**R’lyeh by the artist Mr. Loach.**

H.P. Lovecraft used the term non-Euclidean in a few of his stories including “The Call of Cthulhu” and “Dreams in the Witch House.” In specific reference to “The Call of Cthulhu” the term non-Euclidean geometry is used to describe Cthulhu’s sunken City of R’lyeh. However, the term non-Euclidean was not used to describe the great cities of the Elder Ones in “At the Mountains of Madness.” This article compares these two alien cities to one another and discusses the non-Euclidean nature of R’lyeh.

I have already discussed what Euclidean and non-Euclidean means in a pervious article but for the sake of this discussion these terms will be briefly reviewed. Simply put the term Euclidean refers to 2-dimenional (squares, triangles and circles on a plane) and 3-dimenional (cubes, pyramids and spheres in space) realities. Human architecture is almost entirely based on Euclidean geometry (see below).

**Euclidean three-dimensional space (from http://www.wikipedia.org)**

While human architecture may be heavily Euclidean, other components of our lives are dependent on non-Euclidean geometry, such as the use of Global Positioning System (GPS) technology due to the curvature of the Earth (see below). In addition, much of nature is non-Euclidean in design.

**A comparison between Euclidean and non-Euclidean (elliptic and hyperbolic) Geometries (www.blendspace.com)**

From a Lovecraftian perspective this may seem a little disappointing, however, shown below is an example of non-Euclidean architecture. Such designs can be a little disorienting but as will be discussed in more detail below, based on HPL’s text I hypothesize that the non-Euclidean description of R’lyeh is only a partial attempt to understand the truly alien aspect of the city. However, before we discuss R’lyeh in more detail, I want to briefly review the Elder Ones cities in “At the Mountains of Madness.”

** A truly non-Euclidean view of R’lyeh (www.jennytso.com)**

**House in Abiko, from Renovations of the National Exhibition Centre – an example another variety of non-Euclidean architecture.**

The cites of the Elder Things in “At the Mountains of Madness” were truly strange and alien, being described as “…curious regularities of the higher mountain skyline – regularities like clinging fragments of perfect cubes…” and “…no architecture known to man or to human imagination, with vast aggregations of night-black masonry embodying monstrous perversions of geometrical laws and attaining the most grotesque extremes of sinister bizarrerie.” Other terms used to describe the alien Elder Ones cities included truncated cones, tall cylindrical shafts bulbously enlarged and often capped with tiers of thinnish scalloped discs. multitudinous rectangular slabs or circular plates of five-pointed stars, cones and pyramids either alone or on top of other cubes or cylinders some of which were flatted on the top, and needle-like spires in clusters of five.

**At the Mountains of Madness by Stephan Mcleroy (www.stephenmcleroy.com)**

While the descriptions of the Elder Ones cites are indeed alien, they are primarily Euclidean in nature (e.g. cubes, cylinders, etc.) but with some small inclusion of non-Euclidean architecture. More importantly, they did not give the impression of a geometry being “all wrong” as Wilcox described R’lyeh in his dreams or the dream-place geometry, extra-dimensional impression Johansen had when he landed on the island.

**R’lyeh by the great artist John Coulthart (www.johncoulthart.com)**

R’lyeh appears to be more “alien” to us relationship to the cities of the Elder Ones, which corresponds with our biological relationship between the Elder Ones and Cthulhu (including its spawn). Essentially, HPL was very explicit in stating that the Elder Ones, while being very alien, were still made of the same matter we are; we are residents of the same universe. In contrast, Cthulhu and its spawn are well known to be extra-dimensional entities. They are not of this universe and are not composed of the same matter we are. Thus, their manifestations into our reality is more than likely not their “true” form – simply an interpretation of their appearance in a three dimensional / one time universe. Sort of the way you can draw a representation of a cubic on a sheet of paper. It is an interpretation of a three dimensional object on a two dimensional plane.

**This is a drawing of a cube, interpreting what a 3-dimenional object looks like on a 2-dimensional plane.**

Since Cthulhu and its spawn are extra-dimensional, their architecture is more than likely extra-dimensional as well. This would explain why the geometry of the R’lyeh just does not feel “right” to humans. Being creatures of 3 dimensions and 1-time scale, our senses and previous experiences are making an attempt to perceive Cthulhu and R’lyeh. Sometimes our senses clearly get this extra-dimensionality wrong such as when Parker was swallowed up by an angle of masonry that was acute but behaved as if it were obtuse as documented in the end of “The Call of Cthulhu.”

**R’lyeh by Pal Carrick**

To conclude, while the cities in Antarctica are clearly alien, they were built by the Elder Ones, creatures of our universe and reality. In contrast, R’lyeh seems more alien and “wrong” since it is only a representative manifestation of what it looks like in our reality. Thus, our perception of what is looks like is very different than what is actually looks like in its own multi-dimensional reality. In fact, since we are limited to 3 dimensions and 1 time we can never know what this multi-dimensional city truly looks like. This goes for its extra-dimensional denizens, which includes Cthulhu and its spawn. However, if we could somehow alter, expand and/or increase our senses, maybe we could then see the true form of both Cthulhu and R’lyeh.

Next time we will expand on the concepts of extra-dimensionality, with specific discussions on Cthulhu itself. Thank you – Fred.

**R’lyeh by Decepticoin (www.deviantart.com)**