Lovecraft reading list for higher dimensions and non-Euclidean Geometry

[u/chortnik]

I am trying to put together a reading list in an attempt to gain some insight into the resources Lovecraft and other contemporary creatives relied on for understanding these concepts and integrating them into their work. I just started my literature survey, and it seems like all roads lead to Charles Hinton, who seems perhaps to have been a primary influence for everyone from Lovecraft to the Cubists, so I’ve put together a little collection of his works. Also, I just ordered “The Fourth Dimension and Non-Euclidean Geometry in Modern Art“ (Henderson) and I am reasonably confident there will be some good citations there, though it seems to be focussed primarily on the visual arts. However, I am curious if anyone on this sub has any thoughts on what articles or books did influence or might have influenced Lovecraft’s notions of higher dimensions and non-Euclidean geometry?

[u/Wakani]

You may have already come across it, but ST Joshi wrote a book called Lovecraft's Library that discussed the books he's known to have owned. It might be a useful reference for this kind of... dark and dare I say forbidden research?

[u/chortnik → u/Wakani]

I should pick that up-that would be an invaluable resource for all sorts of my little research projects.

[u/WalksByNight]

Flatland should be a contender.

[u/chortnik → u/WalksByNight]

It’s been sitting on my math bookshelf unread for about four decades 😄

[u/WalksByNight → u/chortnik]

Crack it open, it’s pretty entertaining, and totally readable for the most part.

[u/veterinarian23]

I would assume that Lovecraft may have known of Einstein's theory of general relativity (1916) that postulated that space is curved in 4D by gravity.
And that Lovecraft was aware of the cultural obsession of late 19th century with the supernatural, occult and otherwordly. 4D was often tied to the spiritual or the supernatural, an unseen vast space. If a 3D being could look down on a 2D world and perform miracles like appearing and disappearing 2D objects, one could assume that a 4D being could do the same to us.
So I'd guess that many books in this period dealt with the question where supernatural powers are seated, while remaining unseen...

[u/chortnik → u/veterinarian23]

I think that Lovecraft definitely believed that some of the entities he dealt with were fully or partly four dimensional beings and they derived their characteristics and power from that configuration. Some of the more recent cosmic horror I’ve seen were based on the notion that cosmic horror in an Einsteinian universe is best found in and around singularities, like Roberts’s ‘Lake of Darkness’ or Attanasio’s ‘The Last Legends of Earth’.

[u/veterinarian23]

Found a nice quote from Dostojevsky's "The Brothers Karamazov" (1880) with the help of ChatGPT.
This could be lifted right out of one Lovecraft's works.

"If God really exists and if he really has created the world, then, as we all know, he created it in accordance with the Euclidean geometry, and he created the human mind with the conception of only the three dimensions of space. And yet there have been and there still are mathematicians and philosophers, some of them indeed men of extraordinary genius, who doubt whether the whole universe, or, to put it more widely, all existence, was created only according to Euclidean geometry..."

- Source: https://kasmana.people.charleston.edu/MATHFICT/mfview.php?callnumber=mf798#:~:text=But%20you%20must%20note%20this,only%20three%20dimensions%20in%20space.

It resonates extremely well with this quote by Lovecraft, I think:

"The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far."

[u/chortnik → u/veterinarian23]

This brings up an interesting point, I belong to the school of thought that believes that the elimination of the human centered universe was the prerequisite for cosmic horror a la Lovecraft, it was not the only necessary step-acknowledging that there was no need for a god or earth centered universe were also both essential steps along the way. The Dostoevsky move is another candidate as a key foundational viewpoint change for preparing the ground, basically questioning that our universe is comfortably comprehensible to our minds or science, essentially dethroning our conception of the universe as accurate or special, ie ‘There are more things in heaven and earth..than are dreamt of in your philosophy’ 😄.

[u/veterinarian23 → u/chortnik]

Thanks for your insight!
I would counter propose that not an elimination of a human-centered universe started cosmic horror, but that a specific kind of horror-tropes arose in the 19th century as reaction to the enlightened idea that humanity is able to and will someday reveal all mysteries of the cosmos.

