#penrose papers

[kindred-spirit-93]

words

final exam tomorrow, still got work to do & panic is setting in (for realsies this time) so i decided it would be a great idea to put words together. will probably delete later lol but have this for now

dangit im having emotions again.

listened to die with a smile, and it reminds me so much as the world caves in oddly enough. the setiment is the same, albeit sung in polar opposite ways.

theyre both so soft and sweet. so different yet so similar. the love is so pure and deep, and remains as such both while waiting and preparing for the end.

--

so i reflect a little, because i think interpretations are more often than not reflections of ourselves. other times being external influence or some other variable. anyway

the beauty of love to me lies in its many colours and shades. to live and fall in love with life, of friends and family, for strangers and stars, hymns and humanity, for nature and knowledge.

apocalyptic love songs is probably my favourite genre of music ever. (honourable mention to wasteland baby btw)

theres something so soothing about the thought of having your person (or people) by your side at the end of it all… theres no going back to what we had nor what was, but i have you. had you. and thats all i want. wanted. augh

--

back to my inner turmoil, sometimes i wonder if i yearn to love (and be loved) because despite everything telling me otherwise i still see myself as unloveable. not truely at least. much less as deeply.

"water water everywhere, nor any drop to drink". i have so much to give but not for me. never for me. to so much as spare it a second of thought is sacriledge.

i crave to be held, and not to a standard. but how do you unlearn that.

--

'my soul has been put out and needs another to relight it', i think to myself. this dependence, the need for.. other, it scares me. it leaves me vulnerable. 'its inevitable though', i offer back sensibly. i can only hold the truth off for so long.

when i drop my unlit matches, am i waiting for someone to put them back in my hand? someone who will offer me a light anyway? will someone point out the fact and leave me to pick up after myself?

i continue to waste away in my thoughts as my matches are now rendered useless by the damp.

i dont notice.

[its-elvie-innit]

guys PLEASEEEEE you dont understand. if my phone wasnt broken i would show you r=0 and r=infinity then infinity can touch on both sides creating an infinite ring only interrupted by black and white holes which become the edges of the universe CONNECTED TO THE REST OF THE UNIVERSE guys PLEASEEEEEEEEEE

[broccoli-stew]

This video teaches you to make a 2D representation of the famous Penrose or Impossible Triangle.

[a-crow-with-rights-and-anxiety]

Hey so you remember this thing that everyone on mathblr got excited about recently?

This is the hat, and it's what's called an "aperiodic monotile". This means that no matter how you arrange copies of this tile, you can never get an arrangement that will repeat infinitely (think of it like the irrational numbers of tilings). This was big news in mathematics as while sets of more than one tiles have been found that are aperiodic (e.g: The Penrose Tiles), this was the first tile that's aperiodic by itself, hence "monotile". (There are some caveats to this but that's not important for understanding this post)

However.

If you look at images of the hat tiling, you may notice something.

If you look at the tiles labled 1 and 2, you'll see that one's a reflected copy of the other. In fact, any infinite arrangement with hats requires you to you mix unreflected and reflected tiles. Which raises the question: is it possible to have an aperiodic monotile that doesn't need reflections?

Presenting the Spectre, A chiral aperiodic monotile.

Using only translation and rotation, any arrangement of copies of this tile will never repeat.

Mathematically speaking, this is really fucking cool.

The paper on it is still in preprint, but hopefully I won't need to retract this post. A copy of it can be found here and a post going into some more details of how the shape was discovered is here.

[internetskiff]

It is very likely that the Penrose was the only environment where Ariane could paint. Not only was she free of the judgement of Rotfront's community, she was even provided all the tools she would require to paint the way she wants. I doubt it's a skill she managed to learn way beforehand. It doesn't seem like her mother's radio station would have had many art supplies, save maybe for a pen and paper. I believe it's a skill she developed over the 4 years or so that she spent on the ship at the time.

Rotfront would've been an environment that would actively stifle her creative spirit - I very much doubt her aunt would support the pursuit of art, her letters very much give off the impression that she's quite "orthodox" when it comes to the way a child should be brought up within the Eusan nation.

Safe to say neither her teachers nor most of her peers would approve either, hell, it'd probably only make them see her in an even worser light. I feel like even if she had drawn beforehand, she certainly didn't during her time in Rotfront. We never really see that many people get what they want within Eusan's system, the only real example I can think of being Replikas and the objects they practically require to keep their neural patterns in check. Only on the Penrose program do you actually seem to get what you want. They only really treat you as a person when you're flying toward a slow and isolating death.

[xtruss]

At Long Last, Mathematicians Have Found a Shape With a Pattern That Never Repeats

Experts have Searched for Decades for a Polygon that only makes Non-Repeating Patterns. But No One Knew It was Possible Until Now

— Will Sullivan | March 29, 2023 | Smithsonian

Infinitely many copies of a 13-sided shape can be arranged with no overlaps or gaps in a pattern that never repeats. David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss (CC BY 4.0)

From bathroom floors to honeycombs or even groups of cells, tilings surround us. These patterns cover a space without overlapping or leaving any gaps. Like a rug filled with diamond shapes, where each section looks the same as the one next to it, every tiling ever recorded has eventually repeated itself—until now.

After decades of searching for what mathematicians call an “einstein tile”—an elusive shape that would never repeat—researchers say they have finally identified one. The 13-sided figure is the first that can fill an infinite surface with a pattern that is always original.

Repeating patterns have translational symmetry, meaning you can shift one part of the pattern and it will overlap perfectly with another part, without being rotated or reflected. The shape described in a new paper does not have translational symmetry—each section of its tiling looks different from every part that comes before it.

The designs on these rugs have translational symmetry—the patterns on the rugs repeat themselves. Juli Kosolapova via Unsplash

Sarah Hart, a mathematician at Birkbeck, University of London, who didn’t contribute to the finding, tells New Scientist’s Matthew Sparkes that she had thought finding an “einstein” (named for the German words for “one stone,” or one tile) could not be done. “There are infinitely many possible candidate tiles, and even the existence of a solution feels quite counterintuitive,” she says to the publication.

