#Permutations

[knotty-et-al]

Visualization of the Rubik's cube

[awkward-sultana]

"I am the lawful wife of Sultan Suleiman. I've given him five children. Am I not as precious as a slave to you?"

[vertigoartgore]

Captain Marvel switching places with Rick Jones. Art by ChrisCross, Wayne Faucher, Tanya Horie and Richard Horie for the cover of 1999's Captain Marvel Vol.4 #0 (turning 25 today, feel old yet ?). Also used later as the cover of the tpb Captain Marvel: First Contact (2001).

[burlveneer-music]

My WVUD playlist, 3/25/2025

Steve Reich - Four Organs Flock - In C (Full Length Version) Steve Reich - Music for a Large Ensemble Listening Center - New Riddles Steve Reich - Tehillim, Pt. 1 (Fast) JOBS - You Are the Object Owls - Good Medicine Steve Reich - Traveler's Prayer Battle Trance - Green of Winter III

[verdantachillean]

The 4 horsemen of mathematics to pass the time

[dimachina]

i dont even want to admit how hella mad i am whenever i get drunk and i can’t snap on the keyboard to input Negan’s “ONE” which is four goddamn fucking permutations on the keyboard to input, it’s NOT easy, i need an arcade stick

[entomophagouserisian]

Incoming: some weeb shit I've folded one of my favorite math things into (permutations)

So I recently went back to Revolutionary Girl Utena because my girlfriend hadn't seen any of it yet and I hadn't seen much beyond season 1 (I know it's a foundational work of sword lesbianism and regret not having gone harder on it before).

I was kind of laughing with her about how edgy the translated lyrics of Zettai Unmei Mokushiroku (Absolute Destiny: Apocalypse, the song that plays during the scene where Utena climbs up to the arena every episode) and I noticed that there wasn't a translation for a chant at the end of it that hits my ear in a very pleasing way.

The chant in question:

Mokushi Kushimo

Shimoku Kumoshi

Moshiku Shikumo

The reason there is no translation is that it's mostly gibberish. They took the word "Mokushi" (Apocalypse) and rearranged the syllables in all possible ways to create this particular piece of poetry. The repetition of syllables in this way ends up feeling really good to my brain when I hear it and I have therefore been alternating between trying to memorize it and analyzing its structure for the past few days.

Unfortunately in order to present my process for this analysis I'm going to have to teach you some basics of the mathematical conception of permutations.

(The following aside into math is actually wholly unnecessary to my overall analysis, so feel free to skip to the clearly marked conclusion at the end if it feels like too much or you just don't feel like engaging with it)

A permutation is any reordering of a set of objects. Note that it's just reordering, it doesn't include deletions or the introduction of new elements or new copies of old elements. Commonly if we want to analyze permutations directly, and more specifically to talk about the permutation where the first object goes to 2nd position, second object to 3rd, third object to 1st, we use (123) (read as 1 goes to 2, 2 goes to 3, 3 goes to 1). As well, if the 3rd object stays put and the first two swap places, we would use (12) (read as 1 goes to 2, 2 goes to 1) to describe that. If no change is made, we usually just use (1) (read as one goes to one or the identity) to describe that. (This is very much lacking the rigor and generality that I would've preferred, but this post would've been substantially longer if I'd gone into that much detail, so I'm kind of hoping someone can come in with just this much explanation and understand what comes after)

So my first step in my analysis was to try to record how each of the "words" related to the base/actual word Mokushi (this is admittedly where it would be quite useful for me to change over to hiragana, but I don't know it and don't have a keyboard downloaded for it and don't feel like downloading one just for this post or copy/pasting the hiragana repeatedly, sorry to those of you who study/enjoy Japanese)

So, rewriting the chant as the permutations applied to Mo-Ku-Shi (written this way to emphasize the 3 objects being permuted):

(1) (132)

(123) (12)

(23) (13)

It was fun but didn't get me anywhere (other than verifying every possible ordering was present, but I was already pretty certain of that) so I instead chose to look at what permutation is happening at each step in the sequence rather than just how they compared to the original:

* (132)

(132) (13)

(132) (132)

Here, we see a much more obvious pattern. For all but one transformation, we are permuting by taking the first syllable and pushing to the end, moving the other two toward the beginning of the "word". To hear it, it is very easy to recognize the 2-syllable repeats happening throughout that first pulled my attention. However, this one permutation couldn't be done exclusively if they wanted to cover all possible permutations, as applying (132) 3 times brings you back to the original word, so the third Permutation is instead (13) which just reverses the syllables in this case since there's only 3 of them, but this also notably changes them to a "word" not yet seen which can bring us to the two we are still missing by applying (132) two more times.

