Grounding Three-Dimensionality in Motion

Abstract

It is not known who first came up with the idea of trying to deduce three-dimensionality from a discussion of the motions of bodies or of geometrical figures. It is rather improbable that the beginnings of such an idea go back to ancient geometry where on one hand, as mentioned above, the three-dimensionality of spatial forms was taken for granted but, on the other hand, it was accepted by way of proof in plane geometry to flip a figure out of the plane in order to bring it to cover a mirror-congruent figure. In the first place, there was (as witnessed by the above-mentioned definitions of Euclid) obviously no need, apart from the spatial distinction of length, breadth, and height, for an explanation of three-dimensionality. Second, according to the ancient view, the concept of motion belonged in physics. Mathematics was, in contrast, the science of temporal immutables.