#olver quick

[yesimwriting]

Match Burns

A/n saltburn rewired a part of my brain

also my original idea was way too long for a one-shot so now i'm splitting it into 2 (maybe 3?) parts, if you'd be interested in that pls lmk lol

Summary: Despite your charm and kind disposition, Oliver has never been able to let himself be fond of you. Not with the way that Felix gravitates to you and your obliviousness to the attention. When you're invited to join him and Felix at Saltburn, his wariness of you morphs into an oddly suffocating dislike, until he realizes how to turn you into a way to get 'in' with Felix.

Pairing(s): eventual felix x reader x oliver, current oliver x felix (unreciprocated) and felix x reader (unreciprocated)

Warnings: potential typos (i'm tired yall), first time writing characters so potentially ooc?, canon-level toxic thoughts/plotting, some canon deviation (felix is alive and well to me and it's staying that way), oliver lowkey hating reader,, but kind of in the grown up version of a kid pulling another kid's pigtails when they have a crush lmao

----

The qualities that make the others adore you, that leave them with no choice but to treat you as some kind of dorm hall trapped princess, are the parts of you that make it difficult for Oliver to tolerate you.

You may not be the heir of some great fortune, the kind of commodity that can only be created through generations of pristine breeding and a lifetime of wealth that comes attached to that kind of pedigree. But you do have something.

His peers may see your self sacrificing nature in the ear you're always willing to lend or the time you're willing to give away without a second thought as instinctual kindness. But Oliver knows how to look beyond careful facades, the stained glass people use to warp the way they're perceived. He knows that your too sweet smiles and soft eyes are just your forms of social currency.

And the most off putting part of it all? The only person that can get away with pretending to not notice the way people react to you, is you.

Sometimes, when his thoughts drift to you without his permission, Oliver convinces himself that it's impossible for anyone to not see your softheartedness as the compensation that it is. And then someone--Felix, says something that is so transparently devoted, Oliver knows that it's worked. Give people what they want, and eventually you'll ensnare them.

Oliver let himself believe that he was finally reaching the peak of Felix's favor after being invited to spend the summer at his family's estate. Then, two days into his stay, Felix informed him that you'd be joining them at the end of the week.

The thought of you and your sense of humor that always seems to toe the line between witty and sarcastic; and the warm feel of your hand on his, or anyone's, arm, because when you listen you do so with your entire body; and your bright eyes that seem to see through everything but yourself, at Saltburn seemed to take something from this away from him. You didn't even need a sob story or to flash an indicator of something in desperate need of repair to get invited.

You were just you, and that was enough.

The way Felix told him only strengthened his chargin. She's friends with you, isn't she? I've seen you two together at the library.

The two of you. Not something that Oliver chose. You appeared one day at his side, on a too warm day for late November in Oxford. A too crowded library had the universe dropping you onto his lap. He accepted your presence because of the way the world seemed to light up for those around you.

But now there are no crowds of admirers to divide the attention. There is only Felix and his family, and with just two guests being invited to spend the summer, it'd be easy for the ultra wealthy to turn this into a competition for favorite pet.

It's also more than that. Alone here, it was easy to pretend Felix's attachment to you didn't exist. But now--now he could easily be the second favorite out of a set of two.

----

There was only one part of your arrival that Oliver was looking forward to, and you stole it from him.

He wanted to witness a crack, a wavering in your assuredness. The size of the estate would get to you, would make you--for once--seem small. You'd hesitate, maybe even see Felix in a different way that'd have you rethinking your friendship.

Your eyes had widened, a combination of shock and awe meshing together behind your gaze. Oliver could feel it, the moment that you'd reveal yourself as susceptible to shrinking in on yourself...and then your eyes met his, and the look vanished before it could fully take root.

You grinned at him and then at Felix, abandoning your luggage next to the car that picked you up before approaching them with unashamed enthusiasm. You pulled each of them into a quick hug, your warmth an ache against him. You didn't attempt to suppress your joy until Duncan appeared, standoffish as ever as Felix introduced you. That was just enough satisfaction to make Oliver want it more.

He's still thinking about it now, imagining just what it'd take to leave you vulnerable. You don't sense the resentful nature of his thoughts. You never do. Not even when Felix tells you that you'll be staying in the room connected to his through a shared bathroom.

Felix suggests giving you some time to rest before dinner. You accept the offer, tired from the back forth traveling from the UK to the US. Your visit to your mother had been so brief, you accepted Felix's offer so quickly. Maybe there's more tension in your family than you've admitted.

"She likes you a lot." Felix's low tone snaps Oliver out of his thoughts. It's a strangely nervous statement that doesn't make sense. You're friends with both of them, and if Felix means the statement in the romantic sense, he's wrong. Oliver's in the habit of taking note of the way people see him, and he can't remember instance in which you've ever looked at him like that.

He could see you feeling that way about Felix easily. You're around Felix often and while there is an underlying hint of stiffness when you're around him, it isn't a sign of dislike. You're determined to like him less, you're dedicated to not loving him. An amicable, but ultimately pointless goal. Who doesn't end up loving Felix?

Oliver doesn't know where this conversation is going, so he decides to keep his response simple. "She likes you, too."

"N--" Felix starts to deny the point, but realizes a full dismissal wouldn't be true. You do like him, it's just--it's different. "She trusts you." Felix shakes his head once, still uncertain. "I know we're friends, but sometimes, especially when we're alone, it-it feels like she sees me as a match that's starting burn too close to her fingers."

There it is. Oliver can't blame you for your precautions. Felix has turned the heads so many women--and some men--and he allows them to hang around him openly. His desirability, his options have never been secret. And your only overlap into his world is going to the same college. Oliver's even heard of you deciding to spend the night alone instead of with Felix because you don't always feel safe at those kinds of parties.

You're playing it safe, like a very good girl from suburbia, USA. It's your way of surviving, but Oliver can't quite respect the choice. You're smart enough to realize that loving Felix is like playing with matches, but you're not strong enough to realize that the proximity would be worth a few burns.

"I know we're a little different, but I don't want her to think I'd ever make her do anything." The obliviousness in Felix thinking that this is just about social circles is endearing in an odd way. "How'd you two get so close, anyway?"

Oliver isn't sure so close is the right way to phrase things. Sure, you're attentive and a little touchy, but that's just how people like you move through the world. Besides, if anything, Oliver thinks you choose his company so often because he's never given you the kind of desperate attention everyone else gives you.

Oliver forces a smile, pushing against the thought of being the one to bridge the gap between the two of you. It twists at his stomach. "What? Are you asking me for girl advice?"

Felix cracks a grin, playfully nudging Oliver with his shoulder. "You know how I meant it."

The words are light, but still another attempt at getting a concrete answer. There's an edge there that Oliver's familiar with, an implication of a feeling he's gotten used to. That chest tightening, what's so special about them? And now the Felix Catton is viewing him in that light.

Personal emotions aside, this--you--could be more useful than Oliver thought.

[agaypanic]

Headcanons meeting Oliver Quick and Felix's little second sister catton!reader

Oliver Quick Meeting Felix Catton's Little Sister Headcanons

Masterlist

Request Something!