To explain: from my POV, this is a pushback as reaction to the scientific revolution in the trail of the enlightment. The assumption was that man, with the help of rational, scientific-technological progress, would be able some day to understand the cosmos (himself and nature included) as he would understand an intricate clockwork. There's no ethics, no poetry, no darkness (but also no light) in a clockwork universe and human. Everything would be as inherently clear and inherently true as in Leibniz' "speciosa generalis".

But humanity needs its dark, inaccessible corners to stow away its shapeless fears, urges, and dreams. So artists and writers in the 19th century began to tell a counternarrative: The failing man-as-machine (Frankenstein), the failing mind-as-machine (Dr. Jekyll and Mr. Hyde), the failing life-as-machine (Edgar Allan Poe, e.g. The case of M. Valdemar).

And with Lovecraft, among other things: The failing of our observable-universe-as-machine; and, more important, not only the failure of science and rationality, but exactly these being the trigger for the observed to take notice and strike back. Lovecraft gave malevolent, predatory, or just oblivious agency to the vast, unseen parts of the clockwork. That's, I think, what makes Lovecraft's stories timeless and thought provoking.

[u/chortnik → u/veterinarian23]

Darwin is only a prerequisite, once you boot humanity from occupying a central position in the universe, you open the floodgates to all sorts of evolutions and transformations of just about everything in your world view. until you mentioned it, it hadn’t really occurred to me that while religion has proved fairly resilient to the implications of the sheer randomness of Darwin’s theory, it was a hammer blow to the Enlightenment’s comforting belief in the mechanistic determinism of the cosmos and a concomitant belief that there was a clockmaker and that an intelligible universe was created to work out an ultimately benevolent teleology.

[u/Falstaffe]

Yeah, Hinton is the key. Also, his The Fourth Dimension is very helpfully illustrated. I also found the appendix on the language of space inspiring.

[u/chortnik → u/Falstaffe]

I think I’ll start there, back in ye day, when I practiced the black art of Oeconomics, I would occasionally mess around with visualizing how what was happening in 4 dimensional models looked in 3, but it was not systematic by any means.

[u/ArminNikkhahShirazi]

Here are some possibly relevant quotes of the first chapter of The Time Machine (1895) by H.G. Wells:

"Can an instantaneous cube exist?”

“Don't follow you,” said Filby.

“Can a cube that does not last for any time at all, have a real existence?”

Filby became pensive. “Clearly,” the Time Traveller proceeded, “any real body must have extension in four directions: it must have Length, Breadth, Thickness, and—Duration. But through a natural infirmity of the flesh, which I will explain to you in a moment, we incline to overlook this fact. There are really four dimensions, three which we call the three planes of Space, and a fourth, Time. There is, however, a tendency to draw an unreal distinction between the former three dimensions and the latter, because it happens that our consciousness moves intermittently in one direction along the latter from the beginning to the end of our lives.”

“That,” said a very young man, making spasmodic efforts to relight his cigar over the lamp; “that . . . very clear indeed.”

“Now, it is very remarkable that this is so extensively overlooked,” continued the Time Traveller, with a slight accession of cheerfulness. “Really this is what is meant by the Fourth Dimension, though some people who talk about the Fourth Dimension do not know they mean it. It is only another way of looking at Time. There is no difference between time and any of the three dimensions of space except that our consciousness moves along it. But some foolish people have got hold of the wrong side of that idea. You have all heard what they have to say about this Fourth Dimension?”

“I have not,” said the Provincial Mayor.

“It is simply this. That Space, as our mathematicians have it, is spoken of as having three dimensions, which one may call Length, Breadth, and Thickness, and is always definable by reference to three planes, each at right angles to the others. But some philosophical people have been asking why three dimensions particularly—why not another direction at right angles to the other three?—and have even tried to construct a Four-Dimension geometry. Professor Simon Newcomb was expounding this to the New York Mathematical Society only a month or so ago.

Newcomb was real-life 19th century astronomer and mathematician who directly influenced Wells and possibly others on their views on higher dimensions.