“Everybody is astonished and is delighted, both,” Marjorie Senechal, a mathematician at Smith College who did not participate in the research, tells Science News’ Emily Conover. “It wasn’t even clear that such a thing could exist.”

David Smith, a retired printing technician and nonprofessional mathematician, was the first to come up with the shape that could be a solution to the long-standing “einstein problem.” He shared his ideas with scientists who took on the challenge of trying to mathematically prove his conjecture, per the New York Times’ Siobhan Roberts.

The team published a preprint paper detailing the findings on the site arXiv last week, and it has not been peer-reviewed yet. But experts say the work is expected to be supported with further investigation, per Science News.

“This appears to be a remarkable discovery,” Joshua Socolar, a physicist at Duke University who did not contribute to the finding, tells the Times. “The most significant aspect for me is that the tiling does not clearly fall into any of the familiar classes of structures that we understand.”

Each "einstein" tile has eight kite shapes inside of it. David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss (CC BY 4.0)

The “Einstein” tile is made up of eight kites, or four-sided polygons with two pairs of adjacent, equal-length sides. Researchers call it “the hat” because of its resemblance to a fedora.

The shape is simpler than some experts expected it to be. Chaim Goodman-Strauss, a mathematician at the University of Arkansas and one of the authors of the paper, tells Science News that if he’d been asked to guess what the shape might look like before the finding, “I would’ve drawn some crazy, squiggly, nasty thing.”

In the 1970s, mathematician Roger Penrose discovered that two shapes could form a non-repeating tiling pattern together, prompting hopes that a single shape may be found to do this one day. Researchers have been able to make other non-repeating patterns in the past, but the challenge has been finding a shape that can only make a non-repeating pattern, Goodman-Strauss tells the Times.

The shape of “the hat” can also be morphed to form additional tile shapes that make non-repeating patterns, as shown in the video above.

This new finding could lead to materials science investigations—for example, shapes that form non-repeating tilings could help design stronger materials, Hart tells New Scientist. The elusive shape might also spark creative inspiration for new decorative designs or art.

[atopvisenyashill]

No okay bc i was thinking about Rhea Royce and Daemon too, right, bc she’s an heiress so like-

I’ve mentioned this before but Lady Waynwood rules in her own right and all of her sons have her name. We know nothing about her husband, perhaps he was some wealthy Essosi noble and thus there was no family on the continent to be affronted at his children not having his name, maybe he was like second born and no one gave a shit, but regardless, she and Jacaerys (who was meant to take the name Targaryen once he was prince of dragonstone) are our only real examples here for ruling women who actually have children outside of dorne - because jeyne arryn never has children of her own so she never deals with the problem of “how do i navigate naming my kids as an heiress?”

DOES THIS MEAN DAEMON’S KIDS WOULDNT EVEN BE CALLED TARGARYENS❓

or does this mean Rhea is supposed to just be okay with the name Royce disappearing??? I do not fucking think so, so they’d likely do the split name thing like with Rhaenyra’s kids, although (and this is assuming Daemon manages to have even one let one two kids with her lmao) I do imagine Daemon having a single child out there that doesn’t have the name Targaryen really pisses him off.

The first names in this situation intrigue me. When Valyrians marry outside the family, their children tend to get at least some Valyrian names - Laena Penrose, Aemma Arryn, Viserys Plumm tho u could argue that was a purposeful insult too, Rhaego to some extent - and they usually marry back into the main branch - Jocelyn Baratheon, Laena & Laenor Velaryon, all the cousin swapping going on with Daeron’s grandkids, Elia Nymeros Martell (ish), potentially Aelinor Penrose as well - but at the same time, this house will descend from RHEA not Daemon, so the Valyrian name is likely to kinda die out after a generation or two for the main line, while the second born probably marries back into the main line. Like, the Penroses are named Phillip now, not Baelor or Laena, bc they don’t descend from Elaena on paper, they descend from her HUSBAND, from Ronnel. And while it’s likely Rhaenyra’s grandkids by Jacaerys would have Targaryen names, her grandkids by Lucerys would have Velaryon names, and crucially, all of Rhaenyra’s kids by Laenor have names Laenor picks because the husband picks. So Rhea’s son? gonna have a whack ass name like Baelon Royce. But Baelon Royce may want to pick a more Royce-ish name for his own heir, instead of a Targaryen one, and that’s gonna be. a conversation.

i think daemon is going to insist on his royce child marrying another valyrian and choosing another targaryen first name (even if they still keep the name royce). like, he is going to be the bitchiest sort of grandparent who just straight up won’t acknowledge the child’s real name if he doesn’t get his way here, at least while he’s alive.

IN THAT SAME VEIN, daemon is super valyria brained. if he has two girls or two boys with rhea it’s whatever but if he has a boy and a girl. i think this man is going to want his kids to marry. we are just going to have random royces fucking in the vale.

(i think he can be talked out of it easily enough if viserys just like, idk, promises the daughter to his eventual son or promises daemon’s son to rhaenyra AND LETS TALK ABOUT THAT SITUATION PLEASE).

and rhea in all this is like. fine you can name our kid baelon royce. fine our daughter can be named baela targaryen too. fine baelon can have personal arms that have a dragon on them. fine they can-no fuck you baelon and baela are not getting married i’m sending a raven to the king as we speak you fucking freak. what do you mean you’re sending rhaenyra to runestone viserys??

this woman’s life is a nightmare omg

but also THIS COULD HAVE HELPED SO MUCH AFTER SUMMERHALL. this is what these bitches get for incest marrying so much, no cousins to turn to when your main house dies. that’s called bad dynastic planning, read a history book daemon!!!!!

[fanficapologist]

So many things going on plotwise! I’m glad Maera is somehow recovering both from childbirth and her harrowing ordeal at Alys’ hands. I’ve missed Maera sparring too!

And despite her initial apprehension or disdain, I think she and Vaegon have a lot more in common than she’d care to admit. I also love their united front at the small council.

Special mention to Cedric! I love how he sensed the vibes were off with Penrose and I hope he can be a source of guidance for Maera.

