Lovecraft and Mathematics: Non-Euclidean Geometry

Over the next few articles I will be discussing how HPL incorporated mathematics and physics into his fiction.  However, other subjects, such as astronomy and biology, may crop up from time to time.  Sometime in February discussions will begin on the Yithians.  For this article the focus will be on “non-Euclidean geometry”.

                        Brown University’s Ladd Observatory in Providence, RI

While HPL loved astronomy, he was not a fan of mathematics.  As a student, he thought of having a professional career in chemistry or astronomy but the difficulties he had with algebra made him realize this was not possibility.  In fact, as cited in S.T. Joshi’s I Am Providence: The Life and Times of H.P. Lovecraft (Hippocampus Press, 2013), HPL remarked in 1931,

“In studies I was not bad – except for mathematics, which repelled and exhausted me.  I passed in these subjects – but just about that.  Or rather it was algebra which formed the bugbear.  Geometry was not so bad.  But the whole thing disappointed me bitterly, for I was then intending to pursue astronomy as a career, and of course advance astronomy is simply a mass of mathematics.”

It is interesting to note that HPL was not stratified with the grade he received in Intermediate Algebra during the 1906-07 school year and that he voluntarily re-took the subject the following year.  Unfortunately, based on school records HPL did not receive his high school diploma , finishing only the eleventh grade (Joshi, 2013).  Never completing high school and going to college was always a personal failure in his mind, which he mentions a number of times.  However, HPL clearly had a strong interest in the sciences throughout his life and this was well engrained in his stories, incorporating the most up-to-date scientific knowledge at the time into his writings.

Lovecraft by Greg Nemec

Upcoming articles will go into more detail in the use of mathematics in HPL’s work, however, for this article I wanted to focus on one of his more popular phrases:

Non-Euclidean Geometry– to understand what non-Euclidean geometry is you have to know what is meant by Euclidean geometry.  Euclid was a Greek, born around 300 B.C. and his best known for developing the  math of geometry.  Part of his treatise The Elements, included a series of axioms and notions which laid the foundation for modern geometry.  Non-Euclidean Geometry is simply a modification of one of these axioms or notions.  Two of the more “common” types of non-Euclidean Geometry are hyperbolic geometry and elliptic geometry.  For convenience, each type of geometry is shown below:


Thus, Euclidean space is essentially “planar” geometry.  Straight lines, squares, cubes and angles of 45 and 90 degrees – this is Euclidean geometry and to someone like HPL who was so interested in architecture, nothing exemplified human civilization than their buildings and infrastructure.  Non-Euclidean geometry is not just triangles and squares – the familiar circle formulas of C = 2 π r and A = π r(C = circumference; r = radius; A = area; π is 3.14159…) are very Euclidean.  Thus, the elliptical and hyperbolic geometries do not follow these Euclidean circle formulas and thus are defined as non-Euclidean geometry.

When I first figured this out in high school or college I was sort of disappointed because in my mind Lovecraft’s non-Euclidean geometry looked far more alien than elliptical and hyperbolic geometries however, stop for a moment and think about seeing an entire city built using this type of geometry.  Shown below are some varying examples:


Cover art for The Art of H.P. Lovecraft’s Cthulhu Mythos (by Michael Komarck)

                                                       R’lyeh by John Coulthart (

I love these examples of Lovecraft’s non-Euclidean geometry, particularly in showing what R’lyeh looks like.  All three exude a very alien impression.  However, in my mind R’lyeh would look far more alien.  For example, I see the buildings and structures actually changing shape simply by viewing them from different points of view – something that is obviously very difficult to show in a drawing or painting.  What is truly amazing is how in simply using an unusual phase such a “non-Euclidean geometry” Lovecraft was able to stimulate the imagination of his readers as well as other writers and artists generations later.

Next time I will be discussing the use of mathematics in Lovecraft’s The Dreams in the Witch House.  Thank you – Fred


11 thoughts on “Lovecraft and Mathematics: Non-Euclidean Geometry

  1. Lovecraft-ery looks to me as cover up for chig architecture from Space Above and Beyond, just something like Chiggy van Richtofan ship known as “Abandon All Hope”

    1. I must admit I do not know what chig architecture is – I will have to look that one up. Thank you! Fred

  2. You might find this scientific “paper” on R’lyeh interesting. It tries to account for the temporal and spatial abnormalities of the city.

    Possible Bubbles of Spacetime Curvature in the South Pacific
    Benjamin K. Tippett

  3. I always viewed the cities of as 4 dimensional, which would mean a) the architecture is always changing and b) the buildings could exist in multiple 3 dimensional realities at once, thus explaining how the sailors in Call of Cthulu became “lost in the angles”

    1. I agree with your ideas – I “see” R’yleh in a similar manner. The non-Euclidean geometry is beyond angled dimensions but this does not describe the multi-dimensional structure of R’yleh – I think the non-Euclidean nature only scratches the surface and we can not see the true nature of R’yleh or of Cthulhu itself. Thank you for the comments! Fred

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