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[twocubes]

Consider the relationship graph of a complete binary polycule (complete = every person is in a relationship with every other person, binary = contains people of only two genders). call an edge in this graph gay if both the people in that edge are the same gender, and call it straight if the people in that edge are different genders.

We will say that a binary polycule tends straight if it has more straight edges than gay edges and that it tends gay if it has more gay edges than straight edges.

Show that if a complete binary polycule contains an equal number of people of both genders, then it will tend straight.

In terms of the size of the complete binary polycule, what is the critical gender ratio for straight tendency? (when the ratio of genders is above the critical gender ratio for straight tendency, the polycule will tend straight)

Do there exist complete binary polycules that trend neither straight nor gay? What about binary polycules that aren't complete?

Research problem: are there other conditions on the relationship graph besides completeness that also result in the existence of a critical ratio?

[vacuously-true]

Okay here's my setup:

Here are the proportions:

If the number of men and women is equal, p=1/2, and 4(p-1/2)²=0, which is less than 1/n for any n. So no matter the size of the polycule, if there are an equal number of women and men, it will tend straight.

If p = 1/2±1/(2√n), then the polycule is balanced. For example, n=4 and p=1/4 or 3/4 works. So does n=9 with p=1/3 or 2/3.

Here's a diagram of different p values and whether they provide gay tendency, straight tendency, or balance:

You might notice that for larger values of n, the "straight tendency" region in the middle gets more and more narrow. Here you can see what that region looks like for n from 0 to 10:

In fact, for n>4, the majority of p values give a polycule that tends gay rather than straight.

Suppose we investigate complete binary polycules for larger and larger values of n:

For larger and larger polycules, straight tendency becomes vanishingly rare, and gay tendency becomes the norm.

Here we see the proportion of relationships in a polycule which are gay plotted against p, in the limiting n->∞ case.

Another win for the gay agenda.

[drovak-blog]

This is one more reason as to why I love math.

[prokopetz]

I can never take those "maid and princess" kink scenarios as intended because every time I see one I get a vivid mental image of a scenario where owing to a series of bizarre miscommunications each is convinced they're the one taking sexual advantage of the other.

[prokopetz]

What I'm getting from the notes on this post is that for a lot of y'all your ideal kink scenario is basically an erotic Abbott and Costello bit.

[bigscaryd]

Basically all the kinksters I know are primarily interested in erotic Abbot and Costello bits.

No, that's not entirely true. ************** is somewhat known for what are basically erotic Lucy bits, and I know someone who would trade his shoes for an erotic Marx Siblings bit.

[shabbytigers]

serious underappreciation of the harpo potential here

[bigscaryd]

I will elaborate. Harpo is using the toys extensively and expertly but (a) only toys; (b) they're all funny in some way; and (c) totally silent and grinning. Chico is the only one who is either (a) doing any sado stuff or (b) using any bioquipment.

[anonymousamethyst]

[ryan-sometimes]

I (Brazilian) spent 4 years in the US between ages 18-22 and the questions USAmericans would ask me about Brazil were so funny, because it’d either be something that verges on insulting, like: “do you guys have cars in Brazil?”

Or it’d be something insane like “in Brazil do you have Cracker Barrel freshman orientation homecoming sorority party Walmart shotguns?”

[caffeinewitchcraft]

The Aftermath of the Chosen One

Summary: Dulce is a Hero. The people who made her one better hope they never see her again. TW: mentions of violence, ptsd, panic attacks

————.

She is a villain when the adventure is over. It creeps up on her slowly. The shortened temper, the unnatural laughter, the darting eyes. She looks up at the corners of rooms for demon bats that don’t exist in this world and claws at her own flesh when she doesn’t find them.

Her companions come find her six months afterwards.

What does it look like, a prince and a knight and a mage walking into a McDonald’s? It’s 1 am, closing time, when she finds out.

