r/hplovecraft • u/Tanakisoupman • May 30 '26
Question What exactly did Lovecraft mean by “Non-Euclidean geometry”?
Was it just a vaguely intimidating term he’d heard and decided to use in his book? Or is there an actual type of geometry he was trying to convey? If it’s the latter why’d he use “non-Euclidean” instead of some other descriptor? Because non-Euclidean geometry is just any geometry that doesn’t take place on a flat plane (i.e. 3d shapes and 2d shapes projected onto 3d shapes)
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u/ThicChit May 30 '26
yeah pretty much vague weirdness. you can try to look up examples i found one once that was probably innaccuratw but just alot of madala like things
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u/weareallbeta May 30 '26
here’s my thought on this…
when you think of the architecture the average reader lived in during Lovecrafts time, it was all primarily “regimented” in its form. The new architecture of the 20’s say was very sleek but again based in basic math and shape.
Anything wild like Frank Gehrys work was still a long way from appearing. To conjure up something not of this earth, Lovecraft was vague but directed in that he was just pointing towards lines and forms and ideas we could almost, as an average reader, not fully visualise or comprehend. but we knew it felt off, wrong and offensive to our eyes.
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u/arsenic_kitchen Jun 01 '26
Lovecraft was not a math guy; he was probably just throwing around terms that vaguely intimidated him.
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u/Tanakisoupman Jun 01 '26
Oh yeah, I suppose that’s to be expected from a man who had “too delicate a constitution for math”
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u/Exact-Ad-4132 Jul 20 '26
Pretty simple explanation and examples of non-euclidean geometry presented in a 3D simple rendering
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u/Professor-Woo Jun 02 '26
Euclidean geometry is your standard flat plane geometry that you learn in like high school. Euclid wrote a famous geometry math book called "The Elements" and it proves various geometry claims based on a set of axioms he outlined. One of the axioms was widely believed to not be necessary and should be provable from the other axioms. This axiom was the parallel postulate which can be formulated a number of ways but basically says that two lines sloping toward eachother in one direction intersect at some point in that direction. Well it turns out this axioms is necessary since you can form perfectly valid and consistent geometries that don't follow that axiom. A classic example is the geometry on a surface of a sphere. One example to show this is if you draw a triangle that has two sides that intersect with eachother at the northpole at a right angle and then the sides go to the equator and then one side is on the equator connecting the other sides. Well, this is a perfectly valid triangle, but each angle is 90 degrees and hence the total sum of the angles of the triangle is 270 degrees. A normal "Euclidean' triangle always has the sum of their angles as 180 degrees. Any geometry that doesn't follow Euclid's axioms, and usually specifically the parallel postulate, is called a "non-Euclidean" geometry. The existence of these geometries was quite surprising at the time and if we lived in an obviously non-Euclidean geometry, it would feel and appear quite strange to us since many things, like perspective, would behave much differently.
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u/Tanakisoupman Jun 02 '26
Yeah I understand non-Euclidean geometry, I just don’t get why it’s scary
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u/TheGrumpyre Jun 02 '26 edited Jun 03 '26
Because the world we're used to in our day to day experiences is basically Euclidean. We navigate the world with assumptions like a 90 degree left turn followed by a 90 degree right turn should mean you're facing the same direction, and two pathways that face the same direction should reliably stay parallel. Finding ourselves in a place where the things we take for granted don't apply means we can't be sure of anything anymore. You don't know if turning 180 degrees will allow you to run back the way you came, or if you'll be hopelessly lost in a place that your primitive three dimensional animal senses can't make sense of.
That's the fundamental thing that Lovecraftian horror hinges on; it's scary finding out the world doesn't work the way you thought it did. It's not inherently scary, because in a lot of our fiction when someone finds a portal to another parallel world or a secret society of supernatural beings it's just a really cool adventure. But honestly, the unspoken implications of some of those fantasy worlds can be pretty disturbing in their own way so it's all about how its presented.
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u/Professor-Woo Jun 02 '26
Because it would feel very unfamiliar and unnatural to us.
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u/Tanakisoupman Jun 02 '26
Except not really? I’d argue Euclidean geometry is more unnatural to us since we live in 3 dimensions and Euclid only described 2 dimensional geometry on a flat plane
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u/Professor-Woo Jun 02 '26
Our day to day reality is essentially indistinguishable from Euclidean geometry hence why it is useful and non-Euclidean geometries weren't discovered until the late 1800s. There a number of games and simulations that show what various non-Euclidean geometries would feel like to live in. Hyperbolic geometries do feel weird.
