#induced geometry

[aviancataclysm]

said i'd be working on X but secretly practicing VeritY instead (it's the most doable medium demon for me rn from vibes since it feels easier to get consistent than HeLL, will just take more atts than easy demons............. aside from B we do NOT talk about B) although what the HELL IS THAT SHIP/UFO DUAL???? AT THE VERY END TOO????????? my worst skill is dual if we don't count swing so this is going to be FUN

[bogleech]

All my life I’ve been unable to understanding finding an animal “gross” just for its natural appearance and I still can’t accept that anybody really means it. “Gross” is something an animal might DO or a condition it might be in, like when a dog rolls around in roadkill, right? I can get finding some animals “scary” for how they look or how they move, but....gross? Like an insect, all by itself, is some sort of unclean filthy gag-inducing “gross” to some people? How? What??? You’re saying there are basically unsanitary SHAPES? Specifically for animals? A creature can have a geometry that makes some people nauseated?

Or is it like some people have difficulty contextualizing insects or worms as individual animals and instead hold them in the same mental category as almost like a “substance” or a “texture,” like living “dirt?” Is THAT what it is?

[your-yandere-bestfriend]

　　　　　ₓ˚. ୭ ˚○◦˚.Wet dreams.˚◦○˚ ୧ .˚ₓ

Todoroki Shoto

Based off the song Wet Dreamz by J. Cole.

(Guys do I drop this after a 2 year hiatus or no )

。。。 Though it was the second day of school already, there had already been talk of a new student—most likely gossip overheard from the U.A. staff. Typically a new student wasn’t of much appeal, this was a huge school after all, even though it was prestigious, but what made the U.A. students so chatty about this new student was the fact that she was a foreigner. There had only even been three American students in the long history of U.A. high school, so getting a transfer was not only impressive, due to the fact that she wasn’t required to participate in the entrance exams, and also exciting.

The bell chimed for second blocks end, and next for the students of class 3.A., was the drowse inducing subject. Math. The teachers filtered out in order to teach their proper subject, after all just because this was a hero school didn’t mean that they were excused from engaging in normal, more uneventful subjects. Todoroki sat with perfect posture in the back of the room, awaiting the teachers entrance. His ears perked up when he heard Midoriya speak of the new girl who might’ve been making her first entrance today, though he didn’t quite care for a new student, it honestly had nothing to do with him, he hadn’t found a need for more friends, Midoriya, Uraraka, Iida, and Floppy felt plentiful.

The door slid open, the chattering of the class going still. In walked Cemento, but it wasn’t just him, it was also the new girl, and now that he has seen her with his own eyes, he could understand what the excitement was for. She had mesmerizing, smooth skin, she was delicate looking, with the such pretty eyes, they put his heterochromia ones to shame. Along with her pretty eyes and gorgeous figure her hair was long, around 30 inches, and red just like his left side, Todoroki couldn’t care less if it was real or not. He was sure his mouth was keenly open, but he knew he wasn’t alone, even the girls in the class were shocked at her appearance.

Cemento guided her to the front of the large classroom, in front of the expensive smart board that wasn’t yet displaying geometry problems, thankfully.

Cemento was preparing to give her the go ahead to start speaking but she already took that initiative for herself.

“Hi everyone it’s an absolute pleasure to meet you all! I’m … and I look forward to getting to know each and every one of you,” she beamed.

Sure she was already beautiful but todoroki could feel fire coming out his right side when she smiled revealing a straight line of pretty, white teeth. His multicolored eyes glanced around his classroom, and even the notorious Bakugou was in awe, a sight he has never yet seen.

“It is an absolute honor to have you here … ! Your Japanese is impressive!” Iida stood up moving his arm in the odd robotic like motions, but todoroki doubted anyone missed the telltale pink blush flushed across his pale face.

… bowed in response, traditional Japanese etiquette that she had obviously studied along with the language.

His eyes followed her long legs as she walked to the only empty seat in the room. Right next to him.

[technician-the]

Magneton induced power cut

Do you call animal (pokemon) control or an electrician when this happens?

Magneton was pretty easy to make after magnemite (lol), although I forgot to clear the keyframes on the duplicate bodies and the first time I ran the animation one wandered off >_<

Im trying a new lighting effect, It uses a rotating 2d grid instead of a 3d latus as its base geometry. the plane rotates to always lay between the two points I set as the start and end of the lighting bolt. the result is much less unused geometry, and a faster render time. the lighting formed by is a random path through the grid (using geonodes shortest edge path function), with some additional randomization tacked on at the end to hide the grid structure.

the second gif is my attempt at simulating electromagnetic lines of force in blender. Im using a wave texture, with the coordinates based on the distance from the megneton, and a little vorinoi mixed in for distortion

[duckprintspress]

Celebrate Native American Heritage Month with 7 Queer Books We Love

November is National Native American Heritage Month! We’re celebrating with books (as always, lol). We asked our rec list contibutors for their favorite queer books either by Native American authors or starring Native American characters. Most of these books (maybe all, I couldn’t confirm for all the authors) are both! Contributors to the list are Nina Waters, hullosweetpea, D.V. Morse, Shea Sullivan and an anonymous contributor.

-

Indiginerds edited by Alina Pete

First Nations culture is living, vibrant, and evolving…

…and generations of Indigenous kids have grown up with pop culture creeping inexorably into our lives. From gaming to social media, pirate radio to garage bands, Star Trek to D&D, and missed connections at the pow wow, Indigenous culture is so much more than how it’s usually portrayed. These comics are here to celebrate those stories!

Featuring an all-Indigenous creative team, INDIGINERDS is an exhilarating anthology collecting 11 stories about Indigenous people balancing traditional ways of knowing with modern pop culture.

-

Postcolonial Love Poem by Natalie Díaz

Postcolonial Love Poem is a thunderous river of a book, an anthem of desire against erasure. It demands that every body carried in its pages – bodies of language, land, suffering brothers, enemies and lovers – be touched and held. Here, the bodies of indigenous, Latinx, black and brown women are simultaneously the body politic and the body ecstatic, and portrayed with a glowing intimacy: the alphabet of a hand in the dark, the hips’ silvered percussion, a thigh’s red-gold geometry, the emerald tigers that leap in a throat. In claiming this autonomy of desire, language is pushed to its dark edges, the astonishing dune fields and forests where pleasure and love are both grief and joy, violence and sensuality.

Natalie Diaz defies the conditions from which she writes, a nation whose creation predicated the diminishment and ultimate erasure of bodies like hers and the people she loves. Her poetry questions what kind of future we might create, built from the choices we make now – how we might learn our own cures and ‘go where there is love’.

-

A Snake Falls to Earth by Darcie Little Badger

Nina is a Lipan girl in our world. She’s always felt there was something more out there. She still believes in the old stories.

Oli is a cottonmouth kid, from the land of spirits and monsters. Like all cottonmouths, he’s been cast from home. He’s found a new one on the banks of the bottomless lake.

Nina and Oli have no idea the other exists. But a catastrophic event on Earth, and a strange sickness that befalls Oli’s best friend, will drive their worlds together in ways they haven’t been in centuries.

And there are some who will kill to keep them apart.

-

Never Whistle at Night: An Indigenous Dark Fiction Anthology edited by Shane Hawk and Theodore C. Van Alst Jr.

Many Indigenous people believe that one should never whistle at night. This belief takes many forms: for instance, Native Hawaiians believe it summons the Hukai’po, the spirits of ancient warriors, and Native Mexicans say it calls Lechuza, a witch that can transform into an owl. But what all these legends hold in common is the certainty that whistling at night can cause evil spirits to appear–and even follow you home.These wholly original and shiver-inducing tales introduce readers to ghosts, curses, hauntings, monstrous creatures, complex family legacies, desperate deeds, and chilling acts of revenge. Introduced and contextualized by bestselling author Stephen Graham Jones, these stories are a celebration of Indigenous peoples’ survival and imagination, and a glorious reveling in all the things an ill-advised whistle might summon.

-

The Witch King (Witch King series) by H.E. Edgmon

Wyatt would give anything to forget where he came from–but a kingdom demands its king.

In Asalin, fae rule and witches like Wyatt Croft…don’t. Wyatt’s betrothal to his best friend, fae prince Emyr North, was supposed to change that. But when Wyatt lost control of his magic one devastating night, he fled to the human world.

Now a coldly distant Emyr has hunted him down. Despite transgender Wyatt’s newfound identity and troubling past, Emyr has no intention of dissolving their engagement. In fact, he claims they must marry now or risk losing the throne. Jaded, Wyatt strikes a deal with the enemy, hoping to escape Asalin forever. But as he gets to know Emyr, Wyatt realizes the boy he once loved may still exist. And as the witches face worsening conditions, he must decide once and for all what’s more important–his people or his freedom.

-

Elatsoe (Elatsoe series) by Darcie Little Badger

Imagine an America very similar to our own. It’s got homework, best friends, and pistachio ice cream.

There are some differences. This America been shaped dramatically by the magic, monsters, knowledge, and legends of its peoples, those Indigenous and those not. Some of these forces are charmingly everyday, like the ability to make an orb of light appear or travel across the world through rings of fungi. But other forces are less charming and should never see the light of day.

Elatsoe lives in this slightly stranger America. She can raise the ghosts of dead animals, a skill passed down through generations of her Lipan Apache family. Her beloved cousin has just been murdered, in a town that wants no prying eyes. But she is going to do more than pry. The picture-perfect facade of Willowbee masks gruesome secrets, and she will rely on her wits, skills, and friends to tear off the mask and protect her family.

