ABSTRACT
THE concept of the straight line results from the child's first attempts to relate objects spatially in a system of projective viewpoints or co-ordinates. Strictly speaking, the topological idea of ‘a line’ does not include the ‘straight line’ at all. To transform an ordinary line, the only kind of line recognized by topology, into a straight line requires the introduction, either of a system of viewpoints such as the elements of a line masking each other to form a perspective, or else a system of displacements, distances and measurements. Drawing or imagining a straight line therefore presupposes a projective or euclidean space, so that in actual practice such a notion is far from elementary, whatever may be the opinions expressed in textbooks of geometry. However, this is not very important since their authors are as ignorant of psychogenetics as they are of the logical foundations of their own subject.
