinite processes (like summing infinite series) can yield finite results.

Limits and Infinity

Nature of the Infinite: Calculus heavily relies on the concept of limits, where values approach some end point, often involving infinity or infinitesimally small quantities. Philosophers question what it means for something to approach a value (limit) without ever actually reaching it. What is the status of infinity in calculus? Is it a real, physical entity or a useful mathematical abstraction?

Infinitesimals: In the development of calculus, the idea of infinitesimals—infinitely small quantities—played a crucial role. Philosophers like George Berkeley famously criticized early calculus for relying on "ghosts of departed quantities" that seemed to have no clear ontological basis. Later, the rigorous formalization of limits by Augustin-Louis Cauchy and Karl Weierstrass helped address these concerns, though the concept of infinitesimals remains a subject of philosophical debate.

Mathematical Realism vs. Formalism

Realism: Mathematical realists believe that the objects and structures of calculus (such as limits, derivatives, and integrals) exist independently of human thought, either as abstract objects or as part of the fabric of reality. This perspective raises questions about the relationship between mathematical concepts and the physical world: Does calculus describe real processes in nature, or is it a mere human invention?

Formalism: Formalists, on the other hand, argue that mathematics, including calculus, is merely a system of symbols and rules that humans have devised to model reality. For formalists, the power of calculus lies in its logical consistency and utility, not in the existence of mathematical entities as part of the physical world.

Applications to Space and Time

Mathematics of Motion: Isaac Newton and Gottfried Wilhelm Leibniz, the co-founders of calculus, developed it to study the motion of bodies through space and time. Philosophers ask how calculus models space and time and what this implies for our understanding of reality. Are space and time continuous or discrete, and how does calculus help answer this question?

Relativity and Quantum Mechanics: In modern physics, calculus plays a vital role in theories like general relativity and quantum mechanics. Philosophers of science consider how calculus provides the tools to describe the curvature of spacetime or the probabilistic nature of particles. This brings forth metaphysical debates on the nature of the universe and whether our mathematical tools truly capture its essence.

The Role of Approximation

Calculus as Approximation: In many cases, calculus provides approximations rather than exact answers, especially when dealing with real-world phenomena. Philosophers ask whether this means that calculus only approximates reality, and if so, how accurate these approximations are. What does this say about the limits of human knowledge and the nature of truth in mathematics?

Constructivism vs. Platonism

Platonism: Many mathematicians, such as Kurt Gödel, held that mathematical objects exist in a Platonic realm, independent of human minds. In the philosophy of calculus, this view would suggest that limits, derivatives, and integrals exist "out there" in some ideal form, waiting to be discovered.

Constructivism: On the other hand, constructivists believe that mathematical objects only exist when they are constructed or proven to exist through logical processes. In this view, the objects of calculus, like infinitesimals, do not exist in an abstract realm but are instead tools we create to solve problems.

Historical Development and Philosophical Insights:

Newton vs. Leibniz:

Newton's Fluxions: Newton saw calculus as a way to describe motion and change in the natural world. He introduced the idea of "fluxions" to represent instantaneous rates of change. His view of calculus was closely tied to physical processes, such as the movement of planets.

Leibniz's Infinitesimals: Leibniz focused on the mathematical notation and formal structure of calculus, introducing the concept of infinitesimals. Leibniz’s approach was more abstract, focusing on symbolic representation rather than direct physical interpretation.

Berkeley's Critique:

Criticism of Infinitesimals: The philosopher George Berkeley famously criticized early calculus in his work The Analyst (1734), calling infinitesimals "ghosts of departed quantities." Berkeley’s critique focused on the lack of rigor in the concept of infinitesimals, pushing mathematicians to develop a more solid foundation for calculus, leading to the formal concept of limits.

Modern Foundations:

Limit Theory: The development of rigorous limit theory by mathematicians like Cauchy and Weierstrass resolved many of the early philosophical objections to calculus. By defining limits rigorously, they provided a solid foundation for understanding how calculus could deal with infinity and infinitesimally small quantities.

Non-standard Analysis: In the 20th century, Abraham Robinson developed non-standard analysis, a formal mathematical system that reintroduced infinitesimals in a logically rigorous way. This has revived philosophical discussions about the nature of infinitesimals and their role in calculus.

The philosophy of calculus examines the underlying concepts of change, infinity, and continuity that are central to calculus. It raises questions about the nature of mathematical objects, the relationship between mathematics and reality, and the limits of human knowledge. While calculus has provided powerful tools for understanding the natural world, it also raises deep philosophical questions about the nature of space, time, and motion.

#philosophy #epistemology #knowledge #learning #education #chatgpt #ontology #metaphysics #Calculus #Philosophy of Mathematics #Infinity #Limits #Continuity #Infinitesimals #Mathematical Realism #Formalism #Space and Time #Mathematical Foundations

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thecloudsaremyhome · 18 days ago

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☆Platonic April week 2☆

☆Platonic yandere professor geto x reader☆

Summary: you've been taking Mr. Geto's cours for a while now and can't help but notice something is off about his behavior an how he treats you, but you unknowingly stepped into his webbed trap where escape is not an option

Tw: manipulation, isolation, yandere behavior, yandere themes, geto is a warning in itself, obsessive behavior, coddling, reader has trust issues, delusion behavior, infantilization, reader is stressed, overthinking

Word count: 2k

Everyone loved professor Geto, smart, hadsome, and very professional.

No wonder many of your female classmates swooned over his attention and many of your male classmates craved his praise.

Because he had an air of calmness around him,a voice so soothing that just draws you in and makes you feel safe. With his honey words and rich deep voice.

Well not for you that is, you've always had this bad feeling about your professor, be it gut or Intuition, you don't know.

All you know is to keep your interactions to a limit for your own sake.

You don't actively avoid him nor do you follow him around like. Lost puppy, you are just there.

But that doesn't seem to stop your professor from keeping a diligent eye on you, it may seem like hes just looking out for a student of his when he gives you more attention than the rest of your classmates, but you know its something entirely different.

The way he looks at you with hidden motherly affection in his gaze but what creeps you out the most is the way he carefully masks his obsessive behavior.

The way he seems to notice every little detail about you is the most unnerving part, the way he seems to coddle and worry over you.

And your trying your best to avoid him or politely turn down his invitations on tutoring or extra credit, and his constant coddling and worrying over you.

you've tried to dismiss to the best of your ability. because you know he is trying to slowly lure you into his webbed trap.

And if you fell into that trap, their would be no escape from his suffocating hold.

And the worst part may be is that no one bats an eye at his strange behavior towards you, more than not most are jealous of the extra attention you receive so that leads to you not being able to confine to anyone including your so called friends.

This leads you to feel isolated and more over alone.

Maybe he's intentionally trying to isolate you so you could only turn to him, as crazy as that idea may sound, it may be accurate or you may just be deluding yourself into thinking that either way.

So you continue to hold your all and keep your distance between you and your overbearing professor, which is easier said than done to be honest.

But today really wasnt your day, you woke up 30 minutes late because you forgot to set your alarm the previous night, which leads to you rushing out of your dingy apartment door, to your university.

Once you finally make it to your first class, calculus and to say your professor was pissed was an understatment.

she already seemed like she woke up on the wrong side of the bed as well with her frizzy chocolate brown hair and eye bags under her eyes.

She actively scolded you infront of the whole class, and by the end of it you were almost left in tears by the pure embarrassment of the whole situation.

You can feel tears brimming at your eyelids and your contained sob in your throat, you try to push it down for the sake of your own sanity to not actively cry and embarrass yourself even more.

When she was finallsy done you were dismissed to yur seat which was luckily the back row. So you wouldnt have much attention on you.

But you could still hear the giggles and talks directed at you and that didnt help your ever growing damp mood at all.

So with a heavy sigh you decided to reluctantly ignore the stares and comments your receiving in favor of focusing on the board.

Finally lunch rolls around and you couldnt be even more appier to be relived of a break from the suffocating rooms you call a class.

You decide to get in line and buy lunch today. While your waiting your scroll on your phone to pass the time.

But you dont notice someone rushing past you until its to late and you stumble before accidentally bumping into the person before you, who spills her drink on your worn down mtv shirt.

Thus causes you to let out a groan of annoyance as you quickly apologize and decide that its not worth staying in line anymore.

nor is it worth any further embarrassment. Its like the universe is against you today for some odd reason and you are not aving that.

