#whats np. no problem?
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the disgruntled quiet (he had to do math)
#slay the princess#stp the long quiet#guys im gonna be real i didnt understand binomial distribution#mean = np????? the fuck does that mean#p = q Except when it isnt? why? some of us are more equal than others?#if np > 10 and nq > 10 then use z table??? what#whats np. no problem?#nq must be.... no questions#my art#my doodles
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i should be Doing Tasks instead of sitting here waxing poetic about math but i do think graphs (the discrete math kind) (not this kind 📊📈📉) are the most elegant and beautiful mathematical object
#*slaps roof of graph* this bad boy can fit so much information in it#it's just a set of vertices and a set of edges! and the edges are just pairs of vertices!#that's IT!!!! two sets!!#well also you can add edge weights#anyway then you can take your two sets and maybe edge weights and use them to represent problems#that are probably too hard to solve with current computing technology (see: P != NP)#mathematical equivalent of a corkboard with documents and red string#'this thing is connected to that thing' in its absolute purest form#math#ok. done waxing poetic for now#numbers do not lie#ok one more thing. i have beef with the other kind of graph for having the same name#those are CHARTS#also useful but HRRRHGH GRRR ripping them apart in my teeth. impostors. nobody knows what im talking about when i say graphs because of YOU#ok ok im done
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Are you planning on uploading another fanfic soon? (/np)
kinda!! dont know how soon but yeah the golden hour thing is gonna be another chaptered fic but im gonna wait til january to start posting that bc i want to get the secret santa one out of the way first :0
soooo the next thing ill upload is the secret santa fic and then after that another longer project aaaaand thats. all my plans that i wanna name so far <3
#oh yea i also got another ask from a while back sitting in my inbox asking when ill upload the next smut piece so to that ill also say idk#dont really have anything concrete planned like that sorry to disappoint#anon said 'trying to find something new to jack off to' maybe i should get that reclist done soon huh#inbox#anonymous#hey what does the np mean btw i just know it as shorthand for no problem?
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Just adding a source for that 20% figure:
Up to 40% of ankle sprains go on to develop chronic symptoms, including pain, swelling, instability, and recurrence that persists at least 12 months post-injury. Furthermore, approximately 20% of individuals who sustain acute sprain develop into chronic ankle instability.
OP did a phenomenal job of explaining this thing but in case anyone else wants a source for the rest of the post: NPS, Harvard Health.
If I could give one piece of life advice to my fellow humans, it would be this highly specific little chestnut: "If you ever sprain your ankle, get medical care."
One of the most common things I've heard from older people than myself is, "Oh yeah, I twisted my ankle in (insert grade of school here) and it's never been the same." Or, "I have a bad ankle. I can't tell you how many times I've sprained it." And one of the most common things I've heard from younger people is some variation on, "Yeah, I think I just twisted my ankle. I think I have some old crutches from high school at my parents' house. I'll just use those for a few days."
I didn't learn this until after I sprained my ankle last year, but 20% of ankle sprains lead to chronic ankle instability, which was grimly defined by my doctor as, "an unending cycle of ankle sprains."
Another thing I didn't fully understand is that "sprain" is an umbrella term for any of those ligament injuries. Yeah, you could simply stretch the ligament-- twist it. Or you could tear it. Or you could completely sever it, and those are all sprains. If you're not a doctor, it's likely hard to tell what degree of sprain you have. The worse the sprain, the higher the chance of it healing weird and becoming unstable. If you are having trouble putting weight on your ankle and it's not feeling better the next day, please get it checked out!
I know medical care is expensive and many of us don't have health insurance, but it might cost you more in the long run if you don't get care for a hurt ankle. Otherwise you might spend a lifetime of having to get MORE ankle injuries checked out, missing work or social opportunities due to ankle injury, having to limit exercise, surgeries later in life, and more.
When I hurt my ankle and foot last year, I assumed the broken foot bone would be the bigger concern, but my treatment plan was almost entirely centered around the ankle ligament tear. My doctor said that was the more serious injury and the more finicky bit to heal. I worry when I hear a friend mention they sprained their ankle and were just treating it at home, 'trying to stay off it as much as I can.' That usually means a few days, but I had to stay completely off mine for 4 weeks, followed by a walking boot, a brace, and months of physical therapy. It was intense!
Ankles are annoying because they support your entire darn body and you don't realize how much you need them until you hurt one. So that is the one nugget of wisdom I hope to leave all of you with!
