Silly Goose

I’m just a boy 20M

[marklangnee]

Learning how to draw day 1. Turns out angling the paper on my thigh made the entire thing skewed for one sketch. Out of everything I tried drawing, this is the only one that ended up looking any good lmao

[marklangnee]

The way they teach Gram Schmidt Orthonormalisation (referred to as GS henceforth) is actually criminal. It’s not a plug and chug algorithm, it’s actually very intuitive. Also apologies to anyone who doesn’t know what GS is or does, but that is beyond the scope of a single tumblr post. I would point towards my blog, but that would doxx me, so I won’t do that.

As an EE student, I’ve used a lot of GS. Every single semester, there’s at least one subject that requires it (after the general first year, though Lin Alg was the first place I learnt it), especially my comms classes. While I’m not sure, I’d assume it’s used all throughout engineering, since so much of engg can be reduced to linalg + probability.

In first year—when I first learnt it—I hated it. It felt confusing and kinda useless? One of the problems with learning these concepts devoid of application I guess. It came up in numerical methods with QR decomposition, but it still felt like fluff. It wasn’t until 3rd year ADC (Analog and Digital Comms) that it actually clicked in my head. It only did that because we were finally using real signals versus abstract quantities, so we were forced to see what it was doing. However, it is entirely possible to gain the required intuition with vectors, so I’ll be doing that because I don’t want to explain the inner product in detail.

***

The point of Gram Schmidt *Orthonormalisation* is pretty self evident if you know what orthogonal and normalisation mean (in terms of vectors). I will continue with the assumption that you do know what those are, and what projection is.

So the main idea behind GS is to take a set of vectors and produce an orthonormal basis for them. Thats a lot of word salad. What does it actually mean? Well, what we have are a bunch of arbitrary vectors. That means they look something like {[1,2,3], [-3, 2, 5], …}, vectors that point every which direction, and it’ll give you a basis for those vectors that is a) orthogonal, so that each vector is completely independent from all the others, and b) normal, so that projections are easy.

I think the bit that never got into my head was why it’s so important. Can’t we just use the trivial basis (i.e. {[1,0,0], [0,1,0], [0,0,1]}? That’s already orthonormal, and our vectors are already in that form.

The issue is that the trivial basis is often *not aligned super well with the problem we’re trying to solve.*

Imagine we have some vectors that represent velocity of a body. It’s meant to go in a straight line, but due to wind or other disturbances, it can deviate a bit from the line.

It’s important to remember that our trivial basis *can* describe this. GS doesn’t make any new information, it just makes it easier to spot.

Let’s take it in 2D, where our velocity vectors are {[0.5, 0.5], [0.4, 0.6], [0.3, 0.7]}. We can see that the velocity is aligned with that first vector, with some deviations. This could be because of drag, air resistance, irregularities in how the barrel we’re shooting a projectile out of, or any number of external forces/disturbances. However, we don’t really know how much each of those forces are actually contributing to the motion of the body.

How can we quantify any of this? Well, an approach might be to look at the difference between velocity vectors.

Taking the first vector as our reference, we get {[0,0], [-0.1, 0.1], [0, 0.2]}, from this, we can see that there *seems* to be a pattern.

But what does that pattern represent? Our measurement vectors are aligned to *some* frame, but that frame does not necessarily show us what actual directions are important.

The issue right now is that our measurements have two components. The main trend, and the disturbances. Our standard basis cannot represent this well, there’s a lot of overlap between the two. What we want to do is remove the overlap.

To remove the main trend and see what else is going on, GS comes pretty handy.

Our first step is to define the main trend. Again, we’ll take our first vector (calling the three vectors as u1, u2, and u3 from now) as reference. Its direction is the normalised vector in that direction (calling direction vectors v).

v1 = u1/||u1|| = [1/sqrt(2), 1/sqrt(2)] = [0.707, 0.707]

Now what we do is take our reference direction and see what new direction our next vector introduces.

u2 -> u2 - (u2•v1)v1

Let me explain this step a little more in detail. u2•v1 is the projection of u2 along the direction of v1. That is, how much of u2 is pointing in the same direction of v1. Now, if we subtract that portion from u2, we get the component of u2 that *isn’t* pointing in the direction of v1. It’s pointing in a *new direction*.

u2 -> [0.4,0.6] - 0.707[0.707, 0.707]

= [-0.1, 0.1]

Now normalising it, we get:

v2 = [-0.707, 0.707]

That’s the new direction introduced by the second measurement.

