#Eugenia Cheng
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luxe-pauvre · 2 years ago
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There is a myth that math is about getting the right answer, but that’s a very ingressive approach to it; a more congressive approach, and one that is much more prevalent in higher-level math, is that it’s about how you construct rigorous arguments to show that something is an answer. A congressive approach says it’s more important to learn that discipline than to learn the answer; it’s also a more transferrable skill. Math detractors complain that they never have to use school math in their daily lives, which is probably true if the whole focus of their school math was on specific answers about things like triangles and quadratic equations. Unfortunately, math as presented in school is largely the ingressive aspects: getting the right answer, following rules that are imposed on you, a proliferation of facts that you’re supposed to know, and solving problems. If instead the math were congressive — about building arguments, seeing relationships between things, and understanding contexts in which different things are true — then the math would be much more relevant to daily life and much more about genuine mathematical ability.
Eugenia Cheng, x + y: A Mathematician's Manifesto for Rethinking Gender
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anarchistdragonnerd · 2 years ago
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Book recommendation; X + Y (a mathematician’s manifesto for rethinking gender) by Eugenia Cheng
Rather than think about men vs women, consider the power structure in place. She develops the idea of ingressive and congressive people, and it reads very much like mutual aid by Pyotr Kropotkin despite not being explicitly communist/anarchist.
Great read, especially when paired with her other book, the art of logic.
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52booksproject · 2 years ago
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Book 35 The Art of Logic in an Illogical World
RNG produced 160.0- Logic. Offhand I thought about reading Flatland by Edwin Abbott or a Lewis Carol book, but decided to go with something more modern. Eugenia Cheng's The Art of Logic in an Illogical World seemed a good choice.
And it was pretty much. Cheng gets a bit into the nitty gritty of what logic is and various things like what negation vs being opposite is. There are a lot of Venn diagrams and tables and the like. I have to admit I didn't follow some of it very well.
She talks about how she's very rarely found to be logically wrong, mostly by using weasel words apparently. She does argue when you just try to pick apart someone else's argument rather than coming to a genuine understanding where the person is coming from is being selfish. And that sometimes people just will fundamentally disagree on some things like whether people should help each other or just be rugged individuals.
SHOULD YOU READ THIS BOOK: If you want to know about logic and applying it, sure. My one caveat is if you have any trouble with eating disorders. She talks about her weight. A LOT. and tries to defend that complaining about her weight .A LOT. doesn't mean other people should read any weight judgement into her statements. I only half buy that.
ART PROJECT:
I decided to go with a Venn Diagram
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engineeringphilosopher · 5 months ago
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For me it was and is a reference for logical-rational reasoning together with Eugenia Cheng
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analytically · 7 months ago
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If we object to the idea that “men are better,” it’s not that helpful to declare instead that “women are better.” It pits men and women against each other and sets up a prescriptive framework rather than a descriptive one.
(x + y: A Mathematician's Manifesto for Rethinking Gender by Eugenia Cheng)
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la-galaxie-langblr · 1 year ago
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Why is it always "why do you enjoy maths" and never "how was reading Richard Hammack's Book of Proof, a freely available pdf, was it fun learning about set theory and proof by contradiction in your spare time"
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o0oooooo0o · 11 months ago
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uttara bhadrapada is all about honing that cool crystal center within. ppl will find that in association with these natives “most” is the word you will often see next to their name and not always in a socially acceptable way. These natives leave behind gifts to humanity transcending the boundaries of good and evil.