#i dont know WHY i want australian sources on topics like these but i do#like oh no what if it turns out that ankle sprains are different in australia#thats an extremely likely problem to come up#anyway the NPS is australian
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jeff buckley blasting. laying in my undies. thinking about computational complexity theory.
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making me code problems to do with matrices without numpy should be illegal im not kidding
#ewwwww this is horrible. i did it with numpy just to see how much cleaner it is and now i need to convert it back to regular python. gross#tbh in my modules im always using np and scikit. so why can't i always use them#finished the num an problem sheets for the first week tho!! the semester hasnt even started im just scared#why is the computer not infallible... i hate floating point errors just do what i tell u to do correctly lol???#joking. but also#.ramblings
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I've been disabled for almost 29 years. Here's what I've learned.
Tablets sink and capsules float. Separate out your tablets and capsules when you go to take them. Tip your head down when taking capsules and up when taking tablets. Liquigels don't matter, they kinda stay in the middle of whatever liquid is in your mouth.
If your pill tastes bad, coat it with a bit of butter or margarine. I learned this from my mom, who learned it from a pharmacist.
Being in pain every day isn't normal. Average people experience pain during exceptional moments, like when they stub their toe or jam their finger in a door, not when they sit cross-legged.
Make a medical binder. Make multiple medical binders. I have a small one that comes with me to appointments and two big ones that stay at home, one with old stuff and one with more recent stuff.
Find your icons. Some of mine include Daya Betty (drag queen with diabetes), Stef Sanjati (influencer with Waardenburg syndrome and ADHD), and Hank Green (guy with ulcerative colitis who... does a bunch of stuff). They don't have to be disabled in the same way as you. They don't even have to be real people. Put their pictures up somewhere if you want; I've been meaning to decorate my medical binders with pictures of my icons.
Take a bin, box, bag, basket, whatever and fill it with items to cope with. This can be stuff for mentally coping like colouring books or play clay or stuff for physically coping like pain medicine or physio tape.
Decorate your shit! My cane for at home has a plushie backpack clip hanging from the end of the handle and my cane for going places is covered in stickers. All of my medical binders have fun scrapbooking paper on the outside. Sometimes, I put stickers and washi tape on my inhalers and pill bottles. I used my Cricut to decorate my coping bin with quotes from my icons, like "I've seen enough of Ba Sing Se" and "I need you to be angrier with that bell".
If a flare-up is making you unable to eat or keep food down, consider going to the ER. A pharmacist once told me that since my eye flares can make me so nauseous that I cannot eat, then I need to go to the hospital when that happens.
Cola works wonders for nausea. I have mini cans of Diet Pepsi in my coping bin.
Shortbread is one of the only things I can eat when nauseous. Giant Tiger sells individually-wrapped servings of shortbread around Christmas or the British import store sells them year-round. I also keep these in my coping bin.
Unless it violates a pain contract or something, don't be afraid to go behind your doctor's back to get something they are refusing you. I got my cardiologist referral by getting in with a different NP at my primary care clinic than who I usually saw. I switched from Seroquel to Abilify by visiting a walk-in.
If you have a condition affecting your abdomen in some way (GI issues, reproductive problems, y'know) then invest in track pants that are too big. I bought some for my laparoscopy over a year ago and they've been handy for pelvic pain days, too. I've also heard loose pants are good for after colonoscopies.
Do whatever works, even if it's weird. I've sat on the floor of the Eaton Centre to take my pills. I've shoved heating pads down my front waistband to reach my uterus.
High-top Converse are good for weak ankles. I almost exclusively wear them.
You can reuse your pill bottles for stuff. I use my jumbo ones to store makeup sponges and my long skinny ones to hold a travel-size amount of Q-Tips.
Just because your diagnostics come back with nothing, it doesn't mean nothing is wrong. Maybe you were checking the wrong thing, or the diagnostic tool wasn't sensitive enough. I have bradycardia episodes even though multiple cardiac tests caught nothing. I probably have endometriosis even though my gynecologist didn't see anything.
You can bring your comfort item to appointments, and it's generally a green flag when someone talks to you about it. I brought a Squishmallow turkey (named Ulana) to my laparoscopy and they had her wearing my mask when I woke up. I brought a Build-A-Bear cat (named Blinx) to another procedure and a nurse told me that everyone in the hall on the way to the procedure room saw him and were talking about how cute he was. Both of those ended up being positive experiences and every person who talked to me about my plushies was nice to me. If you don't feel comfortable having it visible to your provider during the appointment, you can hide it in your bag and just know it's there, or if you're in a video appointment, you can hold it below frame in your lap.