Now let’s look at the third vector. We’re going to do the same thing. See u3, and remove the components of u3 that align with v1 and now v2.

u3 -> u3 - (u3•v1)v1 - (u3•v2)v2

≈ 0

This means that u3 doesn’t contribute any new information about directions, its information is completely explained by the other two directions.

So our new basis looks like {[0.707,0.707], [-0.707, 0.707]}

The two vectors are orthogonal and normal. So, finding the original vectors in this new basis is as easy as adding the projections in each direction.

So:

ui = (ui•v1)v1 + (ui•v2)v2 =>

u1 = 0.707v1 + 0v2

u2 = 0.707v1 + 0.141v2

u3 = 0.707v1 + 0.282v2

Now it’s much easier to see how the vectors are changing. v1 is staying the same, while v2 is linearly increasing. *This strongly suggests it’s not random and we should try to figure out what it is*.

This is exactly why we shouldn’t use the standard basis. It hid the structure behind the system in the coordinates, since they were coupled. Using the basis we got from GS, it becomes immediately obvious what’s going on.

Like I said earlier, Gram Schmidt doesn’t create any new information, it just makes information easier to understand by giving us a coordinate system that’s tailored to the structure of the system. It stops different pieces of information from talking over each other.

***

I hope you now understand the intuition behind Gram Schmidt Orthonormalisation. It’s about finding all the directions in which data changes wrt a reference so that the numbers are more aligned with the problem at hand. I’ll get down to writing a more comprehensive blog post about it someday. Maybe we can go into least-squares or QR decomposition, since those are used *everywhere*. But for now, that’s it. Thank you for reading!

PS. I’m very new to this, and doing it on mobile, so I apologise if the formatting is off. I don’t think the markdown will render, but oh well. I’m too lazy to go back and correct it all now

[the-auguer]

ghost always heard the other recruits complain about how hard it is to please their girls, how difficult they are, and all the other locker room talk. so he figures most of it is bitching but with a kernel of truth in there somewhere, and he’s glad he isn’t dealing with something like that on top of everything. but then he gets his girl and all he can do is scratch his head when he hears it. it’s all just observation and application, innit? like field work but way easier— no guns, no deaths, no mess. his girl has a favorite food, a favorite flower, a favorite kind of little trinket, and it makes her happy when he brings them to her. he keeps a calendar of all the dates she tells him about, like any good soldier would, to plan around or for them. he figures no girl wants to be worrying about her car, so he takes it to the shop and fills it with gas when he can, drives her everywhere while he’s with her. he doesn’t mind wherever they go, but she does so he picks the places and the things she likes and gets rewarded when they get home. her hips buck when he flicks his tongue or curls his fingers a certain way? noted and catalogued for future reference.

and somehow everything he does is right and gets him kisses all over his face, one happy girl calling him “sweet” of all things. this shit is easy and the rest of those muppets don’t deserve their girls.

[gorejo]

unedited. wrote this while taking a break from finishing his fic bc I forget just how rich Sylus is.

It's rare, but occasionally Sylus gets you mad. And the victim of your rage isn't him... but his bank account — specifically, the black card he's given you to use.

"Serves him right. I hope you go broke," you bitterly muttered, purchasing whatever comes to sight.

Usually, you're adamant about not using his money, specifically this card, despite his constant reminder to use it without guilt.

But when he finally comes home, days without warning or contacting you, with his clothes covered in blood and face full of exhaustion, that breaks the camel's back for you.

The result —

A new dining set, this time plated with gold. -$5k.

A new set of diamonds and pearls. -$9k.

A new Camaleonda sofa set. -$25k.

A Hästens bed set that you'll be using alone. -$150,000k.

So when Sylus gets a phone call asking if these purchases were fraudulent or if he would want to lock his card in case it was stolen, he chuckles while he taps his finger on his desk, smirking.

cute. so so cute.

He informs the banker on the other line, “No, run those purchases through."

"But sir, are you sure...? Whoever this is, they've also purchased 100 kitty plushies?"

