#nonassociational

[strawberry-spiderwebs]

Readymade Color: In the World

The prompt was to take photos of our readymade color in three nondomestic locations associated with the readymade, and three nondomestic locations not associated with the readymade.

Three associated locations:

Three nonassociated locations:

To be honest, I had no idea how to hook my projector in a portable way for shopping malls and other related locations. I also accidentally did these with the everyday monument 🤦🏻‍♀️ so these are not “real” images.

Here are some of the everyday monument ones since I did them:

[21st-century-minutiae]

a couple important details for your record of the ℝ, ℂ, ℍ, 𝕆 post:

division algebras need not be uncountably infinite; any (possibly nonassociative) algebra such that every nonzero element has a left multiplicative inverse and a right multiplicative inverse is a division algebra.

The rational numbers are called ℚ for (the Italian word for) “quotient”, not because ℝ was taken.

Hamilton not only worked with quaternions, but invented/discovered them!

An algebra is alternative if its multiplication has an alternating associator: that is, the associator [x, y, z] = (xy)z – x(yz) is 0 whenever two arguments are equal. This is weaker than associativity.

An algebra is considered to be “over a field k” (e.g. “over the reals”) if it admits scalar multiplication by that field in a manner compatible with its own structure.

The core of the joke is that there are only four alternative division algebras over the reals! This forms a parallel to the four elements mentioned in the Avatar: The Last Airbender opening.

Note that there are in principle more algebras than you get from using the Cayley-Dickson construction (which is what gets the complexes from the reals, the quaternions from the complexes, etc.), so this isn’t just about things stopping at the sedenions.

As it happens, these are also the only four real-finite-dimensional division algebras over the reals (sedenions have zero divisors, precluding them from allowing division), and the only real normed division algebras, as well as the only four algebras satisfying some other properties that wind up being equivalent. (See e.g. one of Hurwitz’s theorems.) So from various (similar) angles, they’re quite fundamental (like the elements).

Feel free to reblog and post all that. I don't mind being corrected. Apparently I was taught the "H/Q/R factoid wrong". Go figure.

Though I thought I had said that they were uncountable infinite divisor algebras, not that divisor algebras were uncountably infinite.

I also completely lost track of describing "divisor" algebra when I was going into details. That tends to happen sometimes. My eclectic mathematical hobby of choice is complexity and formal languages, not abstract algebra, so I can admit my shortcomings.

[dichotomy-of-the-day]

Everything in reality is either nonassociative or associative.

[er-cryptid]

Nonassociative Learning

-- occurs when an organism is repeatedly exposed to one type of stimulus

-- two important types      -- habituation      -- sensitization

-- habit = an action that is performed repeatedly until it becomes automatic

-- in habituation, a person learns to “tune out” the stimulus

-- example = you live near train tracks and eventually become accustomed to the sound and it becomes background noise

-- dishabituation      1. stimulus removed      2. person is no longer accustomed to stimulus      3. if stimulus is presented again, person will react like it’s a new stimulus

-- sensitization is the opposite of habituation

-- there is an increase in responsiveness to the stimulus

-- instead of being able to “tune out” the stimulus, the stimulus produces a more exaggerated response

.

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[kikisfuneralservice]

SHINEE MEMBERS’ REACTION TO BEING IN A CLUB

hello hello!! this is my first official post that i hope reaches its target audience! all of what i plan to write will be ot5, AS WELL AS IT IS A WORK OF FICTION. like i said, this blog is ot5, so i will write for all five members!!

this is for shits and giggles only!!! just goofin’ around, so nothing serious! :)

enjoy and maybe leave a like if you did! :)

**THIS IS PURELY A WORK OF FICTION AND NONASSOCIATIVE TO ANYTHING SHINEE OR SM ENTERTAINMENT: THIS IS PURELY FOR ENTERTAINMENT PURPOSES ONLY**

ONEW (JINKI)

is not a party animal

actually just doesn’t go to parties at all

he just prefers staying inside with a nice book and a cat on his lap ok!!!!!!

is the friend who follows you around bc he doesn’t know where to go or put his hands so they swing awkwardly by his sides

“it’s so loud in here! how can you hear anything??”

