ABSTRACT
The Euclidean group has practical as well as formal virtues. It is the natural group for men to adopt who are mobile agents, who see things from different points of view, and move them around from one position to another. A very different, more specific, approach depends on the independence of our concepts of shape and size. Elliptical and hyperbolic geometries, although consistent and possessed of many merits, have the demerit of linking the concept of shape with that of size in such a way that we cannot have two figures of the same shape but different sizes. We may argue that it is a necessary condition of our being able to apply the concept 'same shape though different size' that our geometry should be Euclidean. A Euclidean geometry has no natural unit either of area or of length, and therefore is less committing, and constitutes a better conceptual framework, just because it forecloses the answers to fewer physical questions.
