I was recently looking through an archive of early
Dungeon magazines, and found a fascinating article in issue No. 6, July/August 1987, which featured a great example of a non-Euclidean dungeon called
The Forbidden Mountain by Larry L. Church. If you all can find a copy of that issue, I highly recommend it. The article begins with a discussion of spherical and hyperbolic geometries, and their implication for how a dungeon mapped on an ordinary piece of graph paper would in fact play (see figures 1, 2, and 3). Next he imagines briefly the possibilities of dungeons in arbitrarily curved space (figure 4), and produces a diagram of a dungeon that is effectively on a Moebius strip (figure 5)! Gary Gygax was known to have had a great deal of respect for gamers' minds, believing them to have above average intelligence and creativity. It's striking to me that so early in the magazine's history they would put such a sophisticated thought in their magazine. It speaks to the great deal of respect the magazine had for the intelligence of their readers. I'm suspect that respect is gone today.
I also can't help but wonder if their inclusion of a non-Euclidean dungeon in the first year of publication suggests that at least among homebrew dungeon designers, such machinations were more common than one might guess from early modules.
Both H.P. Lovecraft's
The Dreams in the Witch House and
The Call of Cthulu used non-Euclidean geometry as a device to make their horrors seem alien, with access to unfathomable knowledge which humanity is only able to touch upon. It was a common theme in all his stories. Since even in his time, the ideas of alternative formulations of geometry were well developed, it's implicit in his stories that humanity had already gone "too far," in its search for knowledge. The Theory of Relativity was something we were not "meant" to know. The ability to manipulate space itself would almost certainly be a hallmark of powerful magic or divine intervention. I was also thinking about when I was eleven and learning to play D&D while also teaching myself to program in Ye Old BASIC with Lyne Numbers on my ATARI XE computer. I remember carefully keying in a program called "Hunt the Wumpus" and taking pride in how I'd made the Wumpus' lair into a Moebius strip.
Dr Who's TARDIS would be impossible without non-Euclidean geometry.
As a dungeon master's tool, geometrical tricks are probably about the dirtiest, least expected trick you can pull. Particularly with all the advanced graphics tools we have now, there's no reason for us to feel constrained to two or three dimensions. None the less, it seems that we've all succumbed to the tyranny of our graphics software, which invariably seems to produce a flatter, less, mindbending world. Non-Euclidean dungeons could be examples of weird "funhouse" sorts of magical effects, or else inspire horror and awe in the tradition of H.P. Lovecraft, were a dungeon becomes a weird arrangement of higher dimensional objects, time and space lose their conventional meaning, and serves to make humans feel weak and pitiful in the face of superior beings from the outer reaches.
Maybe it's just me, but growing up I felt like my friends and I all shared an uncomfortable fascination with the alternative formulations of space and time. In highschool I read Albert Einstein's
The Theory of Relativity, and Rucker's
Geometry, Relativity and the Fourth Dimension. In college one of our textbooks was
Spacetime Physics by Taylor and Wheeler. Contemplating non-Euclidean geometries was an important part of my intellectual growth as a young person. Dungeons and Dragons was one place where people could perform
gedankenexperiments and develop a visceral feel for them. I suspect the experience was more widespread than is commonly acknowledged. Maybe it's also just me, but it seemed like non-Euclidean geometry was everywhere then. Maybe I've just lost touch with geeky kids.
So... my next dungeon will be non-Euclidean.