Unfazed, Sylus responded, "That’s just my future wife throwing a tantrum. She’s cute, no?”

"I-I see."

How adorable and naive were you to think this would ever bother him — no, it excited him even more whenever you decided to challenge him, especially when you didn't allow him to touch you ever since he's gotten back.

And before he ends the call, he orders, "Send me a list of what she purchases, and make a transfer into that account so she could spend more."

Not too long after, you receive a text from him.

From: Don't You Dare Get Weak And Call Him First 🔪

I expedited that bed, Kitten. But why don't we put it to good use and give your new plushies a good show, Sweetie? Tonight.

[cruxhing]

non british reader making fun of simon for being british

“Why do you guys put curry on Chinese food?” you asked randomly while you were helping Simon clean his gun collection.

Simon’s hand pauses over the barrel and slowly looks over at you; the rag just barely hovering over the barrel, “… Wot,” he says flatly. Simon’s questions were never questions; always questions formed into statements.

You looked over at Simon, setting down the dirty rag and shrugged, “like— I was craving Chinese food so I tried finding the closest restaurant that does take out… Most of the dishes had curry on them— Also, why is everything fries? Even the Chinese restaurants serve fries with curry on top,” you rambled, almost ranting at this point. “I wanted some actual spices, not soft fries with bland curry. While I’m at it, your guys’ curries look so gray. Like there’s no color to it.”

Simon stilled for a second. Was this an insult? Or were you just curious? Naive, maybe? “… It’s chips, first of all,” Simon replies with a huff before he went back to cleaning his gun, “and secondly, you hadn’t had proper Chinese if you’re complainin’ about curry on chips.” He gave you a side glance before quickly looking away, “and it’s fusion. Proper or not, it’s still Chinese.”

You sat there momentarily, watching how Simon’s fingers run through the crevices of the barrel, “oh my gosh, and the way you just said it— You guys always say ‘let’s get Chinese’ instead of ‘let’s get Chinese food’ too… Kinda makes me concern for your schooling system here.”

Simon’s eyebrows twitched. He didn’t know whether to laugh or cry (in frustration) at this point. “‘s just how we talk. Don’t look much into it,” he grumbles out, biting back a smile. He looked back at you and set down the cleaned barrel on the table, “any other comments ‘bout us Brits or are you done?” he asks, leaning back on his chair.

The cleaning was long forgotten, the rag and weapons resting on the table beside the two of you. “Also, the way you guys wash your dishes? Yeah, no—“ you shook your head in disapproval.

Simon raises an eyebrow.

“You guys don’t rinse off the soap,” you told him flatly. Simon almost looked petrified at that comment, staring at you with wide eyes. “I went on a whole deep dive on it because it was shocking to hear!” you instantly say, almost defensive at the fact that he didn’t believe you.

Simon pinched his nose bridge and let out the longest sigh you’ve heard. He doesn’t know why he sticks around you so much; you were too annoying for him and yet, here he was. “Alright, well— I don’ do that, so I dunno where you’re getting this information from,” he replies flatly, rubbing his temple now. He’s regretting asking you if you knew any more stereotypes and cultural differences.

You picked up the rag and stared toying with it, “and you guys also—“

“‘nough of your shenanigans, this conversation is over,” Simon cuts you off, full blown smiling at this point. Which, wasn’t much. It’s just the inner corners of his lips twitching up. He turns away from you and grabs another clean rag from the pile before picking up the old one, “one more shite that comes outta tha’ mouth of’ours and I’m goin’ to off myself,” he says, throwing the dirty rag in your face. 

[kadzhi]

one good thing about december on this hellsite is that this gif will be making its rounds again

[lilskippity]

141 out at a bar, nicer than their usual shitthole pubs, when a pretty little bird catches Simon’s eye..

[rawkuna]

୨୧ frat!sukuna finally found out who’s been bothering his shy girl at work

you didn’t tell sukuna at first.

it didn’t seem like a big deal, not really—just one of those gross, persistent things you learn to brush off when you work customer-facing. you sit at the front desk of the campus library three days a week. quiet shifts, gentle lighting, cute little name tag. it’s your favorite job you’ve ever had. until he started showing up.

naoya zenin. third-year. entitled. smug. and annoying in that specific way that makes your stomach twist. he doesn’t do anything—not really. not enough to report. but every time he leans over the counter and asks if you “moan like you read,” or offers to help you “stretch out those tight little legs,” you feel your skin crawl. you tell him you have a boyfriend. he laughs. says, “you’re too sweet for a guy like that.”

you still don’t tell sukuna.

not until he notices the way you keep your voice soft when someone walks in behind you. the way you keep glancing toward the doors. the way your hands tremble just a little when your phone lights up and you ignore it instead of smiling.