A/N: i have no idea if felix or venetia is the oldest sibling, so i made the birth order venetia, felix, reader. reader is a freshman at oxford. im american and although ive been to europe a few times, i dont know much about english terminology and such. kinda short compared to my other headcanons since it’s just meeting headcanons

***

He didn’t really think much of you at first

Mainly because he didn’t know who you were

Or, more specifically, who you were related to

You shared a freshman class at Oxford

“Hi, is this seat taken?” Oliver’s focus was pulled from meticulously setting out his supplies for class when he heard your voice. He looked up at you, a bit guarded, but relaxed slightly when he realized you couldn’t cause any harm. 

“No…” He murmured, looking around the classroom. He realized that the seats were completely filled, except for the one that was right next to him. “No, you can have it.”

You let out a small noise of appreciation, setting your bag on the desk and settling into the seat. Oliver figured that would be the end of it, and went back to preparing for the lecture that was about to start.

But then your hand came into view, waiting for him to grasp.

“I’m Y/n.” You said cheerfully. Definitely too cheerfully for an eight am class. 

“Oliver.” The boy responded, shaking your hand. He noted it was soft and delicate. 

“Nice to meet you, Oliver.”

Then Oliver’s sights latched onto Felix

He set the foundation by letting the rich boy borrow his bike, completely unaware of the fact that Olver was the one to pop his tire

Then he went to a pub with Michael Gavey, where he knew that Felix would be

When Felix called him over, Oliver was surprised to see you sitting next to Felix, his arm draped over the back of your chair

“Ollie!” Felix grinned, a bit buzzed as he looked up at his timid friend. He couldn’t help but notice that his gaze kept flitting over to you every few seconds. “Sit, sit, sit!”

“Ollie?” You repeated the nickname, turning away from your conversation with Annabelle so you could see who Felix had been making friends with. These days, it was like all you heard was ‘Ollie this’ and ‘Ollie that,’ yet you had never seen him.

It turns out you’d been sitting next to Felix’s new best friend for the past couple of weeks without even knowing it.

“Hi, Y/n.” Oliver waved a bit shyly at you and sat down in the free seat on the other side of Felix.

“You know each other?” Felix asked, head going back and forth between the two of you. 

“Yeah, he’s in one of my classes.” You answered, tilting your head as you looked at Oliver fondly. “I never would’ve guessed that your Ollie was my Oliver.”

“Small world,” Felix added with a laugh.

Oliver couldn’t help but squirm at the unintentional possessiveness. Felix’s Ollie. Your Oliver. He liked the sound of it, although he was much more fond of being possessive himself than possessed.

“So, how do you two know each other?” Oliver asked, feeling the judging stares at everyone around the large table except for you and Felix. From across, there was a scoff.

“They’re brother and sister, genius.” Farleigh chided, taking a drag from his cigarette.

Siblings? Oliver thought, his eyebrows raising. Everyone thought it must have been in embarrassment, not knowing you your best friend’s sister was. Especially when they were so popular.

But no. In reality, Oliver was altering his scheme a bit. Maybe he was able to kill two birds with one stone. Have the handsome Felix Catton and his little sister.

[alaffy]

Only Murders in the Building, Ep. 4x06 - Escape from the Planet Klongo (spoilers)

Congratulations to those who figured out the murderer, or one of the murders. I had seen some guesses.  It will be interesting to see the explanation, especially with that twist at the end.

Just a quick recap.  The Trio go to Glen’s hospital room in order to try and wake him up.  They are also kind of bigots (well, Mabel isn’t, but the other two…good lord).  The nurse isn’t impressed.  But Mabel is able to convince the nurse to call Mabel if Glen wakes up.  

One of the, ahem, so-called gifts for Glen is a case of beer that Sazz gave to Oliver the night she died.  I can’t be the only one who would have immediately checked the case for clues, right?

Anyway, they run into one of the stuntmen from the bar.  They find out that Glen was not Sazz’s protégé, but the person Sazz called in when the protégé screwed up on the movie set.  However, the only people who know who this person was is Sazz, Glen, and Ron Howard.  So, yes, Sazz and Glen were the intended targets.  

Anyway, the trio pretend to be extras in order to get onto the movie Ron is directing (with Oliver thinking Ron would remember him from decades ago when they shared a meal at a certain restaurant).  Mabel, however, leaves because she gets a call that Glen is awake and wants to speak with her about the protégé.  

Glen is then killed by the murderer, because the nurse had called Glen’s emergency contact number.  It was Sazz’s number and so the murderer knew he was awake.  Charles and Olver get into a huge argument (that’s a good subplot about Charles realizing that he’s afraid of Oliver drifting out of his life now that he’s getting married.  It has a nice moment, but….).  Anyway, they go to a restaurant.  Rod Howard goes to the same place and recognizes Oliver.  He tells them what happened on the film set.

Meanwhile, Mabel is being hounded by the Script Writer.  He’s hoping Mabel will help him with the script as, according to the Producer, the scripts keep getting worse and worse (the Producer even telling Mabel that she doesn’t even see the script she fell in love with anymore).  Mabel agrees to help, but she also decides to get a beer.  And guess who’s case she happened to take with her?

Ron shows Oliver and Charles a picture of the Stunt Man, as he has pictures of everyone he’s ever banned from set.  And, sure enough, it’s the Script Writer.  At the same time, Mabel finds the original script for the movie.

Which leads to an interesting revelation.  And, of course, all of this will be confirmed next episode, I’m guessing.  So, the Script Writer is not a failed Stuntmen seeking revenge (he only took the Stuntman gig because he wanted to hand his script to Ron Howard).  He also isn’t the original writer of the movie script; Sazz is.  

And it makes sense.  It explains why Sazz knew about the movie before it was announced and who was working on it.  Also, earlier in the season, it was mentioned that Sazz was retiring from the Stuntman business and that she had something lined up (her park, yes, but this also could be what she was referring to).  It also explains why Sazz, when referring to Winney and the notes, kept using the term “plot holes.”  

They also said she was trying to get away from someone who kept taking from her.  My guess is she blamed herself for the accident on set and was trying to help him become successful as a script writer.  Perhaps even going so far to write the script for him.  But something happens and she realizes he’s using her.  And what she wanted was to tell The Producer and Charles the truth about the script and so he killed her.  And the reason he killed Glen is because Glen recognized him as someone who was close to Sazz.

Except…

The Script Writer has to have an accomplice (he still wouldn’t have had time to kill and clean up) and I have a feeling it might be one (or both) of the Brothers sisters.  We do see one of them with the exact same type of shoe print that was left in Dudenoff’s apartment. However, when it was revealed that they didn’t know Dudenoff was dead (because it seemed like Sazz and Dudenoff were killed by the same person), they ceased being suspects.

But given Dudenoff’s history of collecting lost souls, it is realistic to assume that they had visited his apartment before and maybe had even lived in one of those many empty apartments.  Furthermore, it would also explain how they got into Dudenoff’s apartment and how anyone knew about the working incinerator.    

The question is, though, why would they be willing to help the Script Writer commit murder?

[nightskylonging]

Lord of Chaos notes:

Taim's vibes are horrendous. Everyone knows this. I forgot just how bad they were.

Aiel vs. wetlands humor - I thought Rand's joke was funny, at least.

Mat is remarkably good with Olver!