Get a small bucket, fill it with stuff, and stick it in your bed (if you have room for it). I filled a bucket with Ensure, juice boxes, oatmeal bars, lotion, my rescue inhaler, etc. in October 2023 in anticipation of my laparoscopy and I still have it in my bed as of January 2025.
If your disability impacts your impulse control (e.g. ADHD, bipolar disorder), you should consider setting limits around your spending -- no more than X dollars at a time, nothing online unless it's absolutely necessary, and so on. Or, run these purchases by someone you trust before committing to them; I use my BFF groupchat to help talk sense into myself when I buy stuff.
Feel free to add on what you've learned about disability!
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becoming a you're welcome warrior instead of a no problem-er whenever im doing something for someone im slightly unhappy with
#not a reblog#something something generational divide between ppl who say ur welcome instead of no problem#even though these phrases are both meant to express the same thing they're still perceived differently#smth smth np is of course ill help you you can always count on it vs ur welc is yeah i did put in effort to help and you SHOULD be grateful#does this even mean anything#what am i saying bro
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Some of you are falling hard for the Trump/Musk anti-federal worker propaganda. I think part of the problem is that a lot of people genuinely don't know how the federal government works, so here's an overview on the intended and current state of the so-called fourth branch of government, the federal bureaucracy:
Executive agencies are considered to be within the executive branch, officially, but can only be created, disbanded, funded, and have new leadership appointed through congressional approval. Well, in theory that is.
The majority of staff in federal agencies are called "career staff" who are nonpolitical civil servants who do every kind of work you can imagine, from IT to accounting to scientific field work to livestock inspections to nursing at VA hospitals. They do not, typically, change from one administration to the next, which is essential to ensure the government is able to continue functioning without interruption. These individuals of course can and do hold their own political opinions, but there are stringent rules on how, when, and where they can express them. It is arguably the most racially diverse workforce in the country. Many are veterans, and many are disabled.
Each agency is headed by a political office appointed by the president and confirmed by Congress. This includes a Secretary or Administrator and all of their hand-picked office staff, who are called "politicals." However, even before Congress confirms the president's nominee, the president can appoint an interim leader with no approval, who has essentially all the same powers but can't hold the position for very long. In short, even in those offices where a leader has not been confirmed by Congress, they are being led by Trump appointees.
When Trump makes an Executive Order, those orders are immediately dispensed through the executive agencies, who must abide by the letter of the order. I saw someone say NPS was "complying in advance" by taking the T off LGBT, but these changes were made across all agencies in direct response to Trump's "Defending Women" order. Any career who did not follow this order would have immediately been fired with cause, no unemployment eligibility, and in the current environment we also know their position would be permanently dissolved.
This is what we're dealing with right now. Trump (and his puppet master Musk) do not have the authority to dissolve government agencies, but they are trying to gut them, harassing careers and making the public turn against them, conducting illegal firings, threatening them into resigning. When people leave, their positions will disappear. Their intent is to diminish the staff until the agencies are non-functional. That's why careers are picking their battles. We're holding on by our fingernails to keep federal agencies alive and functioning. We're in the midst of a hostile takeover, a literal coup of the US government.
Yes, it's awful the T was removed on the website. We don't want this. But I promise that is small potatoes compared to the other battles being fought. I have trans coworkers being forced back to the office and they don't know what bathroom they can use. Our personal information is being leaked to hate groups. Careers are getting threats and spam to their work and personal emails. Most of us expect to be illegally fired. Soon. Last week was the largest layoff in American history, and it's just the beginning.
Please support federal workers. We are under attack.
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My issue is that everything is an optimization problem. I attempt to select the best option given all known information. This leads me to constantly be seeking more information without ever feeling completely qualified to make a decision, and I am easily overwhelmed, especially when additional factors occur in the midst of the problem. It's an exhausting, overwhelming, and ineffective way to live. I just need to pick something to have for lunch and get on with it.