it’s ok babe :(

is not really having fun until his Song comes on

like HIS Song

that song is gimme more

sry i headcanon jinki as a britney fan

absolutely in his own WORLD busting a fucking move without a care in the world

GONE after one shot

after this, he only trusted water

JONGHYUN

immediately heads to the bar

nothing wrong with that

mans just likes a good drink

he doesn’t pre game he just drinks steadily the whole time until he’s woozy and he’s suddenly dancing to the sound of drunk girls screaming

WILL NOT PARTY SOBER

a party is not a party unless at least everyone is slightly tipsy

requests old fall out boy songs bc why the fuck not

is disappointed when it doesn’t play and instead they play despacito

“look i don’t have a PROBLEM with it, but i just think we need a change of pace”

always has a pep in his step

so SO talkative

which actually makes you wonder if he was sober in the first place

suddenly he’s best friends with everyone

promises to every person he meets to hang out later

(he doesn’t; he forgets and wakes up with a hangover)

KEY (KIBUM)

most DEFINITELY pre games

he pre games for everything basically

life is a party, bitch.

“this is a 5 year old’s bday-“ who tf cares will there be beer?

is the one who sneaks in a flask bc shit is way too expensive in there

“WHY IS THE MUSIC TRASH IN HERE?”

has no filter once he’s drunk

well he’s already drunk before he comes in

will be dancing the whole time even when there’s no music playing

at this point his brain is made of static

the definition of i’m not as think as you drunk i am

a heavyweight but also a poor decision maker as well

living his best like tbh

go, kibum, go!!!!!

MINHO

does not care for clubs that much but will go when asked

“i’ll just be your eye candy”

ends up being the life of the party instead

things never really go as planned with him

is a master at beer pong when given the opportunity

also busts a fat move on the dance floor

will break it down to cardi b like his life depends on it

thinks he has megan thee stallion style knees but ends up twisting his ankle instead

will challenge you to see who can drink the most shots

(he wins)

(and he’ll remind you about it for the rest of the night)

(or week)

a bit of a lightweight but doesn’t act like it

TAEMIN

also a bit of a lightweight and it’s VERY obvious

a bit nervous at first

just the jitters that’s all

hand him a drink when he walks in and he’ll ease in more

once he eases up, he is active for the rest of the night

will dance to ANYTHING

the personal favorites are always shakira

i’m not gonna make the hips don’t lie joke but alas, it is implied

very impressionable

IS the mood maker he sets the tone of the room

is very friendly and open to meeting new people

LOVES to chat

talks extremely fast when drunk so no one can tell what the fuck he’s trying to say half the time, but it’s the enthusiasm that counts

—

thank you so so much for sticking around!!!!!! it means the world to me!

i feel very excited to get back into writing, so please suggest some content if you would like!

[twocubes]

Neither the left-associative nor the right-associative option is particularly natural, so by convention the unbracketed version is used to denote the commutator: wlwlm = ((wlw)lm)l(wl(wlm)) - (wl(wlm))l((wlw)lm) (figuring out the appropriate additive structure on each grading of the l-algebra is left as an exercise to the reader)

hmm, given such an additive structure, that would make sense, although since we’re having associativity problems, wouldn’t it be more natural for it to be defined to be the associator? (wlw)lm-wl(wlm)? idk i haven’t really looked much into nonassociative algebra...

[cern-official]

theoreticalmemes replied to your post “like the other week I learned of quaternions, they’re basically a...”

They have *sometimes* been used to describe things in physics, but their properties can be described just as well with the orthogonal group to describe spatial rotations. Octonions, on the other hand are even weirder, and have been used a little bit in particle physics, but many are skeptical because nonassociativity isn't so sexy and doesn't have much use. However, I'd recommend looking at the work of Cohl Furey because she's rad

okok so I am looking at octonions now very slowly bc there is. so much I don’t know but I did search up Cohl Furey and I think she’s my one of my new role models now

[ittybittytatertot]

As soon as the Anti-Light went "it went all according to plan," I went GDFI because lord knows that nothing can happen in this show without it being part of a web of lies. Gar and all of the Outsiders deserve better than to be played by the Anti-Light.

I’m going to be honest, I like that the line between the good guys’ and the bad guys’ methods are blurring even as their goals differ. I like that struggle between practicality and ideals and the grey morality of where to draw the line.

