Navigation without a fixed Northern point

I don't have a map of the world yet, but this question does not require a map to answer. The world is shaped like a big disk that is concave on each side (like you took two very shallow bowls and put them together). Areas closest to the rim are coldest, areas closest to the centers of the surface are warmest. So, not exactly realistic geology. One side of the disk is Thyressa, the other Thoros. At the moment, we are not worrying about Thoros right now, only Thyressa. Navigators need to be able to get from one area of Thyressa to another area of Thyressa. The center of the surface of Thyressa is South, the rim is North, clockwise is East, and counter-clockwise is West. A compass will point to the exact center of Thyressa's surface with one side, and the other in a straight line to the rim. Because the rim wraps around the entire disk that is the world, where in the rim the compass points to is dependent on the navigator's East/West orientation. There is no fixed Northern point, only a fixed Southern point. My problem is that I have no idea what that does to navigation. If we draw latitude and longitude lines all around the disk, with latitude being drawn as circles radiating out from the center and longitude as straight lines going from one end of the rim to the center, can a navigator figure out where they are with a map and compass? I honestly have no idea. I've never had to navigate by map and compass in the real world, much less some place with different rules.

Compass alone wouldn't be of any help. If there are stars in the sky, things become a lot easier. Even the sun might work for orientation during the day. How exactly that would be done would depend on how your disc moves through space and how the sun moves.

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Originally Posted by Yora

Compass alone wouldn't be of any help. If there are stars in the sky, things become a lot easier. Even the sun might work for orientation during the day. How exactly that would be done would depend on how your disc moves through space and how the sun moves.

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Hmm. I really should decide that now.

The sun and moon are stationary and exactly opposite of each other, Edit: Better idea. The sun is above Thyressa and is stationary, and the world tilts up and down as it spins like a top, so that any specific area of the world will be high relative to the sun as dawn breaks (meaning sun is low in the sky), low relative to the sun near noon (so sun is high in the sky), and back to higher relative to the sun as the afternoon turns into evening. So, the sun will move in an arc from East to West, but areas closer to the center of Thyressa have a noticeably smaller and shallower arc and the sun seems to be moving slower, and such areas receive much more direct sunlight. At night, the sun transforms into the moon, and the same cycle happens, though the moon changes shape through the month. Because the sun is above Thyressa, the central areas are warmer and the areas near the rim are colder. Of course, in order for that to keep the rim cold, the disk that is the world has to actually be bigger in terms of diameter than the sun/moon (Sun is spherical, moon starts as a sphere and contracts into a tiny crescent, then expands back outwards. This process can tell you the time of month accurately. The world has twelve months of thirty days long, and each season is exactly three months long.). I imagine that, given the distance, the sun is maybe half the diameter of the world. There are constellations, which do not move (though the world does, so they should appear to move across the sky). Seasons are caused by the fact that the world moves vertically up and down relative to the sun/moon throughout the year, getting colder as it gets further away, and at any given point in time the entirety of Thyressa is in the same season (The world has no orbit, and neither do the sun or moon. I'm going for a full blown fantasy planet, and the climatology and geology alone violate several scientific laws. Might as well violate some Astronomical laws, too.).

Then yes, you have a means of telling time and date, and combined with the constellations this tells you exactly which radial line you're on. The way in which the sun/moon seems to move can be used to work out how far along that radial to the edge you are.

Good star charts and records of how the world moves over time would be essential for accuracy but there might well be rules of thumb which could be used in less advanced civilisations.