‧₊˚✩彡 🙀
-losing people close to you
-inhumanism
-aliens
-synth
-being non pc
-extreme wealth and 💸💸💸💸💸
-reptilian beings (dragons, snakes,…)
-aquatic beings (mermaids)
-cold, frigid, aloofness, indifference, apathy
-loneliness, disconnect
-underworld
-fantasy
-collateral damage
-humanity
-secret societies
-control & restriction
-evolution
-mysticism
-combat
-reluctant leader
-burden
-deep space, the unknown
-two faced
-blue/iridescent/chromatic/purple
-eccentricity
-cyberpunk
-conspiracy
-high technology
-destiny & fate
-neptune
-pluto
-funeral
-inertia
-legacy
-skeletons in the closet
-in plain sight
-contradiction
-transformation
-war
-cosmic rain
-drugs/psychedelics
-stoners
-plastic surgery
-victimhood
-delusion
-manipulation
-the end
-transcendence
-the chosen one
-apex saturnino
-being ahead of your time/creating something timeless
-aristocracy
-anger
-doomsday
-out of touch
-dreams
-dissolution
-destruction
-innocence
-cunning
-isolation
-apotheosis
-ascension
-kundalini awakening
-Pegasus
-Andromeda
-evil
-genius
-tamasic
-cold blooded
-ethereal essence
-uncanny valley
-alienation
-abandoning humanity
-fixed
-void
-darkness
-time
-being the brain/face of capitalism ngl
-prophecy
-elongation
-escapism
-the ocean
-for the greater good
-tying together future/present/past
-being afforded a greater, more terrible purpose
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Grimes sun & moon in uttara bhadrapada
OTHER NOTABLE NATIVES:🦄
-rihanna
-hillary clinton
-kim kardashian
-anya taylor joy
-antonio banderas
-rose
-taeyeon
-rooney mara
-gemma ward
-rick owens
-jin
-felix
-tyra banks
-salma hayek
-daniel radcliffe
-joaquin phoenix
-rebecca ferguson
-lil kim
-Luca Guadagnino
-sujan stevens
-janet jackson
-steve jobs
-bill gates
-catherine zeta-jones
-andré leon talley
-anna wintour(*)
-eugenia cooney
-ash stymest
-blac chyna
-travis barker
-jane lynch
-IU
-tupac
-jason statham
-riley keough
-wiz khalfia
- jay park
-timothee chalamet
-samantha morton
-Josh McDermitt
-anton riize
-belle kiss of life
-muammar al gaddafi
-ni-ki
-sullyoon
-king krule
-aidan gillen
-josh o’connor
-salvador dalí
-sophie turner
-hayao miyazaki
-john galliano
-ed sheeran
-kendall jenner
-jessica white
-choi woo-shik
-tom brady
-russel brand
-Satoru Gojo
-Shri Ramanujan
-novak djokovic
-alek wek
-nick offerman
-steve-o
-song kang-ho
-cheng xiao
-enya umanzor
-jenny slate
-nicholas hoult
-isabelle huppert
-soobin
-bladee
-dev patel
-james cameron
-city of los angeles
-harry potter
-wanda maximoff
-iron man/tony stark
-jeffrey e*stein
////(disclaimer, lowkey i’m pretty good at guessing between naks but i can’t say for sure that they r ubp moon some of these r just my own intuition/pattern recognition/symbolism unless their birth time is confirmed and i can flat out get their placements wrong but also ppl lie even about their birthday so it is what it is)
///*I will keep updating this list
UBP SUN:🦄
yuji itadori
irene
alexander mcqueen (ubp sun+rahu)
lisa (ubp sun+venus+ketu) +saturn*mercury in revati
quentin tarantino (sun+mercury+jupiter)
cha eunwoo (sun+venus+ketu+saturn)
lady gaga
mina
lee pace
ethel cain
celine dion
diana ross
yasmeen ghauri ubp sun c mercury revati
mariah carey ubp sun c rahu *mercury pisces pbp
eren yeager
keira knightly
steven tyler
MOON RULED BY UBP:🦄
karina (revati sun c ubp mercury+venus gemini moon ruler ubp mercury)
jamie campbell bower (bharani moon ruled by ubp mars)
UBP ASC:🦄
brie larson
che guevara
billie eilish
shakira+venus
KETU IN UBP:🦄
zoe saldana
bella hadid +ubp saturn
jaehyun +ubp saturn lagnesh saturn in ubp
fernanda ly
RAHU IN UBP:🦄
abbey lee kershaw
ASC RULER IN UBP:🦄
zendaya (cap asc ruled by ketu+saturn in ubp)
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fundgruber · 9 months ago
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Dietmar Dath - Neptunation.