So you walk towards your small clutter of friends and sit down reluctantly, your two friends Yoon-Won and Hikari raise their brows in concern clearly sensing the shift in your mood, and Yoon-Won, ever the sweetheart decide’s to ask you.

“hey (nickname) are you alright? What happened?” she says in a soft tone clearly concerned for your well being.

You sigh and hesitantly nod in response with a “im fine” when you now its far from the truth.

You just dont want to bother your frends with your stressful day and burden them, they clearly already have enough on their plate seeing the current eyebags under hikari’s eyes.

They nod knowing your clearly not fine but not wanting to push it further. You three sit in silence for a good few minutes before yoon-won starts up the conversation again.

“(nickname) you should’ve seen mr. geto yesterday, he was completely on edge and it seems like he was gonna loose it, maybe it had something to do with you skipping?”

yoon-won says clearly the gossiper of the group.

You raise your eyebrows in surprise, thats strange.

its true that you did skip yesterday’s seventh period because you didnt feel like dealing with your overbearing professor, but you would never have guessed he would initially act that way especially since you were gone.

For the whole time you've known mr. Geto throughout the semester he was never the type to easily almost loose his cool.

He was the calm and collected type of professor that a semblance of students were lucky to have.

Yoon-won clearly noticing your surprised expression smirks playfully.

“you’re lucky i covered for you and made up a good excuse so mr.geto wouldnt go and get you himself, he seems to really care for you, you know, like a mother hen.”

she says playfully with a mischievous smile. You tense at her words but lightly laugh it off.

You dont have a good about this at all and your gut is telling you that once you walk into his class, you will be having the time of your life and not in a good way.

But yoon-won is right, ghetto has always acted more of a mother hen to you now that you think about it.

From him constantly checking up on you from time to time to his overbearing nature, youve been lucky that youve been able to avoid most of it to the best of you ability by dismmissing him.

But something tells you that this wont last for long, that you will be cornered and a have to accept his weird form of affection.

But you refuse to, because you know you won’t be able to escape his web once he has you.

You snap out of your daze when hikari says your name and you look up to meet his worrying gaze “(nickname) you good? You spaced out their for a minute?”

you look up towards him and nod sheepishly smiling as yoon-won continues on with her rants. You cant help but chuckle lightly.

Shes always been able to lighten your mood even without her realizing it and, maybe the rest of the day will go smoothly? You hope so.

You were wrong, once you enter mr.geto’s class you noticed the already tense atmosphere plagued in the air.

You carefully walk in and look up to notice mr.geto staring at you with a particular polite smile o his face, but you can tell hes not pleased.

Not one bit, from the twitch of his perfectly manicured brows to his slightly downturned dimples and his usually soft amythytst like eyes seem more sharp and predatory.

You know your fucked, and he knows it to.

So you decided to carefully make your way up the stairs and sit down in your seat, hoping and praying that class could begin soon so that he could focus his attention on something other than you for at least a moment.

So you don't have to feel his burning stare on your already shaking form.

You just can’t handle any more of this, you feel like you could burst into tears any second and you would, but you wouldnt give him the pure satisfaction of seeing that, of seeing you oh so broken and try to pick up the pieces, but you know your better than that.

you wont let him take advantage of you being vulnerable, to exploit it for his own twisted benefit because youve already been their done that.

But you dont notice, his softing gaze peering into you nor do you notice the active worry thats happening, in his turmoil of mind, because you refuse to believe, refuse to believe he isant just trying to trick you, trap you in his hold.

Because you refuse to be trapped like a pet in a cage ever again.

And maybe its your trust issues speaking but you refuse to actively belive your so called professor cares for you, eve if all the disturbing signs are their.

You know he wants you for something, maybe to be a child of his in his sick twisted mind. Maybe to manipulate you? You dont know, but you sure as hell don't want to find out.

Maybe that's why you're actively scared to face him after class, because you know you wont be able to escape.

his ever overbearing presence and you know you will break, and the dam of tears will start to fall right out and you wont be able to do nothing about it.

Because you will be like putty in his overwhelming presence and maybe thats what he wants, for you to be modable like putty.

You get snapped out of your daze when you hear the loud blaring noise of the bell indicating the class was over, you quickly pack up you belongings, realizing you entirely spaced out the whole lesson so youll have to borrow notes from hikari later.

But before you could rush out the door and to the comforting embrace of your apartment you hear mr.geto call out to you.

“(name), may i speak with you?”

you sigh in annoyance but expected this to come, you nod your head and slowly approach the manorkery wooden desk placed at the front of the room.

You look up and are faced with his dark amethyst eyes that look like they could ull you under and never let you go, his eyes were always memerizing n a hypnotic type of way.

maybe thats why everyone gravitated towards him. Because he has a hypnotic type of pull to him.

You make eye contact for a second and momentarily regret it as you notice the sharp look in his eyes. You really aren't ready for this. You sigh shakinly and mutter

“y-you wanted t-to speak with me mr.geto?”

you say coming out more timid than you intended to you internally cringe at yourself. God could you sound any more pathetic?

But you dont notice the soft smile making its way onto your professor nor his softing gaze, like hes looking at a frightened animal needing guidance and protection, he clears his throat and nods

“yes (name) i would like to speak with you about your aparent absence yesterday, would you mind informing me of where you went off to?”

You freeze, he knows, he knows you skipped because of him and hes just waiting for you to mess up, to make a mistake.

Because he knows he has you cornered and their is nothing you can do to stop it.

You feel the tears brimming against your eyelids from the current distress of the situation.

No, not now, please not now, you cant take it. You cant cry here, god why wont your body listen to you!

You finally feel the dam break as tears start to soak your cheeks as your eyes start to get red and puffy, you must look so pathetic right now, crying in front of your professor!

God this has to be the most embarrassing moment in your life.

You feel his steady arms slowly wrap around your shaking body as he pulls you into an invoulatarily hug, and you reluctantly corporate. Because what else are you supposed to do?

If you pull away or yell you will only make the situation worse, so you just sit their an accept his comfort, his soft praises and cooing.

And you cant help but let the warmth bloom in your chest, you cant help but soak it in as much as you can, because what else are you supposed to do?

At this point you know you cant escape him, his everlasting comfot hes been willing to give you, his soft words, his praise and affection.

And maybe you dont want to escape, maybe you want to embrace it because thats the only thing you can do as of now.

And its not like you have any other source of comfort, so hes all you have.

And he wants to keep it that way, you dependable on him, because he knows that small little brain of yours is not suited to do grown up work.

thats why he became more overbearing, thats why he became more constant in his checkups on you, because he knew you couldnt handle yourself, he knew you didnt know how to take care of yourself.

And you clinging to him right now proves his point, your helpless without him, without his guidance without his support.

But he doesnt mind, he relishes it more than anything, because you need him and thats enough for geto.

Maybe he would feel more quilty about manipulating everyone around you if you werent clinging to him like a lifetime, but in the end everything worked out as planned, you just needed a little push to relalize that he is all you will ever need.

And thats a fact.

You shouldve never taken his course to begin with.

Authors note: sorry for how short it is!! I kinda rushed at the end! This Isan't proofread so their may be many mistakes but I hope you all enjoyed this as much as I did!

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reneesghostinthelivingroom · 1 year ago

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NorthShore Nowheres part 1

part 2 || part 3

|| Poly!plastics x fem!reader (bit of Cady x fem!reader) (btw I myself am poly)

|| Warnings: loosely follows the movie musical, with reader being Aaron (slight dialogue changes to fit Y/N), light swearing

|| Summary: you're the leader of the NorthShore Nowheres biker gang/clique. The plastics take an interest in you, but so has Cady...

Requested by Anon!

