#its perfectly euclidean

[beauty-and-passion]

TBOB PART 2: OF FLATLAND, EXWHYLIA AND EUCLYDIA (1/4)

Oooooh, this is going to be fun!~

Welcome everyone, to part 2 of my trilogy of posts regarding Bill Cipher, The Book of Bill, all the lore we got, my obsession from 8 years ago rising from the ashes and my other, older obsessions for Flatland, dimensions and backstories in general. Maybe now you get why this part is gonna be long.

Here we will talk about three second-dimensional worlds and what they have in common, starting with Flatland and Exwhylia.

For all disclaimers and bla bla bla, refer to the first post HERE. In addition to them, I would like to add that:

There will be quotes from Flatland because I love this book (there’s a reason if I read it way before knowing Gravity Falls)

Everyone should read Flatland because it’s great (you can find it online HERE)

Everyone should watch the 2017 movie about Flatland on the official YouTube channel HERE. It perfectly portrays how 2D shapes work & how the world works. Also, it’s hilarious, it’s incredibly well made and A Sphere is my spirit animal. I bet he and Bill would’ve been good pals.

<- Previous part - Masterlist

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PART 1: OF FLATLAND

“EDWIN ABBOTT ABBOTT HAS A DECENT IDEA” - Bill Cipher AMA

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A flat world

I call our world Flatland, not because we call it so, but to make its nature clearer to you, my happy readers, who are privileged to live in Space. Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows - only hard and with luminous edges - and you will then have a pretty correct notion of my country and countrymen.

This is how Flatland starts and we immediately learn that this world is like a vast sheet of paper in which the shapes move around.

And there is no concept of above or below:

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. (...) 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.

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A world based on regularity

Soon we will also learn through the words of A Square, that:

our whole social system is based upon Regularity, or Equality of Angles.

So we have a flat world, dominated by Euclidean shapes (yes, Euclidean geometry doesn’t include just regular shapes, but lines too), based on regularity. Your angles should be regular and your sides equal.

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Social classes for regular shapes 

Our Women are Straight Lines. Our Soldiers and Lowest Classes of Workmen are Triangles (...) Isosceles. Our Middle Class consists of Equilateral or Equal-Sided Triangles. Our Professional Men and Gentlemen are Squares (to which class I myself belong) and Five-Sided Figures or Pentagons. Next above these come the Nobility, of whom there are several degrees, beginning at Six-Sided Figures, or Hexagons, and from thence rising in the number of their sides till they receive the honorable title of Polygonal, or many-sided. Finally when the number of the sides becomes so numerous, and the sides themselves so small, that the figure cannot be distinguished from a circle, he is included in the Circular or Priestly order; and this is the highest class of all.

Flatland has a very precise, clear, schematic vision of society: you have six sides? You’re a noble. You have four sides? You’re a gentleman. You have five sides? You’re a doctor (a “physician” in the book). You have three sides? You’re a tradesman. You’re a straight line? You’re a woman. Yes, women are females only.

But what if you are an Irregular?

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About Irregulars

Since Flatland is dominated by Regularity and the idea of being regular, then you can imagine how all irregular/weird/divergent things are treated:

``Irregularity of Figure'' means with us the same as, or more than, a combination of moral obliquity and criminality with you, and is treated accordingly. (...) ``The Irregular,'' they say, ``is from his birth scouted by his own parents, derided by his brothers and sisters, neglected by the domestics, scorned and suspected by society, and excluded from all posts of responsibility, trust, and useful activity. His every movement is jealously watched by the police till he comes of age and presents himself for inspection; then he is either destroyed, if he is found to exceed the fixed margin of deviation, or else immured in a Government Office as a clerk of the seventh class; prevented from marriage; forced to drudge at an uninteresting occupation for a miserable stipend; obliged to live and board at the office, and to take even his vacation under close supervision (...)

So, well, the Irregulars are basically considered criminals and if not instantly killed or confined in a hospital, they live at the margins of society. Yay.

So irregulars (and, in general, deformities) are not accepted. But, like, not at all.

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About color

There is a huge portion of the book about color and it’s extremely cool - but also, too long to quote it entirely here. Long story short: color existed in Flatland, but it was suppressed and now they live in a black and white world. Because I suppose that society wasn’t shitty enough as it was, so why not making it even worse.

(Actually there is an explanation and for their kind of society it makes sense. Still, shitty world)

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About Recognition by Sight

The book vastly explains how these creatures can see and it’s a very clever to see, considering they live in a goddamn 2D world and all they see are fucking lines. And not even colored lines, that could’ve at least helped a bit. Nope, just gray lines. Yay.

Still, they developed a way to see and yes, all they can see are lines, with the edges that fade in the distance. The more blurred they are, the more angles they can find out - thus recognizing if they’re approaching a Square, a Pentagon or a Circle.

All of this works except for women, who are basically deadly spears with a pointy end, so they’re almost invisible. And that’s why they should wag their end all the time, otherwise other shapes might not see them and get pierced through.

Yep, this is fucking hardcore and I love it.

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PART 2: OF EXWHYLIA

“I believe Bill came from a similar world that was mysteriously destroyed” - Ford Pines, Journal 3

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A flat world

Ford drew a perfect image of Exwhylia and we can see that yep, it’s a flat surface, with no above or below. It’s just a plane, exactly like Flatland.

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A world based on regularity

All we know from Exwhylia can be inferred through Ford’s pages. However, two pages are enough to make it clear that this world is based on regularity.

How can I be so sure?

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Social classes for regular shapes 

Ford describes two of these beings as “an upper-class circle” and “a lowly triangle”. So yes, Exwhylia shares the exact same social structure of Flatland: according to your shape, you will get your social class.

It says nothing about women, but considering Ford spent something like 20 seconds inside it, it’s understandable. However, we know for sure that the Exwhylians’ bodies are razor-sharp, because Ford specified it. Pretty cool - and also another reference to Flatland.

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About Irregulars

Ford says that the inhabitants of this world “considered me to be an “Irregular” shape, which is vulgar in their society”.

Sooo… yes, I imagine that this world ostracized Irregulars too, just like Flatland does.

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About color

Ford says nothing specific about it, so we have no idea if the world is black, white and gray or if there are any colors. We just know that there is no sky and no sun.

However, when he talks about what the Exwhylians can see, Ford draws several lines, says that his eyes can’t help him distinguish these objects, but the Exwhylians can and will interpret the lines differently. This implies there is no color, because if there was, Ford would’ve been able to interpret the lines too, by referring to how they were colored.

So yes, there may be no color in Exwhylia.

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About Recognition by Sight

Judging from how Ford describes what the Exwhylians can see, we can safely assume these shapes also use Recognition by Sight, just like Flatlanders  do.

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And with that, we close the premise of what I want to tell about Euclydia. Keep this stuff in mind, it will be useful to understand the topic of tomorrow's post: Euclydia.

Next post ->

(How about a coffee? ☕)

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[max1461]

I'm terminally humanities brained, but I am kind of interested in pure mathematics and POM and generally just more mathematics oriented philosophy stuff/mathematics in general, I haven't studied any kind of maths since Highschool, how should I get into it? Should I read Quine?

Oh, this is a great question and I am very happy you have decided to send it to me! My answer reflects my particular views on mathematics and what it is all about, of course, so keep that in mind.

The number one thing I would like to convey about mathematics to someone coming from the humanities is that mathematics, far more than most fields, is something you do in addition to something you learn. Mathematical thinking has to be practiced, it is a skill that you train. If your primary interest is in philosophy of math, I'm afraid I haven't read very deeply on the subject and probably can't recommend a good starting place. Maybe... Russell? Look into Hilbert's program, and why it failed? But if you want to understand math "from the inside" instead of "from the outside", then you have to do math, and to that end I think "who to read" is the wrong question.

This might sound a bit scary, but I don't think it needs to be. Math is not so hard to do, although it is a very foreign type of thinking to those who are not practiced at it. In fact, this is why I think doing math is important even if your interests are primarily in POM; math is ultimately a human activity, regardless of e.g. what you believe about the ontology of mathematical abstractions, and I believe that in order to understand it fully (to have a picture of it beyond just its ontology) it must be understood as a human activity. Thus, one must do it, at least a little bit. It is, if nothing else, a whole realm of human experience all its own, and I think just about anyone would profit intellectually from spinning their mental gears in a mathematical way here and there.

Thankfully, there are many great places to start if this is your aim. I assume that what we're talking about here is "proof based" math rather than just calculation. To that end, a great introductory book is Velleman's How to Prove It, which will give you some guiding principles and many examples of how to approach a mathematical proof. Beyond that, I think you'll want to pick up an "entry level" introductory text (that is, an introductory text aimed at undergrads, etc.) on any math topic that strikes your fancy, and work through it—making sure that you understand the structure of the arguments (proofs), and attempting as many of the exercises as you can. The exercises are really the most important part. You cannot learn math without the exercises. You cannot learn math by reading it. The only way to learn is to try your hand at it yourself.

