#row vector

[peeterjoot]

Simplifying the previous adjoint matrix results.

[Click here for a PDF version of this (and the previous) post] We previously found determinant expressions for the matrix elements of the adjoint for 2D and 3D matrices \( M \). However, we can extract additional structure from each of those results. 2D case. Given a matrix expressed in block matrix form in terms of it’s columns \begin{equation}\label{eqn:adjoint:500} M = \begin{bmatrix} \Bm_1 &…

[emiihoney-pots]

aren't these two just the perfect duo in terms of unhinged sprites?

[witchofthesouls]

I wish I had digital art skills because I'm haunted by The Primes' Rooster AU, such as:

The sheer hungry look by Liege Maximo licking up the mess upon Sentinel's thighs and pressing his mouth on the most perplexing valve anyone as come across.

A well-bitten Solus smoking a cigarette in the berth, a contented and well-bedded Megatronus next to her slipping on a nice drink through a straw, and Megatronus is sharing that with a slightly dented Sentinel who's between them and has his own super curly straw to sip the cocktail.

Quintus' labs with the Prime recording the procedures. A serious face in one frame, then a "Oh, someone's (it's Sentinel. He has permission to get inside and Quintus is too deep in Science to realize there's another person there.) messing with my valve. Well, the newsparks do need materials and I can't remember the last time I've eaten."

Alpha Trion and the Cybertronian version of Kama Sutra

Vector Prime distantly watching over others clanging with a glass of wine because of his voyeur kink

Sentinel with his own weapon forged by Solus herself. It's a cross between his canon sword and the Skyboom shield.

Short-king Sentinel with his tall-ass Primes and equally tall-ass teenage/adult children.

Starscream's and Sentinel's dramatic BEEF with each other. Literal cockfighting between these two.

And Rooster!Sentinel in Canon!verse, going "Look at me. I'm your sire/geni now." to Orion and D-16.

On one hand, pre-betrayal discovery is Rooster!Sentinel slinging the Cogless versions of two of his sons/grandsons over his shoulders. On the other hand, post-betrayal discovery is Sentinel versus Sentinel. D-16 won't bow before the false Prime, but he'll lower his face because of the resulting selfcest and the filthy, filthy commentary on Megatronus' (his hero's) sexual preferences. (The High Guard peanut gallery chiming in over Megatronus' getting his back blown by Solus and/or Prima.)

[im-tired1124]

So it’s been a solid 366 days since I last drew a full-body lineup of the castoff cast, and wowee has my art style changed to an unrecognizable extent and also hasn’t changed at all

2/10/24 version for reference

[vanishingmoments]

why are people in my math class acting like i'm the teacher's assistant or something when they put us in study groups

[phoenixiancrystallist]

Month 3, day 18

Working on cleanup for the shirt design! Blocked out the letters with their background shapes and color so all the lines are nice and crisp and go where I want them to 🥰

[beesorcery]

this is a lawless land where the 8 ball somehow feels less insane than whatever the fuck is happening in the rest of the setlist

(p.s. i found columbus lol. still need milwaukee and minneapolis though)

(edit hey chat it’s me again. found milwaukee 👍)

welcome to my new ongoing graphic design project post because the old post was getting a little bit long! i am recreating this t shirt design:

with the 8 ball songs instead of the city names! here is the most recent iteration, updated through 3/15 (orlando):

[haxkattpress]

Our Objective Remains Unchanged by @citrusses

"Harry Potter, returning member of the Oxford University Boat Club, has two goals for the spring of 2005: beat Cambridge, and beat Draco Malfoy. Perhaps not in that order."

This has to be one of the most creative and meticulously researched fics I have ever had the pleasure of reading. If you haven't read it yet, don't walk— run! Citrusses is an absolute genius, and kindly gave me permission to bind her masterpiece.

The cover of this bind is made out four different shades of Allure bookcloth cut by my Cameo 4, and the centerpiece is printed and hand foiled. The banners were machine foiled in gold and black with hand foiled rose gold shading. The endbands were hand sewn with Gutermann silk thread.

You can find more pictures and information about my process under the cut.

The amount of inspiration this fic gave me was overwhelming, and Citrusses' writing fully immersed me in the world of competitive rowing. While designing this bind, I was struck by the sheer wealth of Oxford rowing memorabilia available to me. I settled on this 1929 illustration from an official publication on the Oxford and Cambridge Centenary Boat Race for the cover.

"How hard could it possibly be?" I thought, foolishly. The answer was HARD, but I'll get into that later.

Due to the wealth of design options, I believe that this may be the best typeset I have created to date. Thanks to the help of my friend @tsurashi-bindery, I was able to learn the basics of InDesign (kicking and screaming all the way). There will be spoilers in the text of these photos, so try not to read them if you haven't finished the fic!

For the title page, I modified To See the Crews in Training by Charles Pears (1930). I believe that this was part of a series of advertisements for the race in the London Underground.

For the chapter headers, I redrew the crest from an Oxford Oars, Flags, and Arms postcard, presumably pre 1914. I also had some fun creating a mock email using La_Temperanza's How to Mimic Email Windows on Ao3. Cormac's email makes me laugh every time I read it, and Citrusses provided an appropriately pompous subject.

I also had lots of fun editing the oars from the official OUBC logo to serve as dividers and decorations for the page numbers.

Additionally, I got to edit a full newspaper page for the fic! I was very excited find an opportunity to slip Leyendecker's The Finish (1908) in.

The fic ended beautifully, so I wanted to include one last element at the end to capture the atmosphere. I settled on L'aviron (1932) by Milivoj Uzelac. It makes me feel as though Harry and Draco will continue rowing together long after I've closed the book.

I of course had lots of fun sewing the headbands, and got to do it with not one but TWO copies!

Things got tricky when I had to recreate the cover. I had a poor understanding of how vector images worked, and ended up having to redraw it three times. Once I finally cracked and taught myself how to use Illustrator, the program crashed...and I had to redraw it a fourth time!

I set the vector to cut on my Cameo 4, and I assembled the pieces together like a puzzle on my Silhouette mat. I used Allure's indigo, skylight, white, and black bookcloth in the process. I will be making a tutorial video on this method, so I will keep it brief here.

I also cut a piece of bookcloth to 8.5"x 11" and fed it through my inktank printer to print the center design. I then cut it out using the print and cut feature on my Cameo 4. Both of these methods were a first for me, and they were very scary!!

To be perfectly frank, the foiling was a nightmare and I don't want to get into it. I machine foiled the gold, and then foiled black lettering on top of it. I foiled the rose gold shading by hand, and then foiled a thin black outline along the edge of the banners to make them stand out more.

I hand foiled the spines (because I'm scared of measuring), painted the exposed board (to hide any gaps in the inlays), and used transfer tape to lift my design from the Silhouette mat and onto the cover.

One more fun detail— my copy and the author's copy are sisters! The dark blue and the light blue are inverted on the author's copy, making it distinguishable from mine. This is the first time I have made an author's copy for a fic, and I was admittedly incredibly nervous. I always worry about what authors will think of my work, but Citrusses gave me an incredible amount of encouragement and support throughout the process! Thank you for trusting me with your precious fic!

This story is a work of fanfiction and can be read on Ao3 for free. My bind and typeset are for personal use only and not for sale or profit. Keep fandom free!

[covid-safer-hotties]

Also preserved in our archive

by: Beck Levy

“Maybe now vocalists will finally start bringing their own mics,” I tweeted in the first days of March 2020. My virtual audience was mostly friends I met by participating in subcultures in and adjacent to the DIY tendency of hardcore punk rock. In those early days, we on the cultural fringes shared a sense that the pandemic, in its capacity as a social intervention, could meaningfully disrupt the oppressive ruling order.

When I booked and played shows before COVID-19 hit, I tried to harness energy and rally when crisis arose. Touring band is lost on the road? I was ready to DJ to keep people from leaving between sets. No one came to unlock the club? Let’s play in the parking lot. The last show I’d played, just weeks earlier during Mardi Gras, was on a trailer being pulled by a dump truck. We’re responsive to shifting circumstances, right?

I couldn’t get a clear look at the new terrain through the brutal haze of my first-wave infection. I was disoriented, waking up breathless, fevered, delirious from nightmares about drowning in my own blood. I could not fathom taking any action that would contribute to COVID-19 circulating, and my symptoms made me believe I would be a risk to my community. With home tests scarce, every flare had me conceiving of myself as though I might be a biological weapon.

