PHYSICAL ILLUSTRATIONS 289 



plane, are just as much facing the hard facts of experi- 

 ence as those who start from consciousness as a device 

 for reading the indications of spectroscopes and micro- 

 meters. 



Physical Illustrations. If the reader is unconvinced that 

 there can be anything indefinite in the question whether 

 a thing exists or not, let him glance at the following 

 problem. Consider a distribution of matter in Einstein's 

 spherical "finite but unbounded" space. Suppose that 

 the matter is so arranged that every particle has an 

 exactly similar particle at its antipodes. (There is some 

 reason to believe that the matter would necessarily have 

 this arrangement in consequence of the law of gravita- 

 tion; but this is not certain.) Each group of particles 

 will therefore be exactly like the antipodal group not 

 only in its structure and configuration but in its entire 

 surroundings; the two groups will in fact be indis- 

 tinguishable by any possible experimental test. Starting 

 on a journey round the spherical world we come across 

 a group A, and then after going half round we come to 

 an exactly similar group A' indistinguishable by any 

 test; another half circle again brings us to an exactly 

 similar group, which, however, we decide is the original 

 group A. Now let us ponder a little. We realise that 

 in any case by going on far enough we come back to the 

 same group. Why do we not accept the obvious con- 

 clusion that this happened when we reached A'; every- 

 thing was exactly as though we had reached the starting- 

 point again? We have encountered a succession of 

 precisely similar phenomena but for some arbitrary 

 reason have decided that only the alternate ones are 

 really the same. There is no difficulty in identifying all 

 of them; in that case the space is "elliptical" instead of 