Expect your reading speed to be slow, and new concepts to be confusing. Expect to read things over and over, and fiddle with them in your head, before they make sense. Well, I mean, if you're anything like me or like most people. I think one of the biggest reasons people get turned off to math is that most of it just doesn't make any sense the first time you encounter it; it won't make sense until you've thought about it a lot.

One way or another, if you have a background in philosophy and are used to parsing and evaluating careful arguments, you will have a leg up on many people getting their introduction to proofs.

As for what topic to start with... you could always start with Euclid's elements, which is still a perfectly solid introduction to Euclidean geometry even after 2500 years. It does not quite meet modern standards of mathematical rigor (in other words, its proofs have gaps by modern standards), but realistically this is not a big deal: the basic thinking style is the same, and the gaps are somewhat subtle and technical IIRC, so I don't think it will really affect the beginner experience. On the other hand I believe at least a couple of Euclid's proofs are genuinely flawed (that is to say, they aren't just uncareful in their presentation, but are actually invalid in their structure), so maybe it's better to start with a modern work first.

Some books that I think are good for a beginner:

Graham, Knuth, & Patashnik, Concrete Mathematics — The focus of this book is on mathematical tools for computer science, but even if that is not your interest it's still a great book. It deals mostly with familiar concepts such as whole numbers and sequences (you might have encountered, e.g., the Fibonacci sequence), but is great for learning to problem solve and think mathematically.

Rudin, Principals of Mathematical Analysis, ("Baby Rudin") — If you want trial-by-fire. A lot of math undergrads have this as the textbook for their first proof-based math class, and it's notoriously challenging. Its topic is the field of real analysis, the rigorous foundations of calculus. I... wouldn't start here if I were you, honestly, but it's definitely a classic.

Some graph theory text. Some people seem to be recommending Wilson's, which has the convenient feature of being available online here. I haven't read it, but looking over it, it seems fairly gentle. There are a lot of pictures, and proofs don't enter the picture until a couple of sections in. Graph theory has the advantage of being very visual and having basically no prerequisites, so this might be a nice place to start.

Some abstract algebra book. If you're looking for a really clear presentation of the way mathematics is done today, starting with axioms and proving theorems deductively from them, etc., there is probably no place where it is more straightforwardly visible than in abstract algebra. The first math book I ever attempted was Herstein's Topics in Algebra; not the most beginner oriented, but certainly not inaccessible, and hey, it worked out for me! If this one is not to your liking there are a million books on e.g. introductory group theory you could look into, or the very canonical Dummit & Foote, or so on.

Uh yeah I think that's all I got. Anyone else feel free to put any more thoughts or recommendations in the reblogs!

[random-ln-stuff]

New New Theory:

The Little Nightmares Universe looks like this:

There’s our world on one side, The Eye’s Nightmare Domain on the other side, and the Nowhere is right there in the middle. “Two flows from one, and here (in Nowhere), is whole again”

The Nowhere is a place with many connected but individual places with unique functions. I imagine that as being a place where each individual location has its own unique THING that the people there are drawn to and a specific person who runs that place. The Maw has Gluttony as its vice and the Lady runs it, the Pale City is addicted to TV and Escapism and the Thin Man Runs it, ETC.

The Spiral though, is a specific part of Nowhere that’s slightly overlapping and closer to the Eye’s Domain, so things are different. More Non-Euclidian. It’s a “cluster of disturbing places” layered on top of each other, with travel between these areas being particularly difficult and travel outside of the Spiral as a whole being downright impossible (hence why Low and Alone are trapped there with them using Mirrors to travel throughout the Spiral).

Also found in the Spiral are many things that the regular Nowhere just doesn’t normally allow, like the Giant Baby that seems to be mechanical in nature. Sure the Nowhere can have things that are just off with reality, like the Nest having strange gravity and the Signal Tower’s warping of time, but in most places reality is somewhat similar in nature to our world. The Maw still follows Euclidean Geometry, The Pale City is perfectly stable reality-wise unless you enter the tower, which is alive and follows its own rules, etc.

Actually, I think each of Noone’s dreams have been placing her in various places in the Nowhere, both closer and farther from reality and the Eye. More specifically, just like this:

Ep 1:

The Stone Giant is the closest Noone has gotten so far to the Eye and the furthest she’s gone from reality. The things described by Noone in episode one simply don’t make sense compared to the other dreams and the games as a whole. A Stone Giant with a endless snowy field on top, with the inside being run by clockwork, and also there’s thousands of other people chained inside rooms, a workshop and a entire courtyard, just inside the Giant.

The Lady In Chains also makes it obvious that this entire dream is symbolism for the Lady and The Maw, which doesn’t make sense if this happening in the regular Nowhere because the Lady is already living here. So Episode 1 is located just outside the Nowhere, in that zone where the Nowhere begins to break down into raw nightmarish chaos.

Even the child Noone encounters here may not be an actual child. Their hair is described similarly to the Lady’s own Shadow Magic, a feature that no other child seen so far has, and it’s possible that this child may also just be a product of the Eye’s Nightmarish, Random Chaos.

Ep 2:

Episode 2 seems to take place in the actual Nowhere. It’s similar, VERY similar, to the Maw and how Guests are brought there, like suspiciously similar, but I’ll give it the benefit of the doubt just this once.

Ep 3:

Episode 3’s Mall is literally just the Signal Tower pre-signal tower. A sentient mass of flesh desperately trying to keep Noone distracted from reality to prevent her from leaving. However, I’ll say that this dream seems to be closer to reality because not only does the Mall pull real things from reality to keep Noone happy, those things are objects that Noone personally knows about and likes. A doll that she’s always wanted, a movie she’s seen 100 times, clothes including the dress she first wore to the institution, etc.

The Mall Signal Tower Flesh Walls are also heavily implied to be near the Ferryman in terms of Power, being one of the only entities to react to his presence and possibly being the thing that pulled Noone into this specific dream just this one time. So the Flesh Walls can definitely come this close to reality, with the Ferryman and (unseen so far) North Wind probably being the only others that can.

Ep 4:

I’d we don’t see a circus in Little Nightmares 3, I’ll eat my own hat. A unique antagonist and location never seen before with no symbolism or any obvious connections to previous monsters. Even the Ferryman fails to appear in this dream. This is obviously a location in the Spiral.

[ckret2]

Were there any health effects for Bill as a child, being able to see into the third dimension? I know you mentioned its a uncommon to rare condition in his home world, known enough to make a science of it, but after you mentioned Bill can as a human strain his eyes to see into the 4th but it makes them bleed I’m curious. It fit the human ancient history of assuming someone with a condition is spiritually aligned. I mean besides the effect of seeing inside people and sort of around objects which I feel would probably mess with perception.

Less "uncommon to rare" and more "rare to extremely rare." It's known, but in terms of proportions of the population, if it were a debilitating health condition in the US, it would be in "no pharmaceutical company bothers to make medicine to treat this because the customer base is too small for it to be worth their effort" territory.

Bill's condition was only identified because the most characteristic symptom is angles that don't add up like they're supposed to. For example, in Euclidean geometry, every single triangle, without exception, has 180º degrees. If you have a triangle that measures 60º, 60º, and 61º—so 181º—and yet all three sides measure as PERFECTLY straight, that's bizarre enough to dig into, especially in a society that's historically shown so much interest in shapes' angles.

This is first and foremost known as the You've Got Weird Mathematically Impossible Angles condition, and because of that it got disproportionate resources for research thrown at it in spite of its rarity; "plus these people can see through walls" is a strange bonus symptom that was identified later when they realized everyone with this condition reported such visions. It's rare enough Bill grew up with the expectation that he'd never meet somebody else with the same condition.

So, in his home dimension, it's not an eye thing; it's a whole body thing. All of him bends slightly into the third dimension. In a human body, he doesn't have the same "condition," so he's straining JUST his eye to look into the fourth dimension; which is why it's so damaging to a human eye.

As you'd imagine, yeah, there are gonna be some health side effects to a condition that means your whole body is slightly bent weird. His mom had a condition that I've been imagining as some cross between Ehlers-Danlos syndrome and scoliosis, if you were to try to apply those to a sentient line segment; and Bill's hypothesized that his mom's condition contributed to the fact that he "bends" out of the second dimension. He doesn't have THE SAME condition, but there's some symptom overlap.

Like, back pain. And the emotional pain that comes from people constantly recommending stretches for your back pain that would make your back worse. If he hadn't gained godlike power, he probably would have gotten arthritis early. If he'd ever needed surgery, doctors would've found his organs are just a little bit wrongly placed. Probably rooked up his digestion somewhat, since the organs designed to absorb sunlight evolved expecting light to fall on perfectly flat panels, not a slight dome. And also: other things I haven't thought of!

But nothing extremely debilitating. Probably nothing he even would have gone to a doctor for, until the arthritis. Just a bunch of tiny inconveniences, slightly weird corner angles, and the ability to see through walls.

As far as he was concerned, the biggest negative impact on his life was that it made TV & movies hard to watch, because he's used to seeing the world as shapes but TV only shows the flat lines that normal shapes looking "forward" can see. And also the devastating social isolation.

[june-fallout]

My Beautiful Morning No. 1,452

Writing/backstory snippet for June Fallout

1.4k words

Fallout New Vegas

Be wary of: misogyny, delusions, mild horror.