Friends texted their fears to me frantically: “Is music over? Are shows done?” I thought back to informal and unconventional gigs, the freedom and potentiality those moments held, and reassured my friends, sequestered in our separate biomes. I said and believed: “Music always finds a way, youth culture always finds a way, underground culture always finds a way.”

Slowly, reimagined, remote, and socially-distanced events returned. In lieu of Jazz Fest, New Orleans radio station WWOZ charmed us with “festing in place” on the airwaves. I did a solo set in a virtual anniversary showcase for my old record label. Another friend live streamed a show from a cavernous church. I’d guessed performances mediated by technology might salt the wound, but desperate for connection, I treasured those experiences.

I watched my place in the world creep away from me. There were rumors of scandalous secret shows during lockdown. But the first real sign was pictures on Instagram of people traveling and touring again. Scroll to that last image: a row of COVID-19 tests, all negative, smug. Or positive, chagrined but only a little; a mismatch to the scale of: “For fun I traveled as a disease vector and personally participated in the proliferation of an airborne pathogen that can kill or maim.” Was it a character limit? A limitation of character?

The world passed me by, carouseling through normalization phases, like COVID-19 tests phasing their way out of tour posts. I watched scenes regroup from my new vantage point in biopolitical exile. Pandemic gloom catalyzed a spate of reunions, which is wholesome and beautiful except for the fact that at least one band knowingly toured with a member who tested positive.

Was I overreacting? While COVID-19 left me with an immune system that attacks my body, my mind attacked itself with this question. I’d traded amps for this mental feedback loop. The counterargument was implicit: people need unfettered access to music more than we need safety.

Live music came back. It just didn’t bring me with it.

I didn’t see a critical mass of bookers, venues, or bands advocating for COVID-19 safety with measures like outdoor shows, improved ventilation, livestream options, or just adding tests and masks to the earplug bin at the door. Some hand disinfectant; a little hygiene theater at conventional venues. The will just wasn’t there. I thought our deal was fuck the state, we’ll do it our way. I found myself slipping through the subcultural safety net that exists for outcasts who are slipping through the cracks of mass culture and late capitalism.

Of course, punk was already inaccessible to some. And I actually believe a certain amount of gatekeeping is necessary to protect punk from posers, jerks, and cops. But among the nebulous community clustered around shows, the sexism and racism people have experienced has always been very real, to the tune of entire zines, books, films about that exclusion. I monitored my heartbreak, critically. Resource-scarce, informal, and underground operations often exist at a quagmire of conflicting access needs. Was the sting of betrayal just this painful because it affected me, directly? Can the subaltern mosh?

There was a brief period where my baseline had plateaued, and I enjoyed medium-functionality between flares. Clinging to my modest recovery, a memorial service was my first congregant risk. That was the last time I tried to play guitar. I got the twisties, psychic vertigo from grief and from the contradiction of my setting and my experience, but the band played on, complete with a brass section. And at that otherwise beautiful event, I was ceremoniously reinfected by an asymptomatic tuba player. My health has been steadily deteriorating ever since.

Isolation is hard: it can feel like rejection, it can feel real personal. I struggled to adapt. I know I can have a persecution complex, but I also know I’m materially being made surplus. So what do I tell the complex? Are people being thoughtless, or do they explicitly not give a fuck about immunocompromised people like me?

Life is never totally safe, danger is often exciting, sometimes risk is the point. I know that. I’m not (just) a joyless scold. In the era of potentially deadly airborne pathogens, we’re playing with other lives when we make “individual” health decisions—I thought we’d learned that, but there was no such reckoning.

Punks accepted the sociological production of the end of the pandemic, moving in lockstep with the state, sacrificing medically vulnerable people on the altar of pleasure, just as the state had sacrificed us on the altar of capital. I thought our ingenuity would create new forms of shows. Instead, it exposed our limits under duress. To quote the band Allergic to Bullshit, “If this is what we’re for, this is what we’ll get.”

Maybe my shock seems naïve—after all, there’s a difference between “subculture” and “counterculture”—but there’s a reason I expected better. There are visionaries with love, passion, and fearlessness who organize shows in strip malls, caves, skateparks, churches, parking garages; shows with immediacy like distributing free Narcan, and conviction, like benefits toward Palestinian liberation. I await, with diminishing faith, the eruption of that tendency in the bioethical arena.

Since immune ableism is hegemonic, congregating is a question of building a realistic threat model, making decisions with people who are directly impacted by your actions, and taking all possible precautions. I’m encouraged by radical formations with accessibility modifications, particularly those connecting social abandonment, climate crisis, and genocide. I see this reflected in art book fairs that require masking, outdoor Shabbatot, test-first leftist reading groups. Queer and drag events are making adjustments. Mask blocs and clean air clubs collaborate, with limited resources, to make spaces more accessible. These are people who insist on collective health, demanding freedom to live and breathe clean air.

For those of us with severe Long COVID, exclusion from live music represents a profound loss of humanity. This disconnection feeds into my daily despair; in medical terms, my depersonalization/derealization. Having hoped this crisis would push us closer to communism than complacency, I feel whiplash, what Naomi Klein calls “political vertigo.” Millions of Americans with Long COVID have disappeared from the workforce. Data on the underground music scene are unavailable. It’s hard to count ghosts. I’ve wanted to ask: Have you noticed that some of us are gone? Do you ever miss us?

Four years later, I still can’t even make it to a well-filtered show. My last recreational outing ended in hospitalization from merely ascending a steep hill. I hear about shows from my roommate, the only person I see, who is also the only masked person at them. I tell myself I could try to go to an outdoor gig one day, maybe, if my governing health planets aligned. Instead of being an active musician, I pretend I’m like Jandek, a reclusive genius, but really I’m too clumsy and unfocused to play at home.

I do what I do with everything: act like I’m in a different world. It’s not difficult, because I am. The Well do their thing out there, I do mine in here. I moved across the country in search of better healthcare and, homebound, routinely forget I’m not still in New Orleans. Either way I am inside. I gave up and I don’t fight the world leaving me behind. I am back here, rolling the boulder of my body up steep hills.

In spite of everything, I’m glad shows continue. It’s bittersweet comfort knowing freaks are getting raucous in basements, with noise made by other freaks, sprayed with wet yells, aggressively jostling with teens; in a reprieve from control, experiencing music together. I’d die for your right to do that. And thanks to you, I just might.

[darlingyougotthis]

Gravity

Jake “Hangman” Seresin Fanfic

Chapter Two: The Storm Beneath

The morning sun burned through the hangar’s glass, striping the concrete with long shadows. Inside, the Top Gun squad filed into the briefing room, most still shaking off sleep with half-finished coffees and lazy banter.

Jake strolled in last, sunglasses perched low on his nose, the familiar cocky tilt in his step. He looked as he always did—golden, loose, in control.

But he didn’t feel like it.

Because she was already there.

Nova sat in the second row, legs crossed, flight suit zipped to her collarbone. Her Strike Six patch—dark, understated, deadly—rested over her heart. She didn’t speak. She didn’t need to. The guys weren’t even trying to hide it anymore—the sideways glances, the hushed murmurs.

Jake didn’t look at her.

Not right away.

He took a seat across the aisle, a few rows back, and told himself he wasn’t keeping her in his peripheral vision. That his attention wasn’t already bending toward her like gravity.

But it was. She looked composed. Polished. Effortless. She didn’t scan the room. Didn’t try to place herself. She already knew where she stood.

Like nothing from last night lingered—not the dart game, not the way she’d shut down that “ghost squad” comment with a single line, not the way she’d looked at him when she said goodnight.

That look still echoed somewhere in his chest.

Phoenix dropped into the seat beside her, nudging her lightly. “Morning, Ghost Girl.”

Nova huffed a quiet laugh. “You still calling me that?”

“I don’t see you denying it.”

Rooster leaned toward Coyote behind them. “Think she’s as lethal as her badge looks?”

Coyote muttered, “Think she could kill you with her flight helmet.”

Jake didn’t speak, but he was listening. He tapped his boot lightly against the floor, jaw tight.

Then the room shifted—straightened—as Admiral Beau “Cyclone” Simpson entered with his usual no-nonsense scowl. Behind him came Maverick, flight suit half-zipped and eyes scanning the room like he already knew everything they didn’t.

