[DF] Non-Euclidean Architecture in dungeons questions.

[sir_pudding]

Originally Posted by Ulzgoroth

You'll have to know something about the shape and movement of the higher-dimensional in directions orthogonal to 3-space in order to make any useful prediction.

Yeah, but you can deduce some of that from observation as long as the behavior is repeatable.

[Ulzgoroth]

Originally Posted by sir_pudding

Yeah, but you can deduce some of that from observation as long as the behavior is repeatable.

Yes, but what does framing it as higher-dimensional geometry add? It's just weird stuff happening on a regular schedule.

[sir_pudding]

Originally Posted by Ulzgoroth

Yes, but what does framing it as higher-dimensional geometry add?

A cool explanation? Immunity to dispel magic? Excuse for using the sanity rules from Horror?

[Kuroshima]

Well, next time the Psi in my game gets a psi phenomina while in elder thing infested territory, the whole group is going to end up trapped in a hypercube, and the only way to exit it will be to trace an Euler cycle on it... of course, each room will have an encounter each time they go through it...

[johndallman]

Originally Posted by sir_pudding

Actually that's pretty much the opposite of what I was saying. I think HPL used the term correctly. There's no story I can think of where "non-Euclidean geometry" is used to describe something that's clearly Euclidean. He does imply that non-Euclidean geometry can be used to open the way for higher dimensional intersections but that's not the same thing. I think he meant like hyperbolic geometry as Lamech says. Which is still pretty weird, but all in (hyperbolic) 3-space.

Actually, there seems to be an extra reason he used the term. In the first couple of decades of the 20th century, physics went all weird. We're somewhat used to ideas like wave-particle duality, gravity being a bending of space and Schrodinger's Cat, but at the time these ideas were revolutionary and totally counter to what people -even scientists - of the time were used to. And lots of them refused to have anything to do with them. Even in the thirties, the Deutsche Physik movement that the Nazis took up was supported by real and distinguished, if elderly, physicists.

The idea that space itself was curved and thus all geometry is non-euclidean was especially objectionable to people used to the idea that Euclid was fundamentally right and this was natural law. The president of Notre Dame University, a theologian, wrote a book proving by impeccable Catholic logic that space really was Euclidean and therefore Einstein was fundamentally wrong. The book makes no sense in mathematics or physics terms, of course.

So Lovecraft seems to have been exploiting the horror that certain ideas held for people with conventional educations at the time he was writing. The resistance rather went away with the advent of the nuclear age, and the revelation of the true horrors of WWII.

[Anthony]

Originally Posted by Edges

There are infinite possible non-euclidean geometries but at any given point, they fall into one of two categories, elliptical and hyperbolic.

There's the occasional twisted metric (moebius strip), though they may require discontinuities.

[Flyndaran]

Originally Posted by johndallman

...
So Lovecraft seems to have been exploiting the horror that certain ideas held for people with conventional educations at the time he was writing. The resistance rather went away with the advent of the nuclear age, and the revelation of the true horrors of WWII.

That's so true. It just seem like most of his horror would have made modern people go, "Meh." rather than go gibbering insane... while running the heck away from monsters of course.

[Edges]

Originally Posted by Anthony

There's the occasional twisted metric (moebius strip), though they may require discontinuities.

With discontinuities, you run into points with undefined curvature. Barring these points however, all other points are either elliptical, euclidean, or hyperbolic. A mobius strip is generally considered a topological structure and hence can have any curvature. The ones I had the kids cut out of paper in school, for instance, were euclidean. The mobius strip and its cousins are a product of tinkering with how space is connected rather than curved.

Come to think of it, elder horrors could not only have weirdly bent space but strangely connected space as well. There is no limit to how confused a devious GM can make the PCs.

[Jovus]

Originally Posted by johndallman

The idea that space itself was curved and thus all geometry is non-euclidean was especially objectionable to people used to the idea that Euclid was fundamentally right and this was natural law. The president of Notre Dame University, a theologian, wrote a book proving by impeccable Catholic logic that space really was Euclidean and therefore Einstein was fundamentally wrong. The book makes no sense in mathematics or physics terms, of course.

For clarity's sake: the debate is still raging. There's good proof on both ends for and against the idea that we live in Hilbert space (which is what I take most people to mean by 'Euclidean') with some essentially local curvature. The difficulty comes with Minkowski describing Einsteinian relativity as an essentially changing curvature of a time/space continuum.

[Lamech]

Originally Posted by Edges

With discontinuities, you run into points with undefined curvature. Barring these points however, all other points are either elliptical, euclidean, or hyperbolic. A mobius strip is generally considered a topological structure and hence can have any curvature. The ones I had the kids cut out of paper in school, for instance, were euclidean. The mobius strip and its cousins are a product of tinkering with how space is connected rather than curved.

A mobius strip (if you make your space the surface of the strip) is going to violate other postulates of Euclidean geometry.