Requests open!

~~~

The sound of your motorcycle filled the parking lot as you zipped through and parked in your usual spot, taking your helmet off and twisting your head slightly in a way that fixed your hair. For the plastics, who had been watching you from the side steps of the school, time seemed to play in slow motion. Watching as you flick your hair and get off your bike. Your walk radiating pure confidence. The girls shared a look with one another.

"We're all in agreement?" Regina asked her girlfriends, who nodded and looked back at you. Watching as you walked past them, heading up the steps and giving the school's polycue a wink.

You sat in AP Calculus. Not listening to a word Ms Norbury was saying as she stood at the front, hands on her hips and looking out at the rows of students. You simply folded a paper airplane and tossed it at some random kid next to you, making another stifle a laugh as you smirked. The student swatted the paper plane away.

"Y/N L/N." Ms Norbury gave you that signature warning look, which made you roll your eyes and she continued on with her lecture," Chapter one! Limits and their properties. What the heck are limits, you say? If I write out the equation..."

You started zoning out, hand on your chin and elbow on your desk as you stared at the board blankly.

"The limit equals 3." A voice from behind you spoke up, pulling you from your day dreams.

"That's right." Ms Norbury said, sounding surprised. " Let's try another one. Find the value for K for which the following limit exists."

"K equals -3." The girl says again.

"Damn, girl!" Some mathlete kid piped up.

You looked behind at the girl and smirked," Wow. Are you trying to make the rest of us look like dumbasses?"

"No- I'm- I'm not- trying to it's just sort of happening..." She replied, stuttering as she stared at you. Adorable. You laughed.

"Oh? Is that how it is? Okay. Well..." You leaned a little closer," challenge accepted."

You turned around, looking down at your paper with a sigh. The new girl on your mind. Reaching into your bag, you pulled out your pen then gently trailed your hand through your hair as you began working on your paper. Why did you sign up for AP Cal? This class was going to kill you.

Behind you, you heard something fall to the ground and looked to see Cady's pen. You bent down and picked it up, handing it to her with a smile before looking at the board again. You could have sworn you heard music coming from somewhere...

~~~

After school, you were outside with some of your biker gang. Just chatting and hanging out as you fidgeted with your phone. You happened to notice Cady watching you and gave her a small wave. Then turned your attention towards your gang again; when Cady almost got hit by the bus, your eyes widening slightly. You debated going to check on her. But she said that she was okay. Which made you sigh with relief from where you stood a bit away.

~~~

The following day, you and your gang sat at your usual lunchtable. Rough housing with each other, laughing and spreading gossip as you usually do. You glanced over at the plastics table, watching as Regina got up and walked away.

Karen and Gretchen were talking with Cady. "So, have you seen any guys you think are cute yet?" Karen asked.

"Oh, um- not a guy- but well actually there's this girl in my Calculus class." Cady responded.

"Ohhh, a senior! Who is it?" Gretchen replied.

"Ah, Y/N L/N." Cady replied, Karen and Gretchen shared a panicked look.

"You can't like Y/N L/N!" Gretchen said quickly.

"No, no bad, danger." The danger Karen said was loud enough to get your attention, you glanced at them in confusion then rolled your eyes and focused on your group again. Getting shoved by one of your friends who you playfully shoved back and smirked at.

"We're after her so you can't have her." Gretchen states, looking over at you and your gang's table," Crushes are off limits for friends that's just like the rules of feminism."

One of your friends in your gang wrapped an arm around you and started filming a TikTok. Instinctively you winked at the camera then laughed slightly and looked at your friend, who's name was Julia. But no one called her that, pretty much everyone referred to her as Jules. "Jules, girlie. What weird trend are you hoping on now?" You asked with your usual charming smile. Two things you had a reputation for. Being a bad girl. And then your charm, even if you weren't overly popular people still loved you. You just weren't Apex Predator worthy. Possibly like whatever was a few chains down from that, though.

"That one silent review trend. Featuring you." Jules pointed at you and you couldn't help but laugh.

"Definitely tag me in that." She nodded and you gave her shoulder a gentle pat.

~~~

At the end of the day, you and your gang hanged out at your usual bench. With you sprawled out across it and Jules laying across you. You guys were close friends, though there were rumours you were a thing. One of your friends made a joke and you laughed, though it was cut short as the plastics walked over. Regina with her arms folded, Gretchen and Karen following behind.

Regina's intimidation was enough to scare Jules off you (and the rest of your gang). They excused themselves as you sat up, watching the three in confusion. Once again you swore you heard music... with faint jungle sounds?

"Something I can do for you?" You folded your arms, a little annoyed Regina scared off your friends.

"You. Us." Regina gestures to herself, Gretchen and Karen," Date to the movies Friday night. Wear something nice." She looks you up and down, you glance at your baggy jeans and leather jacket before looking at Regina again.

"Is this you inviting me into your polycue?" If you're being honest, you have wanted them for a while. You just didn't want to risk making a fool of yourself. Regina's gaze tells you everything you need to know, so you nod." Alright. Friday night."