-

Black Sun (Between Earth and Sky series) by Rebecca Roanhorse

A god will return When the earth and sky converge Under the black sun

In the holy city of Tova, the winter solstice is usually a time for celebration and renewal, but this year it coincides with a solar eclipse, a rare celestial event proscribed by the Sun Priest as an unbalancing of the world.

Meanwhile, a ship launches from a distant city bound for Tova and set to arrive on the solstice. The captain of the ship, Xiala, is a disgraced Teek whose song can calm the waters around her as easily as it can warp a man’s mind. Her ship carries one passenger. Described as harmless, the passenger, Serapio, is a young man, blind, scarred, and cloaked in destiny. As Xiala well knows, when a man is described as harmless, he usually ends up being a villain.

What are your favorite queer books with Native American representation?

Want to chat your favorite reads with us? Join our Book Lover’s Discord server!

Update your Goodreads TBR with any of these books by visiting our queer Native American books shelf  on Goodreads!Shop books with Native American rep using our rec list on our Bookshop.org affiliate page!

[kc5rings]

gear ask: boots vs mitts, which is more fun to you and why?

(also "blackout poetry but with a person" is rewiring my brain a bit so thank you for that)

For boots I’m gonna assume you mean ballet/pony boots since as opposed to just regular boots since mitts is the other option

It’s pretty situational but I’d probably go with mitts being generally more fun

With both options (assuming they are the only gear being used) you severely limit the actions a person can take without actually restraining their body all that much

With ballet boots they pretty much prevent walking entirely unless you’ve had lots of practice or are actually a ballerina. This also makes them a fun choice for a character who is actually a dancer to either show off their mastery or make them struggle where they would normally excel. They are an intense piece of gear and agony for someone who isn’t accustomed to them, fun but very situational

Pony boots are often lumped in with ballet boots as being super intense/painful, but are actually much easier to learn and downright comfortable once you do. Good quality ones are made with running and pulling heavy weight in mind, since that’s what they are often worn for. Great for the workout kink minded petplay fan but again, very situational. Not a great idea to wear real horseshoes inside for example

Mitts though, you can use in most any situation you want. Once a pair of properly fitted mitts are on the wearer is completely dependent on others for even the most basic tasks. A person who’s a workaholic is suddenly completely unable to type but otherwise free to wander and relax, a simple door is suddenly a sweat inducing geometry problem to try and tackle solo and a locked door is impossible even with the key in the room

Our hands are the primary means we have for interacting with the world, removing their use removes a massive amount of agency from a person, which can intensify a scene with other gear or force a person who has trouble letting go of control to accept that they can’t do anything but give in for a little while

[positively-knotted]

Dissertationposting 2: Curvature & Hypersurfaces

(Note: I'm not gonna say anything about what I mean by "curvature", as if you haven't already seen it in some context I don't think you're gonna get much out of these posts :/. But for clarity, I'll only ever talk about scalar curvature and call it R. If you're used to Gaussian curvature written K, this is the same except R = 2K. Oh also all my manifolds are oriented.)

It may not be immediately obvious why we would want to consider hypersurfaces when trying to understand curvature - after all, R³ is flat, but contains surfaces with all kinds of curvature. So a motivating example may be in order. This is in fact the example that spurred all of the developments we'll talk about, and is of particular importance in theoretical cosmology! Maybe I'll say more about that later.

Consider a manifold homeomorphic to the n-torus Tⁿ - or more properly, Tⁿ with a choice of geometry (Riemannian metric). Intuitively, this shouldn't be able to have R > 0 everywhere, in the same way that T² can't. Proving this is surprisingly hard, but one sensible approach would be to try induction. After all, T³ is just T² × S¹, and S¹ is easy to understand. Thought of the other way around, we want to find nice hypersurfaces and do inductive descent until we reach dimension 2, then apply Gauss-Bonnet.

But if any old hypersurface doesn't say much, what about particularly nice ones? The obvious candidates are so-called stable minimal hypersurfaces. These are minimal points for area, in the sense that if you perturb them very slightly, their area must increase (e.g. the meridian of a standard torus in the motivating example). The big result about these is as follows:

Lemma 1.

If Σ is a stable minimal hypersurface in a manifold (M, g) and f is any function on Σ, then [1]

Here the left side is the gradient of f (in the normal calculus sense), and \II is the second fundamental form, a number that tells us something about how Σ sits inside M. You can think of it as a kind of error term, but the important bit is that it's squared, so non-negative. R is the scalar curvature of the ambient manifold M, and R_\Sigma is the induced scalar curvature of Σ.

You've probably never seen this before, even if you've done differential geometry. I don't know why this formula isn't better known, it's super useful, as with clever choices of f it gives big results. Just taking f=1 shows that for a stable minimal hypersurface, the intrinsic curvature has to be greater on average than the external curvature. This is a pretty big step forward!

Ok, so we have our choice of useful hypersurfaces. Now we just need to show that they always exist. And they do! In fact, they exist for each homology class:

Lemma 2.

Let (M, g) be a closed n-manifold, 3 ≤ n ≤ 7. Then for any class α ∈ H_{n−1}(M), we can find a closed stable minimal hypersurface Σ such that [Σ] = α in homology.

Let's unpack this a bit. We can think of hypersurfaces as living in a particular homology class in the usual geometric way. It's a standard result from differential topology [2] that we can in find a hypersurface living in any homology class, and that slightly perturbing it won't change that class. The interesting bit here is that we can always take a stable minimal representative, in sufficiently small dimensions. [3] Annoyingly, this means everything from here on out only applies in dimensions less than 8, even though there's no good topological reason why it isn't true more generally. (It definitely is true more generally, we just need a stronger version of this lemma and that makes it an analysis question.)

Next time, we'll use this to show that Tⁿ doesn't admit positive scalar curvature! Notes below the cut.

[1] Proof of Lemma 1. Start with the usual Gauss equation. Take the trace to pass to Ricci curvature, then again to pass to scalar curvature. It turns out that the irritating terms from varying dimensions cancel out! More detail in the screenshots below:

[2] Remember that there is a bijection between H¹(M) and homotopy classes of maps M -> S¹, pairing [f] with f^*(ω), where ω generates H¹(S¹). We can assume f is smooth, choose a regular value t, and set Σ = f^{-1}(t). Then [Σ] is Poincaré dual to f^*(ω).

[3] The actual argument here is pretty standard for the analysis I'll be omitting. In general, if we want to show that an object in space X with property P exists, we'll pass to a bigger space Y where standard results give us an object with that property; then somehow argue that P implies that it's actually of type X. Here, we pass from submanifolds to currents, and minimise area for currents in a given homology class. By measure theoretic magic, this minimisation forces the singular set of the current to have codimension at most 7, so in dimensions less than 8 it is in fact a submanifold.

[rock-swag-tournament]

pyrite propaganda: pyrite is so amazing i’m not even kidding. in my mothertongue, instead of being called fool’s gold, it’s called cat’s gold and we all love cats right?

also, fossils can become pyritised, meaning that we have literal DINOSAUR FOSSILS that are made of pyrite!!! beautiful shiny golden pyrite!!!

plus pyrite has a lot of chemically similar minerals that are awesome that it can occur with as well. i love chalcopyrite because i love copper (CuFeS2 if im not mistaken) and arsenopyrite is haha funny because its chemical composition is literally FeAsS and it has arse in the name as well (sorry).

it also forms in cubes and im p sure the other shape is a dodecahedron (sorry im not good at remembering geometry and im writing this in a pyrite-induced feverish haze so im not gonna google that rn) and we love 1. minecraft (cubes) and 2. dnd (dodecahedron)

i literally love this rock so so so much i will cry forever if it doesnt win (real)

YES TO ALL OF THIS! And thank you especially for shouting out chalcopyrite i love chalcopyrite.

[queenofcandynsoda]

Carmine the Bloodshed

(Thank you @jknerd~)

TW; Self-harm

Carmine the Bloodshed

Other Names: Carmine the Bloodshed (カーマイン・の・さっしょう Chimamire no Carumin), The Psycho’s Son, The Red Devil, Carmine Spini, R-O-001

Age: 7

Affiliation: Deepground; Shinra Electric Power Company (Formerly), Weiss’ Army

Occupation: Child Soldier, Sniper, Assassin (trainee)

Residence: Deepground Offspring Nursery (formerly), None/Nomadic (currently)

Family: Rosso the Crimson (mother), Cerise (younger sister), Eerie (younger sister), Cordovan and Maroon (younger twin brothers), Jasper (younger brother), Peach (youngest sister), Madder (younger brother), Cardinal (younger brother), Chili (youngest brother), The Restrictor (biological father)

Abilities: Firearm Proficiency (Rifle, Sniper Rifle, Shotgun, Handgun, Assault Rifle), Supernatural Gunmanship (Supernatural Accuracy, Supernatural Reflexes, Supernatural Dexterity, Quick Draw), Glowing Eyes, Knife Proficiency (Switchblade, Razor, Scalpel, Clever, Kitchen Knife), Superior Human Physiology (Flash Step, Supernatural Stealth, Afterimage Creation, Bulletproof Durability, Self-Sustenance, Disease Resistance, Enhanced Intelligence, Supernatural Strength, Healing Coma [after blood loss], Mental Regeneration), Blood Manipulation (Bleeding Inducement, Flammable Blood, Corrosive Blood, Haemokinetic Combat, Blood Bullets), Adaptive Regeneration [after MANY attempts to euthanize him] (Acid Immunity, Poison/Venom Immunity, Water Immunity, Fire Immunity, Explosion Immunity, Blunt Force Immunity, Cutting Immunity), Feign Death, Supernatural Cells, Killing Mastery, Killing Instinct (reluctant), Anatomical Mastery, Weakness Detection, Humanity Retainment, Indomitable Loyalty (to his mother and Weiss), Mathematics Mastery (Geometry, Shatterpoint, Numerical Precision, Calculation, Ricochet), Temporal Sense, Combat Adaptation

Likes: His family, Freedom, Daylight, Collecting souvenirs, Girl-in-the-Picture (Vermillion), Guns, Hot Chocolate, Burgers, Pizzas, Loyalty to Weiss, Target Practice

Dislikes: THE RESTRICTOR, Shinra Company, Professor Hojo, Doctor Fiorenzo Rosales, His Murderous Thoughts, Being controlled, Intense Training, Greedy People, Spoiled Brats

Origins: Carmine is a member of the Off-Color Tsviets and the first son and child of Rosso the Crimson. His biological father is the Restrictor, the cruel overseer of Deepground. From birth, Carmine was forced to train to be the most effective killer that could surpass his mother’s abilities. His body has been pushed beyond its limits to the point it is a wonder how Carmine lived past the age of five. After his birth, his mother attempted to hide him but he was quickly taken away and placed in the Offspring Nursery. Since then, he was subjected to torturous experiments as Rosso gave birth to his siblings due to her body being modified to be pregnant for three months. The mother and son would communicate at every opportunity, even having the chance to see his younger siblings. 

