The trope describes certain places, buildings, artwork, or creatures that defy our Euclidean geometry. Parallel lines might intersect in mind-boggling ways, a cube might not actually made up of right angles, a seeming concave depression might turn out convex instead, the stairs could loop around infinitely, or the Eldritch Abomination standing before you might only be the third- or fourth-dimensional manifestation of something even larger and nastier.
Imagine if M.C. Escher dropped a tab of acid, then got possessed by an inhuman god from The Dark Times of prehistory, and you might start to approximate what we're talking about here. Check your sanity at the door… if you can figure out which way it opens.
A location with only minor use of Alien Geometry might look normal at first, but something's up with it, and you just never quite feel at peace there. Get out a tape measure or Mason's Square, and you'll probably Go Mad From The Revelation. More extreme examples could contain… well, anything.
Game and Story Use
- There's the obvious "ancient city that drives you mad" application. This is where Cthulhu and his buddies sleep away the centuries.
- Just looking at such a place is probably a one-way ticket to psychosis or psychic nosebleeds.
- Better hope it's not a Mobile Maze or Genius Loci, or you might never get home.
- No doubt all sorts of evil tricks can be pulled if this place becomes a battlefield. Various twists might allow those who are native to this realm to teleport or just take logic-defying shortcuts. Heck, bullets might round corners or double-back here, too, so be careful!
- Any Portal to the Past or other Gateway can be spiced up by describing it's architecture as being non-Euclidean and mind-bending.
- Your run of the mill Bag of Holding might end up being pretty disturbing if the place it opens up to is part of Lovecraft Country.
- Magic may turn out to be just the applied theory of Alien Geometry. Wizards may have much in common with Mathematicians and Architects.
- This was implied heavily in several stories by H.P. Lovecraft.
- Hell is sometimes portrayed as having non-euclidean geometry. Because having parallel lines that don't meet at infinity is EVIL!!!
- A warning for GMs … non-Euclidean geometry is an ass bitch to map. Your best bet is to use a series of small area maps and interconnect them by a flow chart, rather than making them details of a single map - or make the PCs move at the speed and bearing of plot: wherever they choose to go, it turns out they end up where you planned. On tactical maps anything goes … possibly … if the area is wierd enough you would be well placed to make the PCs randomly determine their location every time they move whilst any natives can move normally. Don't do this too much though or they'll throw things at you.
- An alternative form of non-Euclidean geometry might be termed thematic or subjective … where direction and distance (and maybe time) are relative and subjective - in a sufficiently subjective location "up" might be a matter of consensus … or purely personal.
- For even wackier thematic geometry consider this concept: "things near Birmingham are near Birmingham" - whether that happens to be West Midlands or Alabama and I can go from Sollihull to Gardendale faster than Sollihull to London or Gardendale to Atlanta.