June woke up in her bed. Plush, soft—the kind of bedding you loved running your arms over, to feel as if you were touching clouds. She arose, yawning and stretching out her arms in perfect harmony as she rolled out of her bed. Pajamas? Of course not. June always woke up in pressed and ironed dresses. Her blonde hair was perfectly curled in victory rolls about her head, never disturbed by laying down. Her face wasn't painted. Her lips were just naturally red, lashes naturally wet and dark, cheeks always symmetrically flushed and without a single blemish.

She looked across the room at the bed of her husband. Because why would a married couple sleep in the same bed? What purpose would that serve?

But a few times...

Oh, the bed was empty again! June put her hands on her hips and sighed. Off to work so early.

She reached to the side of her bed and tied both the apron and the band of pearls around her neck. Sunshine was pouring in through the window, but it was 5:30 AM. June never slept in, but she never awoke in the dark. The high heels she had slept in clack clack clacked around the floor as she made up her bed. It only took seconds. The soft floral scent of the one blanket she had mussed wafted through the air as she tossed it and let it settle back down. It landed perfectly on all four corners.

The clacking went with her into the kitchen. The kitchen. Her sanctuary. A lonely one, but June didn't mind.

June Gar Cleaver opened a fridge to see a veritable cornucopia of food. Eggs, fruits, juices, meats—all she needed to feed her family today. And this fridge would always be full. Never would she have to go hungry. That wasn’t for her to worry about. This was her domain, and she took care of it while the man who took care of her kept it stocked. Crack, psh, fwump, pssss…

All these sounds brought a smile to her face (not one that wrinkled it, of course).

What was it that she would make today? Batter whipped into a fine cream, a low blue light burned into a fire, puddles of cream and clouds turned to bread. They piled, unblemished, on a plate. A great bother of sloshing and glugging filled up crystalline glasses with juice. A knife too sharp to fail fruit and too dull to draw blood arranged little slices into a perfect, flower-like rings on top of the pancakes. Every cracked egg landed with its yolk perfectly centered. Every twist and wriggle of the spatula brought the eggs free, leaving behind not a single drop of their fried white. Bacon simmered in a pan without a single drop of grease escaping.

Another beautiful morning, like every morning that had come before, and every morning that would come after.

Surrounded by the sweet symphony of sizzling, smells, and satisfaction, June surveyed her work with a happy face. It was perfect—almost perfect. She just needed one more thing. “Everyone! It’s time to wake up!” June sang, walking through the non-Euclidean halls of her home that shifted every time she looked at them. Sometimes the doors were closer. Sometimes further apart. Sometimes they were all on one side of the hall, and other times, they alternated. June didn’t mind.

She knocked on one door with a neat, red-nailed fist. “Come on, dear. It’s time to wake up!” No response came from the door, but only the laughter answered. It echoed from every single direction. June didn't mind.

June knocked on the next door. "Theodore!" And the next. Until she had knocked on every, having no response. “Oh come now- breakfast is going to get cold!”

Tentatively, June opened one of the doors. Past the threshold, there was nothing. Just blackness. If she stepped forward, she might fall. The laughs started again, echoing from the blackness. June slammed the door. …No one was home right now. That was fine. She would just put the food away for another day, when everyone came back… Surely she wouldn't have to be alone for much longer, would she? June clicked down the stairs in her high heels, not at all hindered by their height. Why would she be? She even slept in them…

June opened the fridge door, ready to put some of the ham in.

She jolted backwards, finding meat already inside. Not deli meat. June was staring at the mangled remains of some girl, shattered and fragmented and mixed together like puzzle pieces in a box that had been shaken. It was terrible to look at, because… That girl was so ugly.

Whoever had put this girl in there was bad at storage. Why would you put all of a person in there…? Not all of that was edible… Not all of it… There was a head with hair attached, brown hair she didn’t recognize, and open eyes. June slammed the fridge door, feeling sick. She stared at her own reflection horrified to find-

That was not her. That was NOT June looking at her. That was some other girl. Some other girl with mangy brown hair like curtains and dark eyes, and hideous little lines drawn on her skin. Some other girl like the one in the fridge.

The laughter came from the air itself, untraceable in its origin, ever-present, all-knowing.

June Jane Hepburn June Cleaver Jane Garrett She fled. Ahh, it was so typical, wasn't it? A hysterical woman, fleeing from a silly sight. The laughter intensified at her stupid, silly, feminine ways.

The hallways swirled and twisted around her. Doorknobs escaped her grip. Stairs folded out into infinite, kaleidoscopic fractals, opening up with rails like teethy maws ready to consume her. One place was safe. She knew this! This, this is where she was put when everything was wrong--her, the house, anything. Where June had to go when things went wrong, locked inside for however long He saw fit. June didn't mind.

She threw herself towards a corrugated metal door set into the wall of her suburban home marked 09-L.

Jane stumbled into the basement--and finally, things were normal again. She sighed softly, panting, raising her head as her brown shoulder-length waves fell around her freckled face.

And she saw such curious things!

A row of upright glass coffins, each with something resembling a girl inside. An ugly girl too. So pale, and with hair just a bit darker than Jane's. Their faces all resembled hers--at least the ones with intact faces--but Jane couldn't possibly imagine being one of those girls. One was pinned to the sides of the glass, face sloughing off of her boneless body hanging like a wet coat, poorly formed fingers and toes hardly anything more than blobs filled with an even mixture of a human's insides. Two sacks of skin full of uniform plasma hung down, her legs. One girl was normal enough, but had flattened legs. Another reminded Jane of Swiss cheese on ham and rye, with tunnels carved out of her that rats chewed through.

Jane did not feel worried for these doppelgängers. They all deserved it! That was, until she stepped closer...

And saw a reflection, peeking at her. A girl with mangy brown hair, big brown eyes, pale skin, and pink marks stretching across her skin in fern patterns. Jane recoiled. There was a second reflection behind that reflection, the body inside, just like the girl in the reflection, just like the girl in the fridge-

Just like... June.

Every identity she assumed to soothe herself was torn off of her like skin, flapping wetly against the ground as they were tossed aside, leaving her flesh to burn against the air.

June dug her hands into her blonde copper brown hair and her pink tan sunless white skin. She needed to pull this identity off too.

She screamed, because it stayed, and it left her in a room surrounded by her own body staring at her, a room underneath a Vault, a Vault in a desert, a Vault once inhabited by a man who she had not seen in 1,452 days.

But that was alright. June didn't mind.

[unskilledpoint]

Here's a fun riddle to test your brain:

You find yourself in an unfamiliar world. In front of you are three children, each of them perfectly rational. Each child is also guarding one of three doors. Behind two of the doors is a monster that will rip all of your limbs off and leave you to die of blood loss, but behind the third door is a magic crystal that will give its holder the powers of a god. You don't know which door the crystal is behind, and you can't understand the language the children speak, but for inexplicable reasons, you know that they can understand your questions. One of them will always tell the truth, one of them always lies, and if you could ask the third one, they would tell you they always lie. Don't think about it. Each child is also blind and only knows what's behind their own door and what their own true or false role is. But what's interesting is that every time any of them answer a question, they will roll a six-sided die. Whichever number the die lands on, they will cycle their truth roles that many spaces. Like so, of course, if it lands on a three or a six, there will effectively be no change, since after that roll, their roles do a full barrel roll. While you and all three children can always see the number rolled, you don't know which way their roles will cycle.

While pondering this problem, you find a brilliantly crafted flute on a pedestal nearby. You take the flute and read the inscription on the pedestal, which gives you important information. Child one wants the flute badly, and if you give it to him, he will do anything he can to help you win this challenge and receive the crystal. Child two has the ability to communicate in a language you understand using the flute, but only if you know Morse code. Child three is skilled in combat and promises she can use the flute as a weapon to protect you from imminent death if you happen to open a door with a monster. The question is: which child should you give the flute to?

The answer (don't read until you've decided your own answer):

Since you don't know Morse code and you're not planning on opening a door with a monster, you give the flute to child one, believing that even if he's the liar, his perfectly rational actions will certainly be in your favor. You then stand in front of door number three as you and child one realize you both have the same idea. Child one opens his door, revealing a monster behind it, and you realize that your odds of guessing the correct door will increase if you now change your decision to door number two. But before you can ask Child two to open it, child one's body is brutally dismembered by the monster behind the door. Child two runs away screaming, and child three takes the flute from child one's corpse and kills the monster. However, when they return, child two moves to guard door number one, child three moves to guard door number two, and child four moves to guard door number three, and so on and so on up to infinity. It should be mentioned that child four is not perfectly rational and did not previously exist; rather, they were a hypothetical future super-intelligence which plans to revive anyone in the past who didn't help in their creation into a simulated punishment. Since you and child one each helped child four come into existence, you two are spared, while children two and three enter a simulated reality.

