How does navigation work on a flat world? Admittedly this is not a question that comes up outside flat earth societies, at least not in the real world, but fantasy worlds aren’t always spherical. Tolkien’s Middle-earth, for example, started off as a flat world, but became round during a cataclysmic event. Before that, the Númenóreans (Aragorn’s ancestors, for those not totally up on their Tolkien lore) were held to be the greatest seafarers in the world: “mariners whose like shall never be again since the world was diminished,” as The Silmarillion puts it. The problem is, a flat earth has implications for navigation: many known methods simply wouldn’t work.

In a piece I wrote for Tor.com, “The Dúnedain and the Deep Blue Sea: On Númenórean Navigation,” I try to puzzle out how they could have navigated the oceans of a flat world. I come up with a solution or two, within the limitations of my math abilities. (I’m sure readers who have more math than I do will be able to come up with something better.) It assumes a certain familiarity with Tolkien’s works, and it draws rather heavily on John Edward Huth’s Lost Art of Finding Our Way, which I reviewed here, not at all coincidentally, last month.