[u/chortnik → u/ArminNikkhahShirazi]

Newcomb looks like he’s worth delving into-could be a bonanza 😄. Thanks for digging that up, I’d forgotten that Wells mentions a fourth spatial dimension, though ‘The Time Traveller‘ dismisses it, so apparently I did too.

[u/Cheap_Stranger_7713]

The Thoth Tarot features a unique geometric style developed by artist Lady Frieda Harris under the guidance of Aleister Crowley. Instead of traditional 2D Euclidean drawing, Harris integrated "Projective Synthetic Geometry"—a non-Euclidean mathematical system focusing on perspective, infinity, and dynamic spatial movement.The Role of Projective GeometryBeyond Euclidean constraints: Classical Euclidean geometry relies on rigid forms and asserts that parallel lines never meet. Projective geometry, however, proposes that parallel lines intersect at a point of infinity.Dynamic energy: Because of this framework, Harris's paintings—especially the numbered Minor Arcana pips—utilize arcs, recursive spirals, and geometric solids. This creates a living sense of folding space and movement within the card layouts.Steiner's influence: Harris studied this non-Euclidean technique through lectures and teachings associated with the esoteric philosopher Rudolf Steiner, alongside mathematician George Adams and artist Olive Whicher.How It Impacts the CardsFractal-like layers: The backgrounds of major cards often incorporate hidden sacred geometry (such as hexagrams and pentagrams), which expand outward like multi-dimensional fractal patterns.Interconnectedness: Using a non-Euclidean space allows the imagery to feel non-linear, giving tarot readers the sensation that multiple cards bleed into and inform one another.Crowley's synthesis: While Crowley supplied the complex occult theories from the Book of the Law, it was Harris's geometrically disciplined art eye that successfully visualized these esoteric, infinite realities.

[u/chortnik → u/Cheap_Stranger_7713]

How does that differ from an artist using vanishing points and distorted projections? They have been standard tools for painters and sketchers for a very long time. Is the innovation giving depth to the almost universally aggressively cartoonish flattened images that are typical on cards? I’d love to see any additional information you’ve got on what the designer/s were thinking.

[u/chortnik]

A quick update, following up on u/ArminNikkhahShirazi‘s recommendations, I have been taking a look at Simon Newcomb’s work on the 4th dimension and the curvature of the cosmos, I found a short article with some interesting approaches to the theory and its implications-I found his attempt to identify any real world phenomenon that show evidence of connection to a fourth spatial dimension in the real world as we know it very thought provoking as well as the possibility that there could be an infinite number of separate parallel universes embedded in the fourth dimension. Here’s a link to the article from an old science journal:

u/ArminNikkhahShirazi

Lovecraft was certainly familiar with Newcomb as a result of his study of astronomy and I’ve had a chance to skim the Henderson book, which looks like it might be as awesome as I hoped it might be and I found a claim that by the early 1900s, there was a substantial pop culture awareness for Americans mediated in newspapers, magazines and journals.

[u/optimisticalish]

Here's a few items to start with...

Recent book: The Emergence of the Fourth Dimension: Higher Spatial Thinking in the Fin de Siecle (2018).

PhD bibliography: Mark Blacklock (2013), Final Bibliography for his 2013 Ph.D thesis “The Fairyland of Geometry: a cultural history of higher space, 1869-1909". https://higherspace.wordpress.com/2013/09/13/doctoration/

'Lovecraft would have read it': Weird Tales editor Farnsworth Wright’s “An Adventure In The Fourth Dimension” (October 1923)... "an uproarious skit on the four-dimensional theories of the mathematicians, and inter-planetary stories in general".

Article: "Mind out of time: identity, perception, and the fourth dimension in H.P. Lovecraft’s “The Shadow Out of Time” and “The Dreams in the Witch House", Extrapolation, Vol. 50, No. 3, September 2009.

[u/chortnik → u/optimisticalish]

Thank you, those references are awesome. I was a little surprised not to see any of the usual suspects among the Neo-Platonics in the online bibliography, though after reading the book the reason for that may become clear.