“Dulce!” Prince Amor clanks through the fronts doors. He’s wearing the Royal Armor, the set that seems to glow from within with the Holy Light of his Blessed Ancestors. The crown on his head is as gold as his eyes. Everything about him looks fake under the artificial dining room lights, but he doesn’t notice. His golden eyes are locked on her. “At last, we’ve found you!”

She’s covered in a fine mist of oil, slashes of burns from the heat lamps marching up her arms. Her black pants are grey under a dusting of spilled flour and she knows her short, brown hair is frizzed up after her eight hour shift. She blinks at the three walking into the dining room and can’t find the words.

“I told you I’d find her,” Mage Kira says proudly. Her black dress looks like it belongs in a gothic version of the Nutcracker. She waves her flowering wand over her head. “Dulce’s magic has always been so distinctive, I knew it would be easy to find her in the Mundane World!”

Mundane world, Dulce thinks. That’s what they think of Earth. Mundane. Run-of-the-mill.

Not special.

Not worthy.

Dulce’s stomach cramps so badly that she sways on the spot. Why did she send the other girl home? Things would be so much easier if she had another human here.

Keep reading

[faustandfurious]

It’s strange how online is the only place you can properly vent about chronic illness, because IRL there’s the issue that if you don’t have Symptoms at the moment, you feel like an attention seeker if you talk about it, and when you do have Symptoms, you have to clench your teeth together through the pain and explain very calmly to the very concerned bystanders that this is normal, calling an ambulance will solve nothing and make everything ten times more stressful, going to the urgent care clinic will solve nothing and make everything ten times more stressful, and what is the polite way of saying «please leave me the fuck alone until I’m better if all you’re going to do is freak out next to me and demand I reassure you that I’m okay when I’m on the bathroom floor cold sweating and retching»?

Meanwhile, online people will go «man, that sucks», and you go «yeah it sure does» and that’s that and it kinda helps a bit

[faustandfurious]

I guess the takeaway here is that if you are the family member/partner/friend of someone with chronic illness, one of the most productive conversations you can have with them at a time when they’re not experiencing severe symptoms is «what do you need from me when you’re having a flare/bad day/week?»

Some people want sympathy, a hand to hold, someone to bring them a glass of water, a hot water bottle, a blanket.

Some people want to be left alone. Maybe the best thing you can do is go into the other room and do the dishes or whatnot.

Learn what the «normal» symptoms are so you’re able to stay calm when they appear.

Recognise that for most chronic illnesses there’s nothing you can do to make things better, it’s not your responsibility to try to fix things, and the most you can or should do about the medical side of things is offer to come along to medical appointments if the person with the illness wants you there (and they might not, for reasons that have nothing to do with you as a person).

And remember that it’s not your illness, and two people suffering instead of one won’t make anything better. If your loved one lashes out verbally at you while in the middle of a symptom episode, you can recognise that they’re stuck with an illness they never asked for and barely know what to do with themselves, but you’re also allowed your own boundaries, and if the person with the illness isn’t willing to have a conversation afterwards about how to prevent them taking their frustration with their illness out on you, you’re allowed to take a step back for your own well-being.

[prokopetz]

Penis nomenclature is one of the less-discussed hazards of having very particular tastes in erotic fanfic. I once ran across a story that improbably had both the exact pairing and the exact kink I was looking for, only to get clotheslined at the first sex scene by the fact that the text consistently referred to the lead's penis as their "dork".

[biggest-gaudiest-poltergeist]

heard someone say "who even owns a rolling pin anymore" and my brain froze trying to process it. what does that mean. are u implying rolling pins are outdated technology? did we come up with a shiny new 21st century method of flattening dough of which i remain uninformed? is there now an app on the app store people are using instead??? im losing my mind "who even owns a rolling pin" people who BAKE

[biggest-gaudiest-poltergeist]

in the 2020s people don't own rolling pins they subscribe to Breadr+ to rent an exciting new model every month! explore a wide range of colors, sizes, weights, grips, and materials to find the model that fits YOUR dream lifestye!!!!!*

*subscription required, Breadr+ rolling pins not currently available for purchase

[ryan-sometimes]

Hate when I miscalculate my vyvanse to coffee ratio and end up feeling like I’m a macbook air being forcefully disabled by a new device update

[dyingroses]

[cheeseanonioncrisps]

“A kiss may be grand, but it won’t pay the rental, on your humble flat, or help you at the automat.”

