The authors found, over the years of research that, characterizing the geometry of the spatial arrangements of object that could be described as in, on, or over is by no means a simple task. Over the course of the project the authors came to the conclusion that it is only possible to make sure of the semantics of spatial prepositions in terms of the relationship between the three activities in the title of the book: saying, seeing, and acting. The functional geometric framework we outline provides just such an account.