Due to the brutal experience he suffered, Carmine has become mentally unstable. He has become hostile to “Shinrites,” meaning people who work for Shinra”, and would aim his rifle at them, believing they intend harm regardless. He tends to be vulgar whenever he feels defensive, especially when it comes to his siblings and mother. This would also lead to profanity and threats of violence. 

Despite these frightening traits, he does his best to create and maintain his humanity. He would make himself bleed daily to remind himself that he is still a living person, not a weapon. Carmine had developed a reputation for trying to escape since he was about four years old. His common method is to use the air vent. This led him to enter various places in the Shinra Tower, such as the Materia Research Facility, SOLDIER Floor, Visual Entertainment Hall, the President’s Office, executives' offices, Hojo's laboratory, and the Skyview Hall, his favorite place. He would collect items, such as office supplies, Shinra/SOLDIER merch, souvenirs, and human teeth from Hojo’s lab. He also managed to collect Lazard’s pens, the Turks’ weapons, Palmer’s luxury eating utensils, Heidegger’s medals, Hojo’s lab equipment, Scarlet’s picture of her daughter, Vermillion, Rochelle’s makeup, Rufus’ coins and shotgun bullets, Junio’s handbags, and President Shinra’s car keys to one of his sports cars. He would then give most of them to the other children in Deepground, such as his siblings and his peers like Fuchsia. There are even times that he took jewelry and fur coats to Rosso in secret. 

When Sonon and Yuffie got captured, Carmine was one of the first to interact with the former. Though their first interaction was brief, the ninja intrigued the young boy. Once they get to meet more formally, Sonon is assigned to fight him, later, he tells him about the “Outside”. Sonon said how Wutai was a great nation before Shinra ruined it and that there was so much freedom. Carmine was amazed by this and would repeat it to the other children. 

Once Yuffie becomes pregnant, Carmine overhears conversations about a potential dissection of the baby, which would lead to its death as they are deemed “disposable”. The boy immediately told Sonon, who then told Nero, Weiss, and Yuffie. The Pure White Emperor then created an escape plan that would lead them into Wutai. Days later, Carmine hit his head hard enough that he got a concussion during training. In the infirmary, when Shelke is assisting in examining him with the doctors, she discovers that Carmine's “obedience” chip has been destroyed. This allows him to go against the Restrictor and gain free will. From there, Weiss sees him as essential to the escape. Soon after, Weiss secretly told the young boy how he could help. 

There are three tasks he needs to do once he escapes;

Seek out Viceroy Sarruf for Weiss to remove him from power for the Kisaragi Family to reclaim control over Wutai

Search for Wutai’s materia, especially the Leviathan materia

Return to help with the breakout once he gets Shelke’s message 

As a way to escape, Carmine forced his body into “Bleeding Sleep” to give the appearance of being dead as blood came out of his mouth and his heart stopped. Several Deepground children, including some of his siblings, pretend to mourn for him. The Restrictor, disgusted by Carmine’s “corpse”, threw him away in the trash truck. Carmine uses “Bleeding Sleep” long enough to wake himself and crawl out of the trash. He looks out of the trash truck to see the sun for the first time, amazed by the sight of freedom. Using this as an opportunity, he jumped out and headed to the nearest town outside of Midgar, Kalm. From there, he learns more about 

Along with getting a red hoodie, black pants, and slightly ragged white sneakers, he also gets a small rifle and stolen materia for any self-defense. 

Now, with all of his equipment, Carmine hopes to complete his tasks to ensure the escape from Deepground and the rescue of his family. As he travels, he learns to become more human and gain experience. 

[bracketsoffear]

Simon (Hawaii: Part II/Miracle Musical) "I promise you, this dude is in EVERY Spiral and Distortion playlist ever. The album tells an ambiguous story, but this trilogy of tracks within is the most obviously Spiral fable ever that isn't from TMA itself. He is a liar and he is deluded: he is a perpetrator and a victim. Every single possible Spiral motif imaginable appears in his story, both aesthetically and thematically.

Simon talks about himself in third-person in the song Murders, and describes himself "in the forest looking to see the trees, but none were there" and seeking the "fountain of infinite mirror", presumably some fractalline Spiral artifact. Simon finds a girl and is paranoid of "terrors or none were there" & a "shadow of nobody there".

In the song "The Mind Electric", he finds himself on trial for the murder of this girl, which he may or may not have commited - he's an unreliable narrator. He pleads insanity, which may or may not be true, and the judge who appears as a holy figure sentences him to electroshock treatment. His brain is fried and he deludes himself into thinking all the hospital workers are holy people and "spiraling down thy majesty". The song's climax is a cry from him: "Someone help me understand what's going on inside my mind / Doctor, I can't tell if I'm not me", before spurting out incoherent phrases.

In the song Labyrinth, Simon retreats into a mind palace in the form of an ever-shifting maze of impossible geometry. He imagines a woman's voice calling: "See how I circle / Imaginary mind, imaginary lines / Let the maze of my design carry you on".

And then he gets time-travel powers and causes 9/11 or something? I dunno, it's a very ambiguous album."

Adam Smith (Torchwood) "Adam is an alien that can only exist through the memories of others, so he infiltrates the Torchwood team and makes them all think he’s been their trusted teammate for years when really it hasn’t even been two days. Adam uses this memory power to distract the team from discovering he’s not real by variously invoking memories of one’s long-lost brother, inducing false insecurities in one, making one in a relationship with him with all the non-con vibes that entails, making one forget her fiancé, and making the one who was closest to catching him believe he’d murdered three women and that Adam was his savior and accomplice. He wove himself so deeply into the team that the only way to get rid of him was to take amnesia pills to entirely erase those two days, leaving the team unnerved and uncertain of what they had done that was so bad they couldn’t remember it"

[cbirt]

Researchers at the MIT-IBM Watson AI Lab have achieved a significant breakthrough in the field of molecular property prediction. By introducing the Grammar-Induced Geometry Framework, the researchers address the challenge of curating labeled data for developing accurate deep-learning models. This framework leverages a learnable hierarchical molecular grammar to capture structure-level similarity, paving the way for data-efficient property prediction crucial for drug discovery and material sciences. The framework demonstrated its excellency for large datasets and extremely limited data, outperforming supervised and pre-trained Graph Neural Networks. This article delves into the Grammar-Induced Geometry Framework, its advantages, and its potential implications.

Fundamentally the framework is based on Grammar-induced Geometry that graphically represents the space of molecules, and every path spanning the root to leaf delineates a grammar production sequence that prompts a particular molecule. Just like following grammar rules, we can formulate diverse sentences, in formal language theory, grammar depicts a set of production rules formulating the procedure of building validated strings from a language’s alphabet. For instance, two molecular structures having a similar substructure would use the same sequence of grammar production rules.

Continue Reading

[madamlaydebug]

Haha! Makes sense. 🤓

📷: Art by Ahmed Elblas

MER: THE GREAT PYRMID OF GIZA

The Great Pyramid Of Giza Known as Mer to the ancient Kemites is the most enigmatic structure on the face of the planet. Mer which translates to the “Place of Ascension” is the only surviving wonder of the ancient world and has inspired much speculation as to why it was built and what was its function.

According the the ancient Kemites themselves the Pyramids served as a ritual center for the Per Ankh schools of initiation. The Kings and Queens chambers were designed to harness resonance frequencies to induce higher states of conciousness. The structure of the pyramid was designed using sacred geometry which allowed the structures to tap into the subtle energies of the earth and the cosmos. The ancients harnessed this enegery for a number of purposes. It is said that the Pharaohs would use the Mer structures which were incased in highly reflective white limestone, capped with gold to "Turn night into day". A feat of such greatness would surely ensure their names and legacies would live on for thousands of years. They were right.

The mathematical accuracy and astronomical information encoded into the structure has baffled scientists for decades. The great pyramid is aligned within three sixtieths of a degree of true north, a more accurate alignment than any other structure on earth. It is not only aligned almost perfectly to the cardinal points, but its placement on the earth is intentional as well placing it directly in the center of the world's landmass.

The level of technological sophistication used to build this great monument far exceeds the capabilities of today’s greatest minds and we could not build anything close to the great pyramid today even with our perceived advanced technology and building machinery. The ancient Kemites did not use the inch as they do in our modern system.