#no but really this is an issue#with larger commitments yes fine do the thinking and research#but the discernment between what requires time and research and what doesn't isn't well developed in my head yet#overwhelmed#plot twist#life my dudes#life#greedy algorithm appreciaton post#not everything is an np problem
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oh hey real quick since it seems were all getting asks from gazans try and be mindful of how you speak and how what you say may be translated, especially through flawed translation like google
avoid acronyms and slang and id go so far as to divide compound words to avoid any confusion
so instead of saying something like "np! ill rb your post to gain more traction" say "it is no problem. i will share your post so my followers can see it"
be specific and be concise, it will help for those who arent fluent in english
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EUROVISION
━━━━ joost klein x f! reader (using a face claim, but you can use your imagination to change her look to anyone you want to)
( social media ) before & during eurovision ; a bit of angst (mention of hate, body shaming etc) ; fluff ; reader isn’t a celebrity; everything is fictional
yourusername



liked by joostklein, wer.ist.aggu and 650 others
yourusername: another day another year with this dude, what will happen if three years ago i wouldn’t had told you that you had shit on your shoe 😻👍
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wer.ist.aggu: wow! great pictures! great people 😅😄
yourusername: i support this guy right there! 👍👍👍 once i told him that i gave him once two euro and asked if he could return it to me, cause it’s been tough with money lately 🫣😁🙏😅 and he gave me one euro without hesitation! 😲 very nice guy 😁👍💪💪💪🔥‼️
wer.ist.aguu: no problem 😉
joostklein: very nice pics, very relatable peace
yourusername


liked by joostklein, appiemussa and 1420 others
yourusername: stream friesenjung and support small businesses! 😄😅
view all comments:
user1: love the song!! new idol
joostklein: great song
joostklein: thanks
joostklein: np
user2: girl can you stfu
user3: isn’t he gay?

joostkleinnews


liked by user4 and 24 567 others
joostkleinnews: some mysterious girl was spotted yesterday at the stage with joost, she was mostly helping the audience. do you think it’s y/n?
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user5: it must be her, cause after the concert i spotted them together
user6: girl- where you stalking them or wtf
user7: gosh, now im not surprised she don’t post her pics
user8: lmaoo true
user9: idk what y’all talking about, she’s super pretty

stuntje


liked by joostklein, yourusername and 5300 others
stuntje: really nice eurovision let’s go 😻
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yourusername: really nice people, really cool song i support 👍
stuntje: im gonna cry now
joostklein: 😉
user10: how can i block y/n comments? 😭
user11: real
joostkleinnews


liked by user12 and 56 878 others
joostkleinnews: y/n spotted on joost instagram story
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user13: lmaoo why she always have this bitch look like girl, you’re trying too hard
user14: exactly!! like you’re no one important so stop
user15: god hate her, joost can be with someone better, someone who will be happy that she’s a part of his life
user16: yes! she doesn’t deserve him


yourusername



liked by joostklein, stuntje and 5718 others
yourusername: this dude will win this freaking contest, mark my words.
comments are turned off

joostklein






liked by yourusername, appiemussa and 332 098 others
joostklein: after first rehearsals, let’s win this eurovision together (with my beautiful support)
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appiemussa: oh, you are beautiful too 🥰
yourusername: we love gay energy
yourusername: love you, will always be your number one fan 💙
user17: aww cuties
user18: love them sm (im sorry y/n for what you needed to go through, but we love you)
yourusername: 💙
#eurovision#joost#joost klein#joost klein x reader#joost x reader#social media imagine#eurovision imagines#fem reader#free joost#face claims#joost klein love#instagram imagine
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Several Sentence Sunday
had idea for the scene in my Tommy feels fic so here it is (it's 2017 so Tommy only recently came out)
“You have a problem with us, young man?” the man asks him with a close to angry look in his eyes.
“I-I,” Tommy doesn’t know what to answer.
Yes, I have a problem with how freely you love each other because even after I came out and started dating openly over the last 6 months I still feel like a fraud. And like I don’t deserve it. Like I don’t deserve to be loved and love someone - that’s what he wants to say. He doesn’t.
“Mitchell, please, let’s get back to our table. I’m sure the young man was just sad that his date never showed up,” the other man puts his hand on his - Tommy suspects judging by similar rings - husband’s shoulder.
“He actually showed up. But it definitely was our first and last date,” Tommy says with a sad smile. “I-I just,” he exhales, and looks at similar kind looks on men’s faces now. “I admired, but also was jealous of the two of you. I was in the closet for years and only really started dating not long ago and it was a disaster. I want to find someone to be like the two of you.”