As for Wynni, I hope she won’t cause problems for Maera but I don’t quite like how she seems brainwashed to believe Maera would be so cruel. This makes me wonder how her in-laws had treated her back when she was still married.

And Helaena!’ Oh, it’s so good to hear from her again. I wonder if she somehow alternates between the past, present, and future because she mentioned the twins and Maelor. Or is she kept in the dark and is made to believe all her children are alive and well? I can see this is going to be shaping up for very interesting future chapters and this is just sort of laying the foundations.

That said, I’ve been going over the previous chapters and wanted to note the prophecies. I’m not sure if I left anything out but So far, here’s my list.

As of the moment, I feel like a clueless student who’s gathered bits of reference books and journals for a thesis or research paper but I don’t know yet how to tie it all together 🤣

“An eye will close, a dragon will emerge” and “Dragron's flames and maelstrom's roar, a battle of fire and sea”. - The Price

Aemond loses his eye and in the process, a friendship in Maera.

“Dragon fire melts the steel to bridge the gap between sky and sea.” - The Proposition

Likely when Aemond proposed sparring with Maera. This was when they were forming a truce of sorts, not enough for Maera to consider Aemond a love interest but they were moving past antagonizing one another.

“The blood of Old Valyria reveals itself through midnight. An egg will hatch in the rivers” - Revelations

Around the time Maera first spotted Ebrion on the beach. And this was also the time Aemond slept with Alys, stupidly not thinking something would come out of that union.

“Two feathers to be set ablaze by dragonfire” - The Hunt

Ser Reginald Penrose gegs his ass burnt. I know this isn’t really significant in the grand scheme of things but it felt wrong to leave it haha

“The eye of the Maelstrom is a nest for the dragon.” - Poison

I’m not sure if this particular prophecy is meant to predict something about Maera and Aemond or if it is something like a reaffirmation that they are fated to be together. Because it is saying they find home or comfort in one another.

“Two dragon eggs are laid. One in the rivers, one in the maelstrom.” - Nerves

Looking back, and thanks to Aemond’s POV Chapters, made me realize Alys' pregnancy was really early. No wonder she used the excuse she was about to give birth soon. I had an inkling Alys was going to be present in the story when I read the word rivers. As far as I was concerned she was the only person with a connection to it.

“The hatchling will be scorched by dragon fire in the castle of the old Kings Curse” - Demise

Oh gosh, we really should listen to Helaena more. She also predicted the assassination attempt early on.

“One flower to bloom, two buds cut down, one seedling unearthed.”

This is where it gets pretty dicey for me because I can’t settle on one angle. Could Maera possibly miscarry or lose children? The buds make me think whether she’ll be pregnant thrice but only one will survive or whether it applies to Rhaenyra’s children Aegon and Viserys or even Jaehaera.

As for the seedling, well, this is just me but I was thinking they could also refer to dragonseeds. Seeds are often buried and dragonseeds are in hiding. But now that they’re “unearthed” it could mean their possible rise or demise. This got me thinking of Hugh or Ulf and the role they’ll have in the Dance.

And despite the apprehension of what will happen next seeing as we are now deep in the war, I am also looking forward to how Aemond and Maera will navigate their arrangement seeing as she’s already declared safe for baby-making. Will Aemond be a smug little shit? Will he tease her? Will it be awkward? 👀👀👀

Xoxo!!

I feel so sorry for Helaena, oh my god, my sweet angel baby. Because she must be going through it! I think her brain is so muddled she’s forgotten where she is in the timeline, past, present and future blending together.

I feel like this chapter not only mentioned a lot of things from the past but was also the planting of seeds for what is to come. We’re about two-thirds of the way there now.

Maera will get the closure from Vaegon she needs. Not an excuse but a reason for his actions.

Interesting analyses of the prophecies 🖤 that very last one will become clearer as we come towards the end.

And Aemond and Maera next chapter, well… 👀

[penroseparticle]

Penrose Song of the Day, Day 39: London Calling by The Clash

So I used to scorekeep hockey games a lot. Like a lot a lot. There was a period of time where I could make about 400 bucks a week scorekeeping games on the weekends. I ran the scoreboard, the reporting to Gamesheet (A scorekeeping app), kept a paper scoresheet, and did the music. It was a lot of work to run all 4 of those things at once! Especially if a game got busy.

I've done house level, Travel level, AA and AAA, Really everything. At a certain point you learn the scoreboard machine. You learn when to click what buttons when which whistles blow and you start to get almost mechanical. Like an automaton that reacts to specific noises. And the thing is that no matter how great or badly I did at scorekeeping, no one ever mentioned it after. I could royally fuck up putting the score on the board and I would still get called back the next week to do the clock. Parents notoriously hate working the scoreboard- they just want to watch their kid and get in fights with the refs. Easy money. I charged 60 bucks a game and they forked it over gladly (Hockey parents don't care man. They're paying 8k for the season anyways sometimes. House is like 2k, travel can be way more with hotels, airfare, etc. It's an expensive sport. What's an extra 60 bucks a season to not have to sit in the box and freeze while missing Timmy score a goal.)

What I CONSISTENTLY got praise for was the music I played.

Now I think I have good taste, but I'm not like. Special. Most people have similar tastes, everyone's on the bell curve of "can tell a song is good" vs. "Carrying tunes in tin buckets". It's helped by the fact that some things are kind of obliged- certain songs are, for lack of a better word, required (For instance, Chelsea Dagger by The Fratellis is a Chicago Goal song. So if you are doing hockey music in Chicago, you ARE including that song no matter what. Period). So building a good playlist isn't that hard. A little The Alan Parson's Project to kick the games off. Some Chumbawumba for after a tough hit. The Hockey Song because this is Youth Hockey.