“All right,” the commander called out, pulling up the screen behind him. “Hope you’re all feeling sharp this morning, because we’re diving straight into classified scenario prep.”

A chorus of “Yes, sir.” can be heard from around the room as Cyclone explains the perimeters of their training.

“What you’re about to see hasn’t been flown before. It’s a prototype extraction op, low-visibility, multi-vector. You’ll be running it in sim, then in air. We’re assigning pairs. These rotations will stick for now.”

He tapped a button. Names appeared on the screen. Jake’s stomach tightened when he read his.

Seresin – Brooke.

He blinked. Brooke. Nova.

One beat of silence passed before he let out a low breath. Phoenix smirked beside Nova. “Lucky boy,” she muttered.

“Pairing decisions weren’t random,” Cyclone went on. “Brooke’s experience with Strike Six makes her a critical asset in scenario building. She has logged over 1,200 hours in black zone operations, has confirmed three air-to-air kills during classified missions, and holds the record for the lowest successful terrain-hugging exfiltration on file. She’ll be leading some of the tactical phases.”

Heads turned toward Nova, someone—Rooster, probably—let out a low whistle. She didn’t react. But, Jake did. He couldn’t help it—the way his brow ticked up, the way his focus narrowed on her profile. Tactical lead? That wasn’t casual. That was trust.

Maverick launched into mission parameters, the room adjusting around the sharp angles of strategy and simulated risk. But Jake was only half-listening.

He was watching Nova.

She sat straight, eyes forward, fingers loosely laced on the desk. When Maverick threw out a question—“What’s the fastest vertical split response in a blind canyon at high-altitude entry?”—Nova didn’t pause.

“Two-point-six,” she said. “Three, if you’re flying with deadweight.”

A low whistle came from Coyote.

Mav gave a short nod. “Correct.”

Jake leaned back in his chair, arms crossed. He was impressed. Too impressed. Maybe that was the problem.

This wasn’t some pretty blonde with a mysterious past and a good aim at the dartboard. This was someone who didn’t just deserve to be here—she could fly circles around half the room. Maybe including him.

“Gear up. Wheels up in 30.” Maverick dismissed them as the briefing wrapped up, chairs scraped and conversations sparked. Rooster clapped Coyote lightly on the shoulder as they passed, muttering something like “Damn, she really is a ghost.”

Coyote rolled his eyes. “Told you.”

Jake stood slower than the rest. He told himself he wasn’t waiting for her to look at him.

He told himself wrong.

She rose gracefully, gathering nothing—she hadn’t even brought a pen. She didn’t need to. That brain of hers probably held more classified knowledge than half the intel office.

And then, just as she passed him, she glanced sideways. Their eyes met. No smile. No word. Just that look. Like she saw right through him.

Then she was gone, boots tapping steadily out of the room like she wasn’t leaving a trail of tension in her wake. Jake let out a slow breath, dragged a hand through his hair, and muttered under it— “Shit.”

The locker room was quiet, filled with the rustle of gear bags and the low creak of hinges as Phoenix pulled her locker open. Nova leaned against the bench, zipping up the top half of her flight suit, blond waves falling down over one shoulder. She looked calm. Almost serene.

She was still new here. But it didn’t feel like it.

Not to Phoenix.

“You really don’t rattle, do you?” Phoenix asked, tossing Nova a water bottle from the top shelf. “Not last night. Not this morning. Not even when Cyclone dropped your kill count like a mic.”

Nova caught the bottle one-handed and smirked. “Why waste energy?”

Phoenix rolled her eyes, grinning. “I swear, Strike Six must teach emotional detachment with flight mechanics.”

Nova chuckled, soft and low. “It’s more like… perspective.”

Before Phoenix could reply, the door opened behind them.

Tiffany stepped inside.

Her heels clicked against the tile, and even out of uniform she looked like she’d walked off a magazine cover—sleek hair, perfect blouse, clipboard clutched in one manicured hand.

“Didn’t realize this was an open meeting,” Phoenix muttered under her breath.

Nova said nothing, just tightened the strap on her gear bag and focused on tucking in the edge of her sleeve.

Tiffany smiled. Wide. Pleasant. Deadly. Eyes landing on Nova.

“Just thought I’d drop by and check on the pilot side of things. Big flight coming up. Heard you’ve been paired with Jake.”

Nova glanced over, expression unreadable. “That’s what the board said.”

“Interesting choice,” Tiffany said, head tilting slightly. “They usually don’t shuffle partners unless there’s… potential.”

Phoenix turned fully now, one brow arched. “I’m sorry, are you implying something?”

Tiffany didn’t even blink. “Of course not. I’m just surprised how quickly things move around here.”

Nova finally looked at her then—calm, open. No edge, no bite.

“I’m just here to do my job.”

Tiffany’s smile tightened. “Naturally. Though it’s a little jarring, I guess… how someone can show up one day and have everyone talking.”

Nova didn’t respond. She didn’t need to.

She just swung her bag over one shoulder, smooth and practiced, then offered Tiffany a gentle nod. “Nice to meet you, by the way. Officially. Professionally.”

Tiffany blinked. “Right. Yes. You too.”

She extended her hand.

Nova took it without hesitation—firm, respectful, brief.

Tiffany’s grip lingered half a second longer than necessary. “I hope your time here is… productive.”

Nova’s smile didn’t quite reach her eyes. “So do I.”

With that, Tiffany turned on her heel and walked out—head high, hips swaying, and a tension in her jaw that didn’t match her parting grace.

The door clicked softly shut. Phoenix let out a breath.

“I don’t know what Jake sees in her,” she muttered.

Nova, still facing her locker, didn’t look up. “That’s not really my business.”

Phoenix scoffed. “She doesn’t like you.”

This time Nova did look at her and shrugged.

“Yeah,” she said simply. “I noticed.”

She grabbed her gloves from the bench and tucked them under her arm, not a trace of bitterness in her voice. Just fact. As if it meant nothing at all.

Phoenix studied her for a moment, then nodded slowly. “You’re kind of a badass, you know that?”

Nova gave a faint smile. “You’re late to that conclusion.”

Laughing, Phoenix followed her out of the locker room, boots hitting the tile in sync. Together, they headed for the sims—two women, side by side, walking into fire without ever needing armor.

The tarmac shimmered under the late afternoon sun, the heat rippling off steel wings and freshly laid jet fuel. Jake “Hangman” Seresin adjusted his gloves out of habit, attention flicking toward the runway.

Then he heard her.

Boots on pavement. Confident, steady, unhurried.

Nova.

Helmet under one arm, Strike Six patch gleaming over her heart, eyes hidden behind aviators that somehow made her even harder to read. She walked past him like he wasn’t even there—but her words landed with precision.

“Try to keep up, Hangman,” she said casually.

Jake’s grin came slow, easy, and way too honest.

“If you’re setting the pace,” he replied, eyes following her, “I won’t complain.”

She didn’t stop. Didn’t look back. But he noticed the subtle rise of her shoulders, the slight pause in her step—just enough to let him know she’d heard it. Then she was climbing into her jet, silent and composed.

Jake shook his head, laughing under his breath. This wasn’t going to be a routine flight. Engines ignited moments later, rumbling under the weight of two high-performance birds preparing to punch through the sky.

Jake launched first, Nova tight behind him. Separate jets. Shared objective. Shared frequency.

“Hangman, airborne.”

“Nova, on your six.”

Her voice crackled into his headset—low, precise, unreadable.

Jake checked his radar, watching her icon slide effortlessly into formation behind him.

“Targets ahead,” he said. “You want high or low?”

“Split left. I’ve got upper sightlines.”

He didn’t hesitate. Jake banked hard into the turn, Nova slipping above him like they were two pieces of the same machine. Her movement was clean. Automatic. Every minor shift predicted the air before it changed.

Strike Six. Ghost team, sure—but her instincts were all too real.

“Ping at nine o’clock,” she called out. “Cut wide. You’ll ride through clean.”

Jake adjusted without hesitation. She wasn’t giving suggestions—she was anticipating and she was right again.

“Sharp eyes,” he murmured.

“Comes with the ghosts,” she replied. He could almost hear the shrug.

Jake exhaled a tight laugh. “Remind me to get one of those Strike Six manuals.”

“There isn’t one,” she said simply. “You either get it… or you don’t.”

They flew tighter. Cleaner. Every shift in position felt choreographed, but it wasn’t. It was trust. Immediate. Natural.

