#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, 12/9/2024

Yui & The Mahadhi Bohemians - Empty Club Okvsho - Where I'm made of Orchestre Tout Puissant Marcel Duchamp - Coagule The Paradise Bangkok Molam International Band - Psych Lam Kor Pas Musique - Obituary Sun Atoms - Narco Polo (feat. Isaac Brock) Alawari - The Mind Speed Limit - Time's Tune (A Run Around the Block) Caixa Cubo - Jet Léguas Steve Coleman & Five Elements - Mdw Ntr Trojka - Romvesen Bananagun - Brave Child of a New World The Last Poets & Tony Allen - This Is Madness Błoto - Szatan The Verge - Gratitude Body Meπa - Etel Painkiller - Dr. Phibes Painkiller - Samsara IV Mozo Mozo - Mozotissimo The Flying Luttenbachers - Id Vomit Brass Against - Immigrant Song Sun Ra Arkestra - Reflects Motion

[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 and stream, 12/2/2024

Devonanon - Blood Laughing (feat. Masayoshi Fujita & Rosa Juritz) Svaneborg Kardyb - St. Pancras The Hardy Tree - September 1975 Yaryu - Sacrifice Scrimshire - Ash ganavya - A Love Supreme, Part 3: Alice Coltrane ganavya - A Love Supreme, Part 4: IONE (feat. IONE) Eve Essex - Room With a View Moses Sumney - Is It Cold In The Water? (feat. ANOHNI) Mark Barrott - Pandora Low Leaf - How to Open a Portal memotone - Catherine, On Fire Cordâme - Ostara Kronstad 23 - Feilbarlig Euglossine - Pastries Ludivine Issambourg - Manoir Sault - Act 9 - Pray For Me Mocky - Stevie's Room Suss - Flight Marysia Osu - melting timbers (feat. Plumm) O.G. Jigg - Jesus Is My Jam Posy - Dreaming In Blue (feat. Jennyfire)

Listen on Mixcloud

[zackbuildit]

We can make a religion out of this!

Visualization of the Rubik's cube

[viragfold]

Permutazioni

MY WORK: LINK

INSTAGRAM: LINK