“who is it?” he asks.

and when you finally whisper it—when you finally tell him, cheeks burning, lashes lowered, voice barely audible over the hum of your apartment—he goes quiet.

the next day, he shows up at the library. not subtle. not discreet. he’s in a black hoodie, chain glinting at his throat, hair messy like he’s fresh out of bed, and a permanent scowl carved into his face. he doesn’t even glance at you when he walks in—just stalks straight to the desk where naoya is leaned over too far, too close, like always.

“you the fucker who’s been talking to my girl?” sukuna asks.

naoya blinks. laughs. “who’re you—”

sukuna doesn’t wait.

he grabs him by the collar and slams him into the desk so hard a stack of paperbacks crashes to the floor. your heart stops. the other students go silent. naoya curses, struggling under the grip, but sukuna doesn’t budge.

“listen real close,” he snarls, voice low. “you look at her again, you breathe in her direction, you so much as think about her when you’re alone in your little twin xl—I’ll break your fucking jaw.”

“jesus—alright, fuck, chill—”

“say that shit again,” sukuna snaps, dragging him an inch closer. “go ahead. see what happens.”

naoya stumbles when sukuna lets him go. stutters something pathetic. grabs his bag and leaves like a coward, face pale, lips pressed tight.

and sukuna finally turns to you.

his expression softens—just a little. like he’s still buzzing with adrenaline, but he’s already back in your corner, already sliding his arm around your waist and muttering, “you should’ve told me, baby.”

you’re still half-frozen behind the desk, your chest tight and your fingers curled into the sleeves of your cardigan, when he finally turns around and walks back to you. no blood. no yelling. but his knuckles are flexing, jaw still locked like it wasn’t enough.

“you good?” he asks, voice low. softer now. just for you.

you nod, barely. and he sees it—how shaken you are, how small you look behind the counter, cheeks flushed and lashes lowered. he breathes out once through his nose like he’s trying to keep it together.

“move over.”

you blink. “what?”

“i said—” he wraps a hand around your waist and lifts you—like it’s nothing, like you weigh less than a thought—settling you right onto his lap as he drops into your chair behind the desk. “you’re not sitting here by yourself the rest of your shift. scoot.”

your knees press together instinctively, hands flailing a little as you try to adjust yourself without exposing anything. he doesn’t help. just tugs you tighter into his chest until you’re practically straddling one of his thighs, warm and flushed and hiding your face in his hoodie.

“sukuna—”

“nah,” he mutters, voice low against your ear. “you’ve been sitting here alone with creeps like that? mm-mm. not happening again.”

you try to argue, but his hand finds your knee and slides just a little higher. not inappropriate, but protective. like he needs to keep skin-to-skin contact just to breathe.

“how many times he come in here?” sukuna asks quietly, mouth brushing your temple. “did he touch you?”

you shake your head, fingers fisting his hoodie tighter. “just… said stuff. all the time.”

he exhales sharp through his teeth. “fuckin’ knew it. knew something was off.”

you sit there for the next hour like that. curled in his lap, legs tucked to the side, his arm draped around your waist like a warning sign to anyone who dares look twice. students come and go. the quiet clack of keyboards hums around you. but no one says anything. no one dares.

and when you reach for your little library clipboard to check someone’s hold status, sukuna takes it from your hand, squints at the name, and grumbles: “this guy borrowed a copy of the art of seduction last month. denied.”

you slap his chest. “you can’t do that—!”