Ishamael was a theologian? For what theology? (This is one of the difficult points of WOT for me. The lack of religion is very unrealistic.)

Alanna. Well. Other people have written better breakdowns of this so I'll just say that it's awful.

So does Herid Fel imply that the Drilling of the Bore kicked off the Third Age? As though in retrospect that's where they reckoned the timeline from?

Rand is absolutely going through it. I wish he would be a little kinder to himself. I know that he won't.

I have a between-reading sessions note here on Galad. I'm not necessarily a Galad hater - I think he provides a very interesting sort of perspective, and seeing how he interacts with the world is interesting. Also, his family situation is so incredibly messed up. Where were his parental figures. (Tigraine left, Tarangail does not seem to have been great, Morgase in her narration doesn't seem to consider him hers - good grief.)

I completely forgot the Egwene and Gawyn stuff. It's... meh.

I'll accept Rand's List being some sort of Compulsion thing.

I don't think Rand realizes he talks to LTT out loud.

Elayne's thoughts on bonding Rand are... iffy. This is something I've noted about most Warder bonds. So. Make of that what you will.

I think there is potential for some kind of Aiel floor time meme. (I also think Rand would benefit from floor time.)

Aes Sedai healing stray cats. Wasn't one of Liandrin's crew in Tarabon known for that?

I am. Concerned. About Aram.

Just to tally some stuff real quick: Rand mutters to Lews Therin, laughs for no reason (this has been a stress response of his for a while), has very changeable moods (at least partially the PTSD), and Perrin notes that he doesn't blink enough (I'd almost say hypervigilance). He would appear to be a few doves short of a coop, and this isn't even as bad as it gets.

Demira Eriff is so real for getting the same six dresses made over and over again for years.

Tylin. Ew.

The description of everything in the Grand Hall in the chapter The Mirror of Mists is so vivid. I love it.

New favorite obscure character: Mahiro.

Rand is dissociating again.

Everyone knows Mat is Olver's bad influence, but to be fair, it was Nalesean who let him be a horse jockey.

Oh. I forgot that Sevanna was creepy about Rand too. (Can everyone just leave him alone?)

Dumai's Wells was so much worse than I remembered.

I had less notes for this book. Most of that is because we're well into the long haul here, another is I'm trying not to post the same complaints for every book. Still don't like most of the romances. I'm excited for A Crown of Swords, I seem to remember that being a good one! (Dreading Mat in Ebou Dar, though.)

[luckhissoul]

they're both looking at him. in the sort of way that tells him that they're expecting an answer. had he ever thought of staying in one place all the time? without moving. stagnant. light, if he was going to do that then he would've stayed back in the bloody two rivers! but the question was a little different, wasn't it? not just standing still. but pulling themselves out of the mess that their lives had turned into. light, but imagine that a day of peace. he spent a good deal of his time out on the road, moving quick with the band. always on the lookout to see if there was a threat, if there was something or someone after them, always stumbling into some battle or another.

had he ever imagined a day of peace? well, who hadn't? but they weren't ever going to be giving that. all this running, all this fighting it was pushing them towards the last bloody battle. and they had no choice. but the way rand asks it sounds almost hopeful. like staying here is a card on the table and all they had to do was turn it over. turn it over and see if they had gotten the right hand. he looks over at olver, who gives him something of a questioning smile. burn it all, but he is waiting on him to say yes. he couldn't blame the kid. he had lost his home, his family. but mat wasn't here to give that back to him. he had just taken him in because he had been on his own. with a breath he moves to rest back in his chair. "who hasn't?" he asks with a small shrug of his shoulders. "but we've have you running off to save someone in less than a week." he adds with a laugh.

He almost expected Mat to respond with amusement, he almost thought that he would laugh and leave it where it was. Because that was a bloody crazy idea, wasn't it? How could they stay here? Rand was the Dragon and staying in Far Madding, a place where Saidin was further from him than it had ever been since Dumai's Wells, could be dangerous. He knew that much. He needed to be out in the world. He needed to find those people willing to throw down their bonds and oaths and bring them into the Army of the Light. That would be the ending that they all needed but was it the one that he needed? That was a terribly selfish thought and he tried to swallow it down but it still persistently nagged at the back of his head.

"Stay." He answered with a small nod of his head, his eyes watching the board before them. It felt like he was playing this game with himself, with the entire world. He was near buckling underneath the weight of it. He finally lifted his gaze to look at Mat and then nodded his head. "Have you ever…well, have you ever thought of it?" He questioned with a light furrow of his brows as he reached out, in spite of Olver's groan, and took up one of the stones to toy with it between his fingers. He looked to Olver who seemed to be scooting nearer to the table and looked up at the two of them with increased interest in what they were saying. "Have either of you thought of it?" Because he had and the feeling was heavy to carry.

[markantonys]

thom: i think mat’s really growing up.

mat: [running into the room with olver] come quick! we need an adult!

[tothedevilsshowclosed]

it’s a strange place. different customs that he’s trying his best to keep up with. there’s rooms here where men aren’t bloody allowed! after his time in ebou dar he had been pretty sure that he had seen every flamin’ thing. but this place was something else. but if there was one redeeming thing about the whole place was that no one could channel in the city walls. no asha’man or bloody aes sedai could use the source. thing like that should make him feel a little more at ease being here. but it hardly didn’t. especially not between rand, who was deep within himself, a little lost. and olver, who wandered too much. he said he didn’t like sitting still. the kid wasn’t even nine years old. and he acted like the world was his for the bloody taking. rand wanted to go looking again. olver wanted to play snakes and foxes. so he’s amusing the kid. watching rand from the corner of his eye. getting his coat on. he had mentioned hunting down the last three of the asha’man. men who had taken it upon themselves to try their hand at killing the bloody dragon reborn. all it had done instead was spark rumor, ruin a perfectly good palace, and send rand on this path. he knew little about said path. it was rocky, too long, and blood and ashes, he would rather be anywhere but on it. he had said as much about a dozen times. but nothing had dissuaded him.  “i’m not going with you.” he says, turning to look at rand over his shoulder. “and if you don’t come back i’m leaving first thing.” olver lets out an annoyed grunt at the interruption in the game. he gives him a quick glance and then looks back at rand. “and you told olver you’d play with him. i’m bored of doing it.”  he had played the game several times since coming here. there was no reason for rand to get off scoff free. olver always seemed to remember when he promised something. even rand, although he watched him with a mixture of uncertainty and awe. not exactly fear though. the three of them together had been in far madding for three days now. three bloody days. mat wondered if they stayed any longer with rand cut off from the source that the madness could be ebbed. blood and ashes, he didn’t want to think of it. he gives olver a brief glance. if rand did agree to stay he just hoped that his sullen nature didn’t rub off on the boy. he had been influenced by too many lately. and, light, the last thing he wanted was him to start acting like rand of all people. 

@caracarnn​

[luckhissoul]

psychology + mental health deep dive !

general mental health related trigger warnings apply.  feel free to include more or exclude those facts / test results that take too much time or don’t apply, you can check out this list for more personality-related quizzes to include!

