From the comparatively simple example of two systems rotating relatively to one another, Einstein shows that the peripheral measurement of a rotating circle, as viewed from the other system, exhibits a peculiarity which does not accompany the radial measurement. For, according to the theory of relativity, the length of a measuring rod is to be regarded as being dependent on its orientation. In the case quoted, the rod undergoes a relative contraction only when applied along the circumference, so that we count more steps than when we measure the circumference of the same circle at rest, that is, in non-rotation. Since the radius remains constant in each case, we get a relatively greater value for π, which shows that we are no longer using Euclidean geometry. Yet, formerly, before such considerations could even be conceived in dreams, this π was regarded as absolutely established and immutable; and observers used every possible means of determining its value as accurately as possible. In Byzantium there lived during the eleventh and twelfth centuries a learned scholar, Michael Psellus, whose fame as the "Foremost of Philosophers" stretched far and wide, and whose mathematical researches were regarded as worthy of great admiration. This grand master had discovered by analytical and synthetical means that a circle is to be regarded as the geometric mean between the circumscribed and the inscribed square, which gives to the above quantity, as may easily be calculated, the value √8, that is, 2.8284271.... In other words, the length of the circumference is not even three times that of the radius. We have the choice of regarding the result of Psellus as an approximation, or as mere nonsense. Every schoolboy who, in a spirit of fun, measures a circular object, say a top, with a piece of string, arrives at a better result, but the contemporaries of Psellus accepted this entirely wrong figure with credulous reverence, and continued to burn incense at the feet of the famous master. It is all very well for us of the present to call him a donkey. We have just as much right in saying that mathematicians differ, not in their natures, but only in the order of their brain functions. If a man like Psellus missed the mark by so much, it is possible that men like Fermat or Lagrange may also have erred occasionally or even consistently. No heavenly power will give us a definite assurance to the contrary, and all of us may be just as false in our judgment of accepted celebrities as were the Byzantines eight hundred years ago in their estimate of Psellus.