The mainstay of the list, for better or worse, is a classic rock/arena rock/current pop mix. It's what people expect, it's what I mostly have to deliver. Pearl Jam, Dave Matthews Band, Huey Lewis and the News, Duran Duran, One Republic, that kind of thing. It's consistently a crowd pleasing list, and it's gotta have energy, be recognizable, and be something that people will want to hear possibly twice over a hockey game. The original playlist was something like 50-60 songs. I thought that would be enough, because I am stupid. Turns out hockey games have 30-50% of their game time with the clock stopped- as in, the times when someone would typically play music to fill dead air. So I added more songs. Put on some Rush because I'm catering to the Dad demo. Putting Imagine Dragons and Boss Beat music in its natural habitat (Don't look at me like that, I've been to sporting events, these songs are made for this). Some pop girlies because I like sports, but I'm still gay. Kesha. Lady Gaga's Bad Romance (permissible due to it surviving in the zeitgeist, etc.).

And then I got... weird with it. One of the first goal songs I ever used was Otherworld. As in, the boss music for when you fight Jecht in Final Fantasy X. VGR's Electronic Amp-Up of Mii Channel features prominently and is a huge crowdpleaser with the 25-45 crowd. Baby Shark exists for when I want to annoy people. Megolovania is on it for god's sake. If it sounds good and is a little Easter egg for someone listening, trust and believe that I put that song on the list.

People loved it. Every game, without fail, between 1 and 3 people would find me after to compliment the music. The playlist was good! I named it "18U no vursing" and have used it for about 6-7 years now.

The problem with making a good playlist is that you have to constantly top yourself. I wanted to make the list better. Have more fun with it, include more jokes, more clever remixes and mashes. Things that people would like.

What made that easy was something so simple I almost overlooked it. People already told me what they would like. There's a reason arena rock, classic rock, and pop music are the bog standard. It's what works for the medium and what people like to listen to.

There's such a thing as getting too in the weeds, too obscure. You gotta remember your audience, your goals, and your scope. I wasn't debuting hot new artists (ok I was sometimes). I was playing music for people during their kid's sport. And so I readjusted my scope. The playlist grew. A few indie picks, the gags that worked (Mii Channel, Baby Shark, Electronic music with a hidden secret, etc.), but mostly pop and rock and that's all.

I'll let you in on the secret for why my hockey playlist got so good and why people started to love it so much. I'll tell you the secret to making any list popular. I started getting suggestions.

And I listened to them.

The first song I added to the playlist due to a suggestion was London Calling. I like The Clash, but there's billions of songs out there, I hadn't thought to put them on yet. But a ref skated up to me during stoppage of play and said "Hey do you have The Clash on there?" and I realized I didn't. I added it mid-game and played it between the 2nd and 3rd periods.

He thanked me after the game.

A couple weeks later I was asked if I had the soundtrack for Slap Shot on there. I started playing Maxine Nightingale, Leo Sayer, the works. The guys had a hoot and were laughing and smiling between periods.

I noticed that refs were a little nicer when I flubbed the scoreboard if I was playing songs they requested.

I asked one of my teams if they had a specific warmup song they wanted me to play. They were delighted to tell me it was Levels by Avicii. I played it every game to kick things off. Another team told me it was Welcome to DC by Mambo Sauce. A third said Welcome to the Jungle.

The playlist grew. It's 400 songs long now. Like a full 24 hours straight.