Die Oktopoden werden uns verbinden, wenn wir es nach oben schaffen
Die Mission ist die Verbindung
Connection, Funktoren zwischen Kategorien von Kategorien, zwischen höheren Topoi
Bei Dietmar Dath ist Mathematik zur sozialen Bewegung, zum Implex geworden, eine Diktatur der Programmierer*innen und der Wissenschaft, in der Topos-Coding der Skill ist mit dem Aufhebung funktioniert, mit dem der Formwechsel der Materie gesteuert wird und die gesellschaftliche Reproduktion. In der Gegenwart codiert er selber seine Science Fiction so, mit dem Aufhebungsfunktor. Da wird dann ein Weltraumsozialismus mit transhumanistischem Gesicht (Neukörper) entworfen, in dem eine neue Politik entsteht, neue Kriege, teilweise als Wiederholungen historischer Tragödien. Die Programmierer*innen und die Wissenschaftler*innen spielen darin so eine große Rolle, weil sie im direkten Kontakt sind mit dem Management und der Spekulation. Sie haben Zugriff auf hochwertige Produktionsmittel und Gelder. Und dann im passenden Moment weichen sie ab aus den Kreisläufen des Kapitals, wie in "Menschen wie Gras", wenn die Gentechnik verfrüht freigelassen wird. Daths Faszination für China würde demnach auch nicht bedeuten das was dort passiert zu idealisieren, sondern es ist einfach ein Staat in dem diese Entwicklungen ein Stück brisanter ablaufen, wo eine KP versucht das Ganze zu steuern.
Die Grundlagen für die Freiheit zum Implex hatte eine Partei im Untergrund gelegt, sie hießen die "Gruppe Pfadintegral" (Gippies), dann die "Internationale" (eigentlich die 'Partei', aber er entschied sich dann doch für die Internationale), in unserer Welt sind das Grillabende von Wissenschaftler*innen und Radikalen, wie Barbara Kirchner irgendwo sagt, oder auch Dath immer wieder anklingen lässt. Dath ist das Aushängeschild dieser imaginären Partei (manchmal sieht man sein Formel-Tattoo auf dem Unterarm) im Hier und Jetzt, in den Büchern ist es Cordula Späth oder andere Heldinnen aus Wissenschaft und Musik. Durch seine Doppelrolle beliebter Feuilletonist bei der FAZ und Genosse der DKP zu sein streut er seinen High-Tech Marxismus in beiden Bereichen, und in Zeitschriften wie der Konkret (gerade zum Beispiel ein Text über eine Museumsausstellung über den Faschismus des 21. Jahrhunderts, genannt der "Wechselbalg", in einer zukünftigen Gesellschaft) oder bei Linken.
Die Topos-Codierung kommt auch aus der Musik, kommt auch aus der bildenden Kunst, nur haben die Gesellschaften, die Dath beschreibt das in ihre Raumgestaltung, ihre Körpergestaltung, die Gestaltung ihrer Beziehungen gelegt. Genauso wie das Gärtnern (in den Rechnergärten) oder das Kochen (deswegen auch die Bedeutung der von Dath beworbenen Bücher der Mathematikerin und Musikerin Eugenia Cheng "How to Bake Pi", und "x + y. A Mathematician’s Manifesto for Rethinking Gender", die in diesem Sinne so viel mehr sind als Einführungen). Darin liegt die verführerische Methodik der Kategorientheorie und der Topologie, Erkenntnis und Transformation auf unterschiedlichen Ebenen durchführen zu können. Und das dann wiederum mit Aufhebung zu verkabeln, mit den Klassikern:
"In early 1985, while I was studying the foundations of homotopy theory, it occurred to me that the explicit use of a certain simple categorical structure might serve as a link between mathematics and philosophy. The dialectical philosophy, developed 150 years ago by Hegel, Schleiermacher, Grassmann, Marx, and others, may provide significant insights to guide the learning and development of mathematics, while categorical precision may dispel some of the mystery in that philosophy." F. William Lawvere, Unity and Identity of Opposites in Calculus and Physics. Applied Categorical Structures 4: 167-174, 1996
Hegelianisch-Marxistische abstrakte Algebra befindet sich dann mutmaßlich im Wettstreit mit anderen diagrammatischen Methoden, wie der Lattice Theorie (vgl. Rudolf Wille, “Restructuring lattice theory: An approach based on hierarchies of concepts” 1982). Wenn seit Emmy Noether die Kartierungen Teil der mathematischen Forschung sind (vgl. Lee, C. (2013) Emmy Noether, Maria Goeppert Mayer, and their Cyborgian Counter-parts: Triangulating Mathematical-Theoretical Physics, Feminist Science Studies, and Feminist Science Fiction), bis hin zu Maryam Mirzakhani (in der Nachruferzählung und in der Raumerzählung "Du bist mir gleich" wird das was diese Mathematik mit dem Denken macht in seiner Tragik und transformativen Kraft