The radical axis, as the only straight line in a pencil of circles, brakes the continuity in the infinite succession of the circles. In the same way, in space, the radical plane is an "intruder" in a pencil of spheres which brakes the infinite succession of the spheres. Therefore, in order to realize the continuity principle in pencils of circles and spheres, we must leave those classical concepts of straight lines and planes as something quite different from circles and spheres, and introduce the new, relativistic, concepts of "straight lines" and "planes" which also are real circles and spheres but with a particular relation to the observer.