Nova called another move. “Thrust down two percent. You’re drifting.”

Jake followed without thinking. A beat later, she added, “Clean correction. Didn’t think you’d actually listen.”

“Only when it counts.”

“You mean when I’m right?” she teased—just enough to twist the knife.

Jake smirked. “You’re not wrong.”

There was a pause in the comms—brief. But not empty.

Then Nova spoke again, voice softer now. “You don’t fly like the rumors.”

Jake arched a brow. “That a compliment?”

“Take it however helps you sleep.”

They dropped low into canyon terrain—tight ridges, red rock shadows, and simulated fire zones. Jake cut between walls like he’d done a hundred times before. Nova was right with him. No errors. No corrections. Just harmony.

Then came the final run. Target acquisition.

“Visual on the mark,” Nova said. “You ready?”

“Always.”

“Then let’s finish this.”

He aligned, locked in, and struck clean.

Nova confirmed it a second later. “Target hit. Smooth shot.”

Jake pulled up into open sky, adrenaline still humming.

“Hell of a run,” he said. “You always this easy to fly with?”

“Only when they can keep up.”

Her tone was still even. But something in it curled beneath his skin like a spark.

Minutes later, both jets touched down—Jake first, Nova gliding in behind.

He powered down his jet, lifted his helmet, and slid out onto the ladder. The heat hit again. So did the buzz still crawling down his spine.

She joined him near the tarmac, helmet still tucked against her hip, eyes calm.

“Nice flying,” she said, meeting his gaze.

And then, with just the faintest smile:

“Jake.”

It hit harder than it should have.

Not Hangman.

Just Jake.

Before he could reply, she turned and walked away—like she hadn’t just unbalanced his entire axis with two syllables and a smile.

Jake didn’t follow. He just stood there, watching her go and thinking, she’s dangerous.

The debrief room buzzed low with chatter, but Jake barely registered it. His gaze was locked on the footage playing across the screen—silent, stunning, undeniable.

Nova’s jet carved through the sky like she owned it. Every move was instinct. Every pivot, every shift, every call—it was all just ahead of where it needed to be. Not rushed. Not guessed. She wasn��t reacting. She was reading the sky.

“Look at that,” Rooster muttered beside him, chin propped in his hand. “She’s already banking before the radar even picks up the threat.”

Jake didn’t respond. His jaw ticked once, eyes locked on the way Nova’s jet sliced low through the canyon like she knew exactly where the danger would be.

“Damn,” Rooster said. “That’s not flying. That’s something else.”

“She flies like she’s dancing,” he said quietly, the words slipping out before he could catch them.

Rooster tilted his head. “That’s either poetic or horny, and I honestly can’t tell which.”

Jake’s mouth twitched. “She’s precise. I’ve never seen anyone fly like that.”

Nova’s voice crackled over the recorded comms. “Cut thrust two percent. You’re drifting.”

Jake watched his own response—fluid, immediate. He hadn’t questioned her in the moment. Just followed. Trusted.

He hadn’t done that with anyone else. Not like that.

“She doesn’t hesitate,” Jake murmured. “She just knows.”

Rooster leaned back in his chair. “It’s hot.”

Jake didn’t respond at first. Then - quietly, almost as if he wasn’t aware he said it. “Yeah…”

Rooster glanced at him, brow raised. Jake didn’t look away from the screen.

Rooster added, more softly this time, “Careful, man. That kind of attention’s hard to hide.”

Jake’s mouth twitched. Not quite a smile.

“It’s just flying,” he said.

But he said it too fast. Too flat. And his jaw clenched a beat too long. Rooster didn’t call him out on it. He just looked back at the screen. At the woman carving through simulated death zones like she was painting in the air.

“Sure it is,” Rooster murmured.

Jake didn’t reply. He didn’t have to because somewhere between her voice in his headset and the way she said his name after they landed, he knew damn well— It wasn’t just flying.

[mathematical-cheese]

Yeah I did wonder that as I was writing it. Honestly it's more of a reason to trick people into learning a bit about homology than to actually answer the question so I didn't worry too much about it in the end

I will be honest, I haven't actually learnt the embedded S¹ thing yet (which would certainly have made things easier)

Why Straws Have One Hole: An Introduction to Homology Part 2

In this post I'll discuss simplicial complexes and how we can use them to make our test for holes simpler and motivate the definitions for simplicial homology! The post is more technical but I have tried to motivate each step.

Simplicial Complexes:

A common theme in topology is to build up our spaces from smaller, simpler spaces. One way of doing this is to use simplices! These are generalisations of triangles to all dimensions:

Image is taken from here

An n-simplex has n+1 verticies and is denoted by its vertices in square brackets: <e₀,...,eₙ>. A simplicial complex is made by gluing simplices together such that the intersection of two simplices is also a simplex that is included in the complex. We also require that any n vertices can define at most one n-simplex in the complex. If some vertices e₀,...,eₙ in a simplicial complex, K, define an n-simplex <e₀,...,eₙ> that is in K, we call <e₀,...,eₙ> an n-face of K.

An example of a simplicial complex is a square where each vertex of the square is a 0 simplex and each edge is a 1-simplex. If instead we considered a solid square, we wouldn't automatically get a simplicial complex because the 2 dimensional part isn't made up of 2-simplices. We fix this by adding an addition 1-simplex bewteen one pair of diagonal points which gives us a simplical complex with four vertices, five 1-simplices and two 2-simplices:

We can construct a great number of spaces using simplices! This construction is only up to homeomorphism but that's all we care about! A simplicial complex that is homeomorphic to a space is called a triangulation of that space. Importantly we can triangulate a straw:

This is the simplest triangulation because having fewer simplices would lead to us having different simplices described by the same vertices.

Simplicial Homology

So why do we care about triangulations? The key here is to notice that the boundary of an n-simplex is a simplicial complex made up of (n-1)-simplices. For example, the boundary of a 2-simplex is a simplicial complex made of three 1-simplices. The idea is to modify our test to only involve simplices because then we only have to check finitely many things! This is where things start to get a bit more technical but I will try my best to motivate each step!

Firstly, we need to introduce a convention in the way we describe simplices. We pick an order for the vertices in our complex to be listed, e.g. for the triangulation of the straw we could pick the order a,b,c,d,e,f. Then any time we write a simplex we must list the vertices in that order. For example, with the order above, <a,b,d> is how we describe the left most 2-simplex. The reason we need this is we are about to start thinking about simplices in a more abstract way and we need a systematic way of writing them.

Now for arguably the weirdest (but most powerful) step. We want a way to talk about the boundary of a simlicial complex as one object and we want a way to say when a particular simplicial complex has no boundary. The motivation for this is we want to talk find the analogue of a loop that we can use to test for holes, that is we want a one dimensional object that doesn't have a boundary. Since we eventually want to count things, it might be prudent to somehow assign numbers to things. As mentioned above, the boundary of an n-simplex can be thought of as the union of (n-1)-simplices and unions of sets are kind of similar to a kind of sum. The idea is to talk about "sums" of simplices. It doesn't really make sense to add simplices but we can sort of just fudge it. This fudging is known as "formal sums" and this is when we say "okay, we don't know what a sum of these things actually is but we study it anyway".

We say the elements of X generate these formal sums.

We then consider the set Cₙ(K) of all the formal sums of n-simplices in a simplicial complex K and we call it the nth simplicial chain group of K and we call elements of Cₙ(K) n-chains. We say that the rank of Cₙ(K) is the number of elements of X. Note that the sum or difference of two chains is again a chain.

The rank of C₂(K) is 1 and the rank of C₁(K) and of C₀(K) is 3.

We can now also give meaning to a simplex that is written in a different order to our chosen order. Given an ordered list of vertices, we can swap two elements around to get a different ordered list. If n is the number of swaps it takes to get an ordered list of vertices into our chosen order, we say that the simplex with vertices written in a different order is equal to the element of Cₙ(K) given by (-1)ⁿ times the simplex with the vertices written in our chosen order.

Now we want to figure out how to represent the boundary as a map from Cₙ(K) to Cₙ₋₁(K) since the boundary of an n-simplex is made up of (n-1)-simplices.

The full representation of this map is a bit detailed so I will stick to the case when n is less than or equal to 2 since that's all we need. The definition of this boundary map only depends on what it does to the simplices because it comes from considering their boundaries. So we will say that the boundary map applied to a formal sum is just the formal sum of the map applied to each simplex, for example

where ∂ is denotes the boundary map. So we just need to define ∂ on simplices.

