Alien Geometries

Posted: February 9, 2011 in Ryan Crutchfield, Threat Quality
Tags: , , ,

My name is Ryan Crutchfield and I am a system architect and application programmer with a master’s degree in archaeology that I never get to use. I am a regular contributor at and my twitter stream (@rc6750) will more than likely bore you to tears.

I have a predilection for stories, usually of the cosmic horror variety, dealing with alien geometries and eldritch locations.  Alien geometry is the use of non-Euclidean geometry to describe places, buildings, artwork, or creatures that defy our very understand of the physical world. In these stories parallel lines can intersect, internal house measurements are longer than the external walls, cubes are not actually made up of right angles, and creatures manifest across multiple dimensions. Alien geometry is slightly different than the similar literary tool of sinister geometry. Sinister geometry is represented by large, perfectly made, unknown objects that leave an unnerving feeling with those who see it: think the monolith from 2001: A Space Odyssey, the sphere from…. The Sphere, or even a Borg cube. However, sinister geometry never crosses that line that bends geometry beyond our comprehension.  These objects are perfect squares, perfect circles, things whose shape, though disturbing, we recognize. It is the realm of alien geometries that crosses that line and tosses our Euclidean view of the world out the window.

I am not going to turn this into a math class in explaining non-Euclidean geometry versus geometry as defined by Euclid but this graphic should tell you everything you need to know. I am just setting the scene.



I have identified what I believe are the three main ways that alien geometries are used within a story: hidden spaces, dimensional crossing, and unnerving visions; I will cover each of them with specific examples. I will try not to get too specific with the details, but there may be minor spoilers in the stories discussed below.

Hidden Spaces (Where Did All Those Tentacles Come From)
Hidden spaces are represented by those times that measurements don’t add up, unseen doorways hide beyond your vision, or perhaps a triangle has more than 180 degrees and has just that much more space to hide something. My favorite example of this is in H. P. Lovecraft’s The Dreams in the Witch House.  In this story Walter Gilman, a student of mathematics and folklore at Miskatonic University (Go ′Pods!), discovers the alien topology of his own bedroom serves as an extra-dimensional portal. This idea of hidden spaces shares some aspects of the next genre of dimensional crossing, but I wanted to specifically mention the way that the room is described and laid out.

“Gilmans’ room was of good size, but queerly irregular shape; the north wall slanting perceptibly inward from the outer to the inner end, while the low ceiling slanted gently downward in the same direction.”

Without going into specifics I will just say that poor Walter Gilman has a difficult time while staying in this room. Also, props to Lovecraft for Brown Jenkin; that thing is nuts.

Another, more modern, story involving hidden spaces is House of Leaves by Mark Z. Danielewski. House of Leaves is a complicated tale about Johnny Truant’s notes on a manuscript of the recently deceased Zampanò which turns out to be an academic study about a documentary film called The Navidson Record, that does not actually exist. Oh, and Zampanò was blind. The Navidson Record is supposedly Will Navidson’s documentary about the strange events happening at his house in Virginia. A closet suddenly appears inside the house one day and in his examination Navidson discovers that the internal measurements of the house are longer than the external measurements. That is just the beginning.

The final example in the genre is Heinlein’s And He Built a Crooked House. This story revolves around an architect who builds a house in the shape of an unfolded hypercube. When an earthquake makes the unfolded hypercube fold in on itself to become a hypercube, it becomes eight times roomier on the inside than on the outside. However, the house’s new topology makes for fun problems when trying to actually leave.

Dimensional Crossing (Now You See Me, Now You Don’t)
A particularly popular use of alien geometries is for enabling a character or creature to cross the very fabric of space and time, perhaps travelling between alternate realities in the process. A classic example of this is Mimsy Were the Borogoves by Lewis Padgett. In this story, children’s toys from the far future travel to 1942 and end up in the hands of a couple of children. The toys have non-Euclidean features that the adults in the story can’t even being to comprehend, but as the children continue to play with the toys, their minds become programmed to this new geometry and use their new knowledge to create a tunnel to the dimensions where the toys came from. Another example is The Translated Man, which uses the concept of Aetheric Geometry. Aetheric Geometry is one of the heretical sciences of this world, and was used to translate a ship name the Excelsior into the alternate universe of Aether and back again. Well, that was the theory; in practice it turned out very poorly.

Unnerving Visions (What The Hell Was That)
Unnerving visions are those things that break Euclidean geometric rules, and when viewed have the ability to drive the person mad. H. P. Lovecraft’s work is filled with examples of this. Another famous example of this is from Flatland: A Romance of Many Dimensions when the two dimensional A. Square meets the three dimensional Sphere and it almost drives him insane. A more subtle use of unnerving vision can be found in Laird Barron’s The Imago Sequence. In this story a series of photographs called the Imago Sequence, when viewed, cause feverish dreams and other unpleasantness.

A Challenge
Since I am such a huge fan of alien geometries, my challenge today is for everyone to use this more in your stories. Yes, it is that simple. However, for some real life examples of how using alien geometry will make any story better, I have put together alternative versions of three movies currently in theaters right now. (Note: I haven’t actually seen any of these movies, I am making an assumption based on the information available to me that they do not include alien geometries.)

No Strings Attached
According to the IMDB, this movie is best summed up like this:

“A guy and girl try to keep their relationship strictly physical, but it’s not long before they learn that they want something more.”

Holy crap, that sounds pretty horrible. How about this instead?:

“A guy and girl try to keep their relationship strictly physical, but when the geometry of their house shifts, it’s not long before they learn that physical contact will never be the same.”

The Roommate
What does the IMDB have to say about this movie?

“College student Sara finds her safety jeopardized after she’s assigned to a dorm room with a new roommate, Rebecca.”

What in the hell; this sounds like a remake of Single White Female. Lets punch this up a bit.

“College student Sara finds her safety jeopardized after she’s assigned to a dorm room with a new roommate, Rebecca. When Rebecca steps into the closet one day and disappears, the hunt is on to find what secrets these walls hold.”

Season of the Witch
The IMDB summary:

“14th-century knights transport a suspected witch to a monastery, where monks deduce her powers could be the source of the Black Plague.”

I am not going to lie, this actually sounds kind of cool, but lets see what we can do with it regardless.

“14th-century knights transport a suspected witch to a monastery, where monks deduce her powers could be the source of the Black Plague. While the monks debate her fate, the witch opens a portal to another dimension unleashing the true source of the plague upon the world.”

As you can see, it does not take much to create a more interesting story by adding alien geometry, and I look forward to my challenge being accepted. Come on writers, let us see what you can do!
  1. Is that really what Season of the Witch is about? Jesus fuck I fear for my future.

  2. megann says:

    hey, i stumbled upon your blog while searching for the name of a Lovecraft story that was evading my memory. just wanted to say that after reading this, i’ll be visiting again.

  3. braak says:

    Did you figure out which one you were looking for?

  4. AM says:

    I did not know there was a clasification/ genre for House of Leaves other than ‘blow your mind’. Thank you for the clarification, RC.

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