, and then after going half round we come to an exactly similar group
indistinguishable by any test; another half circle again brings us to an exactly similar group, which, however, we decide is the original group
. 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 conclusion that this happened when we reached
; everything 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 “spherical”. But which is the real truth? Disregard the fact that I introduced
and