They used the royal cubit which is one 25 millionth of the polar diameter of the earth which is the exact distance from the north to the south pole. If you chop that distance into 25 million pieces you get the royal cubit.

The length of a base side at the base socket level is 9,131 inches which translates to 365.242 royal cubits. This just happens to be the earthly year right down to a quarter day. The measurements of the length and width of the perimeter of the great pyramid corresponds to an exact fraction of both the longitude and latitude measurements at the equator. Scaled up this means the great pyramid directly corresponds to the circumference of the equator as well as the measurements from the equator to the pole, making it a scale model of the northern hemisphere.

If you take the location of the Great pyramid as a coordinate this number sequence matches the speed of light traveling through space measurement in meters per second. None of this is a coincidence and the vast information encoded about the earth and its relation to the cosmos points to the fact that these ancient Africans were far more advanced than we could ever imagine and the methods in which they collected and incorporated these high sciences into their structures and cities still escape scientists today.

Today I give thanks to the ancient Kemites and those that came before for their contributions of Mathematics, Sacred Geometry, Architecture & Astronomy. I am grateful for these gifts you gave to the world.

Black Genesis by Robert Bouval and Thomas Brophy

https://www.amazon.com/Black-Genesis.../dp/159143114X

𓊵𓏏𓊪 𓋹 Hotep Be at peace

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"I have not spoken angrily or arrogantly. I have not cursed anyone in thought, word or deeds." ~ 35th & 36th Principals of Ma'at

[rjalker]

no, this is what it looks like when I copy and paste that entire section of the book :)

Section 15. Concerning a Stranger from Spaceland

From dreams I proceed to facts.

It was the last day of the 1999th year of our era. The pattering of the rain had long ago announced nightfall; and I was sitting in the company of my wife, musing on the events of the past and the prospects of the coming year, the coming century, the coming Millennium.

[Note: When I say "sitting", of course I do not mean any change of attitude such as you in Spaceland signify by that word; for as we have no feet, we can no more "sit" nor "stand" (in your sense of the word) than one of your soles or flounders.

Nevertheless, we perfectly well recognize the different mental states of volition implied in "lying", "sitting", and "standing", which are to some extent indicated to a beholder by a slight increase of lustre corresponding to the increase of volition.

But on this, and a thousand other kindred subjects, time forbids me to dwell.]

My four Sons and two orphan Grandchildren had retired to their several apartments; and my wife alone remained with me to see the old Millennium out and the new one in.

I was rapt in thought, pondering in my mind some words that had casually issued from the mouth of my youngest Grandson, a most promising young Hexagon of unusual brilliancy and perfect angularity. His uncles and I had been giving him his usual practical lesson in Sight Recognition, turning ourselves upon our centres, now rapidly, now more slowly, and questioning him as to our positions; and his answers had been so satisfactory that I had been induced to reward him by giving him a few hints on Arithmetic, as applied to Geometry.

Taking nine Squares, each an inch every way, I had put them together so as to make one large Square, with a side of three inches, and I had hence proved to my little Grandson that—though it was impossible for us to SEE the inside of the Square—yet we might ascertain the number of square inches in a Square by simply squaring the number of inches in the side: "and thus," said I, "we know that 32, or 9, represents the number of square inches in a Square whose side is 3 inches long."

The little Hexagon meditated on this a while and then said to me; "But you have been teaching me to raise numbers to the third power: I suppose 33 must mean something in Geometry; what does it mean?" "Nothing at all," replied I, "not at least in Geometry; for Geometry has only Two Dimensions." And then I began to shew the boy how a Point by moving through a length of three inches makes a Line of three inches, which may be represented by 3; and how a Line of three inches, moving parallel to itself through a length of three inches, makes a Square of three inches every way, which may be represented by 32.

Upon this, my Grandson, again returning to his former suggestion, took me up rather suddenly and exclaimed, "Well, then, if a Point by moving three inches, makes a Line of three inches represented by 3; and if a straight Line of three inches, moving parallel to itself, makes a Square of three inches every way, represented by 32; it must be that a Square of three inches every way, moving somehow parallel to itself (but I don't see how) must make Something else (but I don't see what) of three inches every way—and this must be represented by 33."

"Go to bed," said I, a little ruffled by this interruption: "if you would talk less nonsense, you would remember more sense."

So my Grandson had disappeared in disgrace; and there I sat by my Wife's side, endeavouring to form a retrospect of the year 1999 and of the possibilities of the year 2000, but not quite able to shake off the thoughts suggested by the prattle of my bright little Hexagon. Only a few sands now remained in the half-hour glass. Rousing myself from my reverie I turned the glass Northward for the last time in the old Millennium; and in the act, I exclaimed aloud, "The boy is a fool."

Straightway I became conscious of a Presence in the room, and a chilling breath thrilled through my very being. "He is no such thing," cried my Wife, "and you are breaking the Commandments in thus dishonouring your own Grandson." But I took no notice of her. Looking round in every direction I could see nothing; yet still I FELT a Presence, and shivered as the cold whisper came again. I started up. "What is the matter?" said my Wife, "there is no draught; what are you looking for? There is nothing." There was nothing; and I resumed my seat, again exclaiming, "The boy is a fool, I say; 33 can have no meaning in Geometry." At once there came a distinctly audible reply, "The boy is not a fool; and 33 has an obvious Geometrical meaning."

My Wife as well as myself heard the words, although she did not understand their meaning, and both of us sprang forward in the direction of the sound. What was our horror when we saw before us a Figure! At the first glance it appeared to be a Woman, seen sideways; but a moment's observation shewed me that the extremities passed into dimness too rapidly to represent one of the Female Sex; and I should have thought it a Circle, only that it seemed to change its size in a manner impossible for a Circle or for any regular Figure of which I had had experience.

But my Wife had not my experience, nor the coolness necessary to note these characteristics. With the usual hastiness and unreasoning jealousy of her Sex, she flew at once to the conclusion that a Woman had entered the house through some small aperture. "How comes this person here?" she exclaimed, "you promised me, my dear, that there should be no ventilators in our new house." "Nor are there any," said I; "but what makes you think that the stranger is a Woman? I see by my power of Sight Recognition——" "Oh, I have no patience with your Sight Recognition," replied she, "'Feeling is believing' and 'A Straight Line to the touch is worth a Circle to the sight'"—two Proverbs, very common with the Frailer Sex in Flatland.

"Well," said I, for I was afraid of irritating her, "if it must be so, demand an introduction." Assuming her most gracious manner, my Wife advanced towards the Stranger, "Permit me, Madam, to feel and be felt by——" then, suddenly recoiling, "Oh! it is not a Woman, and there are no angles either, not a trace of one. Can it be that I have so misbehaved to a perfect Circle?"

"I am indeed, in a certain sense a Circle," replied the Voice, "and a more perfect Circle than any in Flatland; but to speak more accurately, I am many Circles in one." Then he added more mildly, "I have a message, dear Madam, to your husband, which I must not deliver in your presence; and, if you would suffer us to retire for a few minutes——" But my Wife would not listen to the proposal that our august Visitor should so incommode himself, and assuring the Circle that the hour of her own retirement had long passed, with many reiterated apologies for her recent indiscretion, she at last retreated to her apartment.

I glanced at the half-hour glass. The last sands had fallen. The third Millennium had begun.

Section 16. How the Stranger vainly endeavoured to reveal to me in words the mysteries of Spaceland

As soon as the sound of the Peace-cry of my departing Wife had died away, I began to approach the Stranger with the intention of taking a nearer view and of bidding him be seated: but his appearance struck me dumb and motionless with astonishment. Without the slightest symptoms of angularity he nevertheless varied every instant with gradations of size and brightness scarcely possible for any Figure within the scope of my experience. The thought flashed across me that I might have before me a burglar or cut-throat, some monstrous Irregular Isosceles, who, by feigning the voice of a Circle, had obtained admission somehow into the house, and was now preparing to stab me with his acute angle.

In a sitting-room, the absence of Fog (and the season happened to be remarkably dry), made it difficult for me to trust to Sight Recognition, especially at the short distance at which I was standing. Desperate with fear, I rushed forward with an unceremonious, "You must permit me, Sir—" and felt him. My Wife was right. There was not the trace of an angle, not the slightest roughness or inequality: never in my life had I met with a more perfect Circle. He remained motionless while I walked round him, beginning from his eye and returning to it again. Circular he was throughout, a perfectly satisfactory Circle; there could not be a doubt of it. Then followed a dialogue, which I will endeavour to set down as near as I can recollect it, omitting only some of my profuse apologies—for I was covered with shame and humiliation that I, a Square, should have been guilty of the impertinence of feeling a Circle. It was commenced by the Stranger with some impatience at the lengthiness of my introductory process.

STRANGER. Have you felt me enough by this time? Are you not introduced to me yet?

I. Most illustrious Sir, excuse my awkwardness, which arises not from ignorance of the usages of polite society, but from a little surprise and nervousness, consequent on this somewhat unexpected visit. And I beseech you to reveal my indiscretion to no one, and especially not to my Wife. But before your Lordship enters into further communications, would he deign to satisfy the curiosity of one who would gladly know whence his Visitor came?

STRANGER. From Space, from Space, Sir: whence else?

I. Pardon me, my Lord, but is not your Lordship already in Space, your Lordship and his humble servant, even at this moment?

STRANGER. Pooh! what do you know of Space? Define Space.

I. Space, my Lord, is height and breadth indefinitely prolonged.

STRANGER. Exactly: you see you do not even know what Space is. You think it is of Two Dimensions only; but I have come to announce to you a Third—height, breadth, and length.

I. Your Lordship is pleased to be merry. We also speak of length and height, or breadth and thickness, thus denoting Two Dimensions by four names.

