The Maya imagined both the visible and the conceptual in three-dimensional form. Thus their painters had to represent the third dimension on flat surfaces. Seven ways of showing solid form were invented: combined front and profile views, overlapping, foreshortening, “half-view,” variations in line weight, arbitrary shading, and detached contour lines. Two ways of showing spatial depth were invented: overlapping and raising the level in the composition. Pottery painters never attained perfect command of space representation. Representation of space and form in art is a product of the same kind of speculation and experimentation which produces geometry and philosophical conceptions of space. The Maya lacked the conception of dimensions and never formulated the relationship between even length and width. This restricted their arts; in painting, for example, representations of space and form could not be formulated but had to be reinvented each time they were used.