“Let it have been drawn”: the role of diagrams in geometry http://intellectualmathematics.com/blog/let-it-have-been-drawn-the-role-of-diagrams-in-geometry/ podcast and transcript (part of a series on Greek geometry) talks about how important actually drawing diagrams likely was for the ancient Greeks. The author Viktor Blåsjö suggests an "operationalist" interpretation: that rigorous procedures for drawing things are how you establish facts, not the abstract logic by itself.

(mumble, mumble, "embodied cognition", mumble, mumble)