#<- enjoys math

[libraryofgage]

After checks calendar 84 years, I am once again offering Smart Steve content lmao

Listen the writer's block has been hitting recently if you couldn't tell, but I'm still happy with how this came out.

As always, if you see any typos, no you didn't :P

----

So.

Steve Harrington is smart.

Like, smart smart.

Like, the kind of smart where he not only understands shit, he can explain complicated shit to Eddie without sending his brain into a coma.

It's been two weeks, and Eddie is still trying to come to terms with this discovery. He's four tutoring sessions in and a little spark of surprise still rocks him whenever Steve can easily explain a new topic using the stuff Eddie likes.

He explained velocity using D&D spells. He explained electrical circuits using the concept of plugging a guitar into an amp. After asking a few questions about Lord of the Rings, Steve Harrington managed to explain the in-depth concepts of magnetism using the fucking One Ring.

How the fuck is Eddie supposed to be normal about any of that? Ignoring the sheer fact that Steve is capable of it, how is Eddie supposed to feel about the...the willingness to learn what Eddie understands best and meet him on that level?

If the answer is awed and practically starstruck, he's ahead of the game.

"Hey, you doing okay? Kinda spacing out over there, man."

Eddie blinks, the textbook in front of him coming back into focus. Steve had been explaining the concept of momentum, but his words just floated in one ear and out the other because Eddie was once again consumed by the absurdity of the situation.

It's not like he can say that, though. So, instead, he settles for a grimace and pushes the textbook away. "I think I'm all fried out for physics," he says, looking up at Steve.

"Oh," Steve says, blinking a few times before nodding. "Yeah, sure, uh, sorry."

"Wait, what are you sorry about?"

Steve looks away, an awkward frown tugging at his lips. "I...probably wasn't explaining it too well, huh?"

"Woah, woah, no way," Eddie says, putting a stop to that train of thought before it can leave the station. He turns in his chair to face Steve directly, ignoring how the metal rod that attaches it to the desk digs painfully against his shin. "Listen, Stevie, I've never understood physics more than when you explain it. Like, I don't know, man, whatever you're doing works."

Steve must have been more worried than he let on, because Eddie can literally see the tension draining from his shoulders. "Great," he says, rubbing the back of his neck as he glances away. "Seriously, that's great. I'm glad nothing's been confusing."

"Yeah, so, nothing you did," Eddie says, feeling like he needs to reiterate that point to drive it home. "Honestly, you could probably even make me understand geometry. Not like our teacher is doing shit to help."

"Do you...not understand geometry?" Steve asks, looking a little unsure like he can't tell if that's a joke or Eddie's attempt at suggesting another class he needs help in. This one is a class they share, which means Steve will have seen Eddie's floundering attempts at answering questions, and he feels a whole new burn of embarrassment course through him.

"Do you?" Eddie asks in return.

"Yeah. It's just, like, angles and shit, man."

Eddie stares at him for a moment, eyes narrowing and trying to figure out if Steve is somehow, subtly, making fun of him. But of course he isn't. If Eddie has learned nothing else, it's that Steve doesn't ever think Eddie is actually stupid or deserving of ridicule. He just thinks Eddie hasn't been taught properly, which is more on the teacher than him.

After a moment, Eddie twists around to dig in his bag. He pulls out his geometry homework, slaps it on the desk, and gestures at the triangles and squares and other shapes with unidentified angles and side lengths. "I have literally no clue what the fuck is going on here," he says.

Steve moves closer, looking over the sheet with a slight frown. Eddie knows this face by now. It's the one Steve makes when he's searching for the relevant knowledge in his own brain, pulling it to the front so he can easily identify the gaps in Eddie's understanding. "So, how would you start?" Steve finally asks, offering his pencil.

Eddie takes it, twirls it between his fingers a few times, and looks over the questions. He eventually chooses one asking him to find the length of a side. "I know this one. It's the equation with the squares and shit," he says, carefully writing it out and plugging in numbers under the triangle.

"Right. Pythagorean theorem. A squared plus B squared equals C squared."

"Yeah. That," Eddie says, working through the math on a separate sheet of paper instead of in his head. He can do easy addition and subtraction, but one of the first things Steve did was get him used to using scratch paper. His brain doesn't feel quite as crowded by numbers anymore; now it's just crowded by the endless rotation of bites of knowledge and equations that have nothing to do with the work at hand. It's like his brain can recognize that it needs to remember something, but can't identify what exactly, so it just offers up everything.