As for the Team and the Outsiders and other nonassociated heroes or villains not knowing what’s going on, when you have revolutionary/rebel/whatever you want to call it groups, operating so that no one or very few people know the whole picture is important for keeping everyone safe and the whole operation functioning.

Someone gets kidnapped and tortured for information? That’s bad but at least they don’t know the names of the leaders of another team. Someone is a spy? At least they can’t access all the information the group has.

Keeping secrets isn’t ideal but it is practical. And in the world YJ has created, with legal restrictions and telepaths and espionage, it is also necessary in a way that the secrecy of the s2 undercover plan was not.

I also want to point out that the narrative itself is not framing the League/Team/Batman Inc. secret collaboration as a good or heroic thing. It is presented as an ethical dilemma with potential consequences and how it will play out I can’t say but I can say that’s how stories work. You have characters, you give them problems, you see what happens.

[goingintopsychology]

implicit/procedural/nondeclarative memory

unconscious recall

priming: one stimulus influences a response to a subsequent stimulus, without conscious guidance or intention (ex. doctor -> nurse, rather than doctor -> bread), neocortex

procedural memory: skills and habits, basal ganglia

classical conditioning/associative learning: 

skeletal musculature (cerebellum)

emotional responses (amygdala)

conditioned responses 

nonassociative learning: habituation and sensitization

reflex pathways

source

[vetupdate]

今日読んだ日常診療に役立ちそうな論文20220130

Retrospective evaluation of systemic hypertension in dogs with nonassociative (primary) immune-mediated hemolytic anemia (December 2016 to April 2019): 26 cases

https://doi.org/10.1111/vec.13128

原発性免疫介在性溶血性貧血の犬の全身性高血圧症の回顧的評価

ICUに入院している原発性IMHAの犬26頭とコントロール群として特発性てんかんの治療やモニタリングでICUに入院している23頭の犬を設定。

収縮期血圧　SBP≧160mmHgを高血圧とし、重篤な高血圧をSBP≧180とした。

平均SBPはIMHAの犬で明らかに高い(161mmHg、コントロール群138mmHg)。

入院期間中を通じて高血圧である犬は50%、重篤な高血圧は11.5%。一日以上の入院で高血圧を示した犬は69.2%、重篤な高血圧を示した犬は34.6%。

犬ではIMHAと高血圧の関連がある。

ヒトで自己免疫疾患と高血圧が関連があるとの報告があった。

犬で高血圧は炎症性疾患や免疫介在性疾患と因果関係があるかもしれない。

IMHAの犬では血圧のモニターが必要である。

高血圧の治療が必要であるかもしれない。

全く考えたことがなかった。

これからは血圧測定をしよう。

[oumaimaoriflame]

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[novasciencepublishers-blog]

International Journal of Mathematics, Game Theory and Algebra

Volume 26 Issue 2 2017

The International Journal of Mathematics, Game Theory, and Algebra is an international journal devoted to new advances in all branches of mathematics, game theory and applications, and pure and applied algebra and geometry including Field Theory and Polynomials; Commutative Rings and Algebras; Algebraic Geometry; Linear and Multilinear Algebras; Matrix Theory; Associative Rings and Algebras; Nonassociative Rings and Algebras; K-Theory; Group Theory and Generaliza-tions; Topological Groups, Lie Groups; Geometry; Differential Geometry.

The journal publishes research papers on these or closely related subjects containing original results with proofs. Survey articles of high quality also will be published at the discretion of the editorial board.

Click the link for more: https://novapublishers.com/shop/international-journal-of-mathematics-game-theory-and-algebra/

[thousandmaths]

Miscellany from MCC 2017

Hey folks! If you’re new here, these “miscellany” posts are all about writing down all of the talks at a conference which I enjoyed, but for whatever reason my notes aren’t good enough to write full posts. Normally I do these as the last post of a conference but I’m breaking protocol this time because of reasons.

------

Jia Huang, Nonassociativity of Some Binary Operations

Huang gave a very good talk, it’s just that I happen to have already written about it because of Hein’s presentation at the GPCC in 2016: they were collaborators on that paper.