Child four simulates the two children piloting individual spherical, frictionless cows flying at the same altitude on one axis over a Euclidean planet with a diameter of 50 kilometers. Child two's cow travels at 10 kilometers per day, and child three's cow travels at 20 kilometers per day, starting on Sunday. Child four tells them that at some point during the next five days, they will crash into each other on a day they won't expect. They realize that they won't crash on Friday since making it to Friday will no longer make the crash date unexpected. The same logic eliminates Thursday and Wednesday. Then child four tells them that they will be unconscious for nearly the entire flight. Four will flip a coin, and if it lands on heads, they will both wake up briefly on Monday, and if it lands on tails, they will wake up once on Monday and then on Tuesday with no memory of previously waking up. When they wake up, they have the option to turn exactly 180 degrees without decelerating in hopes of avoiding a crash. They don't know where they start relative to each other, and they're still blind. Additionally, two and three both have the opportunity to throw each other under the bus.

Initially, it is determined that when they crash, they will both wake up injured on a deserted island. If they choose to screw each other over, they will survive the crash unharmed, while the other will stay in a two-week coma before waking up. If they both screw each other over, neither will survive the crash. Both being completely rational, they each elect to screw the other over, but child two was currently the liar, so he accidentally tells child four he won't screw child three over. The simulation of child 1 has now become God and begins an epic battle against child One Prime who has another instance of the God Crystal. Their battle tears apart the multiverse holding time and space over itself several times until child one in perfect rationale directly observes Child 2, causing the superposition to collapse, deleting the entire multiverse that was entangled with him as promised for giving him the flute. Child one then hands the crystal to you, both of you knowing it was all part of the master plan.

If you carefully follow the logic in any other scenario, you will realize that this is the only scenario where you are guaranteed to receive the crystal.

What do you want me to say to this.

[desceros]

There were multiple instances in Euclidean Line where I forgot it was a one shot, I'd scroll all the way back up thinking "damn how long is this mf chap- ITS ONE PIECE????" And I'd struggle to find my place again as I scrolled back down

I struggle with making my chapters too *short* and your proper one shots are book length 😭

joke answer: IM JUST THAT GOOD FLEX EMOJI

normal answer: well. to be clear i answered that in reference to my own work. there are many fics i've read where the chapters were, say, 500 words, and they felt perfectly appropriate for that fic. so i would encourage you not to compare yourself to me, especially since i'm an outlier on my works to say the least! lmao

constructive answer: if you're unsatisfied with the lengths of your chapters, i'd encourage you to examine what is driving those feelings.

are you wishing you could make multiple scenes flow more smoothly together, but they feel discombobulated when you put them in the same chapter? are you struggling with wanting to go further into detail on what happens during a fic, but it feels stilted when you try? are you seeing works that you admire with longer chapters and comparing yours to theirs and coming up with feelings of inadequacy? are your chapters actually too short for what you want to convey, or are you comparing yourself to others at the detriment of your confidence?

examining this will help you find what needs fixing or adapting if you really want to write longer chapters. or, it'll show you that actually, you're fine, the tone of your fic is just right, and you're just harming yourself by looking outwards for comparisons instead of within.

[elamimax]

Principles of Non-Euclidean Romance

Okay, because I wanted an excuse to post this: An Eldritch abomination (Sammaël, for convenience) has split off a piece of itself (Sam) to experience music (it has already cried to Bonnie Tyler's I Need A Hero and can you honestly even blame it) but now it seems it has to reconceptualize all of its ten dimensions while in a frail little human form. This is actually quite well into the story, so if you were already planning on reading this novella, there might be (will be) spoilers. Enjoy!

Sam floated in the nothing, the nothing before waking up, when unconsciousness is a blanket slipping away. But Sam was not an ordinary person, and her consciousness wasn’t either. She held onto the blanket, and looked into the Darkness, which has less in common with regular darkness and more with the traditional abyss. The biggest difference is that the Darkness screens its calls. Sam stared into the Darkness. It stared back. This wasn’t going to keep working, was it? No, the Darkness seemed to say, although it didn’t say anything, of course. It isn’t. So, what then? Sam thought. The world was falling apart, on a bigger and bigger scale. Reality was beyond fraying, it was tying itself into knots to keep from turning into spaghetti. If she kept repeating the same pattern, it was only a matter of time before she was just a pair of eyeballs in a bowl of soup, bubbling up letters to talk. She was going to have to do something different, this time.  Yes, the Darkness didn’t say. You are.

But what? She looked up, although ‘up’ was a ridiculous concept when you were floating in the nothing between sleep and dreams. Up there* was Sammaël. Her original identity. The One she came from. She wondered if it could see her** and how different it was from her now. Was she her own person, or was she a small aspect of a larger creature? And would it be best to return to it, after all? She’d caused all of this, hadn’t she?

*ish **It can, and it waves at her. She can’t see it.

Yes. She thought and tried to imagine the universe, all of it, and found herself failing. Okay, fine, this meaty human brain didn’t have a way to easily conceptualize it. That was something she’d learned to accept, but she knew how to do this when she had thought herself into being aeons ago. She’d start from scratch, if she had to.  She imagined a dot. No dimensions. A point. Points were easy. Every entity could be represented by a dot. It was both every dimension and none. It was the zero and the one. Then, a line. Infinite points adjacent to each other, on one axis. A line, going from somewhere to somewhere, infinitely long and infinitely thin.  One dimension. Then, another line next to the first. And another, and another. Infinite lines, adjacent to each other, until there was a plane, perfectly visible in her mind. Planes were easy. You could draw stories on them. Write on them. They were easy to imagine.  Two dimensions. Still very easy. So stacking planes on top of each other was also easy. Stacking them above and below until this infinite plane covered every conceivable corner of the imaginary space. This was now imaginary space, stretching up, down, left, right, forward and backwards. Space. Three dimensions. This was where things got tricky. She reduced space to a point. For ease of imagination, she turned the point into an apple. All of space. As an apple. She imagined the exact same apple, one unit later. In the same space, but still different. All coordinates the same, except the fourth. The apple, but a little older. She imagined it older and older, rotting and falling apart, and then younger, becoming first red again, then green, and then turning into a bud, then nothing. Then, she imagined every point next to each other. A line. Time. 

Four dimensions. She took a deep breath. Now she had to go quantum, and going quantum was one of those things that was usually a bad idea unless you were an interdimensional horror from beyond the bounds of reality. It never ended well for superheroes and action heroes, after all. Across all of time, there had been trillions of quantum particles, existing in superposition until they collapsed. And every one of them could have collapsed in a different way. Every single one branching off from the original line. Every single one adjacent. Parallel. Infinite lines, next to each other. Creating a plane.  Five dimensions. Sam stood on the time plane and looked up. This bit was easy, at least. The universe was built on numbers, and all those numbers were reducible. The distance between atoms. The strength of covalent bonds. Up and down, infinite planes made of infinite timelines, and almost all except the one she was on mostly useless. If the universe had been slightly different, it would’ve been incapable of life. Sometimes even incapable of fission, or forming planets. But they were there. Spacetime. Six dimensions. She took a deep breath. Floated in the void for a bit. Now she had to get… conceptual. Weird with it. But it was fine. She’d done this before. Sure, back then she’d eaten concepts alive, and they had been a tasty cheat-day treat, too. Now, she wasn’t even sure about chocolate. But she could do this. Couldn’t she?  

Yes, the Darkness implied. You do. All of spacetime existed. In a single point. An apple in an apple. No, that didn’t help. A hypercube. A cube extruded from itself in every possible direction. Slightly better, but useless. She tried, instead, to imagine a field. Now, she imagined one next to it, but where concepts were slightly different. A tree in a point in space and time. The same tree, shifted across all axes, and then… then just one more. An idea. The tree not growing apples, but pears. Then oranges. Then nuts. Then pineapples. Bananas. Carrots. Potatoes. Further. Trees growing smaller trees. Every conceivable concept. Growing on a tree. And then all of them in a line. Every concept. As fruit on a tree. All in a line.  Seven.  Then, every concept instead of every concept. Lines adjacent. A plane of concepts. Everything that could be. Everywhere. All at once.  Eight.  And then, everything that can’t. Up and down. Infinitely. Nine. Squeemp. The final axis of dimensionality. Sam realized she’d been holding her breath, which was a hell of a feat when she wasn’t even technically breathing. But the idea made sense, now. She could see it. The nine base dimensions. And now, the fracture. But it was going up, wasn’t it? Space itself seemed to be fine. Space falling apart was usually a lot of nothing. Nothing and nuclear fission.

And then, everything that can’t. Up and down. Infinitely. 

 This was different. The cause was time. And that was simple to pinpoint too. There was a tear, across reality. Someone had ripped it like a cheap cloth, and now the whole thing was bleeding in on each other, and it wasn’t going to last much longer like this. And Sam knew she had done all of this. She had rewound time, that first time. Not as Sammaël, who was all-present and powerful. Sam, before she’d known she was Sam, limited by a frail human body and a frail human mind to go with it. She’d shattered reality, and it was killing her over and over again. She was at the center of it. She was going to have to fix it.  Yes.  She was going to have to go back. Back back. Not just in Time, or Space, or Squeemp. Reduce all of them to a point. Go a step back.  Ten dimensions. But she couldn’t do that.  No. But someone else could.  Yes.

