#quotienting

[isomorphismes]

Hadamard knew in 1898 that negative curvature and simply connectedness for surfaces embedded in 3-space force uniqueness of geodesics joining two points—implying that any segment of geodesic is also a shortest path.

But there is a long way toward the modern statement: “on any complete abstract Riemannian manifold of ≥0 curvature of any dimension, curvature is the quotient of its universal covering by a discrete group of isometries.”

Marcel Berger, Riemannian Geometry during the Second Half of the Twentieth Century

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Hadamard, 1898 being Les surfaces à courbure opposées et leurs lignes géodésiques

[3liza]

my general position on public nuisance is "you should do your best not to irritate or inconvenience other people unless there's a good reason" and then litigate the "good reason" on a case by case basis. i think that's the best anyone can do. the definition of "good reason" varies wildly depending on context, your background, culture generally, what data you have as a participant or a bystander, and local laws, and all three of these things are relevant factors

for example it really does lower my level of reactive, irritable stress with my neighbors to know their names and general schedules. i don't know why but it really does bother you less if Kyle Upstairs is having a party a little too late and you can hear Bulletproof through the ceiling, as opposed to if you're on year three of living underneath some anonymous fuckhead you want to kill. it's like oh Kyle's cousin is visiting and they're just chilling out maybe they lost track of the time. this makes all the difference. as usual the best advice is to form community with the people around you no matter what, even if you are entirely self-interested it will benefit you in the end. well that's all I got

[poorly-drawn-mdzs]

What a lovely family portrait👨🏻‍👨🏻‍👦🏻🖼️

Enhanced image of A-Yuan's first sword flight.

[more-mathematics-mor-lam]

Telling my cat if he doesn’t shape up, I’m going to inject him into the quotient torus

[ceilidho]

sex worker soap that reader hires to take her virginity and teach her about sex. is this anything

[suburbanbonfire]

welcome to the big leagues, boy

(prints here)

[mindblowingscience]

Researchers have linked spending more time playing video games with a boost in intelligence in children, which goes some way to contradicting the narrative that gaming is bad for young minds. While the difference in cognitive abilities was a small one and isn't enough to show a causal relationship, it is enough to be notable – and the 2022 study was careful to factor in variables including differences in genetics and the child's socio-economic background. Meanwhile, watching TV and using social media didn't seem to have a positive or negative effect on intelligence. The research should prove useful in the debate over how much screen time is suitable for young minds.

Continue Reading.

[sepia-stained-sunset]

3rd Year Hinata constantly agonizes over whether or not Tsukki likes him (he very obviously does) and makes it everyone else's problem until Kageyama is literally gripping Yamaguchi by the shoulders and begging him to join them on their walk home because he genuinely cannot stand this. Yamaguchi just tells him that he can deal with one year of this, he's been dealing with the same thing from Tsukki for two.

[ashfae]

For anyone else going bonkers waiting for @mumblesplash to drop the last part of the Tetris Spoilers Prologue, here, have a distraction. @melibemusca, this is for you; thanks for the encouragement. <3

[fromville-divorce-lawyer]

Here's my From season 4 theory:

So we know Tabitha has dreamed about being in Fromville as a girl who was dressed in a cape at the red stones, and Jade saw the guy dressed in old rags and missing an eye at the same stones. I don't know what time period this is, but I saw a person somewhere mention they look dressed from the same period.

Both are also seeing civil war soldiers. (Tabitha not directly. She was Miranda when she saw them.)

So they both seem to have memories from lives in Fromville far into the past.

I think the monsters from the 1950s being the OG ones who sacrificed their children is a misdirect. Jade & Tabitha's visions/memories go back further than that, so the place has been around a lot longer. I think Jade and Tabitha have reincarnating since the beginning of this place, and the people who first sacrificed their kids are older than the monsters. They're actually the things in the forest that are worse than the town.

Now why are Tabitha & Jade reincarnating rather than becoming whatever the other people became?

Well, it's because Tabitha made a promise to the Boy in White to defeat the Man in Yellow by fulfilling a quest.

What quest you ask? Why, the quest to obtain the hottest husband possible.

Wait, wait. Hear me out.

Henry looks like he was a good-looking dude at 35, and Jim is a blue-eyed hottie himself, so Miranda & Tabitha were obviously well on the way. It just was not quite enough.

Then Tabitha gets to Fromville and meets Jade who (based on empirical data collected via Tumblr poll) is becoming exponentially more fuckable each season. By season 4, Jade's fuckability will be reaching critical levels. Fifth season, it'll be unchartable. Tabitha will have achieved her goal of most fuckable husband to ever live.

Then, everyone gets go home. Remember when we get to season 5 that I called it!

Okay. Sorry, I'm kidding about the Jade fuckability part. But for real, I don't think that the 1950s monsters are the original people who made the deal for immortality.

My theory is that it started hundreds of years ago. With help from the Boy in White, (original)Jade and (original)Tabitha were able to reincarnate so that they can try to save their daughter. (The image on the talisman is either Jade & Tabitha with the sun & moon representing rebirth or MIY & BIW with the sun and moon representing opposing forces. I'm leaning toward the second.)

Now, each cycle restarts when both Jade & Tabitha arrive. (Miranda and Christopher were the two cars that arrived in the past, and although Victor talks about it like he remembers it happening but doesn't seem like he was in one of the cars, I think that's a misdirect, because it would have been too obvious if we knew Mirand and Christopher were the last people to arrive in the same day.)

Each cycle gets to make a choice. If they choose to sacrifice their children, they become a new monster in the forest. In the 1950s cycle, they chose to make the sacrifice, forming the town and turning the people into monsters.

