A Tale of Two Lovecraftian Cities

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)

Cthulhu and Dagon: Residents of R’lyeh

In the Call of Cthulhu, when R’lyeh rises from the Pacific Ocean, it is hypothesized that the structure that broke the water’s surface was “only a single mountain-top, the hideous monolith-crowned citadel whereon great Cthulhu was buried, actually emerged from the waters.”  If this is true, then R’lyeh itself may be an incredibly huge City populated by millions of slumbering Spawn of Cthulhu and the section that broke the water’s surface may be only a small tip of the entire necropolis.

R’lyeh by Vain138

In the story Dagon the protagonist escaped a German sea-raider and found himself adrift in the Pacific Ocean.  After drifting for days, his boat ends up on a slimy, rotting expanse of “hellish black mire.”  After a few days brooding on the boat, he leaves and travels over the exposed plain to set out for a mound in the distance.

A view of the mound on the exposed plain in Dagon (illustration by Mark Foster)

Once reaching the summit of the mound the protagonist looks down into a pit or canyon.  As he travels down the slope on the edge of the pit, he sees a gigantic piece of stone that was clearly not the work of Nature.  As he is examining the strange hieroglyphs and drawings on the large monolith in the moonlight, a large flabby thing rises from the water.  The thing looks similar to some of the creatures shown on the monolith.  It had a generally human body shape covered in scales, glassy bulging eyes, and webbed hands and feet.  The thing, supposedly Dagon, flung it’s gigantic arms around the monolith and bowed it’s head in almost a religious manner.  At this point the protagonist goes mad and runs back to his boat.

Dagon at the monolith (illustration also by Mark Foster)

Both R’lyeh and the monolith in the story Dagon are found in the Pacific Ocean.  It is possible that they are both part of the same structure?  Is it possible that R’lyeh was the upper part of Cthulhu’s City and that the monolith in Dagon and the top spire of one of the highest structures in R’lyeh?  This would all make sense if indeed Dagon is one of the “Spawn” of Cthulhu.  Maybe Dagon was out “testing the waters” so to speak when it first emerged from the Pacific in 1917.  Was Dagon a “scout” before R’lyeh came up from the bottom of ocean in 1925?

Dagon by Jeff Remmer

Future articles will provide additional analysis of both R’lyeh and Cthulhu.  However, next time I will shift gears a little and talk about how Einstein’s ideas on the Universe impacted HPL and the development of his stories.  Thank you – Fred

The Architecture of R’lyeh

R’lyeh is the sunken city where Cthulhu is entombed.  In a previous article on non-Euclidean Geometry I briefly mentioned R’lyeh; however, here I want to go into more detail on this sunken alien city described in HPL’s great tale The Call of Cthulhu.

A vision of R’lyeh by Paul Carrick

As described in The Call of Cthulhu, the crew of the Emma landed on an unknown island on the 23rd of March 1925.  The island was the alien Cyclopean city of sleeping Cthulhu and his Spawn.  The first thing observed as the crew approached the island was a “great stone pillar sticking out of the sea.”  As they approached it, the crew found a coastline of mud, ooze and weeds (I am assuming the “weeds” were a combination of seaweed, tubeworms,  crinoids, coral and other sessile marine life).

R’lyeh by Paul Mudie

The narrator of the story, Francis Wayland Thurston, hypothesized that the city the sailors landed on was “only a singlel mountain-top, the hideous monolith-crowned citadel whereon great Cthulhu was buried, actually emerged from the waters.”  Everything was incredibly huge – greenish stone blocks of unbelievable size and colossal statues and bas-reliefs (in the image of Cthulhu) were observed.

In addition to the immense size of the structures the geometry or the “angles” of the city were all wrong, at least for the human species whose architecture is firmly grounded in Euclidean geometry.  The city seemed to made of non-Euclidean geometry and loathsomely redolent spheres and dimensions apart from our own.  As I mentioned in a previous article, non-Euclidean is simply geometry not confined to straight lines at right angles, triangles, squares, circles, etc.  Any example of what this non-Euclidean geometry looks like in R’lyeh was given in the sailor’s account – “….in those crazily elusive angles of carven rock where a second glance shewed concavity after the first shewed convexity.”

Concave is simply curved inward like a cave, where convex is the opposite and a shape stick out (from http://www.concretecountertopinstitute.com)

So, look at the two sets of buildings below – the buildings on the left are concave, while those on right are convex.  So imagine looking at one set of those buildings and at one moment the structure is convex and the next it is concave.  Or imagine looking at the structure and as you are walking by it actually changes before your eyes from concave to convex, simply based on your point of view.  In addition, unlike a hologram this is a real structure and the shift from concave to convex is not consistent or predictable.  Some structures look the same while others are shifting in shape and structure, with no repeatable pattern.   Still others may change in shape at one point in time and then stop such changes.