“Oh, son,” Mitchell says with a smile and gentle pat on his shoulder, “trust me, you don’t find love like that, you make it. Am I right Thomas?”
“Oh, absolutely.” Thomas smiles at him and then at Tommy, “I’m sure you will find someone you will love so much and really feel like you can make life with. Eventually. Don’t rush the universe, young man. It knows when to give it to you.”
“Yes. Concentrate on loving and accept yourself fully for now, son. Then, when you’re ready, that good man will be here and you two will build something special,” with last pat on his shoulder Mitchell leads Thomas back to their table and Tommy with the last look at their happiness, gets up and out of restaurant.
Love myself first? Ok, let’s try.
Tommy finds the number of his old therapist.
np tagging @bewilderedbuckley @wikiangela @hippolotamus @diazsdimples @devirnis @bi-buckrights @typicalopposite @perfectlysunny02 @queerbuck @queerdiaz @evanbi-ckley @repressedqueen @racerchix21 @theotherbuckley @theweewooshow @pirrusstuff @powersuitup @aringofsalt @saybiwithme @diazheartsbuckley @honestlyeddie-im-bi @half-oz-eddie @kinardsevan @kinrdevan @lavenderleahy @leashybebes @loveyouanyway @monsterrae1 @marvelousbuckley @cliophilyra @cal-daisies-and-briars and anyone who wants to
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Was wondering if you have any thoughts on the long awaited Hakuno(n) FGO debut? Especially the gender differences because they really amped that up this time around
Harmless is the best way to describe it. Nasu had so much fun with their dialogue without getting too lost in the sauce like he did for Ciel. Maybe I could do with less EXTRA gameplay jokes, but eh, it's fine at worst and legitimately funny at best. The senpai posturing didn't do anything to me, but it never got grating.
The thousand years of offscreen backstory for the deathbed Hakunos in the chapter was probably the biggest problem since the framing clearly suggested I was supposed to emotionally connect with something there, but we don't have enough information to know what. Surely this scene will become good when we go back to it after Extella 2 (I won't).
The gender differences are something that intrigued me because I never played male Hakuno so I don't know if it was always like that. What stood out to me is that a lot of the boy's lines have tangible "trying so hard not to say anything offensive" restraint. This shows mainly in the way he comments about women, but even outside of that, we have the NP lines contrasting the boy's peaceful "Don't tell Pieceman" with the girl's unhinged "Sesshouin must die".
Meanwhile, the girl is 100% the Hakuno I know in all of her complete inability to give a fuck. She's quickly intimate with Fujimaru, openly calls Nero and Tamamo her wives, makes boob jokes about Lip, and can look Chaldea's domesticated Archer in the face and say "my goat is washed". All around perfect. Iconic. Sesshouin must die.
Also, it was well documented in this very blog that I was 100% a Berserker Nightingale truther before the Enkidu line ruined my day. Thanks for asking.
#fate grand order#kishinami hakuno#i didn't even notice I had accumulated 3 different fgo hakuno asks#i thought this was just 1 until i reread the one i picked to answer and noticed the enkidu mention was missing
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Stardrinker
Title: Stardrinker
Author: SomeonexSomeone
Word Count: 2.5k
Pairing: Sirius Black x bestfriend!reader, minor James Potter x Slytherin Pureblood np!reader
Summary: Sirius is your best friend, but James...James is your sun.
Warnings: angst, mentions of suicide, mentions of traditional values and arranged marriages, happy ending
Authors Note: hello again! This is kinda a prequel kinda a companion piece to Suneater. Originally I wrote Suneater from readers POV but i am a sucker for the male pov in romances because idk i want to be loved and devoted or whatever so here is what Suneater almost was, with some minor additions
if you or anyone you know needs help, please call 988 (USA) or contact your local hotline. You are loved, you are needed.
Companion piece: Suneater

Sirius is one of your best friends. Well, maybe best friend wasn’t the best way to put it. Sirius was the light of your life, the reason you were able to hold out for as long as you did, a comfort in the dreary place you called home. He was the one who kept you company at stuffy Pureblood events, dressed in clothes that only fit if you stayed as still as possible. He was the one who gave you reassuring looks from across the room as your parents paraded you around the room, sickly fake smiles on their faces that would drop the moment you returned back home. He made those parties somewhat enjoyable as he mocked those around him with little to no tack behind their backs, easily slipping into rehearsed conversation when they looked towards him again. He was the one who would cut into your dances as much as he could, even if customs looked down on him for doing so, just to make sure you didn’t end up in the arms of a Pureblood twice your age, the type who would grab at your hips in a possessive way and allude to buying you from your parents (because, let’s be honest, being on the marriage market in your circle was nearly the same as being cattle put up for auction).