When he's done, Eddie shows Steve his work, the answer circled at the bottom of the scratch paper. "Perfect," Steve says, flashing a smile that makes Eddie's heart lurch dangerously. "Okay, so that's solid. What about this one."

He points at a right triangle with only one angle listed and the other marked as unknown. "No fucking clue," Eddie says.

"This one is asking for the unknown angle. It'll just be some subtraction."

"It's only giving me one angle, Stevie," Eddie points out, gesturing to the angle marked as 53. "What the fuck do I do with that?"

"Well, the main thing is that a triangles angles will always add to 180. Also, this is a right triangle," Steve explains, taking the pencil from Eddie to circle the L-shaped corner of the triangle. "This angle will always be 90 degrees on right triangles. Should I keep going?"

"No," Eddie says slowly, drawing the word out as he takes the pencil back. "I'm starting to get it. Lemme try."

Steve waits patiently as Eddie hesitates before adding the angles together and subtracting that from 180. When he gets to a solution of 37, he gestures for Steve to check.

"That's right," Steve says, nodding as he points to another triangle on the sheet. "For this one, I'll teach you about the SOH CAH TOA trick."

Eddie nods, paying as much attention as he can, but he can't help feeling a little distracted by Steve's happy smile and relaxed posture. He's never seen Steve like this during class, and he's struck by the sudden notion that nobody else will see Steve like this, either.

------

When Steve gets home, he drops his bag in the hallway, grabs a soda from the kitchen, and collapses onto the couch.

A few National Geographic and Scientific American magazines are still spread out across the coffee table. A brief glance reminds Steve that none of the stories were particularly interesting in these editions.

He pops the tab on his soda, takes a sip, and glances at the phone on the end table next to him.

Steve had noticed something today. Eddie's shirt. Most of the band shirts Eddie wears are popular enough that Steve sort of knows them. Metallica, KISS, and AC/DC were recognizable since he's passed their albums on display in record stores.

Today's band, though. He didn't recognize that one. What the fuck was Manowar?

After a few seconds of thought, Steve reaches out and grabs the phone. He's just doing research. Wanting to understand the music Eddie likes is reasonable. That's how Eddie learns. There's no other reason for Steve dialing the number of an old classmate.

The phone rings a few times before picking up. "Amare residence," a girl says, sounding distracted.

"Hey, Dee. It's Steve."

"Hmm, Steve. Steve. ...Steeeeve. Oh, is this Steve Harrington, deserter of friends for the woes of public education?"

Despite everything, Steve can't help an amused smile. "Yeah, that Steve," he says. He doesn't apologize, since he knows that's not what she wants. If she was actually angry, she would've hung up.

"Well, how kind of you to grace me with your voice," Dee says, sounding distant like she's set the phone down. "I suppose I can give you until I finish braiding my hair."

"Great. You know about metal, right?"

"Like iron? Duh, Steve, I'm not thirteen."

"No, like, heavy metal."

"Iron is pretty heavy."

"Music, Dee. Heavy metal music."

"Oh! Aren't you a Tears for Fears kind of boy? What are you doing asking about heavy metal?"

Steve starts to answer but stops himself. He doesn't know why. Dee tutors kids all the time. Everyone in their private school group did. That's how they made money. She'd understand that he's trying to learn more about Eddie's interests for tutoring purposes.

So why can't he just say that?

"This long pause says you're thinking about lying to me," Dee says. "Don't bother, Steve."

"Well, I do want to know for the guy I'm tutoring. But not just because I'm tutoring him."

"Awww, are you trying to make a friend?" Dee teases.

Steve grimaces, wondering why his stomach twists slightly at the question. "Yeah, kind of. I want to know more about the stuff he likes. And he likes heavy metal. So, ya know, I thought of you."

"Well, you've come to the right place," Dee says. "And I love talking music, so I guess we can keep talking even after I'm done braiding."

A relieved smile tugs at Steve's lips. "Thanks, Dee, I appreciate it. So, first question, what's Manowar?"

-------

Tag List!

@estrellami-1, @ravenfrog,

[leona-florianova]

‘Must I put on silk stockings?’ ‘Certainly you must put on silk stockings. And do show a leg, my dear chap: we shall be late, without you spread a little more canvas.’ ‘You are always in such a hurry,’ said Stephen peevishly, groping among his possessions. A Montpellier snake glided out with a dry rustling sound and traversed the room in a series of extraordinarily elegant curves, its head held up some eighteen inches above the ground. ‘Oh, oh, oh,’ cried Jack, leaping on to a chair. ‘A snake!’ ‘Will these do?’ asked Stephen. ‘They have a hole in them.’ ‘Is it poisonous?’ ‘Extremely so. I dare say it will attack you, directly. I have very little doubt of it. Was I to put the silk stockings over my worsted stockings, sure the hole would not show: but then, I should stifle with heat. Do not you find it uncommonly hot?’ ‘Oh, it must be two fathoms long. Tell me, is it really poisonous? On your oath now?’ ‘If you thrust your hand down its throat as far as its back teeth you may meet a little venom; but not otherwise. Malpolon monspessulanus is a very innocent serpent. I think of carrying a dozen aboard, for the rats – ah, if only I had more time, and if it were not for this foolish, illiberal persecution of reptiles … What a pitiful figure you do cut upon that chair, to be sure.