To motivate the definition, we consider a 2-simplex <x,y,z> with the order x,y,z. Starting at x, we can think of the boundary as a loop that goes from x to y, then from y to z then from z back to x:

So we could represent the boundary as the formal sum <x,y>+<y,z>+<z,x>. Then written in our chosen order, the boundary is <x,y>+<y,z>-<x,z>. That is ∂(<x,y,z>)=<y,z>-<x,z>+<x,y>. In the first term, we remove the first vertex, in the second term we remove the second vertex and multiply by -1, and in the third term we remove the third vertex and multiply by -1 twice. So it would seem sensible to that the pattern here is the nth term in the boundary of a k-simplex is the simplex where the nth vertex is removed and we mutlipy by (-1)ⁿ⁻¹.

So the boundary of a 1-simplex <x,y> is <y>-<x>. But the boundary of a 0-simplex is always 0 since 0-simplices are just points and have no boundary!

We also have that the boundary of the boundary of a 2-simplex is 0. This makes intuitive sense since the boundary itself has no points at the edge of it but we can show this still works in our abstraction to formal sums:

Now we have two special types of formal sums: those that have no boundary and those that are the boundary of something else. We call an n-chain that has no boundary an n-cycle and we call an n-chain that is the boundary of an (n+1)-chain an n-boundary. We can extend the first above argument to show that boundaries are always cycles, i.e. the boundary of a boundary is always 0. 1-cycles are what replace loops in our earlier test, that is we want to find 1-cycles that aren't 1-boundaries! An obvious yet important example of a boundary is 0, 0 is the boundary of 0 (we'll use this fact later). Two other important facts are the sum of n-cycles is also an n-cycle and the sum of n-boundaries is also an n-boundary. If c and c' are both cycles, then ∂(c+c')=∂c+∂c'=0+0=0 and if c=∂b anf c'=∂b', then c+c'=∂b+∂b'=∂(b+b').

Let's take a step back to summarise what we have so far. We have found a test for holes in a space but it didn't really allow for easy calculation of the number of holes in a space. So we restricted our view to simple spaces and have found a way of abstractly representing the building blocks of those spaces. This abstraction has allowed us to reframe our test for holes into a purely algebraic question!

But how can we be sure this test still works? Let's consider a circle. Using our first test, we can just take a loop around the circle. Then this loops isn't the boundary of anything since it bounds a disc of the same radius but this disc isn't part of the circle. So the circle has a hole. Now we triangulate the circle using three vertices and 3 edges, i.e. a triangle. If we label the vertices as <x>, <y> and <z> we already know an example of a cycle: <y,z>-<x,z>+<x,y>. Even though this calculation was done for a 2-simplex, it only involves the 1-simplices so it is valid in this situation too! But in this case, we don't have any 2-simplices in our space so this cycle can't be the boundary of anything! Conversely, suppose we get a positive result using our simplicial hole test, i.e. we've found a cycle that isn't the boundary of anything. Then we can construct a loop in the space using this cycle and this loop wouldn't be the boundary of anything so the first test would also be positive!

The final step that actually lets us count things is to define the homology groups! What we want to do is find cycles that aren't boundaries. Algebraically, we do this by considering cycles to be "the same" if their difference is a boundary. That is, we say two n-cycles c and c' are homologous if there is some (n+1)-chain b such that c-c'=∂b. We have that all n-boundaries are homologous to each other. Say both c and c' are n-boundaries and that b and b' are (n+1)-chains such that c=∂b and c'=∂b', then c-c'=∂b-∂b'=∂(b-b'). The since b and b' are (n+1)-chains, b-b' is an (n+1)-chain so c and c' are indeed homologous. In particular, 0 is a boundary so every boundary is homologous to 0. So now suppose that c is a cycle that is homologous to 0, then there exists an (n+1)-chain b such that c-0=∂b. So c=∂b and hence c is also an n-boundary. This means that a cycle is a boundary if and only if it is homologous to 0. So now if we want to find cycles which aren't boundaries, we look for cycles which aren't homologous to 0.

We define the homology class of a cycle c to be the set of all the cycles which are homologous to c and we denote it [c]. For example, the homology class of 0, [0], is the set of all boundaries! We can also define a notion of addition of homology classes: [c]+[c']=[c+c']. That is, the sum of two homology classes of two cycles is the homology class of their sum. We call the set of all homology classes of a cycles of a simplicial complex K, the (first) homology group of K and write H₁(K). If H₁(K) only has one element, i.e. H₁(K)={[0]} every cycle must be a boundary and K would have no holes. But if K has a hole, H₁(K) would have more than one element.

We are actually now quite close to being able to count the number of holes a space has! Let's come back to the example of a circle. Intuitively, a circle has 1 hole and we've already seen that we have one cycle which isn't a boundary: <y,z>-<x,z>+<x,y>. But by the way we defined the boundary, we also have that

for any integer n. So for any non-zero integer n, we can find a cycle that is not a boundary. In particular, if m doesn't equal n, then n(<y,z>-<x,z>+<x,y>) is not homologous to m(<y,z>-<x,z>+<x,y>) since their difference is (n-m)(<y,z>-<x,z>+<x,y>) which is not a boundary unless n-m=0, which is not the case here since n doesn't equal m. Moreover, I claim that any cycle in a circle must be of this form. Remember, this cycle represents the loop going around the triangulation of the circle once. The only way we can get loops in the circle are obtained by going around the circle a whole number of times (where going in the opposite direction gives us a "negative" loop). Any other path you try to take will end up with not having the same start and end point and so would have a boundary! So there is a homology class of the circle for each integer. Moreover, adding these cycles represents going around a loop n+m times so adding the homology classes together is somehow the same as the regular addition we know for the integers! In formal terms, we say that H₁(circle) is isomorphic to the integers. Like how homeomorphism is the notion of "the same" for topologists, isomorphism is the notion of "the same" for algebrists! The important part of this is that all of the homology classes can be expressed as an integer multiple of [<y,z>-<x,z>+<x,y>] just like how an integer can be thought of as an integer multiple of the number 1. In this sense, we say that [<y,z>-<x,z>+<x,y>] generates H₁(circle), i.e. H₁(circle) has 1 generator. This cycle came about as a loop around the hole in the circle so it is sensible to guess that the number of generators corresponds to the number of holes!* This is how we will go about showing that a straw has 1 hole in the next part! That is, we shall figure out what the first homology group of a straw is and find out how many generators it has!

*technically, we actually count the free generators of H₁ since the torsion elements represent something else but it won't matter for what we're doing. Alternatively, we could have defined homology over a field to get vector spaces which naturally don't have any torsion but this doesn't feel quite as natural as doing homology with integral coefficients.

[bumblekastclips]

Happy Throwing Him Thursday!

KYLE CROUSE: Next question is from @rabbithaver. “In 2018, you wrote IDW Sonic #14, which contained panels of Silver being thrown by the ankle by Metal Sonic. On May 19, 2022, tumblr user @catgirlkirigiri posted those panels with the caption, 'Happy Throwing Him Thursday.' Now, every Thursday, Sonic Tumblr celebrates by partaking in throwing Silver. Each week, participants render their followers' dashboards unusable by reblogging those panels dozens of times in a row. People have drawn fan art. There are multiple videos of people throwing their Silver plushies, including one of him being hurled off a five story balcony. In celebration of the two year anniversary of the first Throwing Him Thursday, would you both please rank Sonic characters based on how far you think you, personally, could throw them?” [TRANSCRIBER’S NOTE: The balcony mentioned was seven stories, not five, which is much funnier.]