STRANGER. But I mean not only three names, but Three Dimensions.

I. Would your Lordship indicate or explain to me in what direction is the Third Dimension, unknown to me?

STRANGER. I came from it. It is up above and down below.

I. My Lord means seemingly that it is Northward and Southward.

STRANGER. I mean nothing of the kind. I mean a direction in which you cannot look, because you have no eye in your side.

I. Pardon me, my Lord, a moment's inspection will convince your Lordship that I have a perfect luminary at the juncture of two of my sides.

STRANGER. Yes: but in order to see into Space you ought to have an eye, not on your Perimeter, but on your side, that is, on what you would probably call your inside; but we in Spaceland should call it your side.

I. An eye in my inside! An eye in my stomach! Your Lordship jests.

STRANGER. I am in no jesting humour. I tell you that I come from Space, or, since you will not understand what Space means, from the Land of Three Dimensions whence I but lately looked down upon your Plane which you call Space forsooth. From that position of advantage I discerned all that you speak of as SOLID (by which you mean "enclosed on four sides"), your houses, your churches, your very chests and safes, yes even your insides and stomachs, all lying open and exposed to my view.

I. Such assertions are easily made, my Lord.

STRANGER. But not easily proved, you mean. But I mean to prove mine.

When I descended here, I saw your four Sons, the Pentagons, each in his apartment, and your two Grandsons the Hexagons; I saw your youngest Hexagon remain a while with you and then retire to his room, leaving you and your Wife alone. I saw your Isosceles servants, three in number, in the kitchen at supper, and the little Page in the scullery. Then I came here, and how do you think I came?

I. Through the roof, I suppose.

STRANGER. Not so. Your roof, as you know very well, has been recently repaired, and has no aperture by which even a Woman could penetrate. I tell you I come from Space. Are you not convinced by what I have told you of your children and household?

I. Your Lordship must be aware that such facts touching the belongings of his humble servant might be easily ascertained by any one in the neighbourhood possessing your Lordship's ample means of obtaining information.

STRANGER. (TO HIMSELF.) What must I do? Stay; one more argument suggests itself to me. When you see a Straight Line—your wife, for example—how many Dimensions do you attribute to her?

I. Your Lordship would treat me as if I were one of the vulgar who, being ignorant of Mathematics, suppose that a Woman is really a Straight Line, and only of One Dimension. No, no, my Lord; we Squares are better advised, and are as well aware as your Lordship that a Woman, though popularly called a Straight Line, is, really and scientifically, a very thin Parallelogram, possessing Two Dimensions, like the rest of us, viz., length and breadth (or thickness).

STRANGER. But the very fact that a Line is visible implies that it possesses yet another Dimension.

I. My Lord, I have just acknowledged that a Woman is broad as well as long. We see her length, we infer her breadth; which, though very slight, is capable of measurement.

STRANGER. You do not understand me. I mean that when you see a Woman, you ought—besides inferring her breadth—to see her length, and to SEE what we call her HEIGHT; although that last Dimension is infinitesimal in your country. If a Line were mere length without "height", it would cease to occupy Space and would become invisible. Surely you must recognize this?

I. I must indeed confess that I do not in the least understand your Lordship. When we in Flatland see a Line, we see length and BRIGHTNESS. If the brightness disappears, the Line is extinguished, and, as you say, ceases to occupy Space. But am I to suppose that your Lordship gives to brightness the title of a Dimension, and that what we call "bright" you call "high"?

STRANGER. No, indeed. By "height" I mean a Dimension like your length: only, with you, "height" is not so easily perceptible, being extremely small.

I. My Lord, your assertion is easily put to the test. You say I have a Third Dimension, which you call "height". Now, Dimension implies direction and measurement. Do but measure my "height", or merely indicate to me the direction in which my "height" extends, and I will become your convert. Otherwise, your Lordship's own understanding must hold me excused.

STRANGER. (TO HIMSELF.) I can do neither. How shall I convince him? Surely a plain statement of facts followed by ocular demonstration ought to suffice. —Now, Sir; listen to me.

You are living on a Plane. What you style Flatland is the vast level surface of what I may call a fluid, on, or in, the top of which you and your countrymen move about, without rising above it or falling below it.

I am not a plane Figure, but a Solid. You call me a Circle; but in reality I am not a Circle, but an infinite number of Circles, of size varying from a Point to a Circle of thirteen inches in diameter, one placed on the top of the other. When I cut through your plane as I am now doing, I make in your plane a section which you, very rightly, call a Circle. For even a Sphere—which is my proper name in my own country—if he manifest himself at all to an inhabitant of Flatland—must needs manifest himself as a Circle.

Do you not remember—for I, who see all things, discerned last night the phantasmal vision of Lineland written upon your brain—do you not remember, I say, how, when you entered the realm of Lineland, you were compelled to manifest yourself to the King, not as a Square, but as a Line, because that Linear Realm had not Dimensions enough to represent the whole of you, but only a slice or section of you? In precisely the same way, your country of Two Dimensions is not spacious enough to represent me, a being of Three, but can only exhibit a slice or section of me, which is what you call a Circle.

The diminished brightness of your eye indicates incredulity. But now prepare to receive proof positive of the truth of my assertions. You cannot indeed see more than one of my sections, or Circles, at a time; for you have no power to raise your eye out of the plane of Flatland; but you can at least see that, as I rise in Space, so my sections become smaller. See now, I will rise; and the effect upon your eye will be that my Circle will become smaller and smaller till it dwindles to a point and finally vanishes.

[ID: A black and white diagram showing a Sphere intersecting a line, with an eye on the right corner of this line labeled “my eye”. At first the Sphere rests with the line intersecting the middle of his body, creating a large circle. This is labeled, “The Sphere with his section at full size”. Then we are shown “The Sphere rising”, with the line now in a lower section, creating a smaller circle. Finally the sphere is almost above the line completely, forming a tiny circle, labeled, “The Sphere on the limit of vanishing”. End ID.]

There was no "rising" that I could see; but he diminished and finally vanished. I winked once or twice to make sure that I was not dreaming. But it was no dream. For from the depths of nowhere came forth a hollow voice—close to my heart it seemed—"Am I quite gone? Are you convinced now? Well, now I will gradually return to Flatland and you shall see my section become larger and larger."

Every reader in Spaceland will easily understand that my mysterious Guest was speaking the language of truth and even of simplicity. But to me, proficient though I was in Flatland Mathematics, it was by no means a simple matter. The rough diagram given above will make it clear to any Spaceland child that the Sphere, ascending in the three positions indicated there, must needs have manifested himself to me, or to any Flatlander, as a Circle, at first of full size, then small, and at last very small indeed, approaching to a Point. But to me, although I saw the facts before me, the causes were as dark as ever. All that I could comprehend was, that the Circle had made himself smaller and vanished, and that he had now reappeared and was rapidly making himself larger.

When he regained his original size, he heaved a deep sigh; for he perceived by my silence that I had altogether failed to comprehend him. And indeed I was now inclining to the belief that he must be no Circle at all, but some extremely clever juggler; or else that the old wives' tales were true, and that after all there were such people as Enchanters and Magicians.

After a long pause he muttered to himself, "One resource alone remains, if I am not to resort to action. I must try the method of Analogy." Then followed a still longer silence, after which he continued our dialogue.

SPHERE. Tell me, Mr. Mathematician; if a Point moves Northward, and leaves a luminous wake, what name would you give to the wake?

I. A straight Line.

SPHERE. And a straight Line has how many extremities?

I. Two.

SPHERE. Now conceive the Northward straight Line moving parallel to itself, East and West, so that every point in it leaves behind it the wake of a straight Line. What name will you give to the Figure thereby formed? We will suppose that it moves through a distance equal to the original straight Line. —What name, I say?

I. A Square.

SPHERE. And how many sides has a Square? How many angles?

I. Four sides and four angles.

SPHERE. Now stretch your imagination a little, and conceive a Square in Flatland, moving parallel to itself upward.

I. What? Northward?

SPHERE. No, not Northward; upward; out of Flatland altogether.

If it moved Northward, the Southern points in the Square would have to move through the positions previously occupied by the Northern points. But that is not my meaning.

I mean that every Point in you—for you are a Square and will serve the purpose of my illustration—every Point in you, that is to say in what you call your inside, is to pass upwards through Space in such a way that no Point shall pass through the position previously occupied by any other Point; but each Point shall describe a straight Line of its own. This is all in accordance with Analogy; surely it must be clear to you.

Restraining my impatience—for I was now under a strong temptation to rush blindly at my Visitor and to precipitate him into Space, or out of Flatland, anywhere, so that I could get rid of him—I replied:—

"And what may be the nature of the Figure which I am to shape out by this motion which you are pleased to denote by the word 'upward'? I presume it is describable in the language of Flatland."

SPHERE. Oh, certainly. It is all plain and simple, and in strict accordance with Analogy—only, by the way, you must not speak of the result as being a Figure, but as a Solid. But I will describe it to you. Or rather not I, but Analogy.

We began with a single Point, which of course—being itself a Point—has only ONE terminal Point.

One Point produces a Line with TWO terminal Points.

One Line produces a Square with FOUR terminal Points.

Now you can give yourself the answer to your own question: 1, 2, 4, are evidently in Geometrical Progression. What is the next number?

I. Eight.

SPHERE. Exactly. The one Square produces a SOMETHING-WHICH- YOU-DO-NOT-AS-YET-KNOW-A-NAME-FOR-BUT-WHICH-WE-CALL-A-CUBE with EIGHT terminal Points. Now are you convinced?