spürbar), dann ist das was die Netzwerk-Coder (z.B. Fan/Gao/Luo (2007) "Hierarchical classication for automatic image annotation", Eler/Nakazaki/Paulovich/Santos/Andery/Oliveira/Neto/Minghim (2009) "Visual analysis of image collections") und Google Arts & Culture in die digitale Kunstwissenschaft eingeführt haben, man kann es nicht anders sagen, das Gegenteil von all dem. Unhinterfragte Kategorien und unhinterfragte konzeptuelle Graphen (also sowohl Lattice Theorie, als auch Topologie ignorierend), werden ohne Binaritäten oder Äquivalente einfach als gerichtete Graphen, entweder strukturiert von den alten Ordnungen, oder, das soll dann das neue sein, als Mapping von visueller Ähnlichkeit gezeigt (vgl. die Umap Projekte von Google oder das was die Staatlichen Museen als Visualisierungs-Baustein in der neuen Version ihrer online Sammlung veröffentlicht haben). Wenn dann das Met Museum mit Microsoft und Wikimedia kooperiert, um die Kontexte durch ein Bündnis von menschlicher und künstlicher Intelligenz zu erweitern - nämlich Crowdsourcing im Tagging, und algorithmisches Automatisieren der Anwendung der Tags, dann fehlen einfach die radikalen Mathematiker*innen, die diese Technologien mit dem Implex der Museumskritik verbinden können, um ein Topos-Coding durchzuführen, das die Kraft hätte den Raum des Sammelns zu transformieren, so das nichts mehr das Gleiche bliebe. Während die heutigen Code-Künstler*innen großteils im Rausch der KI-Industrie baden, bleiben es einzelne, wie Nora Al-Badri ("any form of (techno)heritage is (data) fiction"), die zum Beispiel in Allianz mit einer marxistischen Kunsthistorikerin die Lektüre des Latent Space gegen das Sammeln wenden (Nora Al-Badri, Wendy M. K. Shaw: Babylonian Vision), und so Institutional Critique digitalisieren.
"Was Künstlerinnen und Künstler seit Erfindung der »Institutional ­Critique«, deren früher erster Blüte auch einige der besten Arbeiten von ­Broodthaers angehörten, an Interventionen in die besagten Räume getragen und dort gezündet haben, von neomarxistischer, feministischer, postkolonialer, medienkritischer, ­queerer Seite und aus unzähligen anderen Affekten und Gedanken, die sich eben nicht allesamt auf eine Adorno’sche »Allergie« wider das Gegebene reduzieren lassen, sondern oft auch aus einer ­Faszination durch dieses, einer Verstrickung in sein Wesen und Wirken geprägt war, liegt in Archiven bereit, die ausgedehnter und zugänglicher sind als je zuvor in der Bildgeschichte. Den Tauschwert dieser Spuren bestimmen allerorten die Lichtmächte. Ihr Gebrauchswert ist weithin unbestimmt. Man sollte anfangen, das zu ändern." Dietmar Dath Sturz durch das Prisma. In: Lichtmächte. Kino – Museum – Galerie – Öffentlichkeit, 2013. S. 45 – 70
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Last night I finished reading the book X + Y: A Mathematician's Manifesto For Rethinking Gender by Eugenia Cheng and it's a book that I recommend to many types of people that are on Tumblr. I also think that the brand of feminism I see in the book really bridges the divide between the trans rights crowd and terfs.
Yes, really, hear me out. A major point Cheng makes is to separate one's character from gender. This is the terf view, with the added point that transitioning re-enforces harmful gender stereotypes. However, Cheng is not a terf, she accepts that transgender people are what they say they are and that not being transgender is a privilege. She doesn't go into much discussion about topics like "what is a woman?" or "who can compete as a woman in sports?" because that's besides her point.
She then goes on to separate "ingressive" behaviour-that is, being individualistic and self-serving-from "congressive" behaviour-that is, being collaborative and helping others. Traditionally, "ingressive" behaviour is considered masculine and "congressive" behaviour feminine, but obviously they don't line up neatly with gender like that, these are learned behaviours that anyone can take on, and how "ingressive" or "congressive" one is can be in flux at any given time. Our patriarchal capitalist society values "ingressive" behaviour, which re-enforces current power structures. Cheng advocates for the creation of a more "congressive" society, which she says is feminist because it goes against the patriarchy, but it would challenge all power structures so it benefits all oppressed people, and requires people to work together rather than against each other.