QUICK FACTS ,

diagnoses: n/a - not sure if he’d have anything considered professionally diagnosed as an mental illness.  i’d say he has some form of ptsd and an addictive personality ( gambling, drinking, sex, dangerous situations ) , which my two minute ( so correct me if i’m wrong ) google research told me that those are considered more disorders and not a mental illness.  triggers: n/a - although it’d take a certain level of trust for him not to get mad or low key freak if someone touches his throat. he keeps it covered though.  positive coping skills: naming the stars, spending time with olver (his boy his child *wipes tears* ), spending time alone ( is this a good coping mechanism or a bad one ? ) negative coping skills: drinking, gambling, casual sex, recklessness, there was a knife fight or two, spending time alone ( tossing this on the negative, too ) , making jokes about it, denial. attachment style: Disorganized / Fearful-Avoidant love language: physical touch myers briggs / mbti: ESTP-T

HISTORY EXPLORATION ,

are their diagnoses formal ( via a doctor, therapist, etc. ) or informal ( self diagnosis, a hunch, unrealized, etc. ) n/a - but i’d say any sort of thing that he does have would be unrealized.

have they ever been treated / medicated? no

have they ever been hospitalized or treated on an inpatient basis? no

how old were they when they first started experiencing / realizing symptoms? experiencing early 20s / realizing ? never. 

do they have a family history of mental illness? no

how was mental health handled / discussed in the family? no

what are their thoughts on mental health / their diagnosis? he wouldn’t have any ? 

in what ways has their diagnosis shaped their life or experiences? subtly, in a way he doesn’t notice. 

SYMPTOMS: note that all of the below are, on their own, normative and typical aspects of human functioning. they become “symptoms” when they last longer than “normal” or when they pose a significant impact on someone’s life / functioning.

BOLD  all that are present,  ITALICIZE  those that are resolved or in the history.

depression.    anxiety.    panic attacks.    dissociation.    derealization.    depersonalization.    suicidal ideation.    self harm.    homicidal ideation.    psychosis.    auditory hallucinations.    visual hallucinations.    delusions.    mania.    hypomania.    racing thoughts.    hyperactivity.    attention difficulty.    flashbacks.    nightmares.    hyperarousal.    hypoarousal.    hypersexuality.    hyposexuality.    psychopathy.  risky behavior.    catatonia.    somatic / bodily concerns.    mutism.    phobia.    agoraphobia.    hoarding.    obsessions.    compulsions.    body dysmorphia.    hair picking.    skin picking.     amnesia.    illness anxiety / hypochondria.    sensory loss.    speech difficulty.    comprehension difficulty.    communication difficulty.    tics.   defiant behavior.    irritable mood.    vindictiveness.     aggression.   pyromania.    kleptomania.    paranoia.    attention seeking.    narcissism.    avoidance.    dependency.    pica.    rumination.    food restriction.    food binging.    purging.    soiling the bed.    insomnia.    fatigue.    sexual dysfunction.    delirium.    developmental delays.

explanations / elaborations on any of the above symptoms: suicidal - was very brief period of a few months. hyperactivity is a constant. flashbacks are a mix of his own experiences and memories that aren’t his, like remembering literally dying dozens of times. nightmares - not nightly. low key hypersexuality - mostly just having fun but there’s a line or two where he’s i’m so sad now i’m going to get a woman and thats just -- compulsive gambling / drinking / casual sex. amnesia - he’s missing pieces of his memories, a lot of his childhood is just blurred. defiant behavior - constantly rebelling, would always do something to defy authority.  attention seeking - flashy, wants to stand out, likes to be noticed - guess it makes him feel seen in a way. avoidance - will avoid confronting literally everything he feels so. good or bad for the most part. 

tagged by: @caracarnn​ tagging : @ofimaginarybeings / @inprometheanfire​​ / 

[luckhissoul]

she says it so softly he almost just does it. but light, that would be pretty stupid. he couldn't afford to be a bloody idiot in front of his men. he couldn't just walk back in the litter because she had asked him to. he had to be at the front, that was how it worked. but then his eyes search her face, feeling a little tug on him. he can even feel olver's eyes on him. the boy was always expecting something, wasn't he? a game of stones, a moment, and now this. or amybe this was just to make up for the fact that olver clearly had started to prefer katrina to him anyways.

he offers a small smile before he lets his gaze drift from the pair of them. that's what they were now anyways, a bloody pair. he looks off at his men, lined up and ready to ride on out. it wouldn't be too long of a ride. they knew how to make quick work when it came to traveling. he gives a small shrug of his shoulders, his eyes scanning the rest of the area. it looked safe enough for them to fall behind. he gives a small gesture for one of the red arms to come towards them. there was no such thing as too much caution. he turns to look back at them again, a slight smile on his face. "maybe i might fall back to see how you two are doing."

She's almost relieved that he agreed. She could practically imagine Olver bounding about happily, knowing that he had some freedom from the confinements of the saddle. She had grown up riding, having spent so much of her money on a horse so that she might learn. But she couldn't imagine being a child and being restricted forever in the middle of a saddle. Maybe Mat understood that much also, maybe he had been the kind of child that couldn't be restrained. Light, he really did seem that way, didn't he? "But what about…" She paused, glancing at Olver who still looked hopeful because the entire thing hadn't been asked yet and she felt nervous suddenly because she wasn't entirely sure whether or not he would agree. It was a big ask considering that he was the General of this entire army. She situated the reins and then gave him a soft smile. Would that be enough to convince him, she wondered. No, she hoped. "…well, what if I asked if sometimes, during the march when you are outside your duties, maybe you could join us? I can imagine that you too would feel quite stuffy in the saddle all day."

[self-preservation-fic]

hello. i just miss these two. any ideas what they're up to? <3

I sure do! I’m pretty busy with the other fandom I’m in at the moment, but I keep going back and working on the second part of this fic because it’s been my baby for forever and I’m not about to let it go :’) 

Where the sequel begins, the guys are on Christmas break, Marcus is with his parents + sister, Oliver is off with his own family. The second fic is going to have a darker tone with some family drama. (And some Oliver POV  👀) The main plot will centre around Marcus making his decision on what to do after her graduates and whether he wants to help the Order of the Phoenix out or not have any part in the conflict to come. 

Here’s a snippet from the beginning of the fic, I’m rating it M for some not-explicit sexual content. Please forgive any grammar/spelling errors, it’s still rough! 

+++

Marcus let his door swing open on silent hinges. His room was way cleaner than Marcus had ever kept it. All of his personal belongings tucked neatly away and the covers pulled taut across so taut across the bed he wondered if they were meant to pin him there. He felt like an adult stuck in a dollhouse and this room wasn’t his anymore. Everything of value he’d brought with him to Hogwarts, he didn’t trust it here alone.

Marcus was careful to hang up his suit before pulling on sweats and rifling through his drawers for a shirt. All of his pent up worrying from the train ride here had manifested itself in a nearly compulsive need to run. He had to dig into the bowels of his drawers to find an appropriately ratty t-shirt.

As he searched, he could pick out the careful tread of his mother’s footsteps down the hall. Drafty old houses with minimal insulation were perfect for eavesdropping and terrible for keeping secrets.

“Come in,” he called, snagging a t-shirt when he heard the wrap of her knuckles against the door. He made sure to raise his voice just loud enough for her to hear, not more.

The door creaked on its hinges. “I just want to know--” her voice was cut off by a sharp intake of breath. Marcus froze, shirt halfway on, he was about to hall it over his head when his mother’s voice stopped him.