I. And has this Creature sides, as well as angles or what you call "terminal Points"?

SPHERE. Of course; and all according to Analogy. But, by the way, not what YOU call sides, but what WE call sides. You would call them SOLIDS.

I. And how many solids or sides will appertain to this Being whom I am to generate by the motion of my inside in an "upward" direction, and whom you call a Cube?

SPHERE. How can you ask? And you a mathematician! The side of anything is always, if I may so say, one Dimension behind the thing. Consequently, as there is no Dimension behind a Point, a Point has 0 sides; a Line, if I may say, has 2 sides (for the Points of a Line may be called by courtesy, its sides); a Square has 4 sides; 0, 2, 4; what Progression do you call that?

I. Arithmetical.

SPHERE. And what is the next number?

I. Six.

SPHERE. Exactly. Then you see you have answered your own question. The Cube which you will generate will be bounded by six sides, that is to say, six of your insides. You see it all now, eh?

"Monster," I shrieked, "be thou juggler, enchanter, dream, or devil, no more will I endure thy mockeries. Either thou or I must perish." And saying these words I precipitated myself upon him.

Section 17. How the Sphere, having in vain tried words, resorted to deeds

It was in vain. I brought my hardest right angle into violent collision with the Stranger, pressing on him with a force sufficient to have destroyed any ordinary Circle: but I could feel him slowly and unarrestably slipping from my contact; no edging to the right nor to the left, but moving somehow out of the world, and vanishing to nothing. Soon there was a blank. But still I heard the Intruder's voice.

SPHERE. Why will you refuse to listen to reason? I had hoped to find in you—as being a man of sense and an accomplished mathematician—a fit apostle for the Gospel of the Three Dimensions, which I am allowed to preach once only in a thousand years: but now I know not how to convince you. Stay, I have it. Deeds, and not words, shall proclaim the truth. Listen, my friend.

I have told you I can see from my position in Space the inside of all things that you consider closed. For example, I see in yonder cupboard near which you are standing, several of what you call boxes (but like everything else in Flatland, they have no tops nor bottoms) full of money; I see also two tablets of accounts. I am about to descend into that cupboard and to bring you one of those tablets. I saw you lock the cupboard half an hour ago, and I know you have the key in your possession. But I descend from Space; the doors, you see, remain unmoved. Now I am in the cupboard and am taking the tablet. Now I have it. Now I ascend with it.

I rushed to the closet and dashed the door open. One of the tablets was gone. With a mocking laugh, the Stranger appeared in the other corner of the room, and at the same time the tablet appeared upon the floor. I took it up. There could be no doubt—it was the missing tablet.

I groaned with horror, doubting whether I was not out of my senses; but the Stranger continued: "Surely you must now see that my explanation, and no other, suits the phenomena. What you call Solid things are really superficial; what you call Space is really nothing but a great Plane. I am in Space, and look down upon the insides of the things of which you only see the outsides. You could leave this Plane yourself, if you could but summon up the necessary volition. A slight upward or downward motion would enable you to see all that I can see.

"The higher I mount, and the further I go from your Plane, the more I can see, though of course I see it on a smaller scale. For example, I am ascending; now I can see your neighbour the Hexagon and his family in their several apartments; now I see the inside of the Theatre, ten doors off, from which the audience is only just departing; and on the other side a Circle in his study, sitting at his books. Now I shall come back to you. And, as a crowning proof, what do you say to my giving you a touch, just the least touch, in your stomach? It will not seriously injure you, and the slight pain you may suffer cannot be compared with the mental benefit you will receive."

Before I could utter a word of remonstrance, I felt a shooting pain in my inside, and a demoniacal laugh seemed to issue from within me. A moment afterwards the sharp agony had ceased, leaving nothing but a dull ache behind, and the Stranger began to reappear, saying, as he gradually increased in size, "There, I have not hurt you much, have I? If you are not convinced now, I don't know what will convince you. What say you?"

My resolution was taken. It seemed intolerable that I should endure existence subject to the arbitrary visitations of a Magician who could thus play tricks with one's very stomach. If only I could in any way manage to pin him against the wall till help came!

Once more I dashed my hardest angle against him, at the same time alarming the whole household by my cries for aid. I believe, at the moment of my onset, the Stranger had sunk below our Plane, and really found difficulty in rising. In any case he remained motionless, while I, hearing, as I thought, the sound of some help approaching, pressed against him with redoubled vigour, and continued to shout for assistance.

A convulsive shudder ran through the Sphere. "This must not be," I thought I heard him say: "either he must listen to reason, or I must have recourse to the last resource of civilization." Then, addressing me in a louder tone, he hurriedly exclaimed, "Listen: no stranger must witness what you have witnessed. Send your Wife back at once, before she enters the apartment. The Gospel of Three Dimensions must not be thus frustrated. Not thus must the fruits of one thousand years of waiting be thrown away. I hear her coming. Back! back! Away from me, or you must go with me—whither you know not—into the Land of Three Dimensions!"

"Fool! Madman! Irregular!" I exclaimed; "never will I release thee; thou shalt pay the penalty of thine impostures."

"Ha! Is it come to this?" thundered the Stranger: "then meet your fate: out of your Plane you go. Once, twice, thrice! 'Tis done!"

Section 18. How I came to Spaceland, and what I saw there

An unspeakable horror seized me. There was a darkness; then a dizzy, sickening sensation of sight that was not like seeing; I saw a Line that was no Line; Space that was not Space: I was myself, and not myself. When I could find voice, I shrieked aloud in agony, "Either this is madness or it is Hell." "It is neither," calmly replied the voice of the Sphere, "it is Knowledge; it is Three Dimensions: open your eye once again and try to look steadily."

I looked, and, behold, a new world! There stood before me, visibly incorporate, all that I had before inferred, conjectured, dreamed, of perfect Circular beauty. What seemed the centre of the Stranger's form lay open to my view: yet I could see no heart, nor lungs, nor arteries, only a beautiful harmonious Something—for which I had no words; but you, my Readers in Spaceland, would call it the surface of the Sphere.

Prostrating myself mentally before my Guide, I cried, "How is it, O divine ideal of consummate loveliness and wisdom that I see thy inside, and yet cannot discern thy heart, thy lungs, thy arteries, thy liver?" "What you think you see, you see not," he replied; "it is not given to you, nor to any other Being to behold my internal parts. I am of a different order of Beings from those in Flatland. Were I a Circle, you could discern my intestines, but I am a Being, composed as I told you before, of many Circles, the Many in the One, called in this country a Sphere. And, just as the outside of a Cube is a Square, so the outside of a Sphere presents the appearance of a Circle."

Bewildered though I was by my Teacher's enigmatic utterance, I no longer chafed against it, but worshipped him in silent adoration. He continued, with more mildness in his voice. "Distress not yourself if you cannot at first understand the deeper mysteries of Spaceland. By degrees they will dawn upon you. Let us begin by casting back a glance at the region whence you came. Return with me a while to the plains of Flatland, and I will shew you that which you have often reasoned and thought about, but never seen with the sense of sight—a visible angle." "Impossible!" I cried; but, the Sphere leading the way, I followed as if in a dream, till once more his voice arrested me: "Look yonder, and behold your own Pentagonal house, and all its inmates."

I looked below, and saw with my physical eye all that domestic individuality which I had hitherto merely inferred with the understanding. And how poor and shadowy was the inferred conjecture in comparison with the reality which I now beheld! My four Sons calmly asleep in the North-Western rooms, my two orphan Grandsons to the South; the Servants, the Butler, my Daughter, all in their several apartments. Only my affectionate Wife, alarmed by my continued absence, had quitted her room and was roving up and down in the Hall, anxiously awaiting my return. Also the Page, aroused by my cries, had left his room, and under pretext of ascertaining whether I had fallen somewhere in a faint, was prying into the cabinet in my study. All this I could now SEE, not merely infer; and as we came nearer and nearer, I could discern even the contents of my cabinet, and the two chests of gold, and the tablets of which the Sphere had made mention.

[Image description start: A black and white diagram showing the pentagon shaped house described above, with a compass in one corner showing the house points north. In the main room of the house is the straight line labled, “My wife”, while everyone else is asleep in their own rooms, except for the Page, who is in the study. Outside the house are two thin Isosceles triangle policemen. Image description end.]

Touched by my Wife's distress, I would have sprung downward to reassure her, but I found myself incapable of motion. "Trouble not yourself about your Wife," said my Guide: "she will not be long left in anxiety; meantime, let us take a survey of Flatland."

Once more I felt myself rising through space. It was even as the Sphere had said. The further we receded from the object we beheld, the larger became the field of vision. My native city, with the interior of every house and every creature therein, lay open to my view in miniature. We mounted higher, and lo, the secrets of the earth, the depths of mines and inmost caverns of the hills, were bared before me.

Awestruck at the sight of the mysteries of the earth, thus unveiled before my unworthy eye, I said to my Companion, "Behold, I am become as a God. For the wise men in our country say that to see all things, or as they express it, OMNIVIDENCE, is the attribute of God alone." There was something of scorn in the voice of my Teacher as he made answer: "Is it so indeed? Then the very pick-pockets and cut-throats of my country are to be worshipped by your wise men as being Gods: for there is not one of them that does not see as much as you see now. But trust me, your wise men are wrong."

I. Then is omnividence the attribute of others besides Gods?

SPHERE. I do not know. But, if a pick-pocket or a cut-throat of our country can see everything that is in your country, surely that is no reason why the pick-pocket or cut-throat should be accepted by you as a God. This omnividence, as you call it—it is not a common word in Spaceland—does it make you more just, more merciful, less selfish, more loving? Not in the least. Then how does it make you more divine?