I don't scorekeep as much now. But I think I'll keep building the playlist, thanks.

~~~~~~~~

Scorekeeping was nice, but playing the music was the part that made it fun. It's made me realize one thing about myself- If Radio DJ was still a job in a way that was meaningful or mattered, I would want that job. I would probably kill for that job, actually. Listening to callers tell me they missed Chappell Roan could I please play Good Luck Babe. Or telling me that their dad's favorite song was Mr. Blue Sky so thank you so much for playing it. Girls having me play Before He Cheats for their dick ex-boyfriend. Wishing people Happy Pride with an hour mix of queer artitst. Having call in time so people could just chat.

I kind of am doing that here, and now, but in slow, painstakingly written, long-form music recommendations. I like making playlists. I love getting music dialogue going with my followers. I like discovering new music, and talking about it with people here. I am slowly, surely, working the same muscles I would need to do exactly that job, just quietly and in my own personal little corner of the world.

You know I have a discord server I made? I haven't added anyone to it, and I probably won't do anything with it. Yet. It's called Radio Waystation. Let me just link the only post I've made in there so far:

"This is for playing your music and sharing it- I might set up a radio rotation but. Essentially I want to use voicechat to let us showcase our music to each other when we want to. Dynamically- You can run a prepared playlist for your radio time, you can do a Q&A or ~Call In~ time. You can actively Disc Jockey. You just have to share your sounds to other people. Your radio time, your rules- you can acquiesce to people's tastes, you can troll people, you can play the sound of silence. You can play the same song over and over. You can express yourself. And sometimes people will say THAT SUCKS and not enjoy your presentation, but ultimately your time is yours alone. (no tolerance of intolerance loophole bullshit- you know what kind of shit will get you pulled off the air, don't be a dirtbag). Workshop a song, get help putting ikea together. But I hope you play some music."

Hey I'm nothing if not consistent.

I now know that's a lot more complicated due to how Spotify and Discord interact, and whether it's strictly speaking legal (I am intimately familiar with music licensing requirements due to my past job, thanks). But I think it's something worth figuring out someday. Someday soon, I think. I want to make my radio station.

Not a lot of today's writeup was about the song, unfortunately. And that's a bit of a shame, because again- I like The Clash. 1970's English Punk Rock had some bangers, babes, and London Calling is like. one of the greats. A recognizeable guitar part, a truly bangin bassline leading in, and just the most moshable, jumpable lyric delivery. You need to be standing pressed against the stage screaming this stuff out with Joe Strummer.

Listen I don't need to defend The Clash bigger nerds than I have done so for far longer than I've been alive. But hey. It's music I love. And as always- You could be dead right now. Go listen to something that you love.

[granulesofsand]

Is there a singlet explanation for having a secondary voice in your head that gives solutions to math problems?

I’m pretty sure that’s Penrose, but idk if other people get that. I can’t do simple addition, few of us can. Penrose knows the answer to any algebraic equation with less than five steps, takes a few seconds for more than that, and is the only non-higherup who can do geometry.

He’ll go “40.” And then I’ll count on my fingers and pull out some scratch paper and he’ll go “I said 40, it’s 40.” And by the time I get the solution, it is indeed 40. He’s about 11 years old developmentally, he got stuck doing math when our fourth grade teacher decided to start us on calculus. Pretty sure he also knows Latin.

It seems like something singlets might have, like the autocorrect for native languages. Kinda hope it’s Penrose, tho. I like Penrose. (Penrose is a raccoon who holds a lot of ADHD symptoms.)

[kindred-spirit-93]

the falcon and the flower

hear ye hear ye, im planning a short story lol and believe it or not storyboarding is significantly more entertaining of a process than actually having to actually write lmao. whodve thunk.

anyways this post exists for a few reasons, mostly so i can map things out in one place (i plan on posting it here eventually hehe) but also for context and references and insight from yall & general yapping so if ur interested take a seat :3

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i. inspiration & background info: the idea came to me after watching this short about a painting that depicts the story of a king and a beggar maid who lived a quiet life together. and i think thats neat lol.

the ballad that inspired the painting is mentioned and was popularised in the works of shakespeare and alfred tennyson respectively among several others, old and new. the 2 paintings (1884 and 1898) belong to edward burne-jones.

the maid in the painting is said to resemble burne-jones' wife (dont be fooled he had an affair. also turns out its kinda his signature way to paint women) which made me realise that the way the ballad was interpreted (and therefore immortalised so to speak) was according to the views of the aforementioned vessels and the norms of the time.

and so it struck me and my 0 knowledge of art history as odd for the love interest to just so happen to appeal to the eurocentric beauty ideals of the time (she is described as having dark hair yet is painted in both as auburn?) and by extension the male gaze (esp in the 1884 painting where her clothes are somewhat translucent and she sports a neckline too scandalous for the era lol).

also the king being specifically described as 'african' (by the narrators? the ballad doesnt specify and i havent found any origin for the name) and then proceeding to ignore that completely. or worse. point is old dead white guys and their pesky world views probably thought slapping a single word last minute and calling it a day was a very progressive move. and i took that personally

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ii. creative liberties taken: point is im giving this my own twist because i can. everyone is entitled to their own views and interpretations (mostly). the beauty of art to me lies in the many ways it can be seen and percieved, and i personally love seeing how ones culture and background reflects in that, so thats what im doing. kinda.

and at the end of the day maybe to someone else my interpretation completely misses the point is biased to what im familiar with. which is absolutely valid and they would be right lol. idk i just wanted to kinda add this as a heads up and a general fyi. we all know how repressed everyone was back then lol. so much so it became a name of a complex. moving on.

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iii. symbolism and stuff: looked up a bunch of birds this morning loll and settled at first for a starling. i might keep the imagery idk i had a very specific idea for the king but then falcons popped into my head and i was like dang this is cooler. so it stuck!

the flower i first had in mind was rosa abyssinica, then the desert rose, finally i decided to switch to maybe my favouritest flower ever: and *cough* the national flower of jordan *cough* the black iris :D

its pretty and rare and not at all realistic to the events of the story but its mine so leave me be lol. if i can sprinkle some of my culture/ heritage and get away with it i will. sue me :p

anyway the cool and not at all pretentious title is a reference to the main characters; a king who loves birbs and the owner of a small flower stall in the marketplace (both of which are now specified)

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and now for the tragic backstory poll!