It was after all of this that I properly noted that that middle step reversed the previous "word" and I mentally zoomed out to notice

~~~~Conclusion~~~~

the chant is set up to mirror itself. The pairs 1&6, 2&5, and 3&4 are all the reverse of one another, ordered such that for all but one pair heard in sequence, there is a 2-syllable repetition when moving from one word to the next. (Yes it took me this long to notice it was mirrored. No all that permutation work was definitely not necessary, but forgive a [likely autistic] math nerd for her indulgences.)

It's just a silly chant in a cartoon but it made me happy to see permutations in it and I am sincerely moved by the poetry of making gibberish out of a dark and serious word like apocalypse by listing off anagrams.

[futurebird]

What if the Library of Babel contained books, not just texts.

I love the Library of Babel-- but it's important to remember that it contains all *texts* (up to a certain length) this is not the same as containing all *books* -- books are objects, they can be different shapes and sizes, made of different materials, bound with different bindings-- books have highlighting and margin notes from previous readers, old lending cards with the names of readers and dates.

Books can have illustrations. But we could make a Babel style indexing system for possible print images. Then represent the images as their index number. Now we have illustrations. We could have codes for size, color, cover material, paper weight, illustrations, margin notes, the style of handwriting of the margin notes. It would be a complex system and the final index numbers would need to be much longer. Possibly impractically long. But, a finite thing can be impractically large.

Here is a related question. How many distinct (as in you can distinguish between them yourself) objects can fit in a breadbox?

(Not all at once. I'm asking how many "different" things are small enough to be placed in a breadbox. This is either permutations or philosophy. )

[sidui]

[rachaelmayo]

This is Harmony of Bone and Air from 2014.

I created two versions of this design. The earlier one (below the text block) was shaded with a stipple technique. The one above is the full-color version that lacks any stippling. Both versions have merits and suit my different moods. Some days, I feel like I need the soothing rhythm of lots of dots, and others, I need psychedelic rainbow scales and bones to make me happy.

This 2014 image was colored with Prismacolor pencils - I think I used a mix of Prisma Scholar and Prisma Premier, as I was working on this on-the-go The Prisma Scholar pencils are less fragile, so those are the ones that travelled with me. I've since found a hard case I like, and carry Prisma Premiers. Oh, and he has a 3D bauble in his hand. That bit isn't colored pencil, of course.

Here's the stippled version from 2010:

[dkl9]

derivative of sort

sort: ℝⁿ → ℝⁿ, being a multivariable function, should have a Jacobian matrix of partial derivatives:

as you vary input position, exactly one of the outputs varies just as much, so each column of the Jacobian is 0s except for one 1

each output position is affected by one input (the one which was sorted to that position), so each row is 0s, except for one 1

thus the Jacobian of sort is a permutation matrix

the exception shows up when two inputs are equal, and if either were perturbed, some outputs would swap

(from AN #857)

[vertigoartgore]

2001's Captain Marvel Vol.4 #22 cover by ChrisCross & Anibal Rodriguez.

[brick3621]

@mousegard

A scorpion, not knowing how to swim, asked a frog to carry it across the river. “Do I look like a fool?” said the frog. “You’d sting me if I let you on my back!”

“Be logical,” said the scorpion. “If I stung you I’d certainly drown myself.”

“That’s true,” the frog acknowledged. “Climb aboard, then!” But no sooner than they were halfway across the river, the scorpion stung the frog, and they both began to thrash and drown. “Why on earth did you do that?” the frog said morosely. “Now we’re both going to die.” 

“I can’t help it,” said the scorpion. “It’s my nature.”

___

…But no sooner than they were halfway across the river, the frog felt a subtle motion on its back, and in a panic dived deep beneath the rushing waters, leaving the scorpion to drown.

“It was going to sting me anyway,” muttered the frog, emerging on the other side of the river. “It was inevitable. You all knew it. Everyone knows what those scorpions are like. It was self-defense.”

___

…But no sooner had they cast off from the bank, the frog felt the tip of a stinger pressed lightly against the back of its neck. “What do you think you’re doing?” said the frog.