Concave and Conex buildings (from www.trekearth.com)

One can see how such strange, chaotic changes in the city of non-Euclidean geometry would certainly make one uneasy.  You would question both your sanity and reality.  Is this city, which originated from the bottom of the sea and obviously not built nor designed for humans some strange hallucination?

Angles of R’lyeh by Marc Simonetti (from The Art of H.P. Lovecraft’s Cthulhu Mythos).  This piece of almost “Escher-like” artwork seems appropriate in conveying the confusion and disorientation associated with being at R’lyeh.

Such confusion and disorientation on R’lyeh did result in the death of at least one of the sailors on 23rd of March 1925.  Johansen swore he saw Parker slip and was “swallowed up by an angle of masonry which shouldn’t have been there; an angle which was acute, but behaved as if it were obtuse.”  Thus, if we are to accept the testimony of Johansen, this shifting or phasing of the buildings and structures on R’lyeh was actually manifested in our reality and not an illusion.  This was beautifully demonstrated in Andrew Leman’s incredible movie “The Call of Cthulhu”, which was filmed as a silent, black and white movie.  I strongly recommend anyone who is interested in Lovecraft and the Cthulhu mythos in general to see that movie – it is fantastic and amazing that they produced such a high quality film on such a limited budget.

At R’lyeh – from Andrew Leman’s The Call of Cthulhu (H.P. Lovecraft Historical Society)

To conclude, R’lyeh not only exhibited non-Euclidean geometries but also exhibited quasi- or alternative forms of quantum mechanics that occurred at the macroscopic level.  This is why poor Parker slipped through an angle he thought was solid.

Next time will discuss the link between R’lyeh and HPL’s story Dagon.  Thank you – Fred

Another view of R’lyeh by Mr. Loach

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:

      From http://www.mathforum.org

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 r²  (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:

From http://www.jennytso.com

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

                                                       R’lyeh by John Coulthart (www.johncoulthart.com)

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

The Spawn of Cthulhu, Part 3 – Additional notes

As previously mentioned there is very little information on the spawn of Cthulhu.  We know they somewhat resemble their Master or Parent Cthulhu and that they came down to Earth with him approximately 350 million years ago.  They battled with the Elder Ones and peace was achieved.  The spawn built the great city of R’lyeh, which then mysteriously sunk into the Pacific Ocean around 300 million years ago.  To this day, Cthulhu and his spawn lie entombed in R’lyeh asleep and sending dreams to the sensitive.

City of R’lyeh by the great Lovecraftian artist John Coulthart

Very little is known about the spawn of Cthulhu; however Hiraku Takeoka, a gentleman from Japan who I have met on Facebook, made a very good point (see below).  Lin Carter, a well known writer of fantasy, science-fiction and horror, contributed to the Cthulhu Mythos, which included the Xothic Cycle.  Mr. Carter was well known to flesh out or “fill in the gaps” in Lovecraft’s mythology but I want to focus this article on the spawn of Cthulhu.

Chaosium’s The Xothic Legend Cycle, Lin Carter’s Mythos fiction (edited by Robert M. Price)

Specifically, according to Mr. Carter’s stories Cthulhu brought a number of other entites to Earth from Xothic, a green binary star.   Some of these entities included Cthulhu’s “mate” Idh-yaa, and their progeny – Zoth-Ommog, Ghatanothoa, Ythogtha and Cthylla (The Encyclopedia Cthulhiana by Daniel Harms).  While this description makes it sound like Cthulhu is the father of one happy “Old One family”, this is a very deceptive interpretation.

Ghatanothoa by the talented artist Mike Bukowski

Biological concepts based on sexual reproduction, such as parents, progeny and siblings, more than likely do not apply to Cthulhu and his spawn.  Nothing is known about the reproduction of these entities; however, the prevailing hypothesis is that they reproduce primarily through mitosis.  That is, they reproduce similar to basic cell division.  Once the cell or individual attains a certain size or volume they split.  It is not known if the conventional Darwinian mechanics of natural selection apply to Cthulhu and his relatives but more than likely Cthulhu is the largest, and thus leader of the spawn.

Following this line of logic, Mr. Takeoka made an excellent point that these “family members” of Cthulhu’s may be larger representatives of the spawn.  Again, if Cthulhu is the largest and oldest of the spawn, he is the leader.  The other family members must be other leaders of the spawn (subordinates to Cthulhu) and have grown to such a size to be named, known and worshipped by humanity and other races in our universe.

Another incredible drawing of a spawn of Cthulhu by KingOvRats

To conclude, not much is known of the spawn of Cthulhu.  However, to date, they are the most “alien” of entities that we reviewed on this blog site.  One thing is for sure, the spawn of Cthulhu is very distinct from the next group of entities we will be discussing – the Deep Ones.  Thank you and Happy Holidays!  Fred