222 ANNUAL, REPORT SMITHSONIAN INSTITUTION. 19 38 



no physical existence that we know of can escape. All that is per- 

 fectly conceivable; and I am not, of course, concerned with whether 

 it is true or not, any more than I was concerned earlier with the truth 

 of the statement that the velocity of light is finite; that is a matter 

 for experiment, and my purpose is served if I can show that the 

 idea of finite boundlessness could be true without violation of ordinary 

 notions. 



Figure l.— Model of finite universe. 

 From "Through Science to Philosophy." By H. Dingle. 



[Courtesy of the Clarendon Press, Oxford] 



We picture, then, a finite universe from which we cannot escape. 

 The next point is that it is impossible for us to know whether we are 

 at its center or its boundary ; in either case we appear to be surrounded 

 by stars on all sides. Obviously an observer at the center (or at A) 

 sees stars all round, but so does an observer at B, for the light of the 

 stars inside is bent, so that he sees then whichever way he looks. 

 The light of a star at S, for example, is bent so that the star appears 

 to be at S 1 . This is a very ordinary phenomenon, exemplified every 

 time we look at a mirror; an object appears in the direction of the 



