Let us first examine the problem from the standpoint of classical science. Consider an observer who walks away from a point on the surface of the earth. He finally comes to a stop after having walked a distance from the point . He turns round, looks back and sees a black line sticking up from the earth at the point , whence he started. The height of the line appears to him to have a certain magnitude; and in order to register this magnitude accurately, he measures with an instrument the precise visual angle under which he sees the black line. He then continues his journey, stops, turns round again and finds that the black line is now seen under a smaller visual angle, hence appears to him to be reduced in height. His first impulse would be to assume that the black line was due to some squirming mirage and, while a reality in so far as it affected his eyesight, yet could be endowed with no objective existence in any impersonal way. Yet, without even returning to the point and investigating the matter more closely, our observer could soon find out that the black line must be produced by some existent entity. He would make this discovery in the following way: By combining the visual angle under which the black line appeared to him with his distance from the point , he would find that wherever he stood, a certain mathematical expression (i.e., ) representative of a length maintained the same invariant value. Something truly objective would have been discovered since, in contrast to visual angle and distance which varied with his position, here was a length which was an absolute since its value transcended his position. He would immediately attribute this absolute to the objective existence of a real rigid pole of length standing at the point . In short, the test of objectivity is invariance for all observers, and this illustration has enabled us to separate the absolute length of the pole from the relative visual angle and distance . Classical science assumed that this test of objectivity would hold in all cases, regardless of whether our observers were stationary or in motion. The theory of relativity tells us that this is not so. The observer in relative motion would always perceive the pole under a smaller visual angle, so that the mathematical expression purporting to give the length of the pole would no longer be an invariant.[71] Under the circumstances we should again be thrown back on the perplexing problem of whether there could exist any kind of universal objectivity holding for all observers in this universe. [Pg 223]