Regina smiles and walks over, kissing your cheek before looking towards Cady who had been watching. She beckons Cady over and then walks away from you. Gretchen and Karen linking arms as they giggle, Gretchen sending you a wink. Your face flushes and you look away, making a mental note to be extra careful. The last thing you wanted to do was piss off all three.

~~~

Feedback is welcomed! Probably going to make this a 3 part story (maybe longer depending), each part being about a half an hour chunk of the movie with extra bits added in between. Just so this doesn't become overly long, yk?

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meangirls-imagines · 1 year ago

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A (Different) Cautionary Tale

a/n: for this story to work the way i wrote it, pretend regina didn't out janis, cady is bi, regina is bi (but obviously leans more towards girls) and aaron is just ✨there✨

regina george.

the queen bee of northshore high school.

everyone wanted to either be regina or be with regina.

everyone except y/n it seemed.

you see, y/n was the older sister of janis, the girl regina used to call a best friend a few years prior but had a falling out with. y/n was a year older than the two, entering her senior year of high school. she was also the complete opposite of janis. she played sports, she had a gpa of 4.0, did extracurriculars. janis didn't do any of that, opting to hang out with damian and spend most of her time in the art room.

regina and y/n had a complicated past. after the falling out between janis and regina, y/n had drove to her house to confront her, only for it to lead to the two hooking up. they became friends with benefits before regina finally got the courage to make y/n hers after two months.

one day at lunch, regina was heading to the table where gretchen and karen already sat, but not before making a pit stop at the table where y/n was sitting with damian, janis, and aaron, pulling the girl up and into a very heated kiss. the whole cafeteria went silent as the two kissed, regina pulling away with a smug smirk on her face. she wiped the lip gloss off of y/n's lips before pecking them one more time and taking her leave.

after much explaining to janis, she begrudgingly gave her blessing and the two became the most powerful on and off couple in the school.

flash forward to now, the couple are currently off and cady heron begins her first day at northshore. she catches regina's eye after making her appearance in the cafeteria, the blonde deciding that she is going to let her sit with the plastics for the rest of the week. confused and excited to make friends, cady agrees and after lunch, heads to ap calculus.

ms. norbury is talking about limits and cady is firing off answers like a rocket when she meets y/n. she feels her heart soar when y/n turns to talk to her. "are you trying to make the rest of us look bad?" cady was at a loss for words. "i'm not trying, its just happening." y/n chuckled a little. "oh, so its like that? challenge accepted new girl." cady blushed and stuck out her hand. "i'm cady." y/n smiled and shook her hand. "y/n. it's very nice to meet you cady." cady smiled as her heart fluttered like never before.

a couple weeks roll by and cady has officially integrated with the plastics. janis and damian's plan to take down regina was in full effect and cady felt her crush on y/n growing every day that passed. with the little help from janis and damien (a very reluctant damien) she talked to y/n enough for the girl to invite her to the annual Halloween party.

in cady's defense, no one told her that she had to dress like a slut until gretchen decided to inform a little too late. while explaining to cady how halloween worked in the states, gretchen's phone vibrated with a text from regina. after cracking under the pressure (all regina did was ask who invited cady), gretchen lets it loose that cady has a crush on y/n. reading the texts makes regina's blood boil and she decides then and there to take matters into her own hands.

she tracks y/n down in the kitchen, the girl looking for something non-alcoholic for cady before the blonde speaks. "we need to talk." y/n turned and scoffed. "thought you were done talking to me after you dumped me for shane over the summer." regina rolls her eyes playfully. "shut up. anyways, you see that girl cady over there?" the two turn to see cady shyly waving their way. y/n nodded. "yeah. i invited her tonight." that sentence makes regina's blood boil even more. y/n was hers and she did not like sharing.

she brushed it off and continued. "well, be careful, she has like a huge crush on you." regina swore she saw y/n's eyes light up at that and decided to kick it up a few notches. she looked at y/n sadly as the older girl looked at her confused. "wow, i didn't think this would be hard for me." y/n looked dumbfounded. "what are you talking about?" regina looked up at y/n with the best hurt look she could muster. "i don't know, i just feel like i have a lot of unresolved trauma with how things ended between us."

y/n scoffed. "give me a break." regina scoffed back and stormed off. y/n sighed, feeling bad about what she said and followed regina. "regina. regina! come on." regina answered back. "leave me alone!" y/n sighed. "can we just talk about this?" she lost sight of regina as it felt like everyone froze in time.

if you were to ask y/n what happened to make her take regina back, she wouldn't be able to tell you because she might have blacked out when her brain processed how hot regina looked as an angel. but the night ended with them cuddled up together in regina's bed after multiple rounds of makeup sex. while the couple were making up, cady made a visit to janis and damian, cementing the plan to take regina down.

6 weeks in and the plan was going poorly. they had given her kalteen bars but they weren't taking the desired effect yet. they had sprayed regina with the sprinklers at the homecoming assembly but all they managed to do was make her look hotter. they had tried to crack gretchen into giving them dirt on regina but the only "big" thing they got was that y/n and regina hook up in the janitors closet during college prep. cady had really learned how evil regina could be when the hair situation came up.

she was at her locker when she saw y/n and regina approach. mustering her best fake smile, she turned to the couple. "hey girl! you sending any candy canes this year?" regina smirked, pulling y/n along with her. "oh, i only send mine to y/n and so most of the time i just get them." she smiled at cady and turned to y/n, who kept toying with her hair. regina looked at her and pushed her hair back, gently scratching y/n's scalp with her pink acrylics just the way y/n liked it. "stop pulling it down! your hair looks so sexy pushed back." regina then turned to cady smirking.

"cady, would you please tell her that her hair looks sexy pushed back?" she leaned her head on y/n's shoulder, smirking at cady. not wanting to explode, cady responded. "your hair looks sexy pushed back." y/n smiled slightly at her and went to thank her but was pulled into a kiss by regina. the two pulled away and regina walked forward, pulling y/n along with her. cady watched with a sigh as the two walked off, watching y/n wrap her arm around regina's waist.

then came the talent show. at this point in time, janis and damian had partially given up with the plan, mainly because janis saw how happy y/n was again and didn't want to ruin it, while damian agreed with her. but cady was too far deep, she had to finish it so she had y/n to herself.

regina was cranky before the talent show due to her new diet and to the fact that y/n wasn't going to be there thanks to an out of town soccer game so no one was safe from her wrath. it didn't get any better when gretchen kept asking her about practicing or when her outfit felt a little tight and it definitely didn't get better when she ate shit in front of the whole school.

regina had never been more embarrassed than she was in that moment. she felt like her life was falling apart. she got up, dusted herself off, and ran all the way to the exit and to her car.

y/n had seen the video by the time the game was over. her heart broke for her girlfriend as the bus headed back to the school. she couldn't wait to get back so she could go and take care of her but she kept watching the video and noticed something. after regina falls and runs off, cady has a smirk on her face, posing for the crowd as the curtain shut. y/n didn't like what she was seeing and she definitely had a bad feeling about the redhead.

when she got back to the school, she immediately got in her car and headed to regina's house. she had bigger problems to worry about.

regina sighed as she grabbed her salad and headed to their usual lunch table. she was wearing sweatpants and was breaking the "rules" but she didn't care. sweats were all that fit her at the moment and she was wearing y/n's soccer hoodie and smelled like her so she didn't care. if she thought falling at the talent show was embarrassing, getting banished from the plastics table was even worse. however, she left with her head held high but everyone had videoed the whole situation.

she ran into y/n who looked over the blonde's shoulder to see cady waving at her with a flirty smile on her face. she glared at the girl and led regina to her table, sending murderous looks at anyone who looked at her girlfriend wrong. regina spent the rest of lunch tucked into y/n's side as the girl rubbed her back.

cady had decided the next day to invite y/n to her "small" get together and even though her gut told her no, y/n decided to take the risk and see if she could figure cady out.

unfortunately for cady, the party was not "small" and half the school showed up at her house. too stressed to function, she took shot after shot before stopping karen and asking if she had seen y/n. she just pointed in the direction of the stairs and cady raced up them, finding y/n in her room, nursing a beer and looking at baby pictures of cady.

cady had tried to make a move on y/n, only to be shut down extremely quick by y/n, who stormed out of the party, running into janis and damian, who was driving his grandma's electric scooter. janis informed her that she won her art show and was looking for cady, who drunkenly stumbled into the front yard, looking for y/n.

janis had exploded on cady, exposing her and her plan to ruin regina's life which caught y/n's attention. now everything made sense to y/n, the kalteen bars, cady dressing just like regina, taking over the plastics, all the pieces clicked into place for the older girl.

cady was a bitchier clone of regina.

y/n allowed damian to take janis for a little joyride to cool her off as she headed to regina's. ms. george had told her that regina had a mild breakdown, which made y/n worry more. she thanked the blonde woman for informing her before heading up to regina's room. she found her curled up in bed, wearing a crewneck sweatshirt that y/n had bought her and holding a pillow to her chest.

y/n's heart broke at the sight as she slipped her shoes off and slid into the bed behind regina. the blonde turned over and buried her face into y/n's chest, allowing the comforting embrace of the girl to calm her down. once she felt that regina had calmed down enough, she explained what happened between her and cady at the party, leaving out the part where janis exposed her. she felt regina tense up when she told her that she made a move on her and relax when she reassured her that nothing happened.

the couple laid in bed for a little longer before y/n finally fell asleep. once she was good and asleep, regina calmly slid out of bed, grabbing the burn book with one goal in mind.

cady heron may have won the battle, but regina was going to win this war.

the next morning, regina had woken up earlier than y/n in order to get everything together. she left a note for y/n before heading up to the school to execute the plan. she dropped the burn book on the ground in the middle of the hallway, waiting for hell to break loose.