IAN FLYNN: [in exaggerated horror] Two years?! KYLE: [laughing] IAN: My poor boy has been yeeted for two years?! KYLE: He’s getting yeeted! He’s getting yeeted like crazy! IAN: I feel bad! KYLE: [laughs] IAN: I’m glad folks are enjoying themselves, but… what have I done to the poor boy? KYLE: [still laughing] Ah, well, I mean, the fandom got a— the fandom got attached to it. To be fair, you know. You did it once. [chuckles] IAN: And really, the credit should go to Tracy Yardley and the other artists for rendering it, but hm… KYLE: True, true. [chuckling] IAN: Half-tempted to sneak in a panel somewhere. [as Sonic] “Happy Thursday, Silver!” [as Silver, panicked as he’s being reminded of his trauma] “WHY?!” KYLE: [erupts into laughter, then as Silver] “What is this?!” [laughs] Man, if you made a reference to Throwing Him Thursday, I think the— I think there’s a lot of Tumblr people who would melt down. In a— you know, in a good way. IAN: [chuckling to himself] Shadow just puts him off a— puts him out a window. [as Shadow] “Huh, is it Thursday already?” KYLE: [laughing] Oh, man… IAN: Anyway, characters that we could throw on a Thursday — or any day, really. KYLE: Any day. I could throw— I could throw— I could take Charmy. [chuckles] IAN: Yeah, Charmy, Cheese… KYLE: But then I’d have to contend with not being able to throw Vector and Espio as they murder me. [laughs] IAN: [chuckles, then as Vector] “Nice arm there, Kyle! Wanna see how [unintelligible] it is?” KYLE: [laughs] Oh! IAN: And I imagine Cream, but only because she wants to, like, take off, so she’s already got her ears ready, and you’re like, out in an open field, and it’s like throwing a kite into the air or something. She’s having a grand time, just, “whee!” KYLE: Yeah, she can fly. [chuckles] IAN: Uh… how heavy is Tails, actually? KYLE: Eh, I don’t think Tails is very, uh, heavy, and he’d fly, so… you know IAN: I’m gonna look this up real quick. KYLE: You could throw Froggy a little bit— [stuttering unintelligibly] a little bit far. You know. IAN: [as Big] “Once.” KYLE: Once. [laughs] IAN: Huh! Actually Tails is like, over forty pounds! KYLE: Okay, he’s a… IAN: That’s not really a throw, that’s more of a heft. KYLE: He’s a beefy— he’s a beefy boy then, huh? Wow. [chuckles, then reading chat] I’m being told that Ray was born to be yeeted. [laughs] IAN: [chuckles] You know that’s what he and Mighty do all the time. KYLE: Of course! IAN: It’s kinda like— it’s like with Cream! KYLE: Yeah. Yeah, yeah, yeah. IAN: [as Mighty] “Ready, little guy?” [as Ray] “Ready!” Woosh! KYLE: Yeah, pretty much, exactly. IAN: How much does Orbot weigh? KYLE: He’s pretty small, but he’s also a robot, so who knows how dense he is? Uh… IAN: If he even has an official weight… [Googling] Uh, he is— holy crap, he’s over sixty pounds! KYLE: Yeah, I was gonna say, he’s probably real dense. He’s got a lot in him. [chuckles] IAN: [sigh] I could probably pick him up and hmph, but yeah, I ain’t throwin’ that. Goodness. KYLE: The irony is that you’d think Cubot would be the dense one! IAN: [chuckles] Well, now I’m curious, if Orbot is sixty-six point one pounds… KYLE: He would be one really heavy bowling ball, at least. [laughs] IAN: Self-steering, no less. KYLE: Yeah! IAN: [Googling] Oh, wow. Cubot’s, uh, almost eighty-six pounds. KYLE: Oh! He’s dense— he’s even more dense! IAN: He’s a hefty boy! KYLE: [laughs] IAN: So, yeah.

KYLE: Nice. [chuckles] Yes. Ah, yes. [reading chat] Cubot, the honorable— or, Orbot, the honorable Whipple. IAN: [snickers] KYLE: Welcome to the Whipple family. [chuckling] I don’t know if we could really throw any of them? I mean, sure, a giant mech could throw Jewel, as we’ve established previously, but I don’t know if I could. She’s pretty— she’s pretty big for a bug. IAN: Yeah, I… she might need to be hefted, not really thrown. KYLE: Yeah, yeah. You could throw a chao. IAN: Yeah. KYLE: You can throw Marine, maybe. IAN: Well, now I’m curious, uh… Charmy’s like twenty-two pounds. KYLE: Why is he so freakin’ huge? He’s a bee! [laughs] IAN: And I would imagine Jewel’s at least that weight, so… KYLE: Y-yeah…? [stuttering] How heavy are pounds on Sonic’s world?! IAN: [laughs] I mean, you could still maybe throw Charmy, but you’d have to put your back into it. You’d have to, like, limber up first. KYLE: Yeah! IAN: And just because we brought it up, you know, the idea is Cream’s just kinda using this as an excuse to be thrown, but— [Googling] she’s twenty-six pounds. She’s barely heavier than Charmy. What in the world? KYLE: [chuckling] What? What?! IAN: But yeah, I could definitely pick her up over my head and kinda, fwoop, and then she’d flap and she’d fly, and she’d have a fun time. KYLE: Yeah, yeah… yeah, yeah, I think they’re all a bit too heavy. It’s that— it’s that dang Beach Ball Head Syndrome they got going on. [chuckles] Those giant heads, you know?

EPISODE THUMBNAIL by @kiimeranova (lines) and @nintendoni-art (colors)! Exclusive Throwing Him Thursday Variant HERE!

—— TRANSCRIBER’S NOTE: Please remember that nothing that is said on BumbleKast is canon! It’s just some guys and their opinions occasionally spitballing ideas. If you don’t like an answer, you don’t have to take it as Word of God or anything like that. It’s all just for fun!

[plague-karm]

Hit horror YouTuber @pastraspec dropped another character bingo template and I think I don’t have to remake one of these ever again since this is pretty well rounded (these aren’t in order except for the top row btw I like these guys for a lot of different reasons :3)

Here’s the original template btw, since it’s blank I might do an album version at some point too lmao

Here’s the character list (god help me)

Kuromi (Sanrio)

Homura Akemi (Madoka Magica)

Phosphophyllite (Land Of The Lustrous)

Shadow The Hedgehog (Sonic)

Marceline (Adventure Time)

Mark Corrigan (Peep Show)

Sisyphus (Ultrakill)

NiGHTS (NiGHTS Into Dreams)

Petey Piranha (Mario)

Rosalina (Mario)

Will McKenzie (Peep Show)

Gabriel (Ultrakill)

Brad Armstrong (Lisa The Painful)

Stocking Anarchy (Panty & Stocking With Garterbelt)

Red Guy (Don’t Hug Me I’m Scared)

Ford Pines (Gravity Falls)

Stanley Pines (Gravity Falls)

Minos (Ultrakill)

Guzma (Pokemon)

My Melody (Sanrio)

Max (Sam & Max)

King Dedede (Kirby)

Spamton (Deltarune)

Tricky (Madness Combat)

Ame Chan (Needy Girl Overdose/Needy Streamer Overload)

Surge The Tenrec (Sonic)

Lloromannic (Sanrio)

Twyla Boogeyman (Monster High)

Draculaura (Monster High)

Donatello (Rise Of The Teenage Mutant Ninja Turtles)

Ryoma Hoshi (Danganronpa)

Aoi Mukou (Totono/You And Me And Her)

Zooble (The Amazing Digital Circus)

Gangle (The Amazing Digital Circus)

Bob Velseb (Spooky Month)

Daisy (Mario)

Kirby (Kirby)

Meta Knight (Kirby)

Leatherface/Bubba Sawyer (The Texas Chainsaw Massacre)

Wallace Wells (Scott Pilgrim)

Bowser (Mario)

Teto Kasane (Utauloid)

Jinx (Arcane)

Madotsuki (Yume Nikki)

Ibuki Mioda (Danganronpa)

Ashley (Warioware)

Ruby Gloom (Ruby Gloom)

Seve (Corn Kidz 64)

Frank Columbo (Columbo)

Thomas Wake (The Lighthouse)

Marcy Wu (Amphibia)

Luz Noceda (The Owl House)

Bee (Bee And Puppycat)

Diane Nguyen (Bojack Horseman)

Phillip Wittebane/Emperor Belos (The Owl House)

Elphaba Thropp (Wicked)

Professor Venomous (OK KO)

Cthulhu (The Call Of Cthulhu)

Mello (Death Note)

SeeU (Vocaloid)

Rem (Death Note)

Gomez & Morticia Addams (The Addams Family)

Serena (MTV Downtown)

Murdoc Niccals (Gorillaz)

Mami Tomoe (Madoka Magica)

Duck (Don’t Hug Me I’m Scared)

Knuckles The Echidna (Sonic)

Salvatore Moreau (Resident Evil Village)

The Beldam/The Other Mother (Coraline)

Withered Chica (Five Nights At Freddy’s)