“i can, actually. i’m dating the librarian. she’s very sweet. very hot. very off-limits.”

you bury your face in his neck. and when he presses a kiss to your hair, still holding you close, you can’t help but smile.

you do love him mean.

but you love him soft, too.

and this is why sukuna's banned from the library smh

[cumtoru-deactivated20260110]

18+ you're the frat’s favorite toy

you’re not technically dating any of them. not officially. not in writing. not in the way that would stop the others from getting a turn.

first it was nanami. soft-spoken, meticulous, always asked first—can i touch you here? is this okay? do you like that?—like he genuinely cared, like he wanted to learn you. he’d kiss your shoulder afterward. wrap his arms around you like a blanket and tuck your hair behind your ear while you caught your breath. he treated you like porcelain, fragile and warm, even when you were soaked and writhing underneath him. especially then.

then it was satoru. god. cocky, talkative, always laughing. his favorite thing was watching you squirm when he said shit like “awh, she’s shy now? wasn’t shy when she was bouncing on my cock like a fuckin’ bunny—” and he’d keep going until your face was hot and your thighs were shaking. he made it fun. sloppy. filthy. filmed you once on his phone and wouldn’t stop showing the others. called you his favorite study break and kissed your tears off your cheeks like they were trophies.

choso came after that. shy. quiet. blushed when you touched him. but that dick? unholy. thick and curved, too much to take all at once, and he didn’t even mean to be mean about it—he’d just grip your hips tight and whimper into your neck like he was the one overwhelmed, even as your eyes rolled back and your legs shook and your cunt drooled all over him. sweet boy. dangerous hips.

then came toji. older. rougher. manhandled you like it was easy. like you didn’t weigh a thing. threw you over his shoulder once and slapped your ass just to make you squeal. he liked you on your stomach, back arched, hand in your hair, fucking you mean—use your words, babygirl. what do you say when you want it harder?—until your voice gave out and your knees were bruised. he'd laugh and flip you over. my messy little thing, he’d say, wiping the drool off your chin.

and then there was sukuna. oh god. he didn’t ask. didn’t wait. just looked at you once across the kitchen after a party, licked his teeth, and said “you’re next.” and you knew—knew in the way your body clenched up, knew in the way the air changed, the way every other guy in the room went quiet.

he made you crawl to him. made you beg for it. laughed when your voice cracked. “what was that, princess? didn’t hear you.” and when you finally gave in, babbling and nodding and letting him drag you into his room by the wrist, he tore you apart. every thrust knocked the breath out of you. he held your throat in one hand, your jaw in the other, hips slamming into yours like he was trying to fuck the memory of the others out of you.

“mine now,” he growled against your mouth, deep and feral. “say it.”

and you did. again and again. especially when he came inside hot and thick and too much—filling you with a groan that rattled through your whole body.

after that? you didn’t really go back to the others. not because you weren’t allowed. but because no one else felt like him.

written by rawkuna do not plagiarize.

me if i was in the frat!jjk universe

[dreaminguponlilypads]

MERRY CHRISTMAS EVERYONE!!! enjoy

You and Simon had been seeing each other for a bit. Nothing big or dramatic. Just dinners, sitting side by side on his couch, watching movies you barely followed. He never called them dates. He just… showed up. Picked you up. Took you home.

He always took you home. Even when it was late. Even when you both knew you didn’t really want to leave. Simon was careful like that. Almost stubborn about it. The last thing he wanted was for you to feel uncomfortable around him. Enough people did.

Last time you went out, he tried to get you to stay. Not very smoothly, though. Just a quiet “you could crash at mine” like it was no big deal. You laughed and said, half joking, “I’m not sleeping in a bed that’s had other women in it.”

You didn’t think about it again.

Two days later, you were about to call him when a message popped up.

It was a photo. In his room. Black shirt. Sleeves pushed up so his delicious forearms were on display, that bastard. One hand on a brand new bedframe, fresh out of the box.

The text under it said,

- Come over. Got a new bed. Bring your toothbrush.

You couldn’t help smiling.

Of course he bought a whole new bed instead of arguing. That man might be the death of you.

But at least you’d die having some fun.

[marklangnee]

5 posts!

WHOS A BOT NOW TUMBLE

[marklangnee]

The shift of interpreting chaotic and lawful on the alignment chart from being the actual laws of the place to being a personal code has been very successful. A similar shift that I would love to see is on the good and evil spectrum. Good and evil are two very charged terms. It feels wrong calling someone evil when they’re not like Stalin levels of bad, but the current delineation of good being nice people, neutral being having the capacity to be selfish, and evil being moustache twirling villains does offer enough resolution on the evil side.