She looked into the Darkness, and Sammaël looked back at her. Had it always been so… terrifying in its formlessness? It didn’t scare her, because she knew it. And she’d conceptualized herself more than half of the way there, and she was even a little proud of that.  I have no need for Pride. “I do.” Interesting.

If you liked this and want to read more, consider picking up the whole book! It's on amazon right here. It's about an eldritch abomination trans lesbian in a time loop.

[nimblermortal]

All right I no longer remember why I was reading about de Sitter space, but I’m getting into a Wiki hole so I’m taking some notes here.

1. “In mathematical physics, n-dimensional de Sitter space (often abbreviated to dSn) is a maximally symmetric Lorentzian manifold with constant positive scalar curvature”

2. A Lorentzian manifold is a type of pseudo-Riemannian manifold

3. “In differential geometry, a pseudo-Riemannian manifold,[1][2] also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate.”

4. “In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus.”

5. “In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.” 

5. This is actually a sentence that makes sense to me, but in case it doesn’t to you: a Euclidean space is basically the sort of space that you’re thinking of with points on a graph. It’s regular, it’s even, it’s got a consistent coordinate system... A non-Euclidean space is, say, if you’re trying to project the Earth onto a map. Even assuming the Earth is perfectly round, trying to get that onto a flat plane leaves you with vastly irregular spacing and, well, all the flaws of the Mercator projection.

So a manifold is a shape, in n dimensions, such that any point on it looks like the space around it is Euclidean, but if you zoom out a bit further it ain’t. “One-dimensional manifolds include lines and circles, but not lemniscates.“ - a lemniscate ~is a figure 8 or an infinity symbol. On either side of the intersection point, it’s basically a circle and works as a one-dimensional line or circle, but at that intersection point, you have to have two dimensions (n+1) to describe the intersection of those lines, so it no longer locally resembles a 1-dimensional Euclidean space at that point.

4. A differentiable manifold is one that you can work calculus on. (I’m going to assume you remember scalars and vectors. If not, a scalar is a number, a vector is a number with a direction, or in graphical senses a ray.) I’m not... super clear on why you need a vector space to work calculus, but then, I’ve always tried to forget visual representations of math as fast as possible because I am a hugely non-visual person and they just confuse me. So it probably has something to do with that, and the way integration represents the area under a curve and differentiation represents its... na, slope or inflection point or whatever.

3. “In the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold M (such as a surface) that allows defining distances and angles, just as the inner product on a Euclidean space allows defining distances and angles there.”

The inner product is the dot product, fyi. If that doesn’t make sense to you... I’m not explaining it here. Sorry if that’s rough, but ultimately I am here for my own understanding and that’s a whole class on matrix arithmetic. Suffice it for here that the inner product lets you take your matrix representation of two curves, do math to them, and come up with a scalar representation of their relation. The metric tensor here is the generalization of that concept, something that lets you define curves’ relationship to each other.

(Note I am using the word ‘curve’ to represent lines and scribbles with arcs, consistent or not.)

“In mathematics, specifically linear algebra, a degenerate bilinear form f (x, y ) on a vector space V is a bilinear form such that the map from V to V∗ (the dual space of V ) given by v ↦ (x ↦ f (x, v )) is not an isomorphism.”

So a non-degenerate metric tensor is one such that the map from V to V* IS an isomorphism. Note that if I am remembering correctly, v is a vector in the space V. I had to remind myself that the dual space is like. Every vector that can exist in V? if you do basic mathematics to them? (Note that I am using phrases like ‘basic mathematics’ very broadly and in a not mathematically-approved sense.) And of course f(x) is a function. And an isomorphism is something that can be reversed with an inverse function.

So then x maps to f(x,v), and v maps to whatever ray or space that original mapping defined, and you can’t undo that. Except that we’re talking a non-degenerate space, so in fact the pseudo-Riemannian manifold that we started out talking about is a manifold (point 5) on which you can work calculus in a way that enables you to describe directions and angles and reverse functions/mappings done in that space. (I am much less confident in that last point.)

That brings me through point 3, but now I have to sleep.

[tamashi-yoken]

ayo cryptid hours?

Item #: SCP-3781, the non-Euclidean Gremlin

Object Class: Euclid

Special Containment Procedure: SCP-3781 is to be contained in its cell, a 4m x 4m x 4m room imitating a college dorm room, and is to be provided with easy to cook noodles every few hours, based on its behavior. SCP-3781′s room must contain the following components as to keep SCP-3781′s erratic behavior at bay:

- A medium screen television with access to streaming services such as Netflix;

- A Nintendo Switch equipped with the games “Animal Crossing: New Horizons”, “Pok��mon Sword and Shield” and whatever new games came out in the last 3 months;

- A digital drawing set including a laptop, drawing table and pen, and any necessary platforms SCP-3781 might request.

If said electronics are absent or non functional, they must be immediately removed and substituted with identical copies as to not cause stress on SCP-3781′s mental state. SCP-3781 is strictly forbidden from using any sort of social media website.

Description: SCP-3781 takes the appearance of a humanoid creature with green skin and a curiously shaped head. Due to mind altering effects surrounding SCP-3781′s vicinity, their head always seems to be perfectly rectangular, in a ratio of 16:9. Scientists are not sure what’s the use for said effect, though it has helped the foundation improve on it’s research on mind altering effects and the fairly safe nature of said SCP.

SCP-3781 presents seemingly erratic behavior, and prefers to stay isolated for the most part. After a large sum of experiments including SCP-3781, scientists came to the conclusion it was content being in confinement.

SCP-3781 does not require sleep, but seems to take great pleasure in doing so - even though it does not seem to sleep regularly. It spends the majority of their time moving around its containment cell, occasionally utilizing the permitted equipment within its cell.

SCP-3781′s main anomalous trait comes from its use of the drawing table and its appliances. By leaving a certain amount of money (preferably in the form of British pounds) and describing a preferred fictional character near SCP-3781′s vicinity will put it into a focus state, in which it will not rest until it has completed an accurate drawing described by your person, which is immediately sent to any electronic devices you possess.

After finishing this process, SCP-3781 will enter a hibernation state for the following 24 hours, after which it will continue its regular functions. It is not known how SCP-3781 is able to deliver archives from different archives without the access to the world wide web, though it seems to be related to its mind altering effects.

You, too, can contribute to the foundation’s research on SCP-3781′s anomalous effects by requesting similar drawings. Please access the following link and leave the appropriate amount of money to fund the SCP foundation!

https://angrymemesandicecreams.tumblr.com/post/668872525690896384/middys-commissions

[iguanalysis]

Psychoses, and Their Projective Surfaces: Clinical Considerations

My main idea for this (ambitious) post is that the three kinds of surfaces onto which psychotic images may be projected are called poiesis, genesis, and sinthome. Projection involves forms of subjective reconciliation with visual logic that compromise the inhibition of belief, forms including delusion, hallucination, and elision.

For any given psychotic phenomenon, the three possible projective surfaces are all four-cornered, but it is never the case that any of them are perfectly “rectangular”. This denotation is because a “moment” is by definition something staggered, or not in conformity with itself temporally, as a particular object of contemplation, whether it was immediately perceived (singular) or retrospectively remembered (individual).

Review the three moments of the Oedipus complex here. (Part 1 of the theoretical framework)

Castration and Frustration / POIESIS

Castration and Privation / GENESIS

Frustration and Privation / SINTHOME

Pictured above are the symbolizations which are defined by any two of the three moments of the Oedipus complex in their relation to one another, and this is because of their essential role in structuring logical development throughout childhood, as well as into and all throughout adulthood. However, qua projective surface, the two terms of the lower level (of the first two of these pictured symbolizations) are swapped around, resulting in a respective form of logical error in the judgment of perception. Respectively, for the symbolization called sinthome, it is the upper level, the moment of frustration, which is swapped around.

From the perspective of “normal” sanity with a lucid perception, however, the attempt to reconcile the projective symbolizations (featuring a reversed lower level or reversed upper level) with the ordinary Oedipal symbolizations of logical apperception naturally results in a misunderstanding of psychosis, one which is prominent in popular culture. One may observe this frequently in visual art, movies, and even in music and writing, where there can be found figuratively “homologous” phenomena.

Visual Processing Abnormalities in Schizophrenia and Real Projective Planes

According to Wikipedia, in studies of schizophrenia, pathological vision phenomena perceived by the patient are consequences of biochemical or physiological deficits in the patient’s visual system. “Visual system” is defined as the parts of the human anatomy which are related to the capacity for a sense of sight.

Examples of visual processing abnormalities in patients with schizophrenia include problems with perception of contrast (surround suppression and contrast sensitivity), problems with motion processing (specifically its relation to surround suppression), problems with eye movement (disorders of saccade and smooth pursuit), problems with contour detection and contour integration (weaker nervous stimulation from perceived collinear stimuli flanking, abnormalities with crowding phenomena, and abnormalities with gaze shifts), and problems with face perception (dysfunctional social interaction and trouble with recognition of emotional expressions).