“Marcus, honey, what happened?”

Shit, he knew what she saw and couldn’t blame her. It wasn’t pretty, the round pink scar on his right shoulder, the skin raised and puckered like a muggle bullet wound. Magic always leaves a mark, Marcus thought ruefully.

“What did you do?” she asked and Marcus could feel the prickle of heat creeping down his back.

“It’s nothing Mom, it was stupid.” He assured, tugging his shirt the rest of the way down and turning to meet her gaze.

Her eyes stuck to his shoulder as if she could see right through him. “That doesn’t look like nothing to me.”

“I was protecting a friend,” he settled, knowing she wouldn’t drop it until he gave her something.

That pricked her interests. “Do I know this friend?”

“No--I don’t know--maybe.” He turned back around and busied himself with grabbing random items of clothing from his luggage for her to give the house elf to wash. No matter where you lived and who you descended from, everyone knew everyone else's business at Hogwarts. He wondered if he told her Oliver’s name if she’d remember going to school with his mother. He wondered how long she’d try to pretend it was okay that they talked.

“Okay,” she acquiesced, quietly, and he let out a nearly restrained sigh of quiet relief.

He handed her the messy bundle he’d collected, and when she took it from him her hands trapped his, holding him tight and forcing him to look her in the eyes for the first time since he’d arrived. Their warm hazel had turned watery. “You know you can always talk to me, I love you so much.” Her bottom lip wobbled slightly and Marcus sighed.

“Mom--” Detaching her hands gently from where they gripped him, he pulled her in over the laundry. She was a tall woman, but even with the bundle pressed between them she still felt small. “Of course I know,” he said, trying his best not to ruffle her perfectly waved hair.

“I just wish you’d write more,” She whispered and he swallowed, sometimes he forgot how long it must be for her in between visits. Time always flew by at Hogwarts and Marcus had always been shit at writing, like he was shit at reading, and it was just easier not to do it most of the time even if he did have something to say. He was blanking now. Lips glued shut.

“I know, I’m sorry.” was all that he could say. It felt lame out in the air between him. All that worry had transformed into leaden guilty in his stomach. There had hardly been any room left to breathe this year between school quidditch, his father--Oliver-- somehow between all of that part of him had forgotten about his mom. “Sorry,” he repeated, and it still doesn't feel like enough.

When she pulled away she waved her hand as if she could dispel her own emotion. Her voice was still thin when she spoke. “Don’t worry about me, I’m just being silly.”

He gripped her shoulders, giving them a squeeze as if he could instill in her the confidence he himself didn’t feel. “Mom, you're not being silly. I should have written, I’m sorry. Okay?”

“Okay,” she said with a nod and he let her shoulders go. The hand not clutching the bundle drifted up to brush his hair back and down the side of his face. “Oh, sweetheart wish you’d talk to me.”

Marcus clenched his eyes shut. He was really not prepared to do this now.  “Mom--”

“Estelle!” Marcus felt her fingers reflexively tense against his cheek at his father’s voice calling from bellow-stairs. He opened his eyes, standing up straighter, not realizing that he’d sagged into her palm.

Stepping back her lip caught between her teeth and he gave her a smile, saying in the most reassuring voice he could muster. “It's alright, I’m okay.”

With a hesitant nod, she turned, stepping from the room and closing the door softly between them. He waited until he heard her heels clicking back down the hall.

Sagging against the door, Marcus let his head thump back against the door. Pinching his thumb and forefinger to the bridge of his now, he suppressed the quelling frustration and anger under his skin, picturing instead a pair of deft arms holding him up. He let out a shuddering breath. He couldn’t leave, he couldn’t and it made him nauseous.

Fishing a flimsy chain out of the pocket of his sweats, Marcus inspected the transfigured metal chain with a small lion gangling from it once again as if he hadn't spent the entire train ride doing so when he thought nobody was watching. It had meant to be a joke, Oliver had produced it from seemingly nowhere and presented it to him with a wry smile. It was the sort of trinket you’d find in Hogsmead shops selling quidditch memorabilia.

“So you don’t forget me,” Oliver had said with an undercurrent of hopeful honesty. He was laid out on Marcus’ bed in his dormitory, looking very at home there, Marcus sat cross-legged on the mattress beside him.

“You shouldn't have,” Marcus had said drily, eyeing the lion as it gave a soundless roar. He put it on anyways, because it made Oliver smile. “And I didn’t get you anything?” Marcus had said, bending over to crowd him against the mattress to press a quick succession of messy kisses to Oliver's face as he had half-heartedly tried to escape.

Eventually, he had stopped the assault, keeping close so that he could more easily study Oliver’s face. It was only Christmas, but he didn’t want to forget a single thing about it. Slowly the smile Marcus had put there slipped from Olver’s face. A warm, square hand reached up to smooth the hair from his face. Marcus allowed himself to melt into the touch, knowing that soon it wouldn’t be there at all. “No, really, you shouldn’t have,” he had said, whispering even though no one was around. He wanted Oliver to know the words were only for him. “Could never forget you.”

The hand in his hair brought him down until his face was pressed to the hinge of Oliver’s jaw, breathing in the comforting scent of his body and trying to pretend he wasn’t about to fall apart.

Fingers carded through his hair as his breath caught and held in his throat. Wrapping one hand around Oliver’s waist the other wormed up under his sweater to feel the warm skin and smooth planes of muscle that hid there. He knew he wasn’t making any noises--he was barely breathing as it was--and yet Oliver was still murmuring shhh noises into his hair.

“Marc, hey, look at me.” Marcuse reluctantly pulled back, just enough to do so while still keeping Oliver close as they lay on their sides. Oliver worried at his lip, his fingers continuing their trail from his brow, down the uneven line of his nose, to the thin set of his lips and the dip in his chin before Marcus caught it and tangled it in his own.

“Hey,” Oliver repeated, looking hesitant and apprehension welled up in Marcus’ chest before he finally stopped worrying at his lip and squeezed Marcus’ hand hard enough to almost be painful. “I love you.”

The rushing sound in his head was so loud he barely heard the pained noise that ripped from his chest. Bending down to press his mouth firmly against Oliver’s own, his brain hazy with want, he repeated I love you, I love you, I love you--over and over in his head. Oliver opened for him willingly, making soft noises against his mouth, his fingers tightening and tugging lightly in Marcus’ hair. Tilted his head, he let himself sink into the soft warmth of his mouth, pushing his hands up further to feel Oliver’s ribs expand and contract tightly under his fingers.

Pulling back he gasped. “I--I--” the words getting trapped in his throat.

“Shhh,” Oliver said, sweeping his thumb over the swell of his bottom lip, then up over the arch of his cheeks. “It’s okay I know.”

Kissing wetly over his jaw and down his neck in apology. He has so many things to apologize for. Rucking his hands up to brush a thumb over his nipple, Oliver’s breath hitched and he full body tensed before relaxing boneless into the bed with a sigh. Pressing a line of kisses down his breast bone, Oliver arched into his touch as he reached the soft dip of his stomach nosing at the fine line of hair there.