One thing he addressed was some possible generalizations (including newer results they have about these). The prototypical example of a $k$-associative function is $a*b = \omega a + b$ for some primitive $k^\text{th}$ root of unity $\omega$. We can also ask about the operations $\omega a + \eta b$, or more generally, by extending to the ring $\Bbb C[x,y]/(x^{k+d}-x^d, y^{\ell+e}-y^e)$, the operation $xa+yb$.

(The latter seems... odd. For instance, $x$ is “basically” a $k^\text{th}$ root of unity, but tweaked so that for some reason the first $d$ powers “don’t count”. It’s not super clear to me what this is supposed to be modeling, although this sort of philosophy feels very much like the intuitive explanations I’ve heard for [higher] tangent spaces in algebraic geometry.)

Kyungyong Lee, A Conjectural Description for Real Roots of Acyclic Covers (collaborator: Kyu-Hwan Lee)

This was the only talk that appeared to be about cluster algebras (although I’m really not sure to what extent it was about cluster algebras). Given an acyclic quiver $Q$ and a module of the path algebra, we say that the corresponding dimension vector is a real Schur root if it has no nontrivial self-extensions, i.e. modules $E$ such that $0\to M\to E\to M\to 0$ is a short exact sequence. (This name does have something to do with root systems, but the details of this relationship are completely beyond me.)

The titular “conjectural description” is easiest to describe in type A, where there are admissible curves corresponding to the path algebra modules, (the link gives the flavor of what an admissible curve is, although the details are different in this setting). In this case, the conjecture is that lack of self-extensions corresponds in the modules happens exactly when the corresponding curve has no self-intersections.

Sheila Sundaram, Plethysm and Characters of $S_n$ Induced from Centralizers

So I keep hearing this word ‘plethysm’ recently and I’ve never really been sure what it means. In this talk I got the answer, if not much else: we define the plethysm of two functions $f[g]$ by treating them as $GL_n$-characters and composing them... so that’s a thing.

Another fun fact that I wasn’t aware of: the multilinear part of the free Lie algebra, considered as an $S_n$ representation, is actually the induced character $e^{2\pi i/n} \uparrow_{C_n}^{S_n}$, where $C_n$ is the cyclic group generated by the long cycle $(1 2 \cdots n)$.

Peter Tingley, Crystal Combinatorics from Lusztig’s PBW Bases

It was a 20 minute talk about crystals. There really wasn’t much chance that it was going to be comprehensible. 

But he did make some some effort to explain why we should care about Lustzig’s canonical basis: in addition to being a crystal basis (okay...), it also descends to a basis for the respectable subquotients of the universal enveloping algebra (okay...), and it it has positive structure constants in types A, D, and E (oh that’s nice).

Jessica Striker, Revisiting Promotion and Rowmotion, Revisited (collaborators: Williams,  Dilks, Vorland, Pechenik, others)

At the last MCC, Anna Stokke talked about promotion. The version that I discussed can be repackaged in the following way: given a standard Young tableau, if it is possible to swap 1 and 2 so that the result is still semistandard, do so. Then if it is possible to swap 2 and 3, do so. Then if it is possible— you get the point. This repackaging allows you to define promotion on arbitrary labelled ranked posets; I’ll leave out the details, but roughly speaking promotion goes “top to bottom”.

In “Promotion and Rowmotion”, Striker and Williams proved that this was (equivariantly) equivalent to rowmotion, which is the same procedure going “left to right”.

In “Promotion and Rowmotion, Revisited”, Striker and friends showed that repeating this idea [“increasing $i$ and decreasing $i+1$, if possible” replacing the swapping mechanism] for increasing tableaux (also discussed in Stokke’s talk), this says something about K-theory.

Finally, in the latest installment, “Revisiting Promotion and Rowmotion, Revisited” [see, it wasn’t a typo!], they showed that it’s actually possible to removed the ranked restriction. Defining promotion in this context is actually a little tricky, and involves a constructing an auxiliary poset that I didn’t really catch.

[er-cryptid]

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[gothamcityneedsme]

when you write long enough the subtextual evolves and becomes so utterly textual that you can never claim it as subtextual again, it becomes core to the methodology of writing the piece. the subtextual inevitably becomes the textual in time, even if readers don’t read between the lines (and don’t realize when the between turns to line itself)