#Permutations

[knotty-et-al]

Visualization of the Rubik's cube

[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).

[awkward-sultana]

"Will Mahidevran and I be the same now?" "Allah forbid." Insp.

[verdantachillean]

The 4 horsemen of mathematics to pass the time

[burlveneer-music]

My WVUD playlist and stream, 9/2/2024

Laurie Anderson - India And On Down to Australia (feat. ANOHNI) The Hardy Tree - All the Hours (radio edit) maya ongaku - Meiso Ongaku 1 Oliver Patrice Weder - Modern Times Krononaut - Silver Silver 英水帝江 (Ying Shui Di Jiang) - Torrents of Rain somethingmaker - Under Melaleucas Andrew Wasylyk & Tommy Perman - Remain in Memory of Full Light Drum & Lace - Plus (feat. Patrick Shiroishi) Tycho & Cautious Clay - Infinite Health Jenova 7 - Deep Star Deception Laurent Bardainne & Tigre d'Eau Douce - Oiseau (feat. Bertrand Belin) Cindy Lee - Dracula Abecedarians - Soil Slowly Rolling Camera - Rebirth Emanative - Paradox Holy Tongue & Shackleton - The Merciful Lake Zaliva-D - Illusion WaqWaq Kingdom - Hado Bataille Solaire - Sauropodes et Acacias

Listen on Mixcloud

[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)

[embervoices]

Now we just need Non Stick Spray Cooking and we're set!

[vertigoartgore]

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

[awkward-sultana]

As we have studied Ibrahim’s career, we have seen the vast power that he gradually gathered into his hands, and we have noted the amazement with which European legates listened to his own accounts of his standing in the state. He was practically the ruler of the Ottoman empire, but there was one fact that he forgot; he was absolutely at the disposal of the sultan and could be disgraced or executed at the latter’s caprice—he was but the shadow of the "Shadow of God on Earth." - Ibrahim Pasha: Grand Vizir of Suleiman the Magnificent by Hester Donaldson Jenkins

[burlveneer-music]

My WVUD playlist, 3/4/2024

Molly Lewis - Cocosette Garden Gate - Touched (Main Theme) The Natural Yogurt Band - Exotic Creatures Don Leisure and Amanda Whiting - Crying Tiger John Surman - Bitter Aloe Matthew Halsall - Newborough Forest Organic Pulse Ensemble - Peace Piece Sons Of Zöku - Möönlight Brittany Howard - Every Color In Blue NCY Milky Band - Magic Polo Kalaha - Tunnel Fabrik Kidding - Komet Ride Orgone - Peace For You (feat. Terin Ector) Konkolo Orchestra - Cover up the Bruises (feat. Nongoma) London Afrobeat Collective - Freedom Champagne Dub - Scrubbing Too Many Zooz X Moon Hooch - Nowhere Else to Go Vital Excursions - Share My Cave Pigbag - Hit the 'O' deck PS5 - Tufo Tomasz Guiddo & Jimi Tenor - Where the Wild Roam Cotonete - Bebete Vaobora feat. Sabrina Malheiros Ghost Funk Orchestra - Eyes of Love BOTTAZZ! - Cardosa Magic In Threes - Cutting Class

[zackbuildit]

We can make a religion out of this!

Visualization of the Rubik's cube

[viragfold]

Permutazioni

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INSTAGRAM: LINK