Marcus wished it didn’t have to be like this, he wondered how long Oliver would put up with it, how far his patience would stretch. Tugging on his hair, Marcus looked up and this time Oliver’s eyes weren't hesitant, but fierce. “I love you,” Oliver said and Marcus felt it burn hot and quick in his chest. Overwhelmed, he gripped Oliver’s hand tighter before pulling it away to make quick work of his belt.

Mouthing a wet spot into the fabric of his boxers, Marcus lingered there before hooking his fingers in and tugging it down. He sucked a possessive bruise into the soft skin of Oliver’s abdomen as he panted wetly above him. Marcus comes with Oliver’s hands wound in his hair, his body curled taught over him and a hand down the front of his pants. He let Oliver come in his mouth, breathing “I love you’s” in a mantra around shaky moans. Marcus squeezed his eyes through the wetness prickling at the corners and moaned in turn.

Marcus blinked back to the present, thumbing the lion in consideration. Everything about it was just so achingly Oliver. Moving over to the mirror over his dresser, he fastened it around his neck. The chain was short but just long enough to tuck under the collar of his shit, hidden away and safe. The metal was cold against his skin, pressing his palm over it, he felt the indentation through the fabric as it slowly grew skin-warm, a heavy comfort against the hollow of his throat.

[neuxue]

Wheel of Time liveblogging: Towers of Midnight ch 9

Mat catches up with an old friend. Or an old not-friend catches up with Mat. 

Chapter 9: Blood in the Air

Well it opens with Mat literally screaming bloody murder, so we’re off to a good start.

He threw himself backward to his feet, hauling the ashandarei up, then spun and slashed—not at the form moving through the tent towards him, but at the wall.

I don’t know why this is so amusing to me, but I’m laughing at the ashandarei being used once again in conjunction with a rather unconventional exit, given that it was granted to him in the first place as, I’m fairly sure, part of his request to be out of the land of the Eelfinn. And then going back for it almost stopped him being able to leave Ebou Dar.

Anyway, somehow he then manages to pull the medallion off his neck and tie it to the blade of the ashandarei all before the inhumanly fast gholam can catch up. Sounds fake but okay.

Though apparently it’s still trying to avoid notice, and also is not immune to a little bit of villainous monologuing, so okay I suppose that buys a little bit of time for some speedy knotwork.

“The one who now controls me wants you more than anyone else. I am to ignore all others until I have tasted your blood.”

I mean, I’m not sure if the gholam plays by the same rules as Aes Sedai but there’s definitely some wiggle room in that command. Just have a quick taste and then you two can be friends. Or Mat can keep it as a pet, depending on how we’re defining personhood.

Or sparring partner? Could be useful to have something absurdly fast and virtually invincible to train against.

Mat agrees on the fighting point, at least, and goes for the attack, because I’m sure this will end well.

Really? Of all the people this thing has killed, including some of your friends and members of the Band, Tylin is the one you’re upset about? Sigh. Fine. That’s a dead horse I don’t particularly need to beat any further, I suppose.

“You didn’t want her; you wanted me!”

Well technically Mat didn’t want her either so they have something in common there.

Okay, sorry, couldn’t resist one last dig.

“A bird must fly. A man must breathe. I must kill.”

That’s a mood. Points for self-awareness, I suppose, though in this series that’s a pretty low bar.

How is the gholam controlled, I wonder? I don’t see this happening, but given that it seems to serve a single master rather than the Shadow in general, it would be cool if there were a way to suborn it to Mat’s will instead, and unleash it on the Shadow’s own armies. That would fulfil its need to kill, and it would actually sort of fit with its dark-trickster kind of nature. But I doubt it.

“I’ve been told to kill them all,” the gholam said softly. “To bring you out.”

Someone needs to give this thing a copy of the Evil Overloard List. Though in fairness I suppose this is less ‘revealing its plans via monologue’ and more ‘delivering a rather chilling threat, given that it knows everyone’s identity’.

And also as a distraction because Mat hesitates for just a second on realising that it knows about Tuon, so all in all a pretty effective gambit.

Or it would be, if not for Teslyn, because she’s still surprisingly awesome. Lifting Mat out of the way with Air—because he’s no longer wearing his medallion and the gholam can’t be affected by the One Power—is some pretty damn clever quick thinking.

And then she attacks it with a chair. Iconic. Is that three times now that chairs have been used as improvised weapons in this series? Four? Whatever the number, I sort of love it. Especially because the image is hilarious every single time.

The object—a chair!—crashed into the hillside beside them. The gholam spun as a large bench smashed into it, throwing it backwards.

This invincible creature of Shadow and nightmare, immune to magic and virtually impossible to fight, being hit by flying furniture.

Credit again to Teslyn though, for immediately coming up with pretty much the only way she could possibly help in this fight. Sure, she’s had time to figure out the loopholes with Mat’s medallion so it’s not completely on the fly, but that’s still some impressive adaptability and problem-solving right there.

Seems the gholam is still avoiding attention, though, because it runs off, pausing only to tear out a pair of throats for good measure on the way.

And now Mat remembers the bloody murder in his own tent that started it all, which turns out to be Lopin, and two random NPCs. Aw, poor Lopin, he just wanted to do laundry in peace.

The gholam had proven itself practically unstoppable. Mat had the suspicion that it could cut down the entire Band in getting to him, if it needed to.

This, and honestly this entire scene, seems very deliberately placed to basically remind us that the gholam is still an unsolved problem. A bit of tag-you’re-it (murder tag? That’s a game, right?), popping up to tear some throats and then run off again, because Our Protagonist hasn’t yet worked out an actual solution but clearly now he needs to.

Which of course begs the question: what is the solution here? How do you defeat something faster and stronger than you are, that also happens to be invincible to magic and indestructible but for a single known weakness?

I suppose that single known weakness, then, should be the starting point here. Which—oh. Mat’s in Caemlyn. And he hasn’t been able to get in touch with Elayne yet, but… Elayne is also in Caemlyn. And knows how to replicate and make ter’angreal. Could she possibly make a weaponised version of Mat’s foxhead medallion? One that could kill rather than maim? Or make copies of it?

Except she can’t even channel reliably at the moment, and also I’m not sure how well she’d be able to study a ter’angreal that by its very nature blocks the use of the One Power on it, so that could present something of a challenge. Still, it’s pretty much the only idea I have.

Unless you could trap the gholam somewhere? Lure it through a gateway? Leash it with the medallion like Gollum with the elvish rope and drag it to the Tower of Ghenjei as a gift for the Aelfinn and Eelfinn?

Hey I’m just tossing out ideas here.

Mat’s worried about Olver, but apparently he’s fine; I suppose it was too much to ask that the gholam might have got to him. Okay, okay, fine, sorry, I’m a terrible person etc. I just… really could not give less of a shit about this kid if I tried, but I suppose that’s a me problem.

Seems like the gholam’s diversifying its skillset, getting into the interrogation business as well as the murder and vampirism one. Always good to have a fallback, I suppose, especially in this economy.

“We’re going to hunt it,” Mat said softly, “and we’re going to kill the bloody thing.”

Cool, sounds fun, what’s the plan? Oh! Maybe you could dissolve the medallion and then inject it into someone’s bloodstream and then get the gholam to eat it…

Sorry, I’ll stop.

Well no, I won’t, but.

“Burn me, I still need to talk to Elayne. I want Aludra’s dragons started. I’ll have to write her another letter. Stronger, this time.”