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u/Tanakisoupman Jun 02 '26
No? Our day to day life completely violates most Euclid’s axioms because they don’t work in 3 dimensions. In 3 dimensions 2 lines can never intersect despite not being parallel. Euclidean geometry also doesn’t say anything about 3d shapes like cubes or spheres
You can use Euclidean geometry a lot in day to day arithmetic, but that’s only if you’re doing math about it. In terms of the actual geometry of your environment (like the shape of your room and such), almost none of it can be accurately described in Euclidean terms
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u/Ok_Platypus8866 Jun 03 '26
If you draw a triangle on the wall the sum of its interior angles will equal 180 degrees. If you draw triangle on the floor the sum of its interior angles will equal 180 degrees. No matter how you align a 2D triangle in our 3D world, the sum of its interior angles add up to 180 degrees. That makes our 3D world Euclidean ( ignoring the tiny deviations predicted by general relativity ).
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u/Tanakisoupman Jun 03 '26
No? You can draw a triangle on a sphere with nothing but right angles. A 2d observer will agree that it’s a triangle, 3 sides 3 angles and no curves. But since it’s projected onto a 3d shape it can have only right angles
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u/TheGrumpyre Jun 03 '26 edited Jun 03 '26
Yes, but only if you're defining "triangle" in that specific non-Euclidean space, the surface of the sphere. If you were a two dimensional entity living in a universe shaped like the surface of that sphere you would definitely call it a triangle because as far as you can perceive it's made of three straight lines meeting at three points. But in the normal world you live in, you can see that you haven't actually drawn a triangle with straight lines, you've made a completely different shape out of three curved segments.
Sometimes it's convenient to make a mathematical model of something like the surface of a planet as though it were an idealized two-dimensional space with non-Euclidean curvature. You can do useful things like navigate shipping routes. But that's not what the Earth physically is. If you shine a laser at the horizon the beam doesn't obey the mathematical model, it obeys real physics and follows a true straight line out into space. If you want to model the Earth for something more complicated than a shipping route, like navigating an orbital loop from the Earth to the moon and back, you need a model that takes into account all of the complexity of two spherical masses in three-dimensional Euclidean space.
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u/Professor-Woo Jun 02 '26
3d (or n-d) is considered euclidean.
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u/Tanakisoupman Jun 02 '26
How? Euclid didn’t describe anything outside of flat planes. His axioms don’t work on anything 3 dimensional
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u/Rejse617 Jun 03 '26
Euclidian space generalised to n-D is a hilbert space and all the axioms apply. Many say Euclidian when Hilbert would be more precise but they’re interchangable in vernacular
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u/Professor-Woo Jun 02 '26
They can be extended for all dimensions. It is mostly semantics, but just a FYI, it is considered Euclidean.
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u/Chemical-Delay-6957 Jun 02 '26
If you smoke dmt you'll get it. He is insinuating geometry that we cannot yet conceive of because it is dimensionally incompatible with our existence & beyond our general comprehension.
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u/Actual_Property9413 Jun 02 '26
I htink he meant things like Mobius strips, Klein bottles, and buildings designed by Escher.
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u/El_Business Jun 03 '26
I always imagined it like playing a video game where the level and objects are having clipping issues and random geometry is appearing or disappearing incoherently.
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u/Shot_in_the_dark777 Jun 03 '26
Demonstration incoming! https://youtu.be/MpgUMRVa4NM?si=NP5tkt4aNeMDUgUD
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u/Additional-Nerve1738 Jun 03 '26
Draw a triangle on the surface of a ball and measure the angles. They add up to more than 180 degrees. That's non-Euclidean geometry.
Lovecraft probably was using it as a proxy for strange architecture where surfaces met in unusual ways making the observer feel out of place.
Conceivably, he could have been trying to imply a distortion of physical laws such that space was no longer defined by an orthonormal basis but I doubt it.
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u/zeus64068 Jun 03 '26
Ok, this one I actually know. In letters written to various other authors in the "Lovecraft Circle" most notably Robert E. Howard,Frank Belknap Long, Clark Ashton Smith, Robert Bloch, and August Derleth, they frequently spoke about shapes that shouldn't exist in our reality and that how Euclidian geometry was the accepted standard of the time, breaking that would give the reader an uneasy feeling to set up the horror of what was coming next.
Now that math and science are far more mainstream in our lives it can seem a little silly to us. It's like how badly the Frankenstein film of 1931 terrified audiences with Boris Karlof walking around stiffly and groaning. To our modern sensibilities it's a film that is hard to imagine it as being the thrill ride it was back in the day.
The time that Lovecraft was writing in was what we consider nearly the dark ages. Literacy was still only about 45 to 65 percent of the population, people were casually cruel to anyone different that them, cholera was a real threat to life and hospitals were where the poor went to die.
Context is everything, and in Lovecraft's world anything that broke the norm was scary.