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uhh-nerya-i-guess · 1 year ago
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Hi
im nerya, or am i.
im a computer science student and i make music as a hobby.. sometimes. or at least i used to? i suppose? i havent been able to make anything for the past year or so.. well thats beside the point. im introducing myself. lets make this upbeat!
im new to tumblr so please be gentle with me, no i did not come from twitter, that is a forsaken place that i shall never set foot in, rather i did not dabble in social media until this point. i decided tumblr would probably be the best place, since i heard yall are quite weird and i like that
ive been reading some category theory books lately (specifically The Joy of Abstraction by Eugenia Cheng) while learning haskell. its been quite a joy, pun intended, i would definitely recommend
ive had an account for a bit but i decided to finally post on here because ive been flooding my friends dms with random babbling, which i do not intend to stop doing, but i think the world might enjoy them too!
funny how tumblr marks "tumblr" as a typo
my current gaming obsession is celeste, (celste :gladeline:), the mods are just so good.
lets uh throw out the part about being upbeat for a moment bc i need to rant. so uh time has been feeling faster and faster lately.. like weeks feel like days and months feel like weeks and everything is just happening so fast. is this normal? am i normal? hopefully so. did i post here before actually? i think i mightve made a "first post" before.. oh yeah i have adhd. anyways yeah time. time is fucking weird, like life has been changing a lot recently and theres a lot of stuff going on. i kind of feel like an outside observer to my own life someties yknow? like everything is happening while im not doing anything and that feels weird, like im watching a movie, i want something new. and that one time i had a haircut and then not recognized myself in the mirror for a sec DOES NOT help me with that feeling.
speaking about adhd i wrote the tags? tag? in the middle of writing that previous segment god help me
uh god that was a rant, uh im not gonna advertise my stuff here but i do stuff occasionally so if dms are a thing here feel free to do that.
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bookclub4m · 1 year ago
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30 Recent Poetry Collections by BIPOC Authors
Every month Book Club for Masochists: A Readers’ Advisory Podcasts chooses a genre at random and we read and discuss books from that genre. We also put together book lists for each episode/genre that feature works by BIPOC (Black, Indigenous, & People of Colour) authors. All of the lists can be found here.
This booklist features books from BIPOC poets published in the past three years.
Chrome Valley by Mahogany L. Browne
Feast by Ina Cariño
Your Emergency Contact Has Experienced an Emergency by Chen Chen
Girls That Never Die: Poems by Safia Elhillo
Content Warning: Everything by Akwaeke Emezi
I Do Everything I'm Told by Megan Fernandes
Living Nations, Living Words: An Anthology of First Peoples Poetry edited by Joy Harjo
Song of my Softening by Omotara James
Spells, Wishes, and the Talking Dead / Mamaht́wisiwin, Pakos̊yimow, Nikihci-́niskot́ṕn : Poems by Wanda John-Kehewin
Burning Like Her Own Planet by Vandana Khanna
Phantom Pain Wings by Kim Hyesoon, translated by Don Mee Choi
Bianca by Eugenia Leigh
Finna by Nate Marshall
Slam Coalkan Performance Poetry: The Condor and the Eagle Meet edited by Jennifer Murrin
God Themselves by Jae Nichelle
You Are Only Just Beginning: Lessons for the Journey Ahead by Morgan Harper Nichols
I’m Always So Serious by Karisma Price
Homie by Danez Smith
Blood Snow by dg nanouk okpik
Promises of Gold/Promesas de Oro by José Olivarez with translation by David Ruano
That Was Now, This is Then by Vijay Seshadri
it was never going to be okay by jaye simpson
Dark Testament by Crystal Simone Smith
Unshuttered: Poems by Patricia Smith
Falling Back in Love with Being Human: Letters to Lost Souls by Kai Cheng Thom
Femme in Public by Alok Vaid-Menon
Time Is a Mother by Ocean Vuong
Find Her. Keep Her. by Renaada Williams
Rupture Tense by Jenny Xie
From From by Monica Youn
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luxe-pauvre · 2 years ago
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Take the example of “strength.” It might initially seem that strength is more ingressive than congressive, but there are different ways to be strong. Traditional strength might be thought of as power, toughness, the ability to be unyielding either physically or emotionally, and thus to overcome others. That is ingressive strength. Congressive strength could be more like flexibility. Some physical materials are strong precisely because they are flexible, whereas something rigid is more likely to break. Congressive strength is like a river altering its course to wind its way through a contoured landscape, as opposed to a waterfall that just pours out. Or deep-rooted plants that can sway in strong winds, compared with a big tree that is more likely to fall down.