Nancy Downs (The Craft)

Ramona Flowers (Scott Pilgrim)

Victoria “Tori” Spring (Heartstopper)

Gonzo (The Muppets)

Frankenstein’s Monster (Frankenstein)

Kinger (The Amazing Digital Circus)

Lord Shen (Kung Fu Panda)

Veronica Sawyer (Heathers)

Dante (Devil May Cry)

Charlie Dompler (Smiling Friends)

Bayonetta (Bayonetta)

Springtrap (Five Nights At Freddy’s)

Crowley (Good Omens)

Cinnamoroll (Sanrio)

Madoka Kaname (Madoka Magica)

Kyoko Sakura (Madoka Magica)

Sayaka Miki (Madoka Magica)

Stephanie (Moral Orel)

Hobie Brown/Spider Punk (Across The Spiderverse)

Jack Skellington (The Nightmare Before Christmas)

Emily (Corpse Bride)

Utena Tenjou (Revolutionary Girl Utena)

Sonya (Kill Me Baby)

Sailor Saturn/Hotaru Tomoe (Sailor Moon)

Soul Evans (Soul Eater)

Peppino Spaghetti (Pizza Tower)

Winfrey (Dreams Of An Insomniac)

Celestia Ludenberg (Danganronpa)

Miu Iruma (Danganronpa)

Death (Puss In Boots: The Last Wish)

Cyn (Murder Drones)

Tabitha (Craig Of The Creek)

Vector The Crocodile (Sonic)

Giroro (Keroro Gunso/Sgt. Frog)

Warwick (League Of Legends)

Choptop (The Texas Chainsaw Massacre 2)

Frankie Stein (Monster High)

Reala (NiGHTS Into Dreams)

Eve (No Straight Roads)

Dr Coyle (ARMS)

Loly Rabbit (I have no clue where she originates from I keep on getting different results each time 😭)

Super Taruco (Nitro +)

Sebastian Solace (Pressure)

Riamu Yumemi (IDOLM@STER)

Gengar (Pokemon)

Gloomy Bear (Mori Chack)

Honey The Cat (Sonic)

A.B.A (Guilty Gear)

Himiko Toga (My Hero Academia)

Octavia Goetia (Helluva Boss)

Breadhead (The Gaslight District)

[deatherella]

Deatherella Does DOTY - Rd 3

A new mid-century oval hairpin leg desk. It's a one-tile desk made from the tabletop from another conversion I did and the hairpin legs are from an awesims conversion by @shastakiss. The legs are steel as they were in the 70's. Lots of formica tops and atomic style formica textures for it, too. My entry was a 1970's based mid century modern travel agency. On the wall is a 4to2 conversion of blacky's Magazine Holder. I made it have two subsets. And, you can see one of the recolors I did of @hcove 's S3t2 MidCentury Dining Chair. I made recolors of the chair in the Pushing Daisies pallette.

Tons of recolors for the Bon Voyage travel poster. Travel posters using places in all Sims games (google search) with some from Vector Stock that I made Sims themed. And a recolor for Mog's shop sign mesh.

A 3to2 conversion of enable_llama's Curve Kitchen. The counters are actually end tables since the originals had no countertops. The left and right curved ends are repo'd to the base couter. There are cabinets, with the curved ends repo'd to the center one. I made a shelf using Mutske's Expedit's Add-Ons' shelf mesh. If you look in the prev showing recolors, you'll see I tweaked the shelf mesh to be the same hieght as the cabinets and took out the divider wood in the middle since the bottom shelf has only one slot. The cabinets, counters, and shelf come in AL woods, and polar formica (found an actual mid-century formica to use) in Pushing Daisies pallette colors, and the original color and recolor. You can, also, see on the edge of the prev, recolors for @thecrimsonsparkles' Simple Magazine Shelf that I edited to have two subsets. I made some add-ons to a cup I converted in the past - three cups and five cups in a row repo'd to the original single cup. They have some travel orientated recolors. There are brochures laying on the desks and table I made using menu meshes by @nekosayuri. from their signs set.

AL woods recolors of curiousB's Awesims Mid Centruy endtables conversion. All necessary meshes included, swatches and previews, too. Download Round 3 Goodies Download Polar Formica textures for your own use.

[positively-knotted]

Some Basic Combinatorics Via Not-So-Basic Topology

Proposition. Let P(r; n,k) be the number of partitions of an integer r into n non-negative integers less than or equal to k. Then P(r; n,k) = P(r; k,n).

This is very easy to see with Young diagrams (count columns vs rows). It's also very difficult to see with topology, but that's more fun. This is probably going to be a bit long, but I think the pay-off is worth it.

The standard construction of (real) projective space Pⁿ is to call it the space of 1-dimensional subspaces of Rⁿ⁺¹. This generalises pretty naturally to the "Grassmann manifold" Gr(n; n+k) of n-dimensional subspaces of Rⁿ⁺ᵏ, so Pⁿ = Gr(1; n+1). Hopefully you believe that Gr(n; n+k) is still a compact nk-manifold. If you want, it's also the quotient O(n+k)/O(n) x O(k).

As well as being a manifold, this is naturally a CW complex. Let's think about how. For each point in Gr(n; n+k) (that is, n-dimensional subspace), it has a unique orthonormal basis where the final non-zero coordinate of each basis vector is positive (easy linalg exercise). Taking this basis, we let d_1,...,d_n be the the "dimension" of the basis vectors (i.e. the position of their final non-zero coordinate, so that (-1,2,0) is 2-"dimensional"). We can assume these are strictly increasing by permuting them. Thus, to each point in Gr(n; n+k), we are associating a unique list of n increasing integers between 1 and n+k.

Let e(d_1,...,d_n) be the subset of Gr(n; n+k) which give those integers. This is actually an open disc of dimension Σ(d_i-i)! Why? To choose the first basis vector, we can pick any unit vector in the upper half-space of dimension d_1. That is, we have a choice in the hemisphere=disc of dimension d_1-1. To choose the ith, we have a choice in a hemisphere=disc of dimension d_i-1, but we have to be orthogonal to the i-1 vectors we have already chosen, giving a choice in a disc of dimension d_i-i. A product of discs is a disc, and we're done!

Checking that this is actually a CW decomposition is kinda tricky, but also unenlightening, it just is true. So let's count how many cells of each dimension it has. An r-cell corresponds to a choice of partition r = Σ(d_i-i), where 1 ≤ d_1 < ... < d_n ≤ n+k. Equivalently, it is a choice of partition r = Σe-i, with 0 ≤ e_1 ≤ ... ≤ e_n ≤ k, by setting e_i = d_i-i. So the number of r-cells is exactly P(r; n,k)!

We're getting close! The final observation is this. Choosing a n-dimensional subspace is equivalent to choosing its orthogonal complement. That is, the map V → V^⊥ is a natural diffeomorphism between Gr(n; n+k) and Gr(k; n+k), and also a CW-isomorphism. (True because everything is naturally defined; slightly tedious to check.) In particular, it has to match up the number of r-cells, so P(r; n,k) = P(r; k,n)! No Young diagrams necessary.

I think this is kinda neat. It's also weird because these Grassmann manifolds completely classify vector bundles on compact manifolds and are how you define characteristic classes, so secretly under all of that differential topology there's really hard partition problems going on.

[dixonsdarkelf]

Finding Myself, Finding You: Chapter One

Main masterlist Series masterlist AO3 link Wattpad link

Story is 18+ for mature content/themes, minors do not interact please

TW/CWs for this story--implied/referenced past rape, canonical violence, non-canonical violence, blood, gore, referenced past suicide, swearing, surgery, excessive drinking, nightmares, vomiting, amputation, medical procedures, non-con medical procedures, referenced past medical torture, referenced past drugging, attempted SA, panic attacks, mental health struggles, referenced sibling death, referenced parent death

Each chapter will have its own TW/CWs listed

This story, Lydia Vector, her family & bestie (c) me, dixonsdarkelf

TWD & its characters (c) AMC & Robert Kirkman, the writer of the comic series

TW/CWs for this chapter--blood, violence, amputation, swearing

“Lydia Rae Vector, Board-Certified in Trauma Surgery!”

The grin that spread across my face caused my cheeks to ache. I looked out and saw my parents and brothers, who fought like hell for their front-row seats to witness their only daughter and sister receive her certification. This was the moment I had worked my entire life for.