and break loose it did. so much so, mr. duvall called an emergency assembly for all junior girls in the gym. regina was still playing the victim card even in the gym as all the girls began the rounds of apologies. once janis went up there, she exposed cady for the fraud that she was, including her plan to try to break y/n and regina up, which made the blonde steam with rage.

regina sent an ugly glare to cady before marching out of the gym, cady hot on her heels. y/n was at her locker when the two stormed by, her gut telling her to follow the pair before it got ugly. cady had chased regina out of the school and to the end of the sidewalk where y/n noticed the bus speeding towards them. with neither of them listening to the older girl and the bus gaining speed, y/n decided to play hero. she shoved regina out of the way before pain erupted throughout her whole body and the world turned black.

"and that's how my sister died."

"quit telling everyone i'm dead janis!"

"sometimes, i can still hear her voice!"

y/n was discharged from the hospital after a week and regina refused to let her out of her sight. going as far as making y/n essentially live with her while she healed. meanwhile, things at school were tense. regina iced out cady, karen, and gretchen, leading her to sit at janis and damian's table at lunch, the trio talking about y/n's recovery process most days.

when y/n was cleared to go back to school, she had to wear a corrective neck collar which garnered stares from all her classmates. but luckily for her, they didn't last long with janis and regina as her guard dogs. with one glare from the ice queen, no one dared to look at y/n wrong. cady had tried to come and apologize but janis wouldn't let her near her sister or regina. regina was grateful for janis throughout this whole process. they had begun to rekindle their friendship and didn't go at each others throats as much.

karen and gretchen had come around to apologize and after much convincing from y/n, regina forgave them, uniting the plastics once more. then came the topic of spring fling. regina was okay with not going, opting to spend the night in with y/n but the older girl told her no. they were going to spring fling, and they were going to look hot doing it.

regina wore a dark blue dress that showed a generous amount of cleavage and skin while y/n wore a suit the same dark blue to match. regina had been glued to y/n's side throughout the whole night. the only time they parted was when regina had to go onto the stage for the announcement of the king and queen.

to everyone's surprise, cady won spring fling queen. after giving out her apology speech and throwing pieces of the plastic tiara to the girls who deserved it, mr. duvall took over the mic. regina walked off stage with a big smile on her face, walking to where y/n stood talking with aaron and damian. once she caught sight of the blonde, she gingerly opened her arms for hug, which regina happily gave.

"i'm sorry you didn't win baby." regina shook her head. "i won before i walked onto the stage. i'm here with you aren't i?" y/n laughed at how sappy the blonde was acting. "oh no, what will the school think when they find out you're actually a big softie?" regina scoffed. "shut up." and with that, leaned up and kissed y/n passionately as confetti rained from the ceiling.

"and with that, our story comes to an end. but remember kids, don't jump in front of a bus, or you'll look worse than my sister does."

"janis!"

#regina george x reader #regina george imagine #mean girls imagines #mean girls 2024

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xyymath · 4 months ago

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Why the Number Zero Changed Everything

Zero: a concept so foundational to modern mathematics, science, and technology that we often forget it wasn’t always there. Its presence in our world today seems obvious, but its journey from controversial abstraction to indispensable tool has shaped entire civilizations.

1. The Birth of Zero: A Revolutionary Idea

The concept of zero didn't exist in many ancient cultures. For example, the Greeks, despite their advancements in geometry and number theory, rejected the idea of a placeholder for nothingness. The Babylonians had a placeholder symbol (a space or two slashes) for zero, but they didn't treat it as a number. It wasn't until Indian mathematicians in the 5th century, like Brahmagupta, that zero was truly conceptualized and treated as a number with its own properties.

Zero was initially used as a place-holder in the decimal system, but soon evolved into a full-fledged number with mathematical properties, marking a huge leap in human cognition.

2. The Birth of Algebra

Imagine trying to solve equations like x + 5 = 0 without zero. With zero, algebra becomes solvable, opening up entire fields of study. Before zero’s arrival, solving equations involving unknowns was rudimentary, relying on geometric methods. The Indian mathematician Brahmagupta (again) was one of the first to establish rules for zero in algebraic operations, such as:

x + 0 = x (additive identity)

x × 0 = 0 (multiplicative property)

These properties allowed algebra to evolve into a system of abstract thought rather than just arithmetic, transforming the ways we understand equations, functions, and polynomials.

3. Calculus and Zero: A Relationship Built on Limits

Without zero, the foundation of calculus—limits, derivatives, and integrals—wouldn’t exist. The limit concept is intrinsically tied to approaching zero as a boundary. In differentiation, the derivative of a function f(x) is defined as:

f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}

This limit process hinges on the ability to manipulate and conceptualize zero in infinitesimal quantities. Similarly, integrals, which form the backbone of area under curves and summation of continuous data, rely on summing infinitely small quantities—essentially working with zero.

Without the concept of zero, we wouldn’t have the means to rigorously define rates of change or accumulation, effectively stalling physics, engineering, and economics.

4. Zero and the Concept of Nothingness: The Philosophical Impact

Zero is more than just a number; it’s an idea that forces us to confront nothingness. Its acceptance was met with philosophical resistance in ancient times. How could "nothing" be real? How could nothing be useful in equations? But once mathematicians recognized zero as a number in its own right, it transformed entire philosophical discussions. It even challenged ideas in theology (e.g., the nature of creation and void).

In set theory, zero is the size of the empty set—the set that contains no elements. But without zero, there would be no way to express or manipulate sets of nothing. Thus, zero's philosophical acceptance paved the way for advanced theories in logic and mathematical foundations.

5. The Computing Revolution: Zero as a Binary Foundation

Fast forward to today. Every piece of digital technology—from computers to smartphones—relies on binary systems: sequences of 1s and 0s. These two digits are the fundamental building blocks of computer operations. The idea of Boolean algebra, where values are either true (1) or false (0), is deeply rooted in zero’s ability to represent "nothing" or "off."

The computational world relies on logical gates, where zero is interpreted as false, allowing us to build anything from a basic calculator to the complex AI systems that drive modern technology. Zero, in this context, is as important as one—and it's been essential in shaping the digital age.

6. Zero and Its Role in Modern Fields

In modern fields like physics and economics, zero plays a crucial role in explaining natural phenomena and building theories. For instance:

In physics, zero-point energy (the lowest possible energy state) describes phenomena in quantum mechanics and cosmology.

In economics, zero is the reference point for economic equilibrium, and the concept of "breaking even" relies on zero profit/loss.

Zero allows us to make sense of the world, whether we’re measuring the empty vacuum of space or examining the marginal cost of producing one more unit in economics.

7. The Mathematical Utility of Zero

Zero is essential in defining negative numbers. Without zero as the boundary between positive and negative values, our number system would collapse. The number line itself relies on zero as the anchor point, dividing positive and negative values. Vector spaces, a fundamental structure in linear algebra, depend on the concept of a zero vector as the additive identity.

The coordinate system and graphs we use to model data in statistics, geometry, and trigonometry would not function as we know them today. Without zero, there could be no Cartesian plane, and concepts like distance, midpoint, and slope would be incoherent.

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algebraic-dumbass · 1 month ago

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this might be a dumb question but like. how do you learn math without a class/curriculum to follow. i have a pretty solid calculus understanding and I want to pursue more advanced math but like im not sure where to start. what even is like category theory it sounds so cool but so scary???. do you have any recommendations on specific fields to begin to look into/whether its best to learn via courses or textbooks or lectures/etc.? any advice would be super appreciated!! dope blog by the way

thanks for the compliment!

first of all it's not a dumb question. trust me i'm the algebraic-dumbass I know what I'm talking about. okay so uh. how does one learn math without a class? it's already hard to learn math WITH a class, so uhhh expect to need motivation. i would recommend making friends with people who know more math than you so you have like, a bit more motivation, and also because math gets much easier if you have people you can ask questions to. Also, learning math can be kind of isolating - most people have no clue what we do.

That said, how does one learn more advanced math?

Well i'm gonna give my opinion, but if anyone has more advice to give, feel free to reblog and share. I suppose the best way to learn math on your own would be through books. You can complement them with video lectures if you want, a lot of them are freely available on the internet. In all cases, it is very important you do exercises when learning: it helps, but it's also the fun part (math is not a spectator sport!). I will say that if you're like me, working on your own can be quite hard. But I will say this: it is a skill, and learning it as early as possible will help you tremendously (I'm still learning it and i'm struggling. if anyone has advice reblog and share it for me actually i need it please)

Unfortunately, for ""basic"" (I'm not saying this to say it's easy but because factually I'm going to talk about the first topics you learn in math after highschool) math topics, I can't really give that much informed book recommendations as I learned through classes. So if anyone has book recommandations, do reblog with them. Anyways. In my opinion the most important skill you need to go further right now is your ability to do proofs!

That's right, proofs! Reasoning and stuff. All the math after highschool is more-or-less based on explaining why something is true, and it's really awesome. For instance, you might know that you can't write the square root of 2 as a fraction of two integers (it's irrational). But do you know why? Would you be able to explain why? Yes you would, or at least, you will! For proof-writing, I have heard good things about The Book of Proof. I've also heard good things about "The Art of Problem Solving", though I think this one is maybe a bit more competition-math oriented. Once you have a grasp on proofs, you will be ready to tackle the first two big topics one learns in math: real analysis, and linear algebra.