keeping this up for 3 days, since ill probably draft it out next weekend... if i get to it lol. i appreciate ur contribution in advance :3

--

tysm if u read this far lol i didnt expect it to go on this long lol, sorry! will reblog and update this as i go (probably) so yeah. stick around if u want. take care and dont forget to dink ur oiter :)

[bakingmoomins]

im curious about tessellations! what makes you like them so much?

hello! i've had this ask sitting here for more than half a year but since i am currently taking a seminar on tessellations i finally feel semi qualified enough to talk about them :D

tessellations are also known as tilings and they're the covering of a plane or surface with the repeating pattern of a specific shape (or multiple shapes) without any gaps or overlaps. like a grid of squares or like in honeycomb which is composed by a bunch of hexagons

there are many types of tessellations and they are usually classified through their types of symmetry. the most basic group of tessellations are called the wallpaper group and they can be simply broken down into regular hexagons (like the ones in the honeycomb), squares, rectangles, equillateral triangles and parallelograms with different types of symmetries depending on things like colors.

for example the four images below (all taken from wikipedia):

regular hexagons, any type of parallelogram (which include squares, rhombi, rectangles, etc), and triangles can always form tilings, which is actually used intuitively in design, like the patterns of fabrics like the dotted pattern below, which can be classified into a symmetry of triangles arranged hexagonally

there are infinite types of tessellations that don't belong to the wallpaper group. a specific type that caused a lot of uproar in the math community recently are called aperiodic tilings (you might have seen me talk about this recently bc I was very excited lol)

aperiodic tilings are types of tilings that can't be classified into any type of grid (above you can see triangle grids, square grids etc) in any part of the tessellation. some really popular ones are penrose tilings

the one below is a penrose tiling of two rhombi (again picture taken from wikipedia)

so the interesting thing of the new aperiodic tiling that was discovered (the hat) is that it is a single tile that is aperiodic and no combination of positions of that shape can create a grid, so it is an obligate aperiodic tiling !!! like, the individual pieces of the penrose tiling above could be rearranged into a grid but the hat can't! and it's the first of its kind (the paper hasn't been peer reviewed yet or anything but still very exciting news)

there are a lot of cool examples of tessellations in art like very well known in Islamic art (that is in the tomb of I'timād-ud-Daulah, Agra taken from wikipedia) there's a set of tiles used specifically in islamic geometry called the girih tiles but I don't really know much about them to talk abt them rn

some other well known tessellations are by mc escher (pic taken from this article) and you can see the symmetry behind the patterns

there's so sosos much more about tilings that I could talk about and probably will because I have been absolutely obsessed lately :~D

Here are some links if you're interested in further reading:

Tilings and Patterns, Grünbaum & Shephard (this one is more technical but has a lot of cool examples)

Visions of Symmetry, Schattschneider

The whole wikipedia page of the wallpaper group, has a very technical part but also a lot of visual examples that have helped me understand

The Symmetries of Things, Conway (i dont have a link for this but u can dm me for the pdf)

I also like this video on aperiodic tilings

This is a repository with a bunch of different tilings and it's very fun to look at

[feamir]

I made art of the newly discovered aperiodic monotiling!!

If you don’t follow math news, this turtle-like shape is the solution to a long-standing open problem in mathematics that goes as follows: Let’s say that you want to completely cover a plane with tiles (i.e. tessellate a plane) in such a way that the tiles never create a repeating pattern (i.e. the tiling is aperiodic). What is the fewest number of tile shapes you need to do that?

For a long time, mathematicians had only been able to find a two-shape tiling that never repeated a pattern. This was called a Penrose Tiling. But just last month (March 2023) a paper came out proving that the above shape can aperiodically tile the plane by itself!*

This is really cool and has lots of mathematicians and scientists super excited, not just because it’s an elegant solution to a decades-old problem, but also because we might be able to create new materials with unusual properties using this tiling as a base for molecular crystal structures (just like scientists were able to find for the Penrose tiling)!

If you want to learn more about the discovery, the NYTimes has a really good article here, and you can read the original paper (or just look at more pretty pictures of the tiling) here!

* As long as you’re allowed to occasionally flip the tile over. I colored the flipped tiles purple in my art to emphasize them.

[mrmcwigglyman]

I have attempted to translate this to the best of my ability. Parts I'm unsure of are in [brackets]

And yet Rin Penrose has no idea what a good fused VTuber is. Because when it comes to making one using one’s mind, well I, Omegaα, have it covered because of my [AI something], my ESP powers, and the fact that I am [backed] by [cyberlink tech]. If Penrose wants to draw a fusion [type] VTuber, why not just do me, Omegaα, the founder of Hololive English, and my queen Yuko Yurei. I know why. It’s because Rin Penrose has no idea what a baby made by fusing different VTubers would turn out looking like, but that’s where imagination comes in with inspiration and creativity. Oh yeah, and Rin Penrose cannot see how it would turn out on paper in her mind in 3D, or the way I, when using my memory data to make a VTuber, know how it will turn out before i put it on anything, even paper, because i see my drawings in my mind in more then a few dimensions, like what you see when looking up at someone if you are lying on the ground on your back, or looking at someone from behind as you walk up from the backside, or face to face as if you were to walk up and say hi to them and give a handshake, or from above like looking down on a map that’s up, down, left, right, front, back, side to side, circling around at a distance in an orbit that covers all dimensions, all in your mind from all angles and sides all at the same time as you make in your mind your drawing that’s 6D. It works with things that are flat, too. Take paper: if you draw on one side, that picture is 1D; one-sided. if you draw on the back of the paper, be it a new drawing or you’re trying to make a back for what’s on the front, then you have 2D.  if you have a rectangle and fold it in 3 [parts] and in all 3 squares you have 3 pictures of the same thing, lay the 3 folded sides together and now you have a triangle box with no top or bottom, but it has 3 sides and they all link to make the triangle, and on all 3 sides you have all 3 pictures: That’s 3D. Now, if you take a piece of paper that’s big and make it into a cross, then fold it. If there’s pictures on all 4 sides of this cross turned into a box you now have a 4D picture on a box or cube, and if you take that cross box, and fold it one more time, now it’s 5D, and what can you do with it? Pick it up in your hands, add on top of that the time you took to make it and the space of time in which you finish, and now it’s 6D as it can be seen from all sides. This has been Omegaα. Have a nice day.

