Are you sure about this path metaphor? I've always thought of it as something hidden that was turned outward to reveal itself—but perhaps that's just me. As to your container, that's probably a more general way of describing something that encloses another thing? Because it makes me think of coming up out of water or earth or a heap of things, not an actual box (as per your "surface"). In an actual box, the typical movement is not
down <=> up but rather
in <=> out. Conceptual metaphors are interesting. —
Cerberus 3 mins ago