Barney, Barney, buck or doe, Has kept me out of Channel Row,’ he sang to the serpent; and, deaf as an adder though it was, it looked happily into his face while he carried it away.

--Master and Commander, Patrick O'Brian

[lala-blahblah]

I get why people headcanon that Trucy would call Edgeworth "Uncle Miles" because it represents how close he is to Nick and Trucy and how he's basically part of the family etc. HOWEVER I cannot help but imagine the shock and horror of passersby who hear Trucy call one man "uncle" and one "daddy" as they watch Nick and Miles interact lovingly in public and come to the conclusion that Nick is openly cheating on his spouse with his spouse's brother.

[whalebearr]

AND THEN WE JUST KEEP ON WINNING ????

[alish-artie]

Imagining Little Mac still being a student and having to go to school after a boxing match like everything's okay is funny to me-

[mediamime]

Supernatural and the Concept of Grace

Hi! It's your friendly neighborhood Media Mime and I'm here with a wall of text about my insane thoughts on how Angels work.

From the TV show Supernatural.

I don't know what I'm doing with my life.

---

These are headcanons, mind you, so they aren’t supported by the show. I just think way too much about stuff like this.

This all stems from how beings from a different plane of existence would be borderline incomprehensible to humans. The whole, true form and voice not being viewable/hearable led to me thinking about them in more abstract forms.

I’m going to give you some weird background stuff below, but feel free to skip to the end if you’re just here for the Grace mechanics and things.

---

My day job is as a Math Adjunct, so you can imagine I have a bit of a fixation on recurring principles, formulas, geometry, and so on.

It’s my jam. 

Specifically, I have a focus on Mathematics in Nature. It's fascinating to me that we see the same shapes and patterns recurring over and over again in all natural formations.

I want to stress that to get into this kind of thing, you don’t actually need a background in Math. There are several resources online that provide examples and visual guides to this field of study. I’ve provided a visual guide below of some of my favorite phenomena as well as a basic (very basic) explanation of the principle. 

I ain’t getting paid for this right now, so you get what you get!

---

Now is also a time to mention that I took some psychedelics in my 20s that made me See Some Shit. This is not meant to be inspirational. I just think I should mention it because you see a lot of Stuff on them, not always Stuff you want to see. You can look up information about psychedelic geometry and skip the hassle of ingesting things you probably shouldn’t.

Don’t do drugs kids, or whatever.

---

The Fibonacci Sequence is where numbers ascend by adding the two previous numbers to itself. This plays a key role in something known as the Golden Spiral. For a very basic explanation, you take a square and draw an arc from one corner to the next and repeat with bigger and bigger squares.

1,

1 + 1 = 2,

1 + 2 = 3,

2 + 3 = 5,

3 + 5 = 8,

5 + 8 = 13,

and so on.

The curve itself is seen in the way plants grow, shells form, and weather formations to name a few. 

(The following are not my images, but they are readily available online. )

---

Tessellations are repetitive polygons (shapes with 3 or more connecting lines, think triangles, squares, hexagons) that form together, without gaps.

In nature, the real world, there are examples of malformations, but Math is an explanation of the ideal principle.

We can see these structures in scales, honeycombs, and so on.

---

Fractals are where we see the same pattern repeat at smaller and smaller forms of itself.

There is a lot of overlap of this with the Fibonacci Sequence (these patterns often appear INSIDE of the spiral), but it is its own concept.

Fun fact, fractals play a significant role in Chaos Theory, which I will not get into here because we would be here all day.

---

Anyway!

Sorry!

Carried away there.

Back to Supernatural (what an insane transition) and how this wraps into my concept of Grace.

---

Angels are filled with this kind of naturally occurring phenomena, a sort of endless collection of patterns. They are essentially manifestations of this idea or at least they process the physical world in this way.

Castiel mentioned eating molecules ONE TIME and well, I ran with it.