Real analysis is about sequences of real numbers, functions on the real numbers and what you can do with them. You will learn about limits, continuity, derivatives, integrals, series, all sorts of stuff you have already seen in calculus, except this time it will be much more proof-oriented (if you want an example of an actual problem, here's one: let (p_n) and (q_n) be two sequences of nonzero integers such that p_n/q_n converges to an irrational number x. Show that |p_n| and |q_n| both diverge to infinity). For this I have heard good things about Terence Tao's Analysis I (pdf link).

Linear algebra is a part of abstract algebra. Abstract algebra is about looking at structures. For instance, you might notice similarities between different situations: if you have two real numbers, you can add them together and get a third real number. Same for functions. Same for vectors. Same for polynomials... and so on. Linear algebra is specifically the study of structures called vector spaces, and maps that preserve that structure (linear maps). Don't worry if you don't get what I mean right away - you'll get it once you learn all the words. Linear algebra shows up everywhere, it is very fundamental. Also, if you know how to multiply matrices, but you've never been told why the way we do it is a bit weird, the answer is in linear algebra. I have heard good things about Sheldon Axler's Linear Algebra Done RIght.

After these two, you can learn various topics. Group theory, point-set topology, measure theory, ring theory, more and more stuff opens up to you. As for category theory, it is (from my pov) a useful tool to unify a lot of things in math, and a convenient language to use in various contexts. That said, I think you need to know the "lots of things" and "various contexts" to appreciate it (in math at least - I can't speak for computer scientists, I just know they also do category theory, for other purposes). So I don't know if jumping into it straight away would be very fun. But once you know a bit more math, sure, go ahead. I have heard a lot of good things about Paolo Aluffi's Algebra: Chapter 0 (pdf link). It's an abstract algebra book (it does a lot: group theory, ring theory, field theory, and even homological algebra!), and it also introduces category theory extremely early, to ease the reader into using it. In fact the book has very little prerequisites - if I'm not mistaken, you could start reading it once you know how to do proofs. it even does linear algebra! But it does so with an extremely algebraic perspective, which might be a bit non-standard. Still, if you feel like it, you could read it.

To conclude I'd say I don't really belive there's a "correct" way to learn math. Sure, if you pursue pure math, at some point, you're going to need to be able to read books, and that point has come for me, but like I'm doing a master's, you can get through your bachelor's without really touching a book. I believe everyone works differently - some people love seminars, some don't. Some people love working with other people, some prefer to focus on math by themselves. Some like algebra, some like analysis. The only true opinion I have on doing math is that I fully believe the only reason you should do it is for fun.

Hope I was at least of some help <3

#ask #algebraic-dumbass #math #mathblr #learning math #math resources #real analysis #linear algebra #abstract algebra #mathematics #maths #effortpost

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mariacallous · 8 months ago

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Today, Aug. 31, Estonians and Latvians celebrate 30 years since the departure of Russian troops from their territories, which ended half a century of occupation. The ongoing war in Ukraine is a daily reminder for Russia’s neighbors that their freedom must not be taken for granted. History suggests that Russians only withdraw from occupied territories for one of two reasons: Either they are driven out by force or their own cost-benefit calculus compels them to leave. In the latter case, the only major territorial withdrawals in Russian history have happened when regime collapse has radically changed this cost-benefit calculus. If Washington fails to recognize this long-established pattern and continues to severely constrain Kyiv’s defense in hopes for some future reset in relations with Moscow, the next wave of Russian aggression is all but ensured.

The Russian empire—whether the tsarist or Soviet variant—collapsed twice in the 20th century: in 1917, when a communist coup dethroned the tsar, and in 1991, when another, unsuccessful coup was the final death knell for the Soviet Union. Both events created a window of opportunity for many smaller nations to break free. Moscow withdrew from many of its non-Russian territories not because it no longer wanted to have an empire, but because it no longer had the means to keep these territories under its control.

Russia is currently occupying more than 42,000 square miles—about the size of South Korea—or approximately 18 percent of Ukraine’s territory. Ukrainians aim at regaining all of it and see full restoration of their territorial integrity as an essential component of a just peace. Yet their hopes to reconquer much of their land have withered, not least due to strict limitations imposed, mainly by the United States, on the Ukrainians’ use of Western weapons. Ukraine’s surprise incursion into Russia’s Kursk region and quick capture of about 500 square miles of Russian soil has changed the outlook: Now, an exchange of territories may become an element of eventual negotiations. Russian leader Vladimir Putin’s calculus is still in favor of continuing the war, but the Ukrainians are finding new ways to increase the cost to Moscow and upend the narrative that Russia is marching towards an inevitable victory.

The historical experience of Russia’s neighbors provides some clues to Ukraine’s chances to regain occupied territories or achieve peace through territorial concessions.

The last Soviet leader, Mikhail Gorbachev, decided to let the Soviet satellite states in Central and Southeast Europe go and allowed an unprecedented degree of openness within the Soviet Union. But even the great reformer Gorbachev was unwilling to give up any of the Soviet republics, including the three Baltic states. A leader of the Estonian national movement at the time, Marju Lauristin, recalled a personal conversation with Gorbachev, in which she explained Estonia’s aspirations for independence and received a straight reply. He could not give away what the Russian nation had gained, she recalled him saying.

The Baltic states grasped the chaos and aftermath of the 1991 Soviet coup to restore their independence, but that was followed by a tense three-year struggle to achieve the withdrawal of Russian troops. Diplomatic efforts took place in parallel with the departure of Moscow’s forces from the former satellite states, including more than 330,000 soldiers leaving East Germany by 1994. As we know, Russia’s withdrawal from Germany was a most humiliating experience for the young Putin, who was traumatized by the East Germans’ peaceful uprising against their communist regime while he was stationed there as a KGB agent.

Estonia was the last European country to secure the departure of Russian troops through a July 1994 agreement between the two countries’ presidents at the time, Boris Yeltsin and Lennart Meri. Both leaders took considerable risks by agreeing to a deal that was unpopular in their respective countries. Many in the Russian opposition, diplomatic establishment, and security services were highly critical of Yeltsin’s decision. On the Estonian side, the deal involved painful concessions, notably allowing retired Soviet military personnel and their families, altogether more than 10,000 people, to stay in Estonia and enjoy social benefits. Similar unpopular conditions were also accepted by Latvia. Although the departure of occupying troops was a dream come true for Estonians, Meri faced criticism at home for the concessions. It took great diplomatic skills and political courage to achieve the final stage of de-occupation, which paved the way for Estonia’s accession to NATO and the European Union.

The motive for Yeltsin was most probably his wish to maintain good relations with the West—especially the economic and financial support on which Russia depended at the time—while the United States and Germany put friendly pressure on him to withdraw his forces from the Baltic states. Any such motive is utterly irrelevant for the current Russian leadership; there is no chance that Western countries could persuade the Putin regime to deliberately leave Ukraine in hopes of improved relations or economic benefits such as sanctions relief.

For some of Russia’s neighbors, giving up territory was the price to pay for independence. However, territorial concessions without being prepared to resist further Russian demands has not been a recipe for stability. In 1939, then-independent Estonia gave in to Soviet demands to establish military bases on its territory in the vain hope of avoiding war. The concessions did not help, and the Baltics were soon occupied and annexed. Finland refused similar demands for the stationing of Soviet troops and was attacked by the Red Army. Yet eventually, Finland sustained its independence after fiercely fighting for it. The Baltics learned a bitter lesson. Today they are prepared to fight back from the first moment of aggression.

Finland gave up one-tenth of its territory as a result of its two wars with the Soviet Union, but it would be wrong to present this as an example of trading land for peace. The Soviet Union did not stop fighting because it was content with the concessions; it stopped because it was unable to defeat the Finns and conquer more land. The Red Army became too exhausted to carry on, not least because it was also fighting on other fronts of World War II.

As part of the armistice agreement that ended the Soviet-Finnish fighting in September 1944, Finland leased to the Soviet Union the strategically valuable Porkkala peninsula, located just 20 miles from Helsinki. Although the lease was set for 50 years, the Soviets returned Porkkala in 1956, which looks like a rare example of a voluntary Russian withdrawal. The decision was part of the thaw under Soviet leader Nikita Khrushchev, who succeeded Joseph Stalin in 1953. The case shows that a new leader who is critical of his predecessor may sometimes be favorable to new openings.

However, in subsequent years the Kremlin continued attempts to subsume Finland under tighter Soviet control, successfully interfering in its domestic politics and forcing it to align much of its foreign policy with Russia’s but failing to push the country closer to defense cooperation. Finland achieved Soviet recognition of its neutral status only as part of the Conference on Security and Cooperation in Europe held in Helsinki in 1975.

Another Russian neighbor, Japan, has also learned that Moscow does not give up territories under its control as a gesture of goodwill. Under former Prime Minister Shinzo Abe, Japan made extensive efforts in the 2000s and 2010s to foster friendly and mutually beneficial relations with Putin’s regime. Abe aimed to finally settle the two countries’ territorial dispute over the four southernmost Kuril Islands, annexed by the Soviet Union at the end of World War II. In the hope of splitting the difference and regaining two of the islands, Japan went to great lengths in courting Putin and avoiding any criticism of Russia, including after Russia’s illegal annexation of Crimea and the start of the war in eastern Ukraine. In March 2022, Russia announced that it did not intend to continue the talks and practically ruled out giving up any of its territories, with Russian Security Council Deputy Chairman Dmitry Medvedev stating that “negotiations about the Kurils always had a ritualistic character”.