During Victor's cycle in the 1970s, neither Miranda nor Christopher remembered their past lives like Tabitha and Jade just did. However, the town was given the same choice. Miranda hid Victor and Eloise from Christopher (she told Victor to hide somewhere Christopher didn't know about), because he was going to choose to sacrifice the children while Miranda wanted to try to set the ones that were already trapped free. Since Victor was hidden, there was no sacrifice, and everyone died instead of becoming a new type of immortal monster.

[aromantic-goldfishdeactivated202]

I need to study the psychology of tumblr users for no other reason than this HAS to be some kind of hivemind type shit

HOW ARE WE DOING THIS

[hunterrrs]

“no chance.” “no? taylor swift?” “it’s, like, unbelievable. i’m not tiktok guy.” “three photos. that’s all you get, each pose. and you’ll have three good ones.” “sit on his lap” “hey! my knees, you know?”

geno and erik terrorizing people 😂

[landoscarey]

lando norris arrived in THIS FIT on a moped should i scream

[fisheito]

alright. 👓 what we got for this weird little step up banner. Why did they have SR yaku and oli on the promo pic?? And what does it have to do with eiden's huey decision???? No matter... let's see if there's anything i'd like to pull for...

& opens updated game &

The only SSRs aster and morv have? . Already have morv, and he's full unlocked. I wouldn't MIND an aster if only to see him slap morv around. but it's not enough to motivate me to throw my contracts... ohhh if only there were a tiny aster SSR.... i want that lil guy fuckin things up...

Ocean breeze yakumo- WAIT, IDOL YAKUMO? THE WETTEST, (arguably) MOST PATHETIC WHIMPERER OF THE YAKUMOS? the yakumo that i did not want during his original run because i wanted nothing to do with him and thus i never Obtained him? YOU're saying i could finally have a soggy beach tankini yakumo in my collection, to manipulate voice lines at will, to replay whatever sad Single Line of Sad Whines he lets out in R2----- THAT YAKUMO? well now i have to read up on the terms and conditions of this banner

[interlude: reading and some judgemental squinting]

They said guaranteed SSR within 70 pulls...BUT IT SEEMS LIKE YOU CAN ONLY CHOOSE THE SSR AT 300? idk bro that seems like a lot to sacrifice for a rerun... what else have we got to work with here

Chocolate fiend retail edmond- does not measure up to white wedding edmond. i remain uninterested

Mother Nature oli- tEMPTING, OK, THE ONE I'VE WANTED SINCE I STARTED PLAYING, , but he probably isn't a great unit like most of the older units BUT MY DEAREST MATRON OF LIFE FLORAL HUNTER OLI..........THE NOSTALGIA HITS HARD

Ropeflinger quincy- no interest

Period cramps kuya- no interest

Loincloth gapmaster garu- tbh i'd be pissed if i got this one because i already have him at 3 stars and if i get just. one single extra of this. that's not enough to ascend himn. it's nto enough to do ANYTHING. either give me plentiful puppy or NONE AT ALL!!!!

Idol apprentice blade- hol up isn't this the blade with that riduclousoly beautiful eiden sprawed alcross the bed that makes you wanna go RRRRRRRHBWRUFFRRAWFBARKRBARKBRAKRKBABRBARK???? ok ok, serious contender,,,, it never hurts to have more blade rooms

Icy equilibrium dante- ?!?! isn't this the one where dante is an absolute loser for eiden and they're so painfully vanilla and sweet that you want to projectile vomit all over the foggy glass? hm. i could use some more bullying dante for his feeligns. yeah, sure , why not

Truth seeker rei- waitwaitwait isn't this another one of rei's lore-important units? the one that dishes out his saian shenanigans, AND sticks him in a locker (where he magically manages to remove his pants but stil retain his powerrfully high goth boots)? hm. also don't remember him being a particular useful unit , but. "cunty boots stay on during sex" rooms are still a delight every time. alright. consider me interested. a bit.

SR yaku- got im SR oli- got im SR quincy- got im

SR kuya- YOU!!!!!!!!!! the AACCCURSED SR that pops up in zerophos' guides, who is weirdly OP and i canNOT COMPLETE THE STAGES BECAUSE I DO NOT HAVE YOU. you supposed "low-rarity-tier" unit with your unfair trigger? skills??? now i BET you would be mighty useful to have but that's just it, innit? the moment i might deign to lure you to my team, and you refuse me. you ignore me more than anyone else ever has in my life. you ignore me more than OG SSR Garu who, to this day, 3 years later, has not dared to look upon me. no. just for that, i'm going to say i'm not interested. get out of here peepaw. i don't need you to complete those freakishly specific challenge trial conditions.

VERDICT? i'm widdle--sorta--maybe interested in 6 of the 11 SSRs , which is not uhhhhhh optimal it's not like i'll come out of this a winner no matter the outcome Lookin 🔬 at these numbers, probably not worth it to me... maybe i'll throw a loose scroll at the banner if i give in to my impulse randomly

but with magical girl blade on the horizon? mm. gotta be smart with these gamblin' odds. may have to bunker down like the crocodile and play the waitin game...

[the960writers]

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A post shared by Mary Robinette Kowal (@maryrobinettekowal)

MICE quotient: Milieu, Inquiry, Character, Event

Mary Robinette Kowal explains what the MICE quotient is and how it works for structuring a story by nesting the elements of it.

[sachermorte]

someone once said that they were convinced that I couldn't leave vienna. like the city limits would bounce me back like a tennis ball thrown against a wall. and tbh it's kind of true. this is the only place on earth I'm functional. imprisoned for all time in a 400km² area. I take one step outside city limits and a secret and evil downtown timer starts that will have me screaming crying pissing throwing up inside a few hours without proper intervention and management. I'm like a vampire who needs to sleep in the dirt he was buried in except I need to sleep with a crushed can of ottakringer tangled in my sheets while I listen to police siren asmr