Like literally the most famous song about how much girls love jewellry is just explaining the importance of getting jewellry for when your partner leaves you penniless and alone.

[ohheyheyitsjj]

The founder of Girl Scouting in the US, Juliette Gordon Low, funded her first troop by selling her pearl necklace, which was her only belonging after her husband died and left everything to his mistress.

She founded Girl Scouts to teach girls self-sufficiency so they wouldn’t have to go through what she went through when her husband died and she didn’t know how to take care of herself.

[penrosesun]

While we’re on the subject, let’s please also remember that historically disenfranchised communities who had to worry about frequently being run out of town often bought expensive jewelry with their limited funds not because they were greedy or tacky or classless, but rather because you can’t sew a real estate investment into the lining of your coat, and the powers that be can’t freeze a diamond necklace the way that they can freeze a bank account.

[prokopetz]

Some of y'all are really out there trying to play the "there's no platonic explanation for this" card on the "what's the odd blowjob between friends" site.

[prokopetz]

At this point I've seen like three unconnected pieces of American media set in a superficially idyllic small town with a big fuckoff lake that functions as a liminal boundary between the Known and the Unknown and in which a major character attempts suicide by drowning, and now I'm wondering if the Liminal Death Lake is just a thing American small towns have.

[prokopetz]

I don't ask much from retro console-style RPGs. All I want is a really jacked woman, a centrally placed combat gimmick that's honestly usually less effective than just doing regular attacks because the action economy doesn't work that way (but I use it every round anyway because it looks sick as hell), and at some point getting to fast travel by being shot out of a cannon.

[prokopetz]

I just had to delete a bunch of dipshits in the replies debating whether Princess Daisy from Super Mario qualifies as "jacked", which has only reinforced my conviction that there's no hope for this site at all.

[vee-dmsr]

[prokopetz]

I don't ask much from retro console-style RPGs. All I want is a really jacked woman, a centrally placed combat gimmick that's honestly usually less effective than just doing regular attacks because the action economy doesn't work that way (but I use it every round anyway because it looks sick as hell), and at some point getting to fast travel by being shot out of a cannon.

[pangur-and-grim]

alright I'm almost finished Project Hail Mary, and I have to say, I don't get why people are shipping the guy with Markiplier when he's already in a perfectly healthy queer-platonic relationship with the alien spider made of rocks

[pangur-and-grim]

that's insane. we need to change this

[caffeinewitchcraft]

I loathe people who litter in general but particularly on hikes because seeing litter on the trail violently rips me away from my maladaptive hobbit fantasies where I'm on my way to a feast day and muttering about the inconsideration of it being held on a mountaintop instead of in the valley which is objectively more convenient for all involved, and instead thrusts me into the mindset of a serial killer who must pick up the evidence their future victim is carelessly leaving along the trail which would inevitably lead the rangers to us prematurely and wouldn't that be a shame? So I pick up their garbage like the trained crime scene expert I am, scouring under bushes for shreds of wrappers, before, satisfied that only nature remains, taking off up the mountain in hot pursuit of my quarry

[prokopetz]

Honestly, it's hard to even get annoyed at some of the folks who come blundering into creative discussions like "this is literally just [thing that does not even slightly resemble what's being proposed]" because their reaction is so clearly the product of an embarrassing lack of literacy. It's like trying to discuss early 20th Century literary fantasy with someone who genuinely can't distinguish between Conan the Barbarian and The Wizard of Oz – at some point you've just gotta feel bad for them!