Let us consider a circular disc rotating with a uniform peripheral speed. According to the deductions from the "special theory" of relativity, an observer situated near the edge of this disc, but not rotating with it, will observe that units of length measured along the circumference of the disc are contracted. On the other hand, measurements along the diameter, which is at right angles to the direction of motion of the circumference, will show no contraction whatever, and, consequently the observer will find that the ratio of circumference to diameter has not the well known value 3.14159 ... but exceeds this value, the difference being greater and greater as the peripheral speed approaches that of light. That is, the laws of ordinary geometry no longer hold true. However, we know other cases in which the ordinary or Euclidean geometry is not applicable. Thus suppose that on the surface of a sphere we describe a series of concentric circles. Since the surface is curved, we are not surprised at finding that the circumference of any one of these circles is less than 3.14159 ... times the distance across the circle as measured on the surface of the sphere. What this means, therefore, is that we cannot use Euclidean geometry to describe measurements on the surface of a sphere, and every schoolboy knows this from comparing Mercator's projection of the earth's surface with the actual representation on a globe. When we come to think of it, the reason we realize all this is because our sense of three dimensions enables us to differentiate flat surfaces from those that are curved. Let us, however, imagine a two-dimensional being living on the surface of a large sphere. So long as his measurements are confined to relatively small areas he will find it possible to describe all his measurements in terms of Euclidean geometry. As, however, his area of operation increases he will begin to observe greater and greater discrepancies. Being unfamiliar with the existence of such a three-dimensional object as a sphere, and therefore not realizing that he is on the surface of one, our intelligent two-dimensional being will conclude that the disturbance in his geometry is due to the action of a force, and by means of plausible assumptions on the "law" of this force he will reconcile his observations with the laws of plane geometry.