One of the consistent motifs in the short fiction of H.P. Lovecraft is the description of creatures and spaces as non-Euclidean. Most readers are still able to identify the horror of these creations (as well as the rampant racism in the stories) but the description itself is highly academic. For many readers this isn’t enough to build a mental image on, most of us couldn’t tell you what makes geometry Euclidean or not. However, Lovecraft’s work remains an icon of the horror genre that continues to be the inspiration for all kinds of stories in a wide variety of media. His use of highly intellectualized descriptions are given enough context that they still have an impact for a lay reader while leaving a deep well of symbolism for more in depth readings.
The descriptions of impossible, non-Euclidean geometries occur as the narrator passes from the normal world into the horrific. This clear delineation between the familiar world and the world of horror makes the reader more likely to accept the unfamiliar descriptors even without a clear definition. The world of horrors should be incomprehensibly terrifying, so a confusing description is actually quite fitting. It also leaves a great deal of room for reader imagination. When making my initial read through of a collection of Lovecraft stories I found the descriptions of unnatural geometries thought provoking and even before doing research I was creating mental images of the cities and creatures of the stories.
When you do eventually get around to research though there is quite a bit to be found. There is quite typical literary analysis of recurring motifs but there are also mathematical papers discussing what a building featuring non-Euclidean geometry might look like. As it turns out Lovecraft was largely self taught and probably encounter non-Euclidean geometry informally, but the study of this branch of math in academic settings continues. A quick read of the Wikipedia page isn’t actually all that helpful for better picturing Lovecraft’s world, but it is interesting to consider the background the author was working from. It is also fascinating to see academics in the arts grapple with this element that is far outside of the area of expertise. I would be curious to send a math major through some of those articles to know how accurate the English papers are.
While the mythos and worlds of H.P. Lovecraft have been appropriated and reinterpreted in a variety of works the focus on geometry as a way of conveying horror is often something that is lost. The numerous video games that have drawn on Lovecraft have to contend with the near impossibility of representing non-Euclidean geometry in a more interesting way than mathematical diagrams. Other works like the recently published novel The City We Became by N.K. Jemisin are very understandably focused on bringing the mythos more in line with contemporary social justice concerns. While the geometrical horror is one of the key elements of building Lovecraft’s defining atmosphere it simply is not the focal point of modern interpretations.
There are a whole host of reasons that the work of H.P. Lovecraft is not particularly accessible for readers. But somehow the academic ugliness of the descriptions is not the primary stumbling block. In fact these unfamiliar terms add to the disconcerting atmosphere that is part of the appeal of Lovecraft’s work. Whether or not you do the background research to better understand exactly what he was talking about these ‘unnatural geometries’ are accessible because they offer a free pass to imagine essentially what ever you want. This perhaps is why the many spin offs of Lovecraft’s work fail to be a captivating as the originals as they make concrete what previously was left open by overly intellectual vocabulary. Usually being too academic in any type of writing is a way to get a large portion of the audience to tune out, it is a hard balance to find and one that is rarely replicated.