Personally, I interpret it as it being from selfless to selfish and I find that it helps me roleplay npcs a lot better. An evil character is someone who would take your lunch from the office fridge or demand a bribe. Further, an evil campaign gets transformed from burning down houses left and right to being more character driven. It signifies a campaign where doing the ‘right’ thing is so longer important.

Alignment is a reminder of a character’s behaviour. It’s a crutch (not saying that’s a bad thing I use it all the time) signifying how you should roleplay a character and this makes it a lot more useful.

[marklangnee]

On a far more positive note, learning is so cool!!! Finding a subject you really REALLY gel with in college is such an amazing feeling I love it. Like yes I find a lot of maths and physics boring, but **that** maths and physics put together with some of the most interesting theory is so fun. Find what you’re passionate about people I’m telling you feeling is like no other.

[marklangnee]

The enshitification of AI is so sad. As someone interested in control systems and theory, seeing a lot of the discourse turning into talks about AI when there are so many more efficient and interesting solutions to the problem is frustrating. I know what AI is, I know how it works, but the actual implementation of it doesn’t interest me. It’s not a solution to everything and it being treated as such makes me feel bad.

It also gives so many people a terrible perception of what AI is and what it’s all about. The use isn’t to make humans obsolete and the vast majority of use cases go under the radar because they’re *boring*. People don’t talk about how cool computer vision is for potato quality detection or how useful it is to make attribution models for marketing post mortems. Everyone thinks it’s about automating writing and drawing and I’ll never forgive the tech bros for championing those use cases.

It’s a tool meant to solve a certain type of problem. Primarily reverse engineering a stochastic or compound and heavily coupled problem. Please understand that before getting mad at me for learning how to implement AI.

[regina-bithyniae]

[str-ngeloop]

new years resolution 2025: do something they can't control or understand

[springrob]

See, "be ungovernable" takes on many forms.

[coolcarsntrucksngunsnusa]

I worked at a company that didn't have asphalt where we worked out in the loading dock area - just a lot of rock and gravel. This area also went out further to what we called the "north lot" where we had steel pipe. One day I was bored and had a black Sharpie and picked up a smooth, palm-sized rock and wrote a number (don't remember what now). I'd do this during slow times or on break. Some single digit, some in the millions and in-between.

Didn't think anything of it. But people started to notice. Someone would stop and pick up a rock and say, "What the hell?"

One day at an employer/employee meeting, one of the supervisors walked in with one of the owners, and they had a bucket full of numbered rocks. "WHAT THE HELL IS THIS?! IF YOU GUYS HAVE TIME TO DO THIS THEN WE NEED TO GIVE YOU MORE WORK! WHOEVER IS DOING THIS, WE'LL FIND OUT AND YOUR ASS IS FIRED!"

No one knew it was me. I quit doing it because I didn't want guys getting more work due to my fun. Worked there about 10 years, and became a foreman. I got fed up with the owners giving workers more work but no raises, and eventually quit.

The owner begged me to stay because I knew a lot of things and always got jobs done ahead of schedule, but I told him these guys deserved more pay. He said, "These dudes only work hard because you are a good foreman. They used to be lazy asses that walked around numbering rocks, remember?"

I looked him in the eye and asked him if he thought I was a lazy ass. "Well, no! That's why I want you to stay!"

I said, "Ted, there was only one lazy ass writing on those rocks and it was me. Those guys out there have always worked hard and deserve to be treated better. You are a rich man and are that way because your crews do good work and deliver but you're too damned selfish to part with a few more bucks to pay them what they are worth. Goodbye." His jaw was on the floor.

A few weeks later, one of my buddies from the company bumped into me and asked me what I'd said to the owner. I said 'Not much. Why?'

"Dude, he gave us all a big raise and gives us more break times. He even apologized to us at a meeting for how he'd been kinda shitty to us at times."

I was like, 'Well, cool. Glad to hear things are better.'

Sometimes you make a difference when you rebel.

[marklangnee]

I’m doing this because apparently tumblr thinks I’m a bot and isn’t letting me send messages to my girlfriend, so I’ll write a quick piece.

I find it so sad that so many people aren’t learning how the gpu works when programming. Like please sir, you have a full ass processing unit in your machine. Learn how to use it, it’s so much fun!