I. "More merciful, more loving!" But these are the qualities of women! And we know that a Circle is a higher Being than a Straight Line, in so far as knowledge and wisdom are more to be esteemed than mere affection.

SPHERE. It is not for me to classify human faculties according to merit. Yet many of the best and wisest in Spaceland think more of the affections than of the understanding, more of your despised Straight Lines than of your belauded Circles. But enough of this. Look yonder. Do you know that building?

I looked, and afar off I saw an immense Polygonal structure, in which I recognized the General Assembly Hall of the States of Flatland, surrounded by dense lines of Pentagonal buildings at right angles to each other, which I knew to be streets; and I perceived that I was approaching the great Metropolis.

"Here we descend," said my Guide. It was now morning, the first hour of the first day of the two thousandth year of our era. Acting, as was their wont, in strict accordance with precedent, the highest Circles of the realm were meeting in solemn conclave, as they had met on the first hour of the first day of the year 1000, and also on the first hour of the first day of the year 0.

The minutes of the previous meetings were now read by one whom I at once recognized as my brother, a perfectly Symmetrical Square, and the Chief Clerk of the High Council. It was found recorded on each occasion that: "Whereas the States had been troubled by divers ill-intentioned persons pretending to have received revelations from another World, and professing to produce demonstrations whereby they had instigated to frenzy both themselves and others, it had been for this cause unanimously resolved by the Grand Council that on the first day of each millenary, special injunctions be sent to the Prefects in the several districts of Flatland, to make strict search for such misguided persons, and without formality of mathematical examination, to destroy all such as were Isosceles of any degree, to scourge and imprison any regular Triangle, to cause any Square or Pentagon to be sent to the district Asylum, and to arrest any one of higher rank, sending him straightway to the Capital to be examined and judged by the Council."

"You hear your fate," said the Sphere to me, while the Council was passing for the third time the formal resolution. "Death or imprisonment awaits the Apostle of the Gospel of Three Dimensions." "Not so," replied I, "the matter is now so clear to me, the nature of real space so palpable, that methinks I could make a child understand it. Permit me but to descend at this moment and enlighten them." "Not yet," said my Guide, "the time will come for that. Meantime I must perform my mission. Stay thou there in thy place." Saying these words, he leaped with great dexterity into the sea (if I may so call it) of Flatland, right in the midst of the ring of Counsellors. "I come," cried he, "to proclaim that there is a land of Three Dimensions."

I could see many of the younger Counsellors start back in manifest horror, as the Sphere's circular section widened before them. But on a sign from the presiding Circle—who shewed not the slightest alarm or surprise—six Isosceles of a low type from six different quarters rushed upon the Sphere. "We have him," they cried; "No; yes; we have him still! he's going! he's gone!"

"My Lords," said the President to the Junior Circles of the Council, "there is not the slightest need for surprise; the secret archives, to which I alone have access, tell me that a similar occurrence happened on the last two millennial commencements. You will, of course, say nothing of these trifles outside the Cabinet."

Raising his voice, he now summoned the guards. "Arrest the policemen; gag them. You know your duty." After he had consigned to their fate the wretched policemen—ill-fated and unwilling witnesses of a State-secret which they were not to be permitted to reveal—he again addressed the Counsellors. "My Lords, the business of the Council being concluded, I have only to wish you a happy New Year." Before departing, he expressed, at some length, to the Clerk, my excellent but most unfortunate brother, his sincere regret that, in accordance with precedent and for the sake of secrecy, he must condemn him to perpetual imprisonment, but added his satisfaction that, unless some mention were made by him of that day's incident, his life would be spared.

Section 19. How, though the Sphere shewed me other mysteries of Spaceland, I still desired more; and what came of it

When I saw my poor brother led away to imprisonment, I attempted to leap down into the Council Chamber, desiring to intercede on his behalf, or at least bid him farewell. But I found that I had no motion of my own. I absolutely depended on the volition of my Guide, who said in gloomy tones, "Heed not thy brother; haply thou shalt have ample time hereafter to condole with him. Follow me."

[ID: A greyscale diagram showing two cubes. The first, labeled 1, has horizontal lines drawn on each face, and dotted lines on the inside to show the perspective. The second cube, labeled 2, has the whole inside scribbled in, making it appear more like a slightly stretched out hexagon than a cube. Image description end.]

Once more we ascended into space. "Hitherto," said the Sphere, "I have shewn you naught save Plane Figures and their interiors. Now I must introduce you to Solids, and reveal to you the plan upon which they are constructed. Behold this multitude of moveable square cards. See, I put one on another, not, as you supposed, Northward of the other, but ON the other. Now a second, now a third. See, I am building up a Solid by a multitude of Squares parallel to one another. Now the Solid is complete, being as high as it is long and broad, and we call it a Cube."

"Pardon me, my Lord," replied I; "but to my eye the appearance is as of an Irregular Figure whose inside is laid open to the view; in other words, methinks I see no Solid, but a Plane such as we infer in Flatland; only of an Irregularity which betokens some monstrous criminal, so that the very sight of it is painful to my eyes."

"True," said the Sphere, "it appears to you a Plane, because you are not accustomed to light and shade and perspective; just as in Flatland a Hexagon would appear a Straight Line to one who has not the Art of Sight Recognition. But in reality it is a Solid, as you shall learn by the sense of Feeling."

He then introduced me to the Cube, and I found that this marvellous Being was indeed no Plane, but a Solid; and that he was endowed with six plane sides and eight terminal points called solid angles; and I remembered the saying of the Sphere that just such a Creature as this would be formed by a Square moving, in Space, parallel to himself: and I rejoiced to think that so insignificant a Creature as I could in some sense be called the Progenitor of so illustrious an offspring.

But still I could not fully understand the meaning of what my Teacher had told me concerning "light" and "shade" and "perspective"; and I did not hesitate to put my difficulties before him.

Were I to give the Sphere's explanation of these matters, succinct and clear though it was, it would be tedious to an inhabitant of Space, who knows these things already. Suffice it, that by his lucid statements, and by changing the position of objects and lights, and by allowing me to feel the several objects and even his own sacred Person, he at last made all things clear to me, so that I could now readily distinguish between a Circle and a Sphere, a Plane Figure and a Solid.

This was the Climax, the Paradise, of my strange eventful History. Henceforth I have to relate the story of my miserable Fall:—most miserable, yet surely most undeserved! For why should the thirst for knowledge be aroused, only to be disappointed and punished? My volition shrinks from the painful task of recalling my humiliation; yet, like a second Prometheus, I will endure this and worse, if by any means I may arouse in the interiors of Plane and Solid Humanity a spirit of rebellion against the Conceit which would limit our Dimensions to Two or Three or any number short of Infinity. Away then with all personal considerations! Let me continue to the end, as I began, without further digressions or anticipations, pursuing the plain path of dispassionate History. The exact facts, the exact words,—and they are burnt in upon my brain,—shall be set down without alteration of an iota; and let my Readers judge between me and Destiny.

The Sphere would willingly have continued his lessons by indoctrinating me in the conformation of all regular Solids, Cylinders, Cones, Pyramids, Pentahedrons, Hexahedrons, Dodecahedrons, and Spheres: but I ventured to interrupt him. Not that I was wearied of knowledge. On the contrary, I thirsted for yet deeper and fuller draughts than he was offering to me.

"Pardon me," said I, "O Thou Whom I must no longer address as the Perfection of all Beauty; but let me beg thee to vouchsafe thy servant a sight of thine interior."

SPHERE. My what?

I. Thine interior: thy stomach, thy intestines.

SPHERE. Whence this ill-timed impertinent request? And what mean you by saying that I am no longer the Perfection of all Beauty?

I. My Lord, your own wisdom has taught me to aspire to One even more great, more beautiful, and more closely approximate to Perfection than yourself. As you yourself, superior to all Flatland forms, combine many Circles in One, so doubtless there is One above you who combines many Spheres in One Supreme Existence, surpassing even the Solids of Spaceland. And even as we, who are now in Space, look down on Flatland and see the insides of all things, so of a certainty there is yet above us some higher, purer region, whither thou dost surely purpose to lead me—O Thou Whom I shall always call, everywhere and in all Dimensions, my Priest, Philosopher, and Friend—some yet more spacious Space, some more dimensionable Dimensionality, from the vantage-ground of which we shall look down together upon the revealed insides of Solid things, and where thine own intestines, and those of thy kindred Spheres, will lie exposed to the view of the poor wandering exile from Flatland, to whom so much has already been vouchsafed.

SPHERE. Pooh! Stuff! Enough of this trifling! The time is short, and much remains to be done before you are fit to proclaim the Gospel of Three Dimensions to your blind benighted countrymen in Flatland.

I. Nay, gracious Teacher, deny me not what I know it is in thy power to perform. Grant me but one glimpse of thine interior, and I am satisfied for ever, remaining henceforth thy docile pupil, thy unemancipable slave, ready to receive all thy teachings and to feed upon the words that fall from thy lips.

SPHERE. Well, then, to content and silence you, let me say at once, I would shew you what you wish if I could; but I cannot. Would you have me turn my stomach inside out to oblige you?

I. But my Lord has shewn me the intestines of all my countrymen in the Land of Two Dimensions by taking me with him into the Land of Three. What therefore more easy than now to take his servant on a second journey into the blessed region of the Fourth Dimension, where I shall look down with him once more upon this land of Three Dimensions, and see the inside of every three-dimensioned house, the secrets of the solid earth, the treasures of the mines in Spaceland, and the intestines of every solid living creature, even of the noble and adorable Spheres.

SPHERE. But where is this land of Four Dimensions?