This does feel like a setup for Elayne helping with the gholam problem somehow via her ter’angreal abilities and Mat’s medallion, given the intersection of all these people and places and events.

Also, Elayne does have a history with multiple letters of varying strength, so I am sort of entertained by the notion of her being on the receiving end this time. And if an epistolary version of Elayne and Mat’s weird friendship is all I get, I’ll take it.

Mat’s plan for now involves sleeping in town in a different inn each night, so… you’d better hope the gholam’s orders regarding avoiding notice don’t change, Mat, or you’re going to end up with a hell of a lot of blood tangentially on your hands. I mean, I’m all for it in the name of self-preservation, but Mat’s a better person than I am.

Oh hi Joline. Can’t say it’s good to see you, and you know it’s bad when Mat and I agree on something. Though she’s come to say her goodbyes, so at least I don’t have to put up with a) her and b) Mat in her proximity anymore.

Mat’s last few lines in this chapter feel… a little more like TGS Mat than like the Mat of the rest of the series, but I can forgive that; it’s a pretty small slip and the rest of this chapter and last have, indeed, been better than last book.

Next (ToM ch 10) Previous (ToM ch 8)

[luckhissoul]

he hears the small voice, unsure if he should go out there or not. who would be calling out like that in the middle of the night? but he gets up anyways, casting a glance at olver who's asleep on the small cot there. he doesn't want to wake him. so he steps out. startled to find another child standing there before him. it takes him a moment to figure if it's a boy or a girl. well, actually he's not even entirely sure when he starts to talk. he could swear the voice is too soft but then on the other hand - it hardly mattered. this wasn't the place for a kid. he already had olver to deal with. and this whole thing could get messy quick.

"gods, you scared me…" he says, letting the flap of his tent close behind him. he eyes the area around his camp before looking at the kid again. "how'd you even get in here?" he knew without having to check that the watch was on guard, they were good at what they did. she must've been pretty clever to slip through. it spikes some paranoia. but would an assassin call out like that, almost aimless to his tent? she's just a kid after all. "what are you doing here all by yourself?"

@luckhissoul gets a plotted starter.

Arya had heard of the band of the red hand at one point and how they had never lost a fight which got her to thinking about things. While she wanted to be the one that drove her blade through the hearts of the people on her list she could see the appeal of back up. She could also see the appeal of being a member of a band with such a reputation perhaps people would think twice about crossing her. All she needed to do was track them down and convince their leader that she would be an asset to their troop. It wasn't like she was without any skills after all.

It had taken her some time, but eventually the lost daughter of House Stark had found them. It was hard to keep herself steady as she approached the camp trying not to bring too much attention to herself as she looked around. Quiet as a shadow. There wasn't a reason to fear them that she was aware of because if they were cruel to children or even women usually there was a warning about associating with them. Calm as still water. Pausing in front of a tent that she was guessing was the leader of the band she took a breath before poking her head in to speak with them. "Hello? Is anyone here?"

[sweetscienceknowledge]

Boxing (A Brief Introduction)

Boxing is one of the few sports that has been around since millennium ago. According to Collins et al. (2020), the history of the sport can be traced back to as early as the 3rd millennium BCE; where boxing was depicted as bare-knuckle contests by the people of Egypt and the Middle East. Similar to everything else, the sport too, had undergone massive changes as time progressed; which makes the present version of boxing entirely different from the one that existed back then.

Today, boxing is comprised of 2 different types; amateur boxing and professional boxing. Amateur boxing is more suited towards up-and-coming boxers. It consists of fewer rounds (3 rounds) and is usually won via outscoring opponents in points. This format is designed mainly for tournaments where amateur boxers compete against one another to win medals and recognition; as can be seen in the Olympics (dubbed as the peak of the amateur boxing scene). 

These tournaments are more often than not treated as an opportunity to represent; be it to represent one's boxing gym in local competitions, or to represent a whole country in prestige international tournaments such as that of the Olympics and Southeast Asian Games. 

Image taken from the London Olympics 2012.

Professional boxing, on the other hand, is the one that is most familiar to the general public. It differs from amateur boxing to a great extent. In professional boxing, boxers compete in a match with rounds ranging from a minimum of 4 rounds (for new professionals) up to a maximum of 12 rounds (reserved for when championship belts are at stake). Due to the larger number of rounds, professional boxers tend to fight at a much-controlled pace, opposite to the quick pace practised in the amateur scene. These matches are often won through either technical knockouts; in which the opponent is conscious but unable to proceed, or through pure knockouts.

These knockouts are often the result of months of preparations, where boxers train to reach their peak performances, tailored to expose and utilise the opposition's weaknesses based on careful and in-depth analysis of their boxing style.

Image taken from the professional boxing match between Mike Tyson and Evander Holyfield (9th November, 1996).

Although amateur boxing lacks decisive wins via knockouts, they often make up for it through constant non-stop actions. This is arguably one of the most intriguing aspects of the amateur boxing scene. Competitors are required to "let their hands go" more frequently as they only have 3 rounds to convince the judges of who the more dominant boxer is. This is especially true when elite amateurs (those with excellent boxing portfolio) are put against one another. Below is a video example of a match between elite-level amateurs Ryan Garcia (Red) and Vergil Ortiz (Blue).

Amateur bout between Ryan Garcia and Vergil Ortiz.

Regardless of the differences between amateur and professional boxing, the beauty of the craft showcased by the competitors will always add to the list of reasons as to why boxing is one of the most reputable and thrilling sports of this present day.

Do you have any favourite boxer? Comment below who and why!

Reference(s):

1. Collins, N., Hauser, T., Krystal, A., Olver, R., Poliakoff, M., Sammons, J. T., & Wallenfeldt, E. C. (2020, May 14th). Boxing History, Rules & Notable Fighters. Britannica. https://www.britannica.com/sports/boxing

(481 words excluding extraneous).

[fateprotected-a]

i’m safely home and liable to pass out. full activity will resume tomorrow. also, they had 09 on the plane so here’s a quick movie tag wishlist

pris during the time she’s actually on planet while the enterprise is being built at riverside (which is bullshit but that’s a rant for later)

pris and pike?? in the aftermath??? kill me 

all of my characters need tags to the time spent limping back to earth at sublight okay. I always need more things set in that recovery period. the slow realization that the emergency is olver but the work is. the work is barely begun. 

[thousandmaths]

Hamiltonian Mechanics (guestpost)

Hi dedicated readers! I'm one of @thousandmaths‘s more notorious colleagues who keeps a blog about math and philosphy. In an elaborate exchange deal, he and I have written guest posts on each others' blogs. You can read his post here.

While working on a farm last summer, I started reading Roger Penrose's Road to Reality, a wonderful book about philosphy, physics, and mathematics with a beautiful set of hand-drawn diagrams. Having studied math and computer science as an undergrad, the only physics course I took was quantum mechanics and I wanted to learn more.

The book didn't disappoint and I would highly recommend it to any student studying the sciences. He always offers the intution behind the mathematics so even if you skip the symbolism, you'll see the general idea. In this post, I want to give a quick introduction to one of the two organizing frameworks of modern physics that Penrose discusses, namely, Hamiltonian mechanics. The best way to learn is by example, so I'll follow a computation from our own Peter Olver's wonderful book Applications of Lie Groups to Differential Equations.