---

A couple of examples I feel strongly about, using Castiel as an easier point of entry than say, Lucifer or Gabriel:

Angels think in a series of sensations, like a form of Synesthesia.  Synesthesia is a concept explored in both psychology and cognitive neuroscience where people express the feeling of multiple senses activating at once. So for instance, the words might leave you with an impression of color or sounds may give you a physical sensation. I think Angels can, and do, adopt a more human perspective the longer they interact in the physical world. This is especially relevant during the time they are essentially made human, but I think the way they interpret information remains abstract. Just a fun fact, if you have Autonomous Sensory Meridian Response (which is usually shortened to ASMR), you have a higher chance, according to some studies, of having a form of Synesthesia. 

---

Angels also think in patterns. For Castiel, in the beginning: His thoughts are very vibrant. Primary colors denote curiosity. The structure of those thoughts are very rigid. He thinks more in straight lines rather than curves. The movement of the thoughts is calculated and repetitive. Learning something for the first time is difficult, so splitting it into individual pieces is easier to comprehend. This is where we get The Face from, you know the one. He perceives things in his own way which makes him socially awkward in human form. As he gets more familiar with the physical world, and the boys in general, his perspective shifts. He has more robust colors dedicated to the people or objects he interacts with and they shift around easier. His thoughts are less linear and more curved and organic. He has less set structure because he isn’t learning as much anymore, he has an understanding he can build off of and make more defined to himself.  Learning to love humanity requires flexibility that doesn’t come naturally to Angels, so he actively works at it.

Seeing souls is easier than interpreting the actual look of people. This is a doozy, but we will take Dean as an example because I’m Destiel/Deancas pilled. To Castiel, Dean looks the way he looks, smells the way he smells, sounds the way he sounds, and so on in physical form. Castiel learns to interpret him in that way as the series goes on, but his soul, the essence of him, has its own set of sensations. The following are not literal, although I’m sure some would translate that way. He sounds like a crackle of fire and a low drum. His colors are darker oranges and blues and greens. He feels like a soft rain and sun on a warm day. He tastes of barrel aged liquor and smoke. He smells like a hearth and earth after it rains. He feels like every aspect of the impala, from the cold metal to the supple warm leather.  Obviously some of these senses shift and change from time to time, but that forms the basis of what Castiel recognizes as Dean.

---

Grace is at least partially visible to other angels and partially felt by humans. Other angels can see each other in their vessels. So they have a concept of what they look like in their true forms, despite being hidden inside of something.  This implies they can experience similar sensations as the other angels they look at, although I don’t like the idea that they can see their “thoughts” necessarily. I would imagine they can “feel” a sudden intense set of emotions/sensations from another angel however, in the way that humans can tell someone’s emotions through facial expression or tone of voice.

---

Humans can learn to experience angels, albeit in a form that is easier for them to comprehend.  Dean doesn’t experience anything special about Castiel when they first meet, outside of the generic information we get about Angels and the obvious senses he can use: seeing, hearing, smelling, (gods I wish tasting was on this list but! Alas!) As Dean gets closer with him, he can start to “hear” him. I like to think he sounds like a pleasant hum or a slight ringing, similar to a wind chime, depending on his mood. Dean, specifically, makes him hum lower than usual. If he were to hum out-loud, it would harmonize with the way his grace sounds. It takes longer to perceive colors, but I think Dean would see the little flashes of blue, similar to the way Castiel’s eyes get when he’s using his powers. This is why I typically put a little blue squiggle between them when I draw them together. Plus other senses, sorry but this is long enough as it is. You likely get the point by now!

---

Anyway, I’m very happy that literally anyone has even a passing interest in my interpretation of these things.

Formatting this was a nightmare and I feel particularly insane today.

[hizerain]

2025.05.05

A mess of notebooks and papers. I've taken to organizing them in multiple piles across my floor. Somewhere slowly functionality over aesthetics has taken over life. My various fragile and beautiful fountain pens swapped for a sturdy indestructible rotring 600 ballpoint. Beautifully kept notebooks exchanged for loose sheets of paper flouncing around. To some extent, I do miss the enforced slowness of the other tools. At the same time, I've always had an aesthetic obsession which has often been suffocating. It has been nice to let go.

[poofpoofpurin]

happy bkdk new year

[far-away-from-tulsa]

rip johnny cade you would’ve loved having a 504 plan and audiobooks

[piccololiker]

love seeing single slug dads in stem ❤️

[aw-dummies-no]

Anyone else ever just sit there thinking about how Bucky was HYDRA's for 2.5 times longer than he'd been his own self?