Eugenia Cheng, x + y: A Mathematician's Manifesto for Rethinking Gender
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palomarmagno · 2 years ago
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antpernas · 1 year ago
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I wish I had the brains to pursue math but alas, it wasn’t meant to be. College algebra was the highest level I completed and I barely passed with a D. But whatever our strengths are, be it math or the arts, I hope we get change the world for the better!
for what its worth i believe anyone can learn anything, i think you just need to associate the concepts youre trying to learn with things you already know. also having a concrete example for more open ended things can really help u wrap ur head around bigger ideas. getting into advanced maths has been hell for me too so by no means do u need to think i am naturally inclined towards it or anything
u also dont need to study it rigorously to learn more about it. if u ever want a more casual delve into math id recommend eugenia cheng and ian stewart. i love their work and i think they do a great job delivering the material in an easily comprehensible way
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jerryjadams · 2 years ago
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Atmosphere Weighs. 2022. Acrylic and watercolor on paper. 8 x 10”. . . . . . . Thinking about more and more abstract concepts is a bit like the high jump. You have to get yourself over a progressively higher and higher bar, and if nobody explains how to do it, you will keep knocking the bar off and want to give up. ~Eugenia Cheng . . . . . . #artwork #painting #abstractpainting #contemporaryart #art #artadvisory #contemporaryabstractpainting #newyork #nycartist #interiordesign (at Brooklyn, New York) https://www.instagram.com/p/Cp7tYtxMCeO/?igshid=NGJjMDIxMWI=
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eimearkuopio · 4 months ago
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This is also what happens when women are expected to look a certain way to be taken seriously and given a chance to do important jobs.
I'm not saying Kamala should be ugly. I'm delighted at her beauty. I'm pointing out that she's lived her whole fucking career backwards in heels, because that was the only option she had, and some of y'all seem to have forgotten that.
It's not that women are so amazing that we can do that and still succeed. It's that the only ones our fucked-up patriarchal society permits to succeed are the rare few who can excel by both ingressive* and congressive* standards simultaneously, and then they get pointed to as realistic examples by patriarchs and as gender traitors by radical feminists.
I don't believe her teeth look like that naturally. I don't believe her eyebrows grow in that shape. Heck, that might be a wig; I'm not saying it is, I'm saying that if her natural hair wasn't "acceptable", society would reject her for showing her natural hair OR for publicly admitting to it being a wig. I would be surprised if she has 20/20 vision, but she'll never wear glasses in public even if she doesn't. She has had holes punched in her ears, but only one per ear, because it's not about self-expression or about austerity. It's about conformity. It's about compliance. It's about trying to hold yourself in an unnecessary stress position because if you can have the strength and the endurance to do so for long enough, you might be lucky enough to "earn" the fundamental human right of having your perspective taken seriously by those in power.
I hope she becomes leader of the free world. No Gods, no kings; I didn't coin the phrase, and I'm not even endorsing it, but I'm pointing out that it's gendered and that the gendering matters in a way that many people do not consider. Smash the kyriarchy! Let the meek inherit that which was promised them.
* Once again, language refers to x+y by Eugenia Cheng; if you want to understand what Paul meant by New Man, I posit he referred to a male who was naturally congressive, and who brought that aspect of himself into everything he did, and then a bunch of ingressive assholes (including Paul!) fucked shit up. I'm a naturally ingressive female, so the other way around. It's going to make it a lot harder to convince me that dying is the best way for me to redeem the world. I'm just going to stick around for as long as I can, doing good in every way God provides an opportunity to and making ingressive assholes who keep telling me to look after myself look bad, and reminding the huge number of congressive rank-and-file people who make up the vast majority of the Body of Christ how Christ actually acted; and you cannot kill me in any way that matters.
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