“Just a precaution,” said the scorpion. “I cannot sting you without drowning. And now, you cannot drown me without being stung. Fair’s fair, isn’t it?”

They swam in silence to the other end of the river, where the scorpion climbed off, leaving the frog fuming.

“After the kindness I showed you!” said the frog. “And you threatened to kill me in return?”

“Kindness?” said the scorpion. “To only invite me on your back after you knew I was defenseless, unable to use my tail without killing myself? My dear frog, I only treated you as I was treated. Your kindness was as poisoned as a scorpion’s sting.”

___

…“Just a precaution,” said the scorpion. “I cannot sting you without drowning. And now, you cannot drown me without being stung. Fair’s fair, isn’t it?”

“You have a point,” the frog acknowledged. “But once we get to dry land, couldn’t you sting me then without repercussion?”

“All I want is to cross the river safely,” said the scorpion. “Once I’m on the other side I would gladly let you be.”

“But I would have to trust you on that,” said the frog. “While you’re pressing a stinger to my neck. By ferrying you to land I’d be be giving up the one deterrent I hold over you.”

“But by the same logic, I can’t possibly withdraw my stinger while we’re still over water,” the scorpion protested.

The frog paused in the middle of the river, treading water. “So, I suppose we’re at an impasse.”

The river rushed around them. The scorpion’s stinger twitched against the frog’s unbroken skin. “I suppose so,” the scorpion said.

___

A scorpion, not knowing how to swim, asked a frog to carry it across the river. “Absolutely not!” said the frog, and dived beneath the waters, and so none of them learned anything.

___

A scorpion, being unable to swim, asked a turtle (as in the original Persian version of the fable) to carry it across the river. The turtle readily agreed, and allowed the scorpion aboard its shell. Halfway across, the scorpion gave in to its nature and stung, but failed to penetrate the turtle’s thick shell. The turtle, swimming placidly, failed to notice.

They reached the other side of the river, and parted ways as friends.

___

…Halfway across, the scorpion gave in to its nature and stung, but failed to penetrate the turtle’s thick shell.

The turtle, hearing the tap of the scorpion’s sting, was offended at the scorpion’s ungratefulness. Thankfully, having been granted the powers to both defend itself and to punish evil, the turtle sank beneath the waters and drowned the scorpion out of principle.

___

A scorpion, not knowing how to swim, asked a frog to carry it across the river. “Do I look like a fool?” sneered the frog. “You’d sting me if I let you on my back.”

The scorpion pleaded earnestly. “Do you think so little of me? Please, I must cross the river. What would I gain from stinging you? I would only end up drowning myself!”

“That’s true,” the frog acknowledged. “Even a scorpion knows to look out for its own skin. Climb aboard, then!”

But as they forged through the rushing waters, the scorpion grew worried. This frog thinks me a ruthless killer, it thought. Would it not be justified in throwing me off now and ridding the world of me? Why else would it agree to this? Every jostle made the scorpion more and more anxious, until the frog surged forward with a particularly large splash, and in panic the scorpion lashed out with its stinger.

“I knew it,” snarled the frog, as they both thrashed and drowned. “A scorpion cannot change its nature.”

___

A scorpion, not knowing how to swim, asked a frog to carry it across the river. The frog agreed, but no sooner than they were halfway across the scorpion stung the frog, and they both began to thrash and drown.

“I’ve only myself to blame,” sighed the frog, as they both sank beneath the waters. “You, you’re a scorpion, I couldn’t have expected anything better. But I knew better, and yet I went against my judgement! And now I’ve doomed us both!”

“You couldn’t help it,” said the scorpion mildly. “It’s your nature.” 

___

…“Why on earth did you do that?” the frog said morosely. “Now we’re both going to die.”

“Alas, I was of two natures,” said the scorpion. “One said to gratefully ride your back across the river, and the other said to sting you where you stood. And so both fought, and neither won.” It smiled wistfully. “Ah, it would be nice to be just one thing, wouldn’t it? Unadulterated in nature. Without the capacity for conflict or regret.”

___

“By the way,” said the frog, as they swam, “I’ve been meaning to ask: What’s on the other side of the river?”

“It’s the journey,” said the scorpion. “Not the destination.”

___

…“What’s on the other side of anything?” said the scorpion. “A new beginning.”

