HyperRogue – A non-Euclidean roguelike

Yeah, Jeff calls it "non-Cartesian". He changes the topology but the geometry is Euclidean. There are also lots of roguelikes doing other experiments with topology, tilings, dimensions (Verdagon 7DRLs, geometry episode of Roguelike Radio, etc.)

Wouldn't any geometry that violates any of Euclid's five postulates be non-Euclidean? Yes, the parallel lines one is the most famous, but surely a geometry that violates any of the other four would be too.

If your geometry has portals, the parallel line postulate will no longer hold. If your portals can have different angles between the entrance and the exit you can straight up cross "parallel" lines, and even if you require them to be oriented at the same angle you'll lose "when given a line and a point exactly one parallel line can be drawn".

Euclidean geometry is an extremely precise geometry, and there is nothing wrong with calling any deviation from it "non-Euclidean". Since Euclidean geometry is a fairly specific point in geometry-space, the only real objection is that calling something "non-Euclidean" doesn't tell you much about what it is, but Euclidean geometry isn't a bad choice for a "default" geometry and at least it tells you it's not that. There is no requirement for it to be continuously curved in some spherical or hyperbolic manner to be "non-Euclidean". Even just permitting a single portal into an otherwise Euclidean geometry would utterly shred Euclid's Elements from top to bottom.

By my examination of the original postulates, not only would portals wreck the parallel line postulate, it in fact ruins 4 out of 5 of them, leaving only that a line can be continuously extended (and that line can still self-intersect, which may in fact violate the definition of a "line" and mean all 5 axioms are busted if you really dug in). It means it is no longer possible to draw a line between any two points (portals can shadow portions of the space such that some points are not connectible), cicles lose a lot of their properties that we rely on (imagine the unit circle, and a portal starting x = .5 and going straight up... they're no longer necessarily continuous), right angles may not be equal to each other any more (portals can change the apparent angles, or give two interpretations rather than one), and of course the parallel line doesn't hold. Putting portals into a geometry fairly comprehensively makes it non-Euclidean.

Super Mario Galaxy is not non- euclidean; it's just a regular 3D projection onto a 2D screen. The spheres you travel on are technically non-euclidean if you consider the surface in a vacuum, but you aren't playing on the surface, you're playing in a full 3D space.

Additionally, 2D sphere surfaces are very understandable because they can actually exist in our 3D world and we're used to them; hyperrogue has a hyperbolic non-euclidean 2D geometry which is impossible in real life, much more confusing, and impossible to display with no confusion. I don't know what Smart Kobold is, but I presume it's also not just a regular 3D game like Super Mario Galaxy.

> some recently introduced EU law

Is it?

It's also available in the official F-Droid repo: https://f-droid.org/packages/com.roguetemple.hyperroid

I like hyperrogue but I think it is arguable that it is not very good as a roguelike; I like it more as a puzzle game. The thing is that in hyperrogue each of the worlds is almost entirely self-contained, and the choices you make in one world, or the order you go through the worlds, do not really impact the overall run in any major way. So it lacks the combinatorial explosion of possibilities that many good roguelikes (incl nethack) have.

Everybody understands that it's an opinion, it's a social convention, no need to spell it out. Just like people saying "broccoli are bad" doesn't need to be subtitled with "it's a matter of taste" or this dress looks ugly implies that it's a subjective take on aesthetics.

Nethavk is much much too baroque, a confusion of ideas and one-turn unavoidable deaths (well, avoidable if you know the secret handshake)[0]. It's like a cupcake recipe that has 40 ingredients and is dripping with extra stuff on top.

Brogue, on the other hand, is perfectly simple but perfectly well-executed, a five-ingredient recipe that lets every ingredient shine.

...Project Silverfish[0] is really entertaining so far...

[0]https://store.steampowered.com/app/2941710/Project_Silverfis...