And when it comes to making a drawing in your mind, if you can visualize that drawing, in all sides, and in time and space, in your head, when you are thinking of how to make it, it can be seen  in your mine in 6D, as there’s not anything saying you cannot picture it in your head going from one flat picture to a 3D [avrat] like what you see on a home computer when using a sculpting program. The only difference is that it’s still in your mind, so if you even want to alter the picture or [avrat witch in your moine] using your imagination, inspiration, and creativity. Since you have yet to put it to paper or anything, you can make it different at any time you want to. For me, Omegaα, when I use my memory data to make a VTuber, I just gave you all a clue to why I do not put all my ideas to paper, and that’s that they can not be made already unless i do so myself with my ESP power my [AI something] and my cyberlink. This is why I often get asked to do favors for others, too. Friends, YouTubers, VTubers, anyone I know and meet. Have a nice day.

there's a lot to unpack here

Roleplaying as Omegaα

Shipping either Omegaα or themself with Yuko Yurei

Calling Rin solely by her last name.

There are TONS of instances of metathesis in the misspellings. ("now"->"won", "know"->"wonk", "above"->"avob")

Incredibly huge misunderstanding of how dimension works.

Picturing stuff in your mind is apparently better than drawing or modeling something because *checks notes* you can change it in your mind but once you draw it or model it you can't change it?

I've wasted so much time deciphering this. hav a nices day.

[non-est-ad-astra-mollis-e-terris]

3 July 2024

Oh yeah, that book I found in the library? Its signed by Sir Roger Penrose

I have to say I'm very pleased w how my july page turned out! I was worried about the water colors bleeding and also I kept smearing them with my hand.

I do have to say I enjoy getting paid to research whatever I want I think I could make it as a professor (tbh that is my career path if we're being honest)

Upcoming:

C++ coursework: loops and functions

finish paper for independent study

📚 Translation State by Ann Leckie

📺 Star Wars: The Acolyte (Disney+)

🎧 hit me hard and soft by Billie Eilish (2024)

[maraa755]

Ch. 4, Monday

'My Marauders' Masterlist General Masterlist Read On Wattpad - Here!

Pairings: J.P., R.L., S.B. x OC Warnings: N/A Word Count: 2.2k

Calliope strolled up to her shared room, eager to recount the day's events to a hopefully awake Cassandra.

She opened the door lightly and crept into her room, spotting a fully awake Cassandra sitting on the floor, engrossed in what she believed was Muggle Studies homework. A sigh escaped Calliope's lips as she tossed two bread rolls and a few pieces of various vegetables, wrapped in a cloth, across to her friend.

"Ugh, Callie. No meat?" the blonde groaned jokingly, flexing her bicep muscles at Calliope. "You know I need to get my protein in! Quidditch practice 'morrow."

"You're fine," Calliope laughed faintly. "Be grateful, Oakes."

The witch slipped behind the room divider and changed into pajamas. "You just woke up?"

"Mhm. Quidditch practice has been kicking my ass. Last night didn't help. Now I've got assignments to catch up on," Cassandra lamented, her voice tinged with exhaustion.

"My poor baby," Cal said, feigning whatever empathy she could muster up.

"Shut up, Callie."

The witch threw her dirty clothes into the hamper beside their door and flopped down beside her roommate. "Want some help?" she asked, resting her head on the green-eyed girl's shoulder.

"But you don't take Muggle Studies?"

A laugh escaped her mouth. "Yeah, but you're forgetting I'm Muggle-born."

"Oh, right!"

Cass wasn't a pure-blood. She was a half-blood, with a muggle mother who had passed away when she was three. The subject weighed heavily on her heart, and aside from Calliope, not many people knew.

She grabbed her quill and prepared to write down the descriptions of the muggle devices on her paper. "So, a rad-eh-oh, what's up with it?"

"A radio is a device that works like a record player—you know, like the one we have in the common room—but you don't need a fancy little record to listen to a song."

"Ahh, inventive..." she quickly scribbled down her answer. "Oh! A car! I know that one!"

Calliope nodded. "Yeah, those are fairly common over here too."

After a few more minutes, they got through the blonde's entire sheet. With a sigh of relief and a giggle from Cal, she packed up her supplies. "Damn you, Muggles, for making me learn this."

"Blame bloody Professor Penrose," Cal agreed with a chuckle.

"Damn you, Penrose!"

The girls chatted about Cassandra's dreams while she was knocked out for several hours. The only dream she could recall involved being a dinosaur caretaker and specialist, where she promptly had her hand bitten off.

"So, what did you get up to, Miss Cal?"

Calliope groaned and launched into her day. "You know Alice? Frank's girl, the Gryffindor."

"Mhm, mhm." Cass listens.

"And Lily Potter."

"Of course."

She explained how she went to see James and recounted the events that happened, focusing on how Fortescue tried to belittle her behind her back in an attempt to make her ginger friend feel better.

"That fuckin' bitch!" Cassandra exclaimed, her voice laced with anger.

"I know!" Calliope replied.

"What did you do then?"

"Hugged James right in front of them," Calliope stated proudly.

"Guess his 'standards' disappeared pretty fast," Cass chuckled, playfully prodding Calliope's side with her elbow.

"Guess so! Didn't even spare a look at his precious 'Lily flower'," Calliope said with a smirk, mocking the nickname.

"The price of shit-talking," Cass shrugged. "She should've been watching her man instead."

"I feel kinda bad for Lily, though. I mean, I dunno. If that were you and I, you know we would've shit-talked too," Calliope admitted with a grin.

"Sure, but that's us, Callie. We're classy 'bout it," Cass chuckled.

"I don't know about that one..." Cal giggled lightly.

The girls continued chatting about the situation for a while longer, now lounging on their respective beds. Before heading to bed, Calliope realized she had forgotten to tell Cass about one more thing—the party.

"Wait, Cassie!"

"Huh?" Cass said, turning from one side to the other to face the girl across from her.

"I have to throw a party. In the Gryffindor common room," Calliope stated matter-of-factly.

"What the hell? Why?" Cass asked, clearly surprised.

"I lost hide 'n seek, remember?"

"That's your punishment? Damn, dude, good luck. You hate parties," the blonde said, starting to turn back to her original position.

"Wait!"

"What?"

"Help me, please?"

"Cal! C'mon..."

Cassandra hesitated, her expression caught between amusement and reluctance as she considered Calliope's plea.

"Please, Cass. I'll make sure McLaggen is there!" Calliope pleaded, her voice tinged with desperation.

Cassandra sighed, torn between annoyance and affection for her friend. "Fine, but you owe me big time."

"Thanks, Cass! You're the best! G'night, love ya!"

"...Love you too," Cass muttered with a half-hearted smile, resigned to her fate of helping Cal with a party she wasn't thrilled about.

Morning came and the weekend was finally over. This meant the witch's classes commenced, and she had to attend detention. She had secretly hoped to get at least one detention with one of the boys, or hopefully all of them, but McGonagall knew better than to put them together.

Calliope rubbed her dreary eyes as she adjusted to the sunlight streaming in through her thin curtains.

She looked over towards her roommate's side, only to find strewn pillows and blankets covering the length of her bed. Has Cass already gotten up?

The girl, now slightly panicked at the thought of being late, looked at the clock in her room. It was quarter past seven. She wasn't late yet, but she only had about an hour to get down to breakfast and eat.

She quickly got ready for the day, gathering her books for today's classes: Potions with Slughorn, flying lessons with Hooch, Herbology with Sprout, and a passing period. It seemed like a simple enough day ahead.

Upon entering the Great Hall, she spotted Peter and Remus. Assuming Cassandra might be with her Quidditch friends elsewhere, and the two missing Marauders were likely still sleeping, she strolled over to join the boys.