___

…”Another scorpion to mate with,” said the scorpion. “And more prey to kill, and more living bodies to poison, and a forthcoming lineage of cruelties that you will be culpable in.”

___

…”Nothing we will live to see, I fear,” said the scorpion. “Already the currents are growing stronger, and the river seems like it shall swallow us both. We surge forward, and the shoreline recedes. But does that mean our striving was in vain?”

___

“I love you,” said the scorpion.

The frog glanced upward. “Do you?”

“Absolutely. Can you imagine the fear of drowning? Of course not. You’re a frog. Might as well be scared of breathing air. And yet here I am, clinging to your back, as the waters rage around us. Isn’t that love? Isn’t that trust? Isn’t that necessity? I could not kill you without killing myself. Are we not inseparable in this?”

The frog swam on, the both of them silent.

___

“I’m so tired,” murmured the frog eventually. “How much further to the other side? I don’t know how long we’ve been swimming. I’ve been treading water. And it’s getting so very dark.”

“Shh,” the scorpion said. “Don’t be afraid.”

The frog’s legs kicked out weakly. “How long has it been? We’re lost. We’re lost! We’re doomed to be cast about the waters forever. There is no land. There’s nothing on the other side, don’t you see!”

“Shh, shh,” said the scorpion. “My venom is a hallucinogenic. Beneath its surface, the river is endlessly deep, its currents carrying many things.” 

“You - You’ve killed us both,” said the frog, and began to laugh deliriously. “Is this - is this what it’s like to drown?” 

“We’ve killed each other,” said the scorpion soothingly. “My venom in my glands now pulsing through your veins, the waters of your birthing pool suffusing my lungs. We are engulfing each other now, drowning in each other. I am breathless. Do you feel it? Do you feel my sting pierced through your heart?”

“What a foolish thing to do,” murmured the frog. “No logic. No logic to it at all.”

“We couldn’t help it,” whispered the scorpion. “It’s our natures. Why else does anything in the world happen? Because we were made for this from birth, darling, every moment inexplicable and inevitable. What a crazy thing it is to fall in love, and yet - It’s all our fault! We are both blameless. We’re together now, darling. It couldn’t have happened any other way.”

___

“It’s funny,” said the frog. “I can’t say that I trust you, really. Or that I even think very much of you and that nasty little stinger of yours to begin with. But I’m doing this for you regardless. It’s strange, isn’t it? It’s strange. Why would I do this? I want to help you, want to go out of my way to help you. I let you climb right onto my back! Now, whyever would I go and do a foolish thing like that?”

___

A scorpion, not knowing how to swim, asked a frog to carry it across the river. “Do I look like a fool?” said the frog. “You’d sting me if I let you on my back!”

“Be logical,” said the scorpion. “If I stung you I’d certainly drown myself.”  

“That’s true,” the frog acknowledged. “Come aboard, then!” But no sooner had the scorpion mounted the frog’s back than it began to sting, repeatedly, while still safely on the river’s bank.

The frog groaned, thrashing weakly as the venom coursed through its veins, beginning to liquefy its flesh. “Ah,” it muttered. “For some reason I never considered this possibility.”

“Because you were never scared of me,” the scorpion whispered in its ear. “You were never scared of dying. In a past life you wore a shell and sat in judgement. And then you were reborn: soft-skinned, swift, unburdened, as new and vulnerable as a child, moving anew through a world of children. How could anyone ever be cruel, you thought, seeing the precariousness of it all?” The scorpion bowed its head and drank. “How could anyone kill you without killing themselves?”

[burlveneer-music]

My WVUD playlist, 3/17/2025

Micro Moon - Border Eva Simó & Myriam Hidber Dickinson - Winds' Wander & Vigil, Folklore Suite No. 2: III. Valley of Thorn Michelle Nicole - March in D'Ornette Mice On Stilts - Edge of the Garden The Fauns - Doot Doot Numün - Awaken Mirrored Daughters - Unreturning Sun Mandrake Handshake - King Cnut Archive - Fool (2024 Remaster) Steven Wilson - Objects Outlive Us: Objects: Meanwhile Alabaster DePlume - A Paper Man Pretty Lightning - Peek A Boo Infierno de Dante - Inseguridad Mighty Jupiter & The Mooncake Band - Interstellar Yacht Futuropaco - Terra Che Non Respire Amy Gadiaga - All Black Everything Collignon - Terra Nigra Bjonko - Enigma (feat. Eliel Lazo) Curtis Hasselbring - Bee Alley On-Ly - Bosco II The Lewis Express - Cold Catch (feat. Chip Wickham) Angelo Outlaw - Time Traveler

[rpaulson]

WHEREVER YOU'RE LOCATED, THERE YOU ARE! +XP

[fjordstan]

imagine fourth wheeling a tricycle