(Source)

A “real projective plane” is defined in mathematics as a “compact, non-orientable, two-dimensional manifold”. This is a basically Euclidean construct, however, whereas the phenomena linked to perception must exist in a three-dimensional, topological reality. In topological terms, then, it is defined using the Möbius strip as its basis: “if one could glue the (single) edge of the Möbius strip to itself in the correct direction, one would obtain the projective plane”. Also: “Equivalently, gluing a disk along the boundary of the Möbius strip gives the projective plane.”

This can be described as a three-dimensional understanding of the flattening of an image. Train tracks that are going off in a straight direction away from where one is standing on them, for example: one sees that in the distance they have a finite “vanishing point” whereat the tracks might simply stop, or they might from there go on infinitely. It is too far away to see which is true, let alone figure out from this that the Earth is round. But the finite point of visual apperception where the tracks seem to merge and “vanish” becomes a kind of mental representation that is different from their physical reality. This is due to the geometry and the limitations of the human sense of sight, even in three-dimensional space.

Psychotic Structures and Their Relation to the Unconscious

Relations, both logical and pathological:

1. Imaginary relation:

In castration–frustration, the imaginary relation is between the real object and the real father.

In poiesis/delusion, the imaginary relation is between the symbolic mother and the real father.

2. Existential relation:

In castration–privation, the existential relation is between the imaginary father and the imaginary object.

In genesis/hallucination, the existential relation is between the symbolic object and the imaginary object.

3. Semiotic relation:

In the square of sinthome, the semiotic relation is between the symbolic object and the symbolic mother.

In sinthome/elision, the semiotic relation is between the symbolic object and the real object.

Delusion and hallucination are classical medical symptoms of psychosis.

“Delusion” is defined by Oxford Languages as:

“an idiosyncratic belief or impression that is firmly maintained despite being contradicted by what is generally accepted as reality or rational argument, typically a symptom of mental disorder.”

“Hallucination” is defined by Oxford Languages as:

“an experience involving the apparent perception of something not present.”

Elision, on the other hand, accounts for the logical ruptures in the structure of perception and its respective cognition that explain how schizophrenia can be better understood from the standpoint of normal, non-pathological consciousness.

“Elision” is defined by Oxford Languages as:

“the omission of a sound or syllable when speaking (as in I'm, let's, e ' en ).

an omission of a passage in a book, speech, or film.

the process of joining together or merging things, especially abstract ideas.”

The relationship to reality which causes suffering in psychotic patients is what is more genuinely pathogenetic than abnormalities, taken by themselves, of visual processing that patients exhibit physiologically and psychologically in cases of schizophrenia. The translation of (understood) perception of the real projective plane into a psychotic symbolization conflicts with a cognized perception of the real projective plane translated into a logical symbolization. In any given symbolization, there is an element of what is unconscious. This is a movement which is mediated by the fixed recognition of a certain kind of relation between two terms found in reality; a third term is found in proximity to this relation, and implicitly points to something hidden behind this relation that is still part of the symbolization nonetheless.

This amounts to the fact that each psychotic “counterpart” to the three symbolizations of the Oedipus complex will have an unconscious product hidden behind the three distinct relations found in the symbolizations of psychotic phenomena, listed above. Those distinct relations are, namely, the imaginary relation found between the symbolic mother and the real father, the existential relation found between the symbolic object and the imaginary object, and the semiotic relation found between the symbolic object and the real object. The respective unconscious products hidden behind these relations are: for delusion, the imaginary object (of cognition); for hallucination, the real father (of disjunction); and for elision, the symbolic mother (of reification).

Mechanisms of the unconscious found in psychosis are surprisingly ordinary-seeming, and coincide with logical apperception. They are, accordingly, cognition, disjunction, and reification. This co-incidence is such by logical necessity, due to the shared nature of reality and the universality of perception as it pertains to symbolizations.

This corresponds to the well-foundedness of the real projective plane as it is defined in topology. Its mathematical definition, on the other hand, features all three psychotic “symptoms”, or processes, in the projective plane’s Euclidean comprehension. It features delusion because it is abstracted as such from reality; hallucination, because it is perceptually immanent and independent of causality; and elision, because its four “sides” reciprocate one another's directions in two-dimensional space without an immovable foundation, or any directional discrepancy in this arrangement (i.e., it is non-orientable).

Plugging Elision into Psychotherapy as the Foundational Structure of Psychoses

It is my hypothesis that in Immanuel Kant's table of concept-categories, each category corresponds to a type of judgment about logical apperception that might bear upon the function of elision in psychotic phenomena. By understanding and defining these connections, the techniques of psychotherapy might improve for psychotic patients, as well as create improvements for the techniques of psychiatric nosography and diagnostics.

It seems like there are hardly any psychiatric patients who might be capable of communicating any precise answers to the questions about these connections which ought to form some part of diagnostic criteria; however, techniques of diagnosis may improve overtime just by making clinicians aware of these connections and trying to put them into practice.

All too often, institutionalization is an indirect form of oppression for patients whose lives could have been made better by somehow being given greater philosophical instruction. How this instruction could be transmitted to the patient successfully is, in my opinion, the most important obstacle facing the eventual progress of psychiatry today, even though such a proposition seems absurd and impractical to implement.

In my own experience, for example, I had a therapist who I underestimated partially due to my prior interest in psychoanalysis; he advised me to study the philosophy of Immanual Kant, but it was a few years before I finally did so, when I was still 22 years old. As a result, my repressed (repeating) behaviors of substance abuse and the malfunctions of the organization of pleasure that are found in clinical depression continued on, and kept repeating. Intelligent though I may have been, I was too deluded that psychotherapy wasn't capable of reaching me, because my true problems must have been somehow more deep-seated than they were “cognitive-behavioral”. Truly it is the latter most of all, even though the former (“deep-seated” problems) were the cause of repeated failures in my adult life, more originally resulting from symptoms of ADHD and gender dysphoria caused by a genetic condition called XXYY syndrome, which is a variant of Klinefelter syndrome.

In my past writing, I have said that “the symbolic mother is genetic, and the symbolic father is poetic.” The genetic problems (ADHD and gender dysphoria) preceded the poetic problems (substance abuse and depression), but the poetic problems bore back upon the genetic problems in such a way as to obfuscate the right understanding I required to develop in a way that was morally effective. Then there are and were the intersections of these two sets of problems with barriers that are more fundamentally societal (ideological and familial) and institutional (financial and occupational).

Thus, even in the 21st century, my therapist encountered the classic problem of resistance to the treatment, just as Sigmund Freud encountered and originally described.

How can this problem of resistance (to the treatment) be examined in connection with the classification of symptoms into both genetic and poetic problems in the context of psychotherapy, as well as be delineated in terms of the psychotic structure of elision, or, the observation of accurate self-judgments which basically escape the patient's notice through denial or misguidance? These classifications are analogous to symptoms of psychosis, even if the problems are not delusional, nor are they hallucinatory.

The unconscious mechanism of elision is reification (of the symbolic mother); the semiotic relation for elision is found between the symbolic object and the real object. Finally, the “third-term” of elision is the imaginary father.

The father function of the imaginary father is repressed in situations where institutional difficulties further complicate the interrelation between my problems here classified as “genetic” (ADHD, gender dysphoria), and my problems here classified as “poetic” (substance abuse, depression). Where obstacles already exist between the genetic and the poetic, even more obstacles are added by the social fabric of reality.

To confront the obstacles which are not “added” by the patient's financial and occupational difficulties is precisely not to see the unconscious mechanism of reification of the symbolic mother, and it is also to single out the imaginary father as what comes into conflict with the semiotic relation involved in elision.

On the other hand, to confront the obstacles which are “added” by the patient's (my own) financial and occupational difficulties is also not to see the unconscious mechanism of reification at work in this complicated interrelation. Thus, the error in the perception of the semiotic relation (between symbolic lack and real lack of the mother's desire) forms a psychotic structure, that of the symbolic mother's (permanent) separation from the imaginary father's phallic and seminal functions. It is not necessarily delusional, nor is it hallucinatory. But it forms the foundation for the possibility of both psychotic projections (delusion and hallucination) by the separation it enacts within reality.

Judgments of the categories of the concept of relation in Kant's philosophy are called “categorical”, “hypothetical”, and “disjunctive”. The semiotic relation found in the structure of elision is visible via its projection onto a real projective surface, and these judgments of relation bear upon these surfaces respectively as Euclidean (categorical), topological (hypothetical), and Kleinian (disjunctive). Their corresponding unconscious mechanisms are, once more, cognition, disjunction, and reification.

Elision is the foundational structure of psychosis because its unconscious mechanism is reification, but the judgment of its own concept of relation (a semiotic relation) is disjunctive. Hallucination, on the other hand, has for its unconscious mechanism disjunction, even though the judgment of its own concept of relation (an existential relation) is hypothetical. And finally, delusion has for its unconscious mechanism cognition, and the judgment of its own concept of relation (an imaginary relation) is categorical.

However, these structures of psychosis are linked to these judgments through elision, unlike their logical, Oedipal, non-psychotic symbolization counterparts (castration–frustration, castration–privation, and frustration–privation a.k.a. the square of sinthome). These symbolizations of visual logic are linked to judgments of relation via their corresponding anti-Oedipal “memories”, or inscriptions. These so-called inscriptions are derived from the “iconic principles” of quantity, proximity, and sequential order, which are in turn derived from the post-structuralist theory of “iconicity”, corresponding to Kant's categories of the concepts of quantity, quality, and modality, respectively.