So far, the West has been surprised by Russia’s ability to bear the heavy cost for its invasion of Ukraine. In Western societies, human life is priceless; in Russia, it is cheap. The Russian regime has been able to rely on seemingly endless waves of expendable soldiers and a harsh redirection of its economy to defense production in ways that would be far too costly for any democratic leader. What can be fatal for a Russian leader, however, is any perceived weakness and the failure to uphold Russia’s greatness. Most Russians want to live in a great country that dominates others, and they are ready to accept sacrifices for this cause, as documented in detail in books by Svetlana Alexievich, Jade McGlynn, and others.

Western leaders have talked a lot about the need to raise the cost of Russian aggression. But they have failed to effectively implement economic sanctions and have still not allowed Ukraine to use Western long-range weapons to attack military targets on Russian territory. By bringing the war to Russia nonetheless, Ukraine has proven that there is space to be bolder and more innovative in making the Russians pay a painful price for their desired greatness—a greatness that is built on invading and occupying other nations.

Russia is not going to withdraw from Ukraine unless it is forced to go—or to pay an unbearable price to stay. There is absolutely nothing in Russian history or recent behavior that suggests Moscow could be expected to negotiate in good faith to reach a compromise. Some territorial concessions from Ukraine may eventually be the price worth paying for peace and freedom—but this remains moot until Russia first gets to the point where it believes that further aggression can bring no gains.

Full restoration of Ukraine’s territorial integrity will likely require another collapse of the Russian empire. It may be years ahead, but Russia’s historical trajectory suggests that it will happen at some point, as the country has shown itself to be incapable of correcting course through evolution rather than revolution. A Western “reset” with the current regime will not be possible without sacrificing Ukraine’s independence and the core principles of the European security order, including the principles of sovereignty and territorial integrity.

Whether losing Ukraine will be the final death toll for the Russian empire, only time will tell. And even then, Russia’s neighbors will always have to be prepared for its violent imperialism to rebound.

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theemptyartdeco · 2 years ago

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Twin Tides (Nate Jacobs)

Summary:

Kaitlyn Arundel, a former prep school princess from New York City, was a pawn in her parents' war of a divorce, had a fire in her that was concealed by a facade of naivety and perfection.

Nate Jacobs is the king of the monsters that once haunted him, a master of control born from his own nightmares.

When their worlds collide, lines blur and reflections emerge, hinting that perhaps, they're not as different as they seem.

Materlist

Chapter 2 Calmness amidst the Storm | Kaitlyn

Warning: This chapter contains prejudice, strong pejorative language and internalized misogyny. (Both of them are deeply flawed characters, read at your own discretion.)

Kaitlyn Arundel belonged to everywhere but nowhere.

To the glamorous New York, to the exotic Beijing, to melancholic Vancouver, Kaitlyn came, breathed and lived. She didn’t mind the habitual change of scenery. Why would she ever? She adored the privilege of flying above the world, rainy wooden scent of the northwestern coast, the foreign and mysterious capital of an ancient civilization and the vibrancy and grandeur of the city where dreams were made of.

But finding herself in a Californian suburban town was something that had almost sent her over the edge of anger and despair.

“Sweet daughter, it doesn’t matter whether you are in New York or anywhere else. Diamond shines everywhere it travels to.”

“Don’t you blame it on me. It’s your father’s fault that I can’t afford your private tuitions and ballet training anymore.”

“I will be sending allowance on your card. Don’t you ever worry. It’s your mother I am punishing, not you.”

“Kaitlyn, I’ve looked into your profile, 4.2 GPA, outstanding volunteering experience. Keep your academic records as it is, you will get into college in no time.”

Getting to a college? Is the man fucking serious? I do not belong to some low life community college. I belong to an Ivy.

“Kaitlyn.”

“Ms. Arundel.”

“I’m sorry,” She adjusted her skirt, forcing the anger and tears down her throat by smiling gracefully, “Please go on.”

“As I was saying, I know transferring across half the country in the middle of your senior year may unsettling,” the principal continued, the appreciation in his voice now laced with a hint of impatience, “But I assure you, there is no need to be.”

“Thank you, Principal Hayes,” Kaitlyn nodded, putting a strand of hair behind her ear, revealing the discreetly ostensible round pearl earring, “To hear this from you offers me great relief.”

Relief my ass.

Every step Kaitlyn took toward the AP Calculus classroom, she felt as if she were Cersei Lannister in Games of Thrones, walking down atonement among stinking peasants of King’s Landing.

Some guys with their poorly arranged shirts smirked at her way, their lustful eyes gazing under her black skirt, while a group of girls whose laughter sounded like those horrendous traffic honking in downtown New York bumped the side of her shoulder, misplacing her expensive shirt.

She peeked back at the the group of girls. Fluorescent pants, their full breasts bouncing blatantly in their tops that served to enhance their youthful sexuality.

They would’ve been sent home, she scoffed, with a slight tilt of her brows, if only this was at the Trinity.

She sat herself in the corner of the first row instead of the centre where she wished to be. She liked attention. Especially the type of attention she receives effortlessly simply by dressing, walking and smiling they way she did. But something about placing in front of twenty ish hormonal teenagers unsettled her. Most importantly, the spot offered her opportunity to observe.

The teacher went on and on about the limit of a function, a notion she had leant in junior year, Kaitlyn’s gaze wandered subtly unnoticeably. One girl was the first of her subject of observation. The makeup on her face was smoky and bold, her winged eyeliner almost reached her brows. She, like almost other girl in East Highland High, wore a short tank top revealing her belly button and petite waist. Then, at least, her eyes finally landed on her breasts, again. They were plump, her round skin rubbed against each other and the rough texture of her top. They captured her attention uncontrollably.

She felt the sensation of her tight, black, push-up bra constraining her flesh like a 19th century corset.

But she loved Victorian corsets.

But it burnt, it hurt.

She returned her mind on the paper, but the image of their horrendous laughter and rude demeanour, the way their breasts bouncing freely and shamelessly played again and again.

Just as she breathed soothingly, preparing to drown herself in the world of mathematics once more, her eyes landed on Nate Jacobs.

Wearing a large blue hoodie, it was obvious in his eyes that his mind was filled with calculations beyond the math.

That night at the carnival, he touched her.

He dared to touch her.

“A lot of men would try to het their hands on a beautiful girl like you. You don’t want to find yourself in that kind of situation.”

Was that a threat?

Nate Jacobs was the image of an archetype she disdained: the arrogant jock, stupid and practically illiterate, actions dictated by sex hormones instead of the brain. Yet the way he spoke to her with the calm and charming mask he had worn , even later that night, the threatening way his gaze locked to that his girlfriend and the way he grabbed her for messing his pride…

For the first time in this dreadful school, Kaitlyn was excited. Among the hormonal driven teenagers, there was a wrestler.

An embodiment of physical strength and strategy.

To be frank, Nate Jacobs had occupied a portion of her mind. A disgust boiled in her stomach as Kaitlyn is recalled the unabashedly greedy look the faces of those pathletic and arrogant high school boys, but Nate Jacobs was everything she liked about men.

Kaitlyn Arundel had made a long mental checklist of the things she liked and disliked about men.

She liked white shirts, crisp and clean, but not the ones that hadn’t seen an iron in weeks.

She liked tall boys, but didn't mind the shorter ones as long as their bodies were in shape.

She hated unkempt appearances, but there was nothing on planet Earth she hated more than fat arms and a round belly.

She liked jeans, snug but not too tight.

She liked sweaters.

She liked confidence, but despised misplaced arrogance, the bluster without the backbone.

She never understood boys who wore makeup, felt it hid more than it showed.

It was one of the things she first noticed about Nate. His confidence didn't just show, it roared.

“Mr. Jacobs, please come with us.”

Her thoughts were suddenly interrupted by Principal Hayes’ voice.

“Maddy fainted, and they found bruises on her neck,” a girl whispered to the person next to her.

“And they think that Nate did it!”

Kaitlyn immediately recalled the image of him dragging Maddy furiously away from the booth after she had called his mom the c word.

To Kaitlyn, the idea of Nate leaving those marks on Maddy wasn’t unsettling. If someone had humiliated her that publicly, she might not have drawn blood, but she'd certainly have sought revenge — maybe by obliterating her future.

An hour later.

“Ms. Arundel, do you consider Nate Jacobs to you a violent individual?”

“No, officer. Nate Jacobs is one of the few who had shown me kindness since my transition to a completely new environment. He is an honest, generous and kind person . I truly believe he wouldn’t do such a thing. He's just not that kind of person.”

Author’s note: after writing this chapter, I realized that her pov, perhaps, is more and disturbing and Nate pov chapters. Even I, the author, got a little disturbed while writing. I know there aren’t as much dramas in the these first two chapters, but I believe it’s essential to take the time to establish their worldviews and give a glimpse of their internal battles. Like Nate, there is a reason why Kaitlyn is the way she is. Her backstory will be explored. Thank you for reading!

Comment pls pls pls! Your comments mean everything to me!

Tag list: @dani-is-a-princess @wabi-sabi1090 @tember1

#euphoria #nate jacobs #nate jacobs x reader #nate jacobs fanfic #fanfic #rue bennett #nate jacobs x you #maddy perez #jules vaughn #jacob elordi

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as-if-and-only-if · 6 months ago

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as of this writing, 538 is predicting by a small margin that Trump will win.

it’s almost a coin toss—53 to 47—and 538 is ultimately just one model. but the trend in Trump’s favor from a month or so ago is clear, and seems to be continuing.

the deadline for registering to vote in PA is today (Oct. 21).

the margins are thin enough that a handful of people in PA (where I am) and other swing states really could change a Trump win into a Trump loss.

a Trump loss—a Harris win—means fewer people dying. it means the climate is less fucked up. it means more people can access reproductive care. it means the rich pay more taxes. it means the genocide in Gaza isn’t made even worse. it means fewer trans people die. it means fewer illegal immigrants are rounded up and deported. for everyone (besides billionaires), a Trump presidency is worse relative to Harris.

voting Harris doesn’t solve everything. it doesn’t even solve these things—it only makes a difference to them. but that difference is measured in lives. the lives of real, breathing people.

these lives will always be worth more than sending a message, or punishing Harris, or feeling good about not voting.

the difference in what actually happens to people will always matter more.