The Lagrangian and Hamiltonian Formalisms

There are two main points of view in modern physics. Named after their alleged founders, the Lagrangian and Hamiltonian formulations are equivalent in a precise technical sense (they are dual) so they are really two different views of the same phenomena. The general idea is that both offer frameworks for deriving the equations of motions for all physical systems, from general relativity to electrodynamics.

In the Lagrangian framework, one writes down an “energy functional” the solutions seek to minimize. A standard computation leads to something called the Euler-Lagrange equations of motion.

In the Hamiltonian framework, one writes down an “energy” that the solutions conserve. A standard computation leads to something called a Hamiltonian system of equations that describe the objects motion.

Here we discuss the “conserved quantity” (Hamiltonian) point of view. This framework requires two inputs:

A Hamiltonian $H$ (a scalar quantity depending on the solution that stays constant over time).

A configuration space $G$ (a space of all possible states of the system).

Requiring only these two pieces for the setup, the Hamiltonian formalism will churn out the equations of motion.

The Hamiltonian Perspective on Rigid Body Rotation

We will extract the equations of motion for the angular velocity of a rigid body $\Omega$ by making the following two choices:

If $u = (u_1, \, u_2, \, u_3)$ is the angular velocity and $I_1, I_2, I_3$ the moments of inertia (their definitions are a story of its own) then set $$H(u) = \frac{u_1^2}{2 I_1} + \frac{u_2^2}{2 I_2} + \frac{u_3^2}{2 I_3}. $$

 The configuration space for a rigid body in three dimensional space is $SO(3)$ (the space of all rotations).

The choice of $H$ might seem a bit arbitrary, but ignoring the normalization factors $I_1, I_2, I_3$, it looks like the usual kinetic energy $1/2 v^2$ in basic physics. Roughly speaking, the moments of inertia track the resistance of a body to rotation (increase in angular momentum via torque).

The choice of the configuration space is clear. Any rigid body floating in space will rotate around a fixed point (its center of mass) and thus at any time can be described via a rotation from an initial orientation. Hence, the motion of of a cube rotating about its center can be described as a series of rotation matrices $R(t) \in SO(3)$.

The Hamiltonian Formalism in Action

Okay, so we have made our two necessary choices. Running through the Hamiltonian formalism will produce the final equations of motion. One can phrase Hamiltonian dynamics in terms of symplectic geometry, but for our purposes, we can take the less jargon-intensive approach of the so-called "Poisson bracket". If $H$ is our conserved quantity chosen above, the Hamiltonian formalism tells us that the angular velocity $u$ evolves as

$$ \frac{du}{dt} = \{ H, \, u \}. $$

The Poisson bracket is thus the key part of the theory. Where does it come from? The Poisson bracket actually accepts two functions so the notation $\{ H, \, u \}$ means that we apply the Poisson bracket to each component $(u_1, \, u_2, \, u_3)$ individually and assemble back into a vector.

A choice of Poisson bracket introduces tons of structure to a manifold. But we can go the other way, and use the structure of a manifold to generate a Poisson bracket.

The space $SO(3)$ of all rotations in three dimension is a in fact a group under matrix multiplication. Moreover, it is a highly symmetric group: a so-called Lie group. That is, it is both an algebraic group and a manifold. These groups are fantastic because they are so shockingly symmetric that restricting attention to infinitesimal perturbations of the identity (tangent space to the 'do nothing' rotation) is enough to (almost) completely describe the group. That is, we can "linearize" the group and lose (almost) no information.

The “linearization” of a Lie group is called its corresponding Lie algebra. A Lie algebra is a vector space with a special operation called the Lie bracket that it inherits from the Lie group structure. In the case of $SO(3)$, the Lie algebra $\mathfrak{so}(3)$ is a three-dimensional space of matrices. This space has enough structure to produce a Poisson bracket. However, we must again pivot to one other space.

The “magical” feature of the Hamiltonian framework is that the correct setting is the dual space $\mathfrak{so}^*(3)$ to $\mathfrak{so}(3)$. Intuitively, we operate in the dual since Hamiltonian flows are described by $\nabla H$ (gradient of $H$). As one learns in differential geometry, the gradient is best viewed as a linear functional (element of the dual space) to ensure coordinate invariance.

Following definitions and such, one computes that the Poisson bracket on $\mathfrak{so}^*(3)$ is given by

$$ \{ H, u \} = -u \times \nabla H $$

where $\times$ denotes the cross product (the geometric reason for this is the subject of another post).

Since $u$ roughly represents the velocity of rotation (it is not precisely the time derivative $R'(t)$ however), we can view the evolution

$$ \frac{du}{dt} = \{ H, u \} = -u \times \nabla H $$

as describing a flow in $\mathfrak{so}(3)$. Expanding our definition for $H$ and the cross product finally gives the following equations of motion

$$ \begin{align*} \frac{du_1}{dt} &= \frac{u_2 u_3}{I_2} - \frac{u_2 u_3}{I_3}, \\\ \frac{du_2}{dt} &= \frac{u_1 u_3}{I_3} - \frac{u_1 u_3}{I_1}, \\\ \frac{du_3}{dt} &= \frac{u_1 u_2}{I_1} - \frac{u_1 u_2}{I_2}. \end{align*}$$

One can then reconstruct the actual trajectory $R(t)$ of the rigid body by standard formulas.

Further thoughts

In addition to simple rigid body dynamics, all of the field theories, from quantum mechanics to fluid dynamics can be extracted from a Lagrangian or Hamiltonian point of view. On the surface, this level of grand unification is almost magical. Does that mean physics is “solved”? After all, for any new theory, one must simply generate an appropriate Lagrangian or Hamiltonian and then “turn the crank" to derive the equations of motion. Nothing could be easier.

Of course, physics is far from “complete” (in many senses of the word) and even in the Lagrangian / Hamiltonian frameworks there is always the problem of choosing the “right” Lagrangian or Hamiltonian to plug into the framework.

More broadly, these frameworks are not truths but merely formalisms and the value of a formalism is precisely how much it guides and organizes our fallible intuition. Penrose hints at some problems with these approaches:

However, I must confess my unease with this as a fundamental approach. I have difficulties in formulating my unease, but it has something to do with the generality of the Lagrangian approach, so that little guidance may be provided towards finding the correct theories. (p 491)

Both frameworks are merely tools for organizing good ideas. As always, there is a “conservation of creativity” in the sense that humans must guess at good models in the first place. No amount of symbol pushes will remove this requirement. At best, abstraction simply focuses our attention on the important features.

[naijawapaz1]

Fergie Olver Bio, Height, Age, Wiki, Net Worth, Married, and Wife

Fergie Olver Bio, Height, Age, Wiki, Net Worth, Married, and Wife

Fergie Olver Quick Facts of Fergie Olver Full Name Fergie Olver Nickname Fergie Marital Status Married Birthplace Moose Jaw, Saskatchewan, Canada Ethnicity White Profession Game show host, sportscaster Active Year 1969-1996 Eye colour Hazel Hair colour Brown Spouse Susan Wheeler.

A famous television presenter Fergie Olveris also an outfielder baseball minor leagues. He is…