[aroaceleovaldez]

why are PJO characters most consistently measured in scales of Michaels?

Like. this is some of the most specific height information we have out of most characters, besides maybe Percy being an inch shorter than Jason. The Michaels Scale...

[mathysphere]

the counting for this was a pain, but boy do I like the look of little lines

A sine wave transformation bookmark, made for @badstitched's charity bookmark project: each variable in the top equation is color-coded to the aspect of the graph that it would affect.

The book's out now to anyone who donates $15 or more to one of a couple different literacy charities-- there's 27 bookmarks in total, all themed around different book genres (mine's in 'nonfiction'!).

Link Here for anyone who'd like to donate and get a nice PDF!

[chongoblog]

Have you heard of the Sum and Product Puzzle, aka the "Impossible Puzzle" because it initially seems like there isn't enough information to go on? I think I have the answer, and I'm mad about it.

I hadn't so I looked it up and here's Wikipedia's summary of it

There's also an explanation, but I didn't look. I wanna figure this out myself.

So let's break it down.

"P does not know X and Y" means that X and Y are not both prime. If they WERE both prime, then P would know the two numbers right away. So if S KNOWS FOR CERTAIN that P doesn't know X and Y, that means that the sum of X and Y can't be made up of two prime numbers. So, for example, the sum can't be 20, since if X and Y are 1 and 19, P would get 19 and be able to easily deduce the values of X and Y.

So we have a bound for the sum here, so we just need to find all numbers that can't possibly be the sum of two primes. I tried to get a good list of all numbers that aren't the sum of two primes through trial and error, but I after I found the first few I just let the OEIS do the rest of the work for me

So our possible sums are: 11, 17, 23, 27, 29, 35, 37, 41, 47, 51, 53, 57, 59, 65, 67, 71, 77, 79, 83, 87, 89, 93, 95, and 97.

Now that doesn't narrow it down a TON, but we can probably do something with this. Now that P knows that these are all of the possible sums, they know FOR CERTAIN what X and Y are. Very interesting. That tells me a lot about the product.

So let's say X is 4 and Y is 7. Then P is 28, and S is 11. Now, other factors of 28 include 2 and 14, which add up to 16 (not on the list), so we could just say that and call it a day, but there's something else that perplexes me. What if P is 24? The factors of 24 are 6x4, 8x3 and 12x2, which give us sums of 10, 11, and 14, and 11 is the only one on the list, so we have new X and Y values for S = 11 that could also apply. And since the S mathematician said he knew what X and Y were upon hearing that P knew, we can safely say S isn't 11, since X&Y could have multiple possibilities.

So, simply put, we need a value of S where there's only one possible P that could work for it. On one hand that still sounds like a LOT of guess and check work, but on the other, I feel like there's a way to find this solution without that.

Doesn't matter. I did the guess and check work anyway, granted it was actually easier when I got to the higher numbers, since most possible factors of P went over the sum of 100, which is one of our limitations. Easiest way to find these unique products is to find the largest prime number (lower than the sum) and use that as one of our two values.

So the conversation goes as such.

S sees that their sum is 17. Knowing that 17 can't be reached as a sum of two primes, S says "P does not know X and Y", which tells P that the sum is one of those numbers we saw up there. P's product is 52, he figures and he only knows two numbers whose sum add up to one of those numbers. So he says "NOW I know the value of X and Y". S hears that and figures that it has to be that one EXACT combination.

X and Y add up to 17 and multiply to make 52 which means that X and Y are 4 and-

...

GOD DAMMIT

[freakinnefor]

you’re so pass remarkable, cal…

[ellraiser]

MUDBORNE IS OUT!!!!

my funky little frog game about genetics, science, frogs, mud, bugs, and dreams is out now!!!

well ok, yea it's been out for just over a week now - but with nearly 15,000 players in the first week to say i've been busy with patches has been an understatement... not only have i been overwhelmed with the volume of bugs (that weren't even tasty ones), but in general i've been blown away by just how much people... actually... like it?

there was a large portion of development were I just lost all faith in the idea, too many things unsolved, so many doubts - i'd spent too much time in my own head that's for sure. but now it's out, and people are loving it, and the reviews have all been just so lovely. thank you so much to everyone who has been playing, it really means the world <3

whether you've played APICO before and enjoyed it, or never seen either of the games, if you love menu management, and frogs, and MATH, then I think you'll enjoy it! (there's also a demo so pls do try before you buy) also there's a story and it's good (imho), and it was my first time doing music and that's not bad either!!

I'm relieved, and finally able to sleep, and I'm glad it's all over and I also can't wait to do it all again! :')