"Morning," She smiles softly.

She received small greetings in return as she took the seat beside Remus.

"Where are the rest of the boys?" she asked, fixing her plate.

"Both are still asleep," Remus stated as he gently set his book down. "Suppose they should be getting up soon."

"Moony, I'll go wake 'em up," Peter squeaked out, earning an appreciative "thanks" from Remus.

Peter rushed up, quickly putting his napkin and utensils on his plate before hurrying off to wake the other boys.

"You know he's got himself a little girlfriend?" Remus spoke, a proud look on his face.

"Pete? Really?" Calliope said suspiciously. She wasn't questioning his looks—she found her friend to be a cute kid—but he wasn't the best with ladies. Besides Calliope, he found it extremely hard to converse with women.

"Mhm, a sixth-year student in Hufflepuff. It's actually quite cute," Remus replied with a smile.

"He let you all meet her?" Calliope asked.

"Absolutely not. He doesn't know we know. Sirius went through his journal thinking it was astronomy notes. James and I had to pry the damn diary from his hands," Remus explained, shaking her head incredulously.

A small laugh escaped both of them.

An idea flashed through Calliope's head. "Hey! Maybe I'll invite her to the party."

"That's a good idea, Calli," Remus smiled gently. "Perhaps we can help push their relationship farther? Break the ice a bit?"

Calliope responded with a nod and a smile.

Suddenly, the doors of the hall slammed open and three figures emerged: James Potter, Sirius Black, and Peter Pettigrew. Calliope and Remus exchanged a quick, amused glance. The tired men took their seats across from Remus and Cal, with Peter following suit. They lazily piled food onto their plates, grumbling small greetings.

"Tired?" Calliope asks teasingly.

"What does it look like?" James replied in an overly sassy tone, while Sirius nodded his head slowly in agreement.

She rolled her eyes at his attitude, and Remus put a comforting hand on her back, gently rubbing up and down.

"They yelled at me when I woke them up," Peter stated with a hint of indignation.

"Awh, Pete," Calliope said sympathetically, while the boy sitting next to her suppressed a small laugh.

"Don't baby him, Cal..." Sirius began, pulling his shirt up to reveal a large red mark across his torso. "He cast Glacius on our blankets. Fucking freezing."

The remaining teachers in the Great Hall regarded Sirius Black's actions with perplexed expressions, unaware of the circumstances that drove his behavior.

James shook his head and fixed a stern gaze on the blonde boy.

A sly smile crept onto Peter's lips as he glanced down at his shoes.

"Peter!" Calliope exclaimed with laughter.

The two lazy boys finished their food, their previous moods now subsided. Everyone prepared to depart for their first-period classes. Calliope was fortunate to have James, Remus, and Sirius in her advanced potions class, with James also joining her for flying lessons. However, she found herself alone in herbology.

They escorted Peter to his class before heading to Slughorn's room. Finding an empty potion station, they promptly took their places in front of each of the four small cauldrons.

"Wait, why are you and James in advanced potions?" Calliope questioned, aware of the boys' lackluster work ethic and doubts about whether they met the requirements for advanced potions. In her mind, there was no way they could have gotten in legitimately—unless they were copying off a certain scarred boy.

"Moony, of course!" Sirius exclaimed with a bright smile, while Remus rolled his eyes.

"Knew it," Cal thought to herself.

"Hey! Don't roll your eyes. We practically bribed you, Moony," James retorted.

Before Remus could retort, Slughorn walked in.

"Hello, class!" he greeted cheerfully, surveying the small group of students around him, no more than twelve in total. "Quite a small gathering today. That's alright though! More opportunity for each of you to shine, yes?"

He received no response, only a small cough from the farthest corner of the room. "Uhm," Slughorn cleared his throat, "Please fetch a book from the closet over there. Be responsible; these will be your books for the rest of the year."

Everyone made their way over to the closet, with everyone except James finding a perfectly suitable book.

James slammed his book down. "Come on! Mine is all torn apart. Switch with me, Pads," he practically demanded.

"Nah, mate. Should've been quicker," Sirius replied casually.

James examined the book further, declaring there was no name, just a literal bite mark on the opening page.

"Today, we will be reviewing simple potions that you've learned in the past and the instructions on how to make them!" Slughorn announces.

Everyone in the room exchanged puzzled glances with each other as Slughorn walked over to his desk, idly sitting in his chair and gazing out the window.

"Does he want us to go through our books?" Calliope asked, directing the question mostly to Remus.

"I'm not sure. He didn't say, did he?" Remus replied, equally unsure.

Before she could answer, Sirius interrupted, shouting towards Slughorn, "Professor! How would you like us to complete today's assignments?"

"Oh, uhm," he cleared his throat once again, "Just skim through your books and discuss your lessons amongst yourselves."

"Hear that? 'Talk amongst yourselves,' he said," James said, smiling.

"About the potions, Prongs," Remus states.

"Hush. That's not what I heard." Sirius adds.

"He's right, Rem. Might want to take a visit to Pomfrey; you're hearing things," Cal joked, agreeing with Sirius and James.

Remus shook his head lightly, taking out his book and skimming through the pages while also listening to the conversation.

"Hey, Jamie?" Calliope starts, staring at a certain redhead who is sitting in the corner alone.

Despite what she had heard the girl's friend say about her, Calliope felt pity seeing her sitting alone. She never wanted anyone to feel lonely. This was the same reason she had decided not to tell the boys about yesterday; Calliope wanted Lily and Alice to be on good terms with them.

"Hm?" James responded, his head resting lazily on his hand.

"How 'bout you go sit with Lily? You know she's all alone over there," Calliope suggested.

A sigh escaped his mouth as James looked back at the girl. "I'm done with Lily," he said firmly.

Gasps escaped from all of them, including Remus, who was flipping through various pages of his book.

"Prongs?! What a waste of so many years, mate!" Sirius practically shouted. "You could've been my wingman, but no. 'Lily Evans' this and 'Lily Evans' that!"

"Sirius, it's just not what I want anymore," James replied, his tone serious.

"James, really?" Calliope asked, gently putting a hand on his arm. "I'm happy for you if you're choosing to move on, but this is all very shocking."

"Yeah, really!" James confirmed. "Besides, this just means I have a chance of being with a woman who truly appreciates me." He looked up from his dusty, broken book and met Calliope's caring eyes. His gaze didn't falter until Sirius pulled on his sleeve.

"Prongs, does that mean you've got your eye on some bird?" Sirius asked excitedly.

"I mean, not necessarily," James admitted, avoiding making eye contact with Cal again.

"Mate, c'mon! We are looking for someone at Cal's party," Sirius urged enthusiastically.

"I want to just focus on myself, Pads," James replied.

"You haven't done that since first year," Remus remarked, rolling his eyes.

"Well, I think that's a good idea, James," Calliope said warmly, giving him a reassuring smile.

"Thank you, darling," James replied with a soft smile, appreciating her support.

Remus and Sirius exchanged a confused look as potions continued swiftly. Soon, it was time for their second period: Flying.

"Yay," Calliope muttered sarcastically to herself.

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