(The link between anti-Oedipal inscriptions and psychotic structures of symbolization might inculcate the Klein bottle and bring it into relation with topological structures used to improve psychotherapeutic interventions somehow.)

— 4/4/2022

[normal-horoscopes]

yeah but like. he was using it in a dumb way. literally every building that exists in the actual world is noneuclidean anyway. maybe hyperbolic doesnt sound as cool but its less asinine. and the phrase non euclidean architecture isnt even like, good writing. its perfectly comprehensible when you say that. he was not using it in a useful way

IM AFRAID MOST ARCHITECTURE IS INDEED EUCLIDIAN

NON-EUCLIDIAN ARCHITECTURE DOES ITS JOB WELL ENOUGH FOR WHAT LOVECRAFT WAS DESCRIBING IF HE HAD A GENIUS IT WAS FOR DESCRIBING ALIEN THINGS IN TERMS THAT WERE JUST FAMILIAR ENOUGH TO ONLY CREATE MORE QUESTIONS

BECAUSE OTHERWISE HIS NOVELS WERE PLOTLESS DRAGGING TAX DOCUMENTS OF GREY PROSE WITH NO CHARACTERS OR PACING

[holy-planet]

The Guide lazily looked out of the ferry and across the black-on-black wasteland, scattered with crumbling castles forgotten by time, sinking into the sea of tar alongside metallic fossils. Littering this organic gloom were queer things of colorful geometry and geometric color.

Occasionally rising from the too-natural grime of the land were artificial flora of forty-five degree angles and primary colors, all photosynthesizing moonbeams. Terrible lizards prowled methodically, animatronic dinosaurs of neon nature and calculated computations grazing polymer ferns and gnawing iron bones. Swooping overhead, plastic bats eat computer bugs, a flitter of light upon the invisible gridwork, echolocative phasers chirping and hooping across a charcoal-puke sky.

And Saints above, all plastic! Perfectly indiscriminate of the kingdoms of life, be it plant or animal, unified by cold plastic and primary colors. Red, yellow, blue- the colors of the hyperdigital anthropology which defied nature, the civilization of the Eno Polystate. An ever-rising architecture of math and madness, directly contrasting and mocking an ever-sinking landscape of muck and mire... a duel and duet of geometry and geography.

The ferry approached the flamboyant rainbow metropolis over the black horizon, and the nature of Eno was becoming increasingly clear. Always rising, always sinking...

From the ferry, the Student ogles. “But... I can’t understand, why is this world like this? Why so digital, so unnatural, so inhuman...?”

The Guide shakes his head, numb to the wonder. “Try to understand, this microplanet is not hospitable, not welcoming. Life cannot naturally form or thrive here, so an unnatural platform is necessary. All physical life outside of the cities are dominantly plastiforms and plastiphages, usually growing as a byproduct of some long-submerged machination, dying equations spewing life into the world like runoff pollution.

“Sometimes however, these things are seeded by artists and natural philosophers, and from these manmade seeds grow a simulation of sentience. Often enough, you’ll see abandoned projects and pieces returning to the earth to die. Beneath us are the unlimited fossils of such things, from microorganisms to ruined cityscapes. Eno is a people, a culture, a civilization- but before all else it is a planet, and one never meant to be domesticated. It consumes all things eventually, and so to survive is to rebel against nature. Do not be disturbed by what you may find here- ironically, the lack of humanity is a formidable show of human spirit.”

As the Euclidean supercity became evermore clear, one could make out a kaleidoscope of indescribable feats once thought impossible by any god. The growing sound of cosmic choirs filled the air parallel to the blinding light pollution. A once vantablack sky grew illuminated by both fires and phasers, a sprawling celebration of sensory overload and a parade of pretentious photon pornography. This place was a hub of the Known Universe’s extremes, countless eternities and forevers condensed down into seconds. Blink, and you miss everything. This place was Wonderland, and as far as its people were concerned, this place was everything.

“This is a parade for the masters of reality to sing and dance and make merry in the streets, blindingly bright and deafeningly loud. This is a theater, a performance of kings and worms. But you are no such king, are you? Indeed, you are a worm. Will you be trampled upon the manic stage, or fall into the depressed cracks to rot? Will it matter? You will not be forgotten, for you were never even known. Kings do not often look down at their boots, after all.

“All the same, know this: There is much to see and much to miss, but I implore you choose your battles wisely. Mind your wandering eye, look away if you must. The things you see here cannot easily be forgotten, your mental virginity cannot be reclaimed. Keep this in mind, or your mind will be lost.”

[gronglegrowth]

30-35 for any oc of your choice?

30: What topics does your oc know the most about? Are these obvious or would these be surprising to others?

Enal: Alteration magic. He has devoted his life to its study, which is no surprise considering that is the type of magic he is seen researching and talking about to others.

Nu-Kinmune: Mirror Logic, which is a given considering Her current status as one; and fashion, which clearly is no surprise - She likes to mirror Her enemies to shreds and look good while doing so.

31: What time of day is your oc most awake? What about most tired? Do they get up at the same time every morning without need of an alarm, or is their sleep schedule all over the place?

Enal: He... doesn’t sleep much. Whenever he does it is usually a short nap, during which he uses ancient magickas to restore both his Vancian spell reserves and himself. Usually, he is quite awake except when his spell reserves are gone, in which case he acts like a walking corpse (even with certain metamagics).

Nu-Kinmune: When not performing Her duties, She tends to have a perfectly normal sleep schedule, and usually wakes up at dawn. Otherwise, She sleeps whenever She can. She feels most energized at day, and most tired in late nights.

32: What five ingredients would you throw into a cauldron to make a potion based on your oc? How would you cook/mix them? What would the potion do?

Enal: A skyshard of the Magna-Ge, a dragon scale, a spell tome, ebony (Lorkhan’s blood), and something blue. One would use Alteration magic to turn each into a powder then mix these powders, heating them into a liquid which is mainly blue with swirls of gold and purple. This potion would allow the drinker to enter some high state of consciousness in which you could perceive both sound and color as tangible objects... or something to that effect. (This is one of the ways Enal sees the world, by the way)

Nu-Kinmune: Any precious gem, shards of a mirror, malachite, gold, and aetherion particles. One would reflect each material onto itself and each other until they are fused together, then alter their state with belief-magic, and the resulting potion would be bright gold and slightly wavy, as if it isn’t really there. Drinking this, would make you dizzy and very unwell unless you were a mer, in which case, it would allow you direct access to the Earthbones, for good or ill.

33: Describe your oc’s favourite environment. Urban or rural? Wild or controlled? What’s the climate like?

Enal: He enjoys large open libraries, spaces between worlds, vast oceans, paradoxical and non-Euclidean spaces. Machinery deep below, clockwork spinning, hum of the rotary, glow of the skyshards, cracking of roots growing up through all of this and on those roots there are newborn crystal flowers.

Nu-Kinmune: Crystal palaces and spires as far as the eye can see; blooming outward like a flower in spring. The air is light and with just the right moisture; breathing its strangely pleasant scent seems to make things dreamy.

34: What would someone blackmail your oc with? Would they be successful in getting what they wanted?

Enal: If you were to blackmail Enal, you would probably blackmail him with the truth that he is not a true god. Of course, he would simply laugh at the thought that you even tried, and erase your memory of knowing this truth.

Nu-Kinmune: Perhaps you would look deep into Her past and find Her unsavory first time with the Thalmor. You would confront Her with this information, you would say you know what atrocities She committed then. And, knowing and accepting the deep weight of Her actions then, you would be successful.

35: How easily does your oc get attached to things? Does everything have a sentimental value to them, or do they see nothing as more valuable than its practical use? What about with people/animals?

Enal: If it is not in any way magical or a gift, he cares not about it. People however, are different. If their personality is interesting and/or they are persistent in getting to know him, he will, eventually, keep that person around.

Nu-Kinmune: She keeps every new thing She can find, especially if it is shiny and precious; an avid collector you may say. In terms of living beings, it is quite easy to at least speak to Her. If She enjoys the conversation, one may find She considers you friend, or more.

[tracybirds]

 You know what, this one is dedicated to my flatmate who is a great guy but also has yet to work out that reading a book about calculus requires allllllllll my attention and making conversation is the exact opposite response you should have to someone trying to read :P

Apparently I was mad enough to wake up at 5am and bang this out xD 

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John’s favourite thing about London was the anonymity. There was a kind of solitude to be found in the midst of a crowd, no-one looking closely at anyone else and everyone hurrying quickly to unknown destinations. The stream of people never seemed to end, tourists marked by the islands that formed around them as they gaped at the sights and saw everything except the annoyed glares of the people forced to alter their course. The shortest distance between two points was a line but only in Euclidean geometry, and so perhaps the book John took out as he ducked into the small café was of greater interest to London dwellers than they might have otherwise considered.