He was the bane of your existence when you were younger. Your parents had always pursued the best course to elevate the family status, jumping from family to family, pledging their loyalty to the highest bidder until they found something better, turning their back without another word. It was obvious, to everyone else around, that your family’s loyalty was like holding water, but with their seemingly random ways of knowing exactly when to jump ship, you were able to keep your head above water with minimal problems. You’ve had more marriage arrangements than most, paraded around every party your parents could make their way into, forced into hundreds of different robes until you could barely remember what any of them looked like.
The Ancient and Noble House of Black was one of the many families your parents tried to cozy up to. It was, to your relief, they were much too confident in themselves to stoop so low as to interact beyond pleasantries with your parents, but it happened frequently enough that you and Sirius came to know each other's faces. Two scared children, standing stiff as a board beside their parents, flicking eyes to judge the other silently. By the time Sirius had decided he wanted to distance himself from his parents, you had already spent too many years glaring at each other to have anything beyond acknowledgement of the others existence.
It was why, when you parents not so subtly berated you at a summer function, you were mortified it was Sirius who found you. The summer before your first year, before the only bit of freedom you ever dared to have, it was no wonder you got a little cocky. The scoff was nothing, easily passed up as a sneeze or a cough, but your parents were furious, hurling hate at you as soon as they got you alone. Your arm still stung from where they had dragged you, wanting to get as much distance from the party as possible to not embarrass them even more, and your eyes burned with unshed tears. You were eleven.
Sirius found you that night, curled up on the floor only minutes after your parents were done with you. They commanded you to remain in the room for the rest of the night, staying far away from any other potential allies, and to hide the disarray they left you in. He rushed into the room without a care to look around, out of breath as if he’d been running, closing the door with a soft click, obviously trying to get some privacy. He leaned against it for a moment, taking a deep lungful of air, before turning. He stopped still when he saw you on the floor.
Neither said a word. Sirius stayed frozen for far too long, eyes flickering between you and the rest of the room, obviously at a loss for what to do. You tried to scooch away from him, but the pain was too much to hide, and a whimper escaped your lips. It was then that Sirius noticed the small drip of blood from your nose, a sign of something he knew all too well. With a pitying look, one you met with a hateful glare, he approached, hand fumbling with the handkerchief from his pocket. You flinched when he reached down, but he only held your chin gently, whipping the blood from your upper lip. He left without another word.
It was a miracle you were able to make it home that night without any further incident. Your parents cooled down, none the wiser to Sirius’s intervention, and prepped you for the next party. The Black’s were there too, of course, but you were far too embarrassed to look Sirius in the eye. But he simply gave you a soft smile and tilt to his head, keeping his pleasantries boring and impersonal. You were surprised, and suspicious.
That is, until Sirius showed up at the last party of the summer with a slight limp and the smallest bit of blood still on his nostril, that understanding overcame you, and you gave him the subtlest of nods, passing a napkin over with the twitch of your nose. From then on, an unspoken pact formed between the two of you.
No words were exchanged during the school year. With Sirius entering Gryffindor, a fact you were both pleased with - a true escape from the pureblood nonsense - and devastated by - you were hoping to have an ally -, it was hard to justify talking to him. Winter and Summers were the only times you were able to sneak a small conversation here and there, but, for someone who loved the sound of their own voice, Sirius was surprisingly good at having a whole conversation with you with just his eyes. It was ridiculous, but for whatever reason, you began to trust Sirius Black.
It was why, during one of the worst moments of your life, you were glad it was him who found you.
Sirius was there when you were on the verge jumping off the balcony that summer night, your parents just having informed you they promised you to a man who could have been your grandfather. The man had leered at you when they left you alone, forcing himself onto you, grabbing everything that would eventually, legally, be his to possess. When you screamed, brandishing your wand, even though it had been drilled into your mind never to pull your wand on a Pureblood of higher status, the man laughed, a vile laugh that made your bones shake, and told you to get all the attitude out of your body before you walked down the aisle; he would not tolerate anything after that. The moment he stepped out, leaving you with nothing but the night air, you unconsciously turned to look at the stars. It was something of comfort, to find a constant like the stars. You took a moment, memorizing them one last time, before climbing up, the least graceful thing you had done in who knows however many years. Your uneven heels rocked you back and forth, a melancholy waltz, before you tipped forward.