~~~~~

I often see a lot of what you might call “moral anxiety” here: attaching extra symbolism to a vote, usually conflating it with “support”.

a vote for Harris is not a signifier of absolute support for Harris or her actions. it is not a sign of allegiance or alignment. it is not a message. any symbolism, any attached meaning, is entirely artificial. such an interpretation is not an actual part of what it means to vote. you are only responsible for the difference your vote could actually contribute to.

and as such, a vote is not the be-all, end-all. it’s just something to keep things from getting worse in one particular extremely significant way.

a vote is first and foremost a practical choice with nonsymbolic consequences—a choice between the two outcomes we’re limited to. and it is only that.

not voting, on the other hand, is only disengagement: only the willingness to allow more suffering, more death, and for a grand prize of nothing at all.

no real, practical consequence can come from not voting that is possibly worth the extra death of even one person.

if a vote for Harris shows anything about you or how clean your hands are, it shows you are willing to confront the reality of our circumstances and what can (and can’t) be achieved by a vote; that you’ve acknowledged the brutal fact that one of only two outcomes will come to pass; that you can act ethically and practically even in suboptimal conditions; and that you’re capable of the necessary ethical calculus of distinguishing bad from worse.

~~~~~

so. we are on the brink of another Trump presidency.

ultimately, when deciding whether to vote, we can stand by to let strictly more people suffer and die under Trump—or we can intervene in the capacity we’re able to.

there are lives to be saved in the difference.

do not give up on them.

vote Harris.

#also if you genuinely think they are the same: they are not. actually compare their policies. do not think in black and white.#believe it or not.#this is massively trimmed down. Will probably post a similar but more thorough version when i wake up #or maybe not!

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huelovening · 1 year ago

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stupid with love

hueningkai x fem! reader

summary: the boy in your calculus class is so cute! but you get awkward when trying to talk to him and it doesn't help that he's your friends ex either. what do you do?

wc: 1208

you really tried to make a move on him, really. but somehow you didn't have enough courage, as you keep telling yourself, "maybe he will notice me first!!"

well, it was kind of true. on october 3rd he even asked you what day it was.

"hey, what day it is?" he turned around, looking at you with his beautiful, big, brown eyes, if you looked even closer, you could see the entire milky way in his eyes.

love sick y/n stuttering out a small "it's october 3rd." your new favorite day.

after first confessing your little crush on huening kai to your newfound friends, they quickly made it known that he was off limits, being wonyoung's ex boyfriend. still, you were allowed to look at him right?

everyday when you would walk into your shared class with him, you would do only what you were permitted to do, ogle the pretty boy sitting in front of you. you hoped that he'd talk to you but you didn't actually expect it! so when he turned around at the end of the class instead of immediately leaving like he usually does, it was a shocker.

"hey y/n, me and my friends are throwing a small party this weekend, i'm not really a party guy, so i'd enjoy your company. will i see you there?"

"yeah! of course.. totally!" you didn't mean to sound THAT excited but who could blame you?

after that you rushed home right away, trying to throw cute outfits together and thinking about how to do your hair. you didn't tell your friends about your encounter with kai, maybe it was better that way.

the day of the party came withing the blink of an eye and you couldn't be more excited. after a final look in the mirror, you decided you were ready and left the house excitedly. at your arrival you were greeted by yeonjun, he was one of kai's bestfriends, his house was pretty big, which was the reason most parties were always hosted at his house. the faint smell of alcohol entered your nostrils quickly, you weren't sure if you were actually about to drink tonight, the idea of it never seeming very appealing to you. maybe you would just look for kai first.

you walked around the big living room eyes scanning for the brunette boy, stumbling across a few drunk bodies. gosh, were you just late or do these people get drunk within 5 minutes? everything about this party was overwhelming, the huge house, the amount of people, the reek of various alcoholic drinks. where was kai?

"y/n! i didn't know we'd see you here!" you turned around, to see sullyoon, one of your shared friends with wonyoung and yuna.

"oh, hi sullyoon! i got invited by this guy, not sure. but i'm glad to see you, are the others here too?" you lied about the fact that kai had invited you, you couldn't risk loosing your friends but at the same time you liked him too much to resist him.

"yeah actually, i think wony went to talk to kai, they seemed really close earlier and yuna is just grabbing more drinks for us" she innocently smiled at you.

what. why would she talk to him? they broke up for a reason, now you weren't sure what to do. do you start looking for them or just pretend this never happened and go home?

you decided on the first option, it wasn't hard to not see wonyoung, wherever she was there would be a bunch of people trying to hit on her. she had so many options why does she feel the need to go back to him?!

you said your goodbyes to sullyoon, telling her you would try to talk to the guy who invited you, which wasn't exactly a lie.

you continued to roam around the house, seeing two familiar faces, talking to eachother, they didn't exactly appear to be having a friendly chat. you observed as she tried to get closer to him, batting her eyelashes at him and you could agnize the discomfort in his eyes, watching him run off.

you don't know what possessed you in that moment but you went to follow his steps. he definitely knew his way around, as he went from corridor to corridor, walking up what seemed like thousands of stairs, until you arrived at some sort of balcony.

he opened the door, you had expected him to close it behind him. but he held it open.

"why are you following me?"

you stayed silent at that, looking at him signalling for you to come outside with him and sit on the expensive chairs the balcony's been equipped with. "are you okay?" you dared to ask, not quite sure what to talk about in this kind of situation.

"i don't know. wonyoung tried to win me back again, using all kind of excusing for leaving me the last time. i'm not attracted to her anymore but it just hurt. i don't want anything to do with her." he confessed to you, honestly filling his voice, like he had some sort of point to prove to you.

you sighed, you haven't known her that long but knew that when she wanted something, her mind was set on it. "she can be a huge deal, i know. i don't think she will leave you alone that fast but it's best to just ignore her, it's the only way to get her to stop. and then, it will be all good!" you tried your best to cheer him up, and he looked up at you, smiling at your enthusiasm.

"you're right, i will be okay" he chuckled. "but.. to be honest, i'm just scared that she'll try to hurt you. i'm sorry to talk about this, since it must be embarrassing for you but she mentioned your crush on me. now that i rejected her she will try to get rid of you, thinking it will do something."

"oh.. wait, so you know? i-.." embarrassment filled your body to the brim, how the hell were you supposed to look at him now?? your first instinct was to stand up, but he went to stop you. "y/n, it's okay. i like you too and i think, if we really try this out we can make it work. what do you think hm?" he hopefully asked. you looked at his hand caressing your's, beginning to smile again.

"i think.. we can do this." you giggled. the moonlight hit you perfectly, enhancing your facial features and kai couldn't help but stare. "w-what's wrong? do i have something on my face, god i keep embarrassing mys-"

"y/n, can i kiss you?"

you thought you would faint at that moment. his eyes reflecting the stars, attentively looking at you, waiting for your response.

you believed you forgot how to speak right now, desperately nodding for him to do what he indicated.

his lips meet yours and oh, how soft they were, it felt like it lasted an eternity and you didn't want it to stop, and kai felt the very same way. as the kiss stopped kai smiled at you.

"let's do this."

#hueningkai x reader #txt x reader #txt imagines #hueningkai soft hours #huening kai x reader #huening kai scenarios #hueningkai imagines #txt soft hours #Spotify

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