My residency was complete. And my boards had been passed. I was officially a surgeon.

The “waterproof” mascara I had spent my last $20 on ran and flaked into my eye, causing it to water more. I take my certificate from the officiator, shake his hand, and look out to the audience once again.

And I see him. Every single time, I see him.

A man stumbling down the center aisle, appearing drunk and disorderly, but he’s covered in blood, and his skin is bluish-grey. Decomposition has clearly already started. That was evident by both the open wounds on his body and the putrid stench that accompanied him. And the rest always happens the exact same way.

The crowd notices him, and slowly, the entire auditorium falls silent. Security starts to come around from the emergency exits, but before they can get to him, the man has made his way to the front row.

And he attacks my mother.

Her screams, the screams of my father and brothers, the screams of the audience and the screams coming from my own throat haunt me. He rips her vocal cords out with one swift bite, and her screams cease as quickly as they began.

And this is always where my nightmare ends.

I wake up in a cold sweat, nothing unusual there. I throw myself upwards, letting out a small yelp and feeling all over myself with my hands, checking for wounds and blood. My mornings went exactly the same way.

Every. single. time.

The small shed I had spent the night in looked even dustier during the day. I used my hands to prop myself up off of the floor and and pulled my backpack, which was my pillow every night, out from behind me. Scooting slightly to my left to get out of the blinding sun coming in through the window, I unzipped it and went through the checklist that I always do, making sure every weapon I had was still in its place.

“Axe, knife, guns, spear,” I said out loud, pulling one of the small guns and the collapsible spear out and setting them on the ground next to me. Checking that the safety was still on for both guns, I checked for my other items. Nothing had ever been stolen from me in the night, but you couldn’t be too careful.

“Journal, water bottle, clothes, food, tools, gauze, lighter, bandages, disinfectant, sewing kit, pills, and my most unique weapon.” Once everything was accounted for, I took the blanket I had been using and folded it as best as I could, stuffing it in on top of everything. I slipped my water bottle out and took the smallest sip, just enough to get rid of my cotton mouth and dry throat. I slipped the gun I left on the floor into the strap on my leg and extended my spear, getting up off of the ground and dusting myself off.

I paused for a moment and listened to the birds chirping outside. I wonder what they were saying to each other, I thought to myself. They seem happy. Of course they did. They don’t have to live through the end of the world in the same way humans do.

My reveling in listening to bird calls was quickly interrupted by the sound of a scream. A human scream. And Walker groans.

I swung my backpack onto my shoulders and jumped to the corner next to the door. I lifted my head slowly, just enough for my eyes to enter the window frame.

There was a man, probably around my age, on the ground, and three Walkers surrounding him. I could see that he had lost his knife in the scuffle, and I imagine he was hesitant to use a gun because he didn’t want to attract more of the reanimated corpses. I readied my spear, took a deep breath, and kicked the door open in one fell swoop.

“Aye motherfuckers!” I yelled, drawing the attention of all three Walkers towards me. I skipped backwards, away from the man, putting a little more distance between myself & the undead. I swung my spear and stabbed the closest one right between the eyes, pulling it out and watching the heap fall to the ground. The other two went down similarly. I paused for a moment, perking up my ears and listening to make sure no others were coming.

Once it was clear, I ran to the man. He was still on the ground, groaning in pain. That’s when I saw the bite on his ankle. My heart sank. But I knew what I needed to do. I ran and kneeled down next to him.

“Hey, what’s your name man?” I said to him, trying to keep my voice as calm as possible. I saw a small glimmer of hope in his eyes.

“A-A-Aaron,” he said, gritting his teeth through the pain.

“Alright Aaron, my name is Vector. I’m a doctor, and I can save you, but we gotta get you inside that shed right there. Can you sit up?” He nodded and used his arms to pull himself into a sitting position. I got up on my feet and put an arm around his back, under his arms.

“Alright Aaron, let’s get you on your feet,” I told him, and I saw him nod out of the corner of my eye. He put his body weight onto his right foot & onto me, and we slowly stood up together. Thankfully, the shed was right by us. I got him through the door and helped him back down onto the floor. Once he was on his back, I moved like lightning to get out my small axe, disinfectant, lighter, bandages, gauze, and two of my shirts, one with long sleeves and a small one.

“Aaron, you probably know where this is going, but I’m going to have to cut your foot off. And then I’m going to cauterize your wound so it hopefully won’t get infected,” I said between inhales, taking the my smaller shirt and tying it into a knot to form a gag. We couldn’t have him attracting any more Walkers. “I need you to take this and bite down as hard as you can. Can you do that for me?”

“Yes…” Aaron said. I saw a couple of tears leave his eyes. He put the knotted shirt into his mouth, laying his head back onto the dirty floor. I poured a small amount of disinfectant onto my axe and onto his leg, just above the bite mark. Some of the disinfectant ran into the wound, and he writhed in pain.

“Alright.” I looked over at him, meeting his eyes, “I need you to stay completely still. Bite down as hard as you possibly can. You got this my man.” He squeezed his eyes shut. I raised the axe up, lining it up with where I was going to make my mark.

“I’m so sorry Aaron,” I whispered, swinging the axe down as hard as I could. Thankfully, his foot and ankle came off with one hit. His blood sprayed across the shed, getting onto the walls and all over both of us.

Despite the muffling of the shirt, his screaming was loud. The tears were flowing. And so was the blood. I grabbed my lighter with my right hand and grabbed Aaron’s hand with my left one, squeezing it to remind him he wasn’t alone.

“I’m going to cauterize it next. This pain is probably going to be worse, but I know you can do this. Just keep breathing through your nose and squeeze my hand when you need to,” I told him. He didn’t nod or acknowledge what I said in any way, but I had to keep moving to stop the bleeding. I flicked on my lighter and held it to his open wound, gliding it back and forth across the whole area. I did this for a couple of minutes to ensure the whole area had been cauterized. For Aaron, I’m sure it felt like hours. He squeezed my hand so hard that I was sure he was going to break it. His muffled screams were the only sound I heard.

“You’re doing great bud,” I spoke softly, “I have padding and gauze that I’m going to put onto it next, then I’m going to wrap it in one of my shirts. Keep biting onto that one for as long as you need.” This time, he opened his eyes, which were bright red from crying, and nodded. I took a couple of pads and pressed them to his leg, holding them in place while I started the gauze wrapping.

“I’m sorry I don’t have an ice pack or anything to help with the burning,” I said. He spat my shirt onto the ground and let out a small chuckle.

“Sorry? You just saved my life.” I took my long-sleeved plaid button-up and wrapped his leg in it, using the sleeves to tie it around his calf. He was still hyperventilating a little.

“Just rest for right now,” I instructed, “once you’re doing a little better, I’ll help you get back to your home base.” He tried to pull himself up to a sitting position, but I lightly pressed on his shoulders to let him know to lay back down, “Stay like that. Just focus on your breathing. I have some water, and I have food if you’re hungry.”

“What did you say your name was?” he asked me. I pulled my water bottle, which was about half-full, out of my bag.

“Vector,” I repeated. I scooted over to him and helped him lift his head enough to sip some water without choking on it. I took my knotted shirt and unknotted it, giving to him to wipe the tears and water off of his face. He rotated his head and looked up at me.

“Vector, why did you help me?” he asked, “you could’ve just killed me, saved your resources. Or taken my stuff and ran.” I squeezed his shoulder reassuringly.

“I took an oath,” I explained, “I’m a doctor. This is what I do.”

“How can I—“ a cough stopped him mid-sentence, “repay you? I can get you food, water, supplies. I have a community. Just say the word and whatever you want is yours.” I leaned back and grabbed my spear, which I had dropped on the way in, and collapsed it fully, rolling back and forth on the floor between my hands.

“Honestly, I could just use directions to a certain place, I must be close to it by now. I’m looking for a safe zone, it’s called—“

“Alexandria.”

I cocked my head at him, my words catching in my mouth and my facial expression displaying my shock. “How did you know that?”

“It’s the only one around here. We’re only a couple miles out” he laughed. Despite my protests earlier, he used his upper body to pull himself up into a sitting position, leaning back against some boxes, “I’m actually from there. I’m a recruiter. I go out with my partner Eric, and we search for survivors, like yourself, and see who would make useful additions to our community. And hell, we could definitely use you.”

I couldn’t believe my luck.

“I’ve been looking for Alexandria for months.”

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