I. I know not: but doubtless my Teacher knows.

SPHERE. Not I. There is no such land. The very idea of it is utterly inconceivable.

I. Not inconceivable, my Lord, to me, and therefore still less inconceivable to my Master. Nay, I despair not that, even here, in this region of Three Dimensions, your Lordship's art may make the Fourth Dimension visible to me; just as in the Land of Two Dimensions my Teacher's skill would fain have opened the eyes of his blind servant to the invisible presence of a Third Dimension, though I saw it not.

Let me recall the past. Was I not taught below that when I saw a Line and inferred a Plane, I in reality saw a Third unrecognized Dimension, not the same as brightness, called "height"? And does it not now follow that, in this region, when I see a Plane and infer a Solid, I really see a Fourth unrecognized Dimension, not the same as colour, but existent, though infinitesimal and incapable of measurement?

And besides this, there is the Argument from Analogy of Figures.

SPHERE. Analogy! Nonsense: what analogy?

I. Your Lordship tempts his servant to see whether he remembers the revelations imparted to him. Trifle not with me, my Lord; I crave, I thirst, for more knowledge. Doubtless we cannot SEE that other higher Spaceland now, because we we have no eye in our stomachs. But, just as there WAS the realm of Flatland, though that poor puny Lineland Monarch could neither turn to left nor right to discern it, and just as there WAS close at hand, and touching my frame, the land of Three Dimensions, though I, blind senseless wretch, had no power to touch it, no eye in my interior to discern it, so of a surety there is a Fourth Dimension, which my Lord perceives with the inner eye of thought. And that it must exist my Lord himself has taught me. Or can he have forgotten what he himself imparted to his servant?

In One Dimension, did not a moving Point produce a Line with TWO terminal points?

In Two Dimensions, did not a moving Line produce a Square with FOUR terminal points?

In Three Dimensions, did not a moving Square produce—did not this eye of mine behold it—that blessed Being, a Cube, with EIGHT terminal points?

And in Four Dimensions shall not a moving Cube—alas, for Analogy, and alas for the Progress of Truth, if it be not so—shall not, I say, the motion of a divine Cube result in a still more divine Organization with SIXTEEN terminal points?

Behold the infallible confirmation of the Series, 2, 4, 8, 16: is not this a Geometrical Progression? Is not this—if I might quote my Lord's own words—"strictly according to Analogy"?

Again, was I not taught by my Lord that as in a Line there are TWO bounding Points, and in a Square there are FOUR bounding Lines, so in a Cube there must be SIX bounding Squares? Behold once more the confirming Series, 2, 4, 6: is not this an Arithmetical Progression? And consequently does it not of necessity follow that the more divine offspring of the divine Cube in the Land of Four Dimensions, must have 8 bounding Cubes: and is not this also, as my Lord has taught me to believe, "strictly according to Analogy"?

O, my Lord, my Lord, behold, I cast myself in faith upon conjecture, not knowing the facts; and I appeal to your Lordship to confirm or deny my logical anticipations. If I am wrong, I yield, and will no longer demand a fourth Dimension; but, if I am right, my Lord will listen to reason.

I ask therefore, is it, or is it not, the fact, that ere now your countrymen also have witnessed the descent of Beings of a higher order than their own, entering closed rooms, even as your Lordship entered mine, without the opening of doors or windows, and appearing and vanishing at will? On the reply to this question I am ready to stake everything. Deny it, and I am henceforth silent. Only vouchsafe an answer.

SPHERE. (AFTER A PAUSE). It is reported so. But men are divided in opinion as to the facts. And even granting the facts, they explain them in different ways. And in any case, however great may be the number of different explanations, no one has adopted or suggested the theory of a Fourth Dimension. Therefore, pray have done with this trifling, and let us return to business.

I. I was certain of it. I was certain that my anticipations would be fulfilled. And now have patience with me and answer me yet one more question, best of Teachers! Those who have thus appeared—no one knows whence—and have returned—no one knows whither—have they also contracted their sections and vanished somehow into that more Spacious Space, whither I now entreat you to conduct me?

SPHERE (MOODILY). They have vanished, certainly—if they ever appeared. But most people say that these visions arose from the thought—you will not understand me—from the brain; from the perturbed angularity of the Seer.

I. Say they so? Oh, believe them not. Or if it indeed be so, that this other Space is really Thoughtland, then take me to that blessed Region where I in Thought shall see the insides of all solid things. There, before my ravished eye, a Cube, moving in some altogether new direction, but strictly according to Analogy, so as to make every particle of his interior pass through a new kind of Space, with a wake of its own—shall create a still more perfect perfection than himself, with sixteen terminal Extra-solid angles, and Eight solid Cubes for his Perimeter. And once there, shall we stay our upward course? In that blessed region of Four Dimensions, shall we linger on the threshold of the Fifth, and not enter therein? Ah, no! Let us rather resolve that our ambition shall soar with our corporal ascent. Then, yielding to our intellectual onset, the gates of the Sixth Dimension shall fly open; after that a Seventh, and then an Eighth— How long I should have continued I know not. In vain did the Sphere, in his voice of thunder, reiterate his command of silence, and threaten me with the direst penalties if I persisted. Nothing could stem the flood of my ecstatic aspirations. Perhaps I was to blame; but indeed I was intoxicated with the recent draughts of Truth to which he himself had introduced me. However, the end was not long in coming. My words were cut short by a crash outside, and a simultaneous crash inside me, which impelled me through space with a velocity that precluded speech. Down! down! down! I was rapidly descending; and I knew that return to Flatland was my doom. One glimpse, one last and never-to-be-forgotten glimpse I had of that dull level wilderness—which was now to become my Universe again—spread out before my eye. Then a darkness. Then a final, all-consummating thunder-peal; and, when I came to myself, I was once more a common creeping Square, in my Study at home, listening to the Peace-Cry of my approaching Wife.

[that-stone-butch]

Your tags made me curious, how would one get into playing Doom with barely any previous experience on such games?

the Chocolate Doom source port (so called because it's not Vanilla Doom, but very close to it) is free to download and supports a lot of total conversion mods if you want. i'd recommend trying mouse look if the original control scheme is too old school for you.

additionally, doom 1+2 have solid ports on platforms such as the nintendo switch if that's your thing.

my general doom 1+2 tips for new players who are more used to modern games are as follows:

hitscanning vs. projectiles: some enemies will 'hitscan' you, which means when they point a gun at you the game will instantaneously scan to see if it hits; there's no dodging if you're in that line of fire at that moment. a projectile, like a fireball, can be dodged if you get out of the way in time. other examples of projectiles are plasma shots and rockets.

that all said: hitscan enemies are a high priority! this is boomer shooter 101; be it the hitscan cultists from Blood, or the chaingunners from Doom, they aren't playing around!

some player projectiles, like the rockets, deal splash damage. keep this in mind; sometimes you don't want to aim for a direct hit.

enemies can be induced to infighting. if you, say, kite an imp's fireballs into a pinky, it will damage it and they may turn on each other.

keep moving! moving, especially circle strafing, is the key to classic doom encounters. you need to bamboozle the hitscanners by breaking up their line of sight, and break up the straight vectors of projectiles.

you cannot jump in doom like in other shooters, and modern players may find this jarring. however, there is a slight bit of time in midair before you start to fall, and a lot of the game is actually designed around this engine limitation. in order to get between two platforms a short distance from each other, you just need to run off of one at the other at high speed. if they're close enough, you'll reach the other platform before you fall.

enemies have pain states, this can be observed in their animations. while for example the super shotgun may damage enemies faster, some are better dealt with by interrupting their attacks with constant damage from a weapon like the chaingun. note which enemies can be stunlocked, how they can be stunlocked, and which enemies *need* to be stunlocked.

the y axis is sheared and you gotta get some practice in with not necessarily aiming up or down, but triggering the game to aim up or down for you. you get a feel over time for when this is going to happen.

save frequently. if you die, you will be forced to restart the level with just the pistol (called 'pistol starting') and the first time a new player learns that will be frustrating.

use the minimap often, and take note of where secrets might be. on higher difficulties, the extra stuff you get in secrets (getting a strong weapon a level or two early, megaarmor, etc) are actually required to keep up.

secrets can often be found by running along walls/level geometry and mashing the use key (this has been lovingly phrased 'wall humping' because of the null sound the player makes when mashing 'use')

pro tip for the cyberdemon: shoot at it until it dies

[beautifulbizarremagazine]

“I am fascinated by natural forms and their order resulting from geometry, mechanics and physical tension. To logical structure/cosmos, I add feeling/chaos. A permanent sense of loss is a fundamental emotion that drives me.. and beauty is equivalent to a loss- freezing of moments in sculpture is a way to trick time and postpone the inevitable.” The emotive and expressive sculptures created by @goornicki.tomasz touch our hearts and souls. This piece highlights ‘counterphobia’ that leads to actively seeking out anxiety- and fear-inducing situations instead of avoiding them. — #beautifulbizarre #tomaszgornicki #sculpture #artist #sculptor #art #figurativeart #counterphobia #mentalhealth #newcontemporary #contemporaryart #contemporarysculpture https://www.instagram.com/p/CoFM_G3I0ha/?igshid=NGJjMDIxMWI=

[transgenderer]

i say i like topology but actually i basically only like metric topology. so its more like geometry. god i love geometry. one of these days im gonna trap one of the geo professors here in a conversation and make them answer this one question that's been bouncing around in my head for ages (can you have a continuous family (like, homotopy but for a whole manifold. is that still homotopy or is that just paths) of isometric embeddings into R^N of some underlying manifold that aren't isometric in R^N (like, the induced metric on them is the same, but youre not just rotating the manifold or whatever))