It had taken many weekends of searching out this place but it had been worth the effort. With its comfortable chairs and perfectly brewed caffé macchiato, John couldn’t think of a place he’d rather spend his afternoons. He nodded to the barista behind the counter as he ordered and quickly nabbed the same corner table he had sat at every day for the last six months. There was a brief opportunity while his coffee was made that people were welcome to talk to him – but they never did. The other customers were creatures of habit and that suited John just fine.

The barista would bring the coffee out to him, and he would smile and accept it gratefully. He wouldn’t drink it all at once, wanting to savour the time before he had to return to the realities of university. He pulled out his book, a popsci non-fiction that had caught his eye in the secondhand book shop with its hideous cover and the intriguing title; Cosmic Topology. It was several years too old to be of any real use and John knew that most of what he learnt from this book would be superseded by the time he reached the level in his degree where they would discuss the shape of the universe in such depth. But there was a good balance of light hearted discussion and just enough mathematics within its pages to keep things interesting. Besides, astrophysics was built upon the successes of previous generations and thus John knew that understanding a historical view of any physics topic could only be of use to him in the future.

Distantly, he heard a bell ringing as the door to the café opened, but he paid it no attention, his mind full of derivations and postulates that leapt out of the page at him. Absently, he pulled his tablet towards him, peering at the words at scribbling down notes of his own to refer to at a later date. He was a model for the focused work he thrived on and so it was with some confusion that he heard the chair opposite him being pulled out from its place at his table. The metallic scrape jolted him out of his thoughts and he glared at the new arrival over the top of his book.

“Hello then,” said a cheerful voice. “What’re you reading there?”

John said nothing, merely raising the book higher to grudgingly allow the stranger to read the title.

“Cosmic Topology,” read the stranger slowly. “What on earth is that all about?”

“Off Earth, technically,” muttered John as he turned the page. He looked up at the stranger, noting her curious face, and sighed. “It’s discussing the non-Euclidean geometry of spacetime. With a particular interest into whether or not the universe can be described as flat considering this effect.”

“Of course, it’s not flat!” she exclaimed. “If the universe were flat it would be like a drawing.”

John ignored her and tried to immerse himself back into the chapter. He wasn’t sure quite where he’d left off, or whether he understood what was happening anymore, so he flipped back to the previous page with a deeper frown.

The stranger was still chattering beside him, oblivious to the fact that she’d lost her audience. Her voice seemed to weasel its way into his brain and trip up his thoughts and he glared at the page as another “don’t you think?” forced him to begin the paragraph afresh as he hummed vaguely in agreement.

He could feel his focus slipping further and further with every word she said and abruptly he drained his coffee in a desperate attempt to restore the peace in his world.

“Phew, down the hatch like that?” she commented. “You got somewhere to be?”

John wanted to yell, just a little, right there in the café. Because the simple truth was no, he didn’t, he always spent two o’clock to three thirty in this particular café and he wasn’t about to change that on the whim of someone who wandered into his life ten minutes prior.

“No,” he said through gritted teeth, and instantly regretted it as this somehow sparked an entirely new conversation.

John was reduced to staring blankly at the pages in front of him, the formulae and arguments swirling in his head like sediment that the constant interruptions refused to let settle.

There was a loud sigh from the chair opposite him and against his better judgement he looked up.

“Sorry, what?”

“I said, do you agree?”

“I, uh,” he stuttered, panic blanketing his mind. What was she talking about? he thought. An image of a teenaged Scott flashed through his mind.

“It doesn’t matter what, John,” Scott said, moodily throwing the tennis ball at the wall. “Women are always right.”

“Yes?” he said cautiously.

That got the stranger’s attention.

“Excuse me?” she said, looking suddenly indignant. “You agree?”

Privately, John thought that perhaps he really didn’t, or maybe he shouldn’t, but he had twenty minutes of lost time rattling inside of him and an opportunity to drive his new attachment away.

“Yes, I do,” he said, looking her straight in the eye.

At this, she stood sharply with an outraged cry and John flinched back as her hand moved fluidly through the air.

On reflection, he was lucky it had been iced coffee she was drinking. The blended slurry had enough mass to showcase her excellent aim and he could see her storming out of the café as he wiped the liquid from his eyes. The smell of coffee was muted but he could already see the stains blooming on his white shirt.

“I’m so sorry,” he gasped at the barista who looked as shocked as he was. “Could I get some napkins?”

He looked mournfully down at his book as they worked together to clean up the mess. It’s pages were already beginning to gum together and he knew he wouldn’t be reading that particular copy for a few weeks. Fortunately, his tablet was waterproof and he smiled wryly as he wiped it down, causing his background to light up, a photo of his family when they had travelled to the Johnson Space Center.

“This is your fault,” he told the grinning image of Scott. “I’m never listening to you again.”

[cheesetheory]

Last night I dreamt

I had a time-travelling DeLorean, like the one in Back To The future, only it travelled through parallel universes as well as through time. It appeared in front of me with the previous owner dead in the driver’s seat (a rotting near-skeletal corpse). Unlike in the movies, the car didn’t keep its momentum after it travelled, and I couldn’t choose where to go, but instead it simply appeared (already stopped) in whatever time/location it chose. Sometimes I would appear away from it, and I’d have to go looking for it.

The first place it sent me was an open semi-marshy paddock, at night. I didn’t get much time to look around though, as I could see a large dark figure moving towards the car from behind, I immediately drove forward and accelerated until the car reached the required 88 mph.

The next place i appeared in was a vent shaft, in what appeared to be a military research facility of some kind (judging by the hallway of numbered hexagonal doors and red flashing lights I saw through the grates). I crawled through it until it opened into what looked like a large concrete elevator shaft, but with the kind of observation window you’d expect to see in a sci-fi testing room on my adjacent side, and an occasional pipe connecting the walls. I couldn’t see the bottom or the top, and there was nobody in the window. There were, however, signs of destruction and decay, as the window was broken in several places, and the inside observation booth was somewhat musty-looking, with the room’s single door on the right side having dried blood stains on it. I grabbed onto a nearby pipe, and manoeuvred myself into one of the larger holes in the window. Walking through the only door led me into a long empty corridor. Despite the place seemingly being abandoned, the lights were still functional, and I could see the relatively pristine white corridor perfectly. There was another door at the end, which opened into a small featureless white room where the DeLorean was parked, and upon stepping inside the car, the walls of the room shifted, lengthening to allow me to drive. I reached 88 mph without a problem.

The next place I ended up was inside my childhood home, at midnight and seemingly several years in the past (I’d say around when I was a preteen). I appeared in the laundry room at the back of the house, and made my way to the hallway. The house was.. longer? Than I remembered? And seemed a bit non-euclidean, but nonetheless I made my way to my room, near the front of the house. I entered my room and saw my little brother sleeping on the top of the bunk bed, while the bottom bunk (where I slept) was empty. I left the room and turned to the front door and, looking out though the door’s small glass panes, I saw that the area past the verandah was simultaneously the hilly country landscape I remembered, and a space-like void. The two weren’t separate, as I could see the void kind of overlaying the scenery, almost like the house was slowly phasing into it. I got outside and was made immediately aware of how cold it was, and that I was only wearing a shirt and track pants. I walked around the side of the house and onto the grass/void(?) where the DeLorean was sitting. As I drove off, I got a feeling that I was leaving something behind, I shrugged it off, since I hadn’t been carrying anything, and hadn’t picked anything up, but the feeling persisted.

The next destination was in an urban/suburban area in the afternoon, next to a shed in someone’s backyard. I started hopping fences and parkouring through the town, seeing nobody around, and eventually making my way to an abandoned factory/warehouse. I looked around, rummaging though trash on the floor until I found an old ornate box that my brain assured me was important, and held sentimental value to... someone, I think. I also got a feeling like I’d accomplished a task, like finishing a fetch-quest in a video game. I made my way out another door, which opened onto a balcony overlooking a parking lot (with only the DeLorean parked there), and a road leading to a large suspension bridge. It was nighttime now, and the balcony overlooked a large body of water (presumably leading to the sea), which the town was built around. There was another person on the balcony, who’s features I couldn’t make out, out of instinct I gave them the box I’d found. They thanked me, and talked about how ‘they’ (referring to some outside entity) loved us, and would ‘save us all’. I then saw the night sky begin to, pulsate? With the stars dimming and brightening in rhythm, and slowly shifting into a flowing stream. I could see chunks of the ground being pulled up and into the ‘star stream’ where they made a spiralling pattern, orbiting the stream as they moved along. I could also see the scenery quickly crumbling into a void similar to the one I saw earlier, and I immediately jumped off the balcony, onto the car. It didn’t look the same as before, in fact, it didn’t even look like a De Lorean, but like another car model entirely, but dream-logic told me it was definitely the same car. Getting in as fast as I could, I drove out of the parking lot and onto the bridge, which had broken apart, with several of its pieces floating in the star stream. I accelerated over the broken bridge, hitting 88 just before I reached the edge.

I was relieved to have escaped, until I released I’d been taken to the same spot I was in when I arrived there, at the same time of day. I started making my way through the town again, but this time I had the overwhelming feeling that I was being followed, even hunted down by what I inexplicably knew was some shadowy organisation/doomsday cult. Then I woke up.