Is your world round? Do the PCs know it.

Psion,
My cosmology is very similar to yours. We were both impressed by a lot of the same ideas in Portals and Planes.

I think my Players are sure the world is round. None of them has given any indication that they suspect otherwise. Despite repeated clues. The general consensus for the population in the game world is that the world must be flat, because everyone that has sailed off in one direction has disappeared. Flat with monsters.

the earth is round, and there are other inhabitable planets in the prime matirial plane.
not many know this, and nither do the pcs.

Hi!

I'm DM of a Planescape-Campaign so its all about planes, not worlds.

Kodam

I put "other." I run a game set in fellow ENWorld poster Vrylakos' campaign world, known as the Shards. The world is comprised of numerous shards of rock, some as small as a small island while others the size of large continents, floating in a seemingly-endless sea of air. High above these shards is the Solar Hearth, or sun, where the gods dwell. The Hearth brightens and dims on a regular schedule, creating day and night. Far below all of the shards is a void called the Beneath, which is entropy incarnate. It is the source of gravity in this world. The various races of the world travel between shards via airship, flying mounts, or other magic.

I keep it simple, round and cheese-holed.

orsal said:

Right. But if you go east, you'll still be going east, and you'll come back to where you started while your direction will have remained east the whole time.

On a torus, the north-south axis would behave this way too, as well as the east-west axis.

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Nah, you can't have both, even with a torus.

OK, I see where the confusion came from. In my original description of the torus, I wrote that it can't have absolute north and south, when what I really meant was that I wanted it not to have absolute north and south.

Umbran said:

About definitions - you may say that the person going north/south never changes direction, because he never really reaches the pole (he cannot, because the axis doesn't actually intersect the surface of the object).

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The way I'm setting up co-ordinates, there *are* no poles, for the same reason that there is no East Pole or West Pole on the earth.

I'm just thinking of a rectangle with wrap-around on both pairs of opposite edges. Directions are inherited from the directions in the plane of the rectangle. If you go north until you hit the north edge of the rectangle, suddenly you're on the south edge and continuing to go north.

Umbran said:

One can just as easily define a singularity line on the torus - lie a plane on top of the donut, the torus/plane intersection will be a line, a circle along the top of the torus. That can be your "pole", and where you chnage from going north to south.

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You could, but I have no wish to do that.

The existence of a north pole and a south pole on the earth are due not to the shape of the earth itself (for, if we take a little license to pretend it's a perfect sphere there is no way to distinguish any point from any other), but rather from certain astronomical phenomena, most notably the motion of the sun around the earth. The same phenomena determine east and west as directions but not as poles. I was thinking of doing something similar with all cardinal directions on my torus-world.

Of course, it is also possible to have a torus with a distinguished circle instead of a distinguished point, and use it to define north and south as absolute directions. For that matter, it would also be possible to have a torus with two distinguished perpendicular circles and thus get all four cardinal directions as absolute directions. But neither of those is how I was thinking of doing it.

This torus-world talk has me wondering what the sky-view would look like. Would you plot such a thing in a normal universe with a sun that it revolves around, etc, or do something different? What would that do to the weather? Would you have the torus rotate along an oblique axis to the inside of the torus gets some sunlight? What would the effects of gravitation and centrifugal force be like? Or would you concern yourself with such real world physics at all?

(To make my bubble worlds worked, I assumed that the "sun" at the center of the bubbles were a repulsive force. Otherwise, the effects of gravity on the inside of a sphere sums out to zero.)

That's an interesting question. I'd assume that the "North Line" (actually a circle, but would be perceived as a line) and the "South Line" on a torus would be the separator between the "Inside" (where you can see the rest of the Torus in the sky) and the "Outside (where you don't). If you're on the outside, and walk north, eventually you'll reach a place where you can see the rest of the Torus on the horizon, and then you would know you are on the Line.

I assume that because, on Earth, the North/South axis is actually the rotation axis (to simplify a bit, because there's geographical and magnetical Norths, and they aren't the same). The most intuitive rotation axis of a torus is in its hollow middle.

Like this ring:


It could also have a rotation axis that pass through the torus itself, like this other ring:


In which cases you would have indeed a North Pole and a South Pole.

Simulating the "videogame" world (with poles at all, be they dots, lines, or circles) is, IMHO, not possible with Euclidian geometry.

And interesting prospect of a Torus is gravity. If gravity is stronger than the "centrifugal force" (that is, the effect created by inertia and rotation) on the Torus, then you can only live on the Outside. In the Inside, you would plummet toward the hollow core. If the gravity is weaker, then it's the reverse -- you can only live on the Inside, on the Outside you would be yanked in outer space for all eternity.

So, let's say you have some sort of magical force thingy that make sure people can live anywhere on the Torus without being sucked outside. It would help explaining why there is still an atmosphere, anyway (unless there is no void, but just an endless Plane of Air -- that's an interesting concept).

Then you could have, because of gravity/inertia, one side that has a weaker Gravity trait than the other. Let say inertia's the boss; then you would have a high gravity Inside and a low gravity Outside.

Yes, it's round. Some of the educated probably know, but to the vast majority of people it doesn't matter, and thus the world is (to them) as it appears - mostly flat.

However, if it every came up, they could probably figure out that it was round without a lot of work.