If youve been next to a port lately, or just strolled down a beach and stared off vacantly into the horizon, you might have, perhaps, noticed a very interesting phenomenon: approaching ships do not just appear out of the horizon (like they should have if the world was flat), but rather emerge from beneath the sea.
But you say ships do not submerge and rise up again as they approach our view (except in Pirates of the Caribbean, but we are hereby assuming that was a fictitious movie). The reason ships appear as if they emerge from the waves is because the world is not flat.