Sirius’ hands clasped around your legs before you could fall, using his momentum to pull you back onto him and the solid ground. Your arms scraped painfully against the stone balcony, tearing through the delicate gloves on your hands and shredding your fine clothes, but Sirius’ body took most of the brunt of your fall. You could barely hear him over the ringing in your ears, too shocked at the fact that you were alive, that you didn’t fall, didn’t crash into the floor below like you so wanted, too overwhelmed to hear him yelling at you, wondering what you were thinking by standing on the ledge like that. Yelling at you for almost taking your life. Your gloves slowly dotted red, then black, as your tears joined to create the most unusual canvas of dotted pain. Suddenly it was too hard to breathe, to let out anything but a wail of despair, enough to render even the great Sirius, the man who always had something to say, to say nothing at all.
He did the only thing he could think of, the only thing he ever wanted anyone to do for him. He grabbed you and held you tight as you sobbed into his arms, begging not to be the one to save your family from ruin, begging to just let everything burn to the ground, setting your body alight so there would be nothing left to touch.
He held you there until the morning light started to peak over the horizon, letting you cry until there was nothing but dry heaves left, until you were too weak to do more than finally let yourself completely rely on him to keep you propped up. Quietly and gently, more than you had ever been afforded before, he helped you stand, flooing the two of you back to your house. Your parents were already fast asleep, too high on the success of setting you up with a match that would bring riches to your decaying family once more to really care where you went. They knew, just as you did, there was nowhere for you to go but the path they made just for you. Sirius shooed away the only remaining awake House Elf to draw you a bath.
“I find that it helps,” he whispered, voice low in order to not bring any unwanted attention. “Hot water does wonders for shaky nerves.”
He moved with practiced ease, steps so quiet you could barely hear the squeak of shiny dragonhide shoes, voice clear was quiet. It was in that moment that you realized he was just like you, trapped in a home that weighed so heavily you could do nothing but let it mold you or crush you, where punishment was more common than gratitude. You noticed the telltale shake of his hands, the same ones you had, the same ones many of your fellow Slytherin’s had - the ones that came from prolonged and constant exposure to punishment curses.
But the smile he gave you that night was nothing but warmth, a rarity in your inner circle. He helped you with your outer layer of clothes, mindful of the way all your strength seemed to have disappeared, turning his head away to give you the illusion of privacy. When he gave you a tight lipped smile, bowing the way so many Purebloods were taught to do on their departure, you panicked, grabbing onto his arm so tightly you nails dug into his skin.
“No, please,” you begged. Tomorrow, you would be proud. Tomorrow, you would hold yourself up once more as you always did, no sign of insecurity to be seen. But today? Today, you had already wasted your will and composure. What was one more unrealistic wish? “Don’t leave me. I…I can’t-”
“Woah! Okay, okay. I won’t leave. I’m right here.” He flushed when you disrobed in front of him, but didn’t let go of your hand, helping you into the steaming bath. The two of you stayed in silence, either too scared to speak or too ashamed, but never letting go. When it was clear you were too overwhelmed to clean yourself, he used his free hand to run a gentle lather over your exposed skin, too delicate to do anything but provide the smallest amount of additional comfort. You fell asleep that night, warmed to your core, at ease for the first time in years.
And when he appeared at the party the following day, his usual smirk gone, in too much pain to do anything but whisper the punishment his parents saw fit to give him after staying out past curfew, it was all too easy to offer the same comfort.
You were there to have an escape from the countless Mother’s trying for his hand, and he was there to deter any more conversations with your fiance. He jostled you jokingly if he caught you in the hallways in between classes, and you always made sure to swing by the Gryffindor table on the way to your own to pinch him in return. On bad days, you seeked each other out, thankfully not needing the bath as neither of your parents could touch you while safe within the walls of Hogwarts. Instead you snuck into the kitchen, snacking on sweet things and improper treats, the kind which you’d never find back home.
Sirius spoke of his friends often, of the comfort they brought him, of the promises they’d kept to always make him feel wanted. Remus was his love, you were his heart, and James…James was his light. He always spoke of James with such awe, reaching his hands out like he was cupping the summer sun in his hands in the only way he could describe his best friend. James made him laugh, made him feel like the cruelty of the world was just a shadow rather than a looming cloud, and made every tomorrow feel joyous rather than dreadful. Even though he had to return him every summer, James was there to hold his hand until he got there, and was the reason Sirius wasn’t being crushed under the pressure of defying his family. Your heart stung when Sirius talked about James, wanting to be that person for him, but with your darkness, there was nothing so bright you could do. If James was Sirius’s sun, and Remus his moon, you were happy to be his stars. Always there, but never the focus.
And then you met James, and everything Sirius said made sense.
The night James confessed to you, it was as if your world was suddenly lit by beaming rays of light when all you ever had were torches. Once the story started, you couldn’t stop. It was the first time, the only time, when you felt you truly had someone who would listen when you spoke your horrible truth, to someone who would actually care what happened to you. Your dormmates knew, but their stories were too alike to your own to be needed to be said aloud. Sirius was there, he was always there, but James…James was new. James was unpredictable, and brash, and quick tempered, and an idiot, but he was also warm. So very warm, that it felt like being gazed upon by the sun when you met eyes. His touch did far more to help than laying outside on a summer day, and when you’re with him, it felt, for the first time, that not everything was tainted by darkness. Even Sirius, your most beloved friend, was no stranger to it.
So, when James pulled you into his warm hug, the kind that promised things would be okay, even if you were sure it never would be, you latched on, and never let go.
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I *think* the deal with Gödel's incompleteness theorems is that it's just a cardinality thing, it's like a pigeonhole principle thing (in spirit; it's not literally the pigeonhole principle). Like that's sort of what diagonalization arguments are, and Gödel has a diagonalization argument. If you set up some system of rules, there will always be consequences of that system that you can't prove because you're limited to "too few possible proofs". I think even Gödel himself said something to this effect somewhere but I can't find it.
It's like. Imagine some sentence in PA that's like ∀nP(n), right. Well it might be unprovable in PA. In fact, Con(PA) is of exactly this form: "∀n(n does not encode a valid derivation of a contradiction)" or whatever, and it's unprovable in PA. But from the outside ∀nP(n) is still true in the sense that, well, no matter how many numbers n you check, you'll never find one that doesn't satisfy P. In fact, any statement of the form ∀nP(n) which is unprovable must be true, because if it were false we could find a counterexample. But we can't make that inference from within PA, we have to make it "on the outside".
I find this sort of unsettling because...
Nevermind. I don't find it unsettling any more. I think it's normal and no big deal. There are definitely interesting issues around this but I think in itself it's kind of no big deal. Especially if you're like, a Curry style formalist and you think of math as the empirical study of the behavior of systems of rules and proofs as repeatable experiments (reducing math to metamath, and making it a science).
It's just all, all Gödel is saying is that mathematical systems are "too small" to directly tell you everything about themselves. Again, *I think*. It's like, no more mysterious than the halting problem, because it literally is the halting problem. I don't think the halting problem is that wacky either. Ok there's no algorithm that tells you whether other algorithms will halt. Sure, an algorithm for a decision problem is a pretty restricted sort of thing. It's not really a surprise that there isn't one that does that.
Anyway the upshot is I don't think Gödel forces us to be any more Platonist than we already are. Like in general, even without Gödel, if you want to be a game formalist, say... and you claim "I've proven φ from the axioms of PA", and you want that to be interpreted in roughly the same way as "I made the move ke4 in a chess game", or whatever... well, to interpret the latter claim, I have to ask questions like "what's a chess game?", "what does it mean to make a move?", and these still get me into the territory of ontology of abstract objects and semantics of claims about abstract objects. So game formalism doesn't save you from this sort of thing. And conversely I don't think Gödel produces any more issues of this kind. If I claim "∀nP(n) is true but unprovable in PA", the thing is it might be hard for me to know I'm right (because ∀nP(n) is uprovable, so I have to investigate empirically, à la Curry's idea), but if the trouble is over the semantics, well, I'm still just making a truth claim about an abstract object (the system PA), so it's like. We're semantically in no more dubious territory than with the claim about making a move in chess or the claim about a totally non-Gödelian proposition proved in PA. It's just that it's harder to establish our claim as true.
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