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 gravitation; 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 indistinguishable by any possible experimental test. Starting on a journey round the spherical world we come across a group , 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 [Pg 290] the real truth? Disregard the fact that I introduced and to you as though they were not the same particles, because that begs the question; imagine that you have actually had this adventure in a world you had not been told about. You cannot find out the answer. Can you conceive what the question means? I cannot. All that turns on the answer is whether we shall provide two separate haloes for and or whether one will suffice. Descriptions of the phenomena of atomic physics have an extraordinary vividness. We see the atoms with their girdles of circulating electrons darting hither and thither, colliding and rebounding. Free electrons torn from the girdles hurry away a hundred times faster, curving sharply round the atoms with side slips and hairbreadth escapes. The truants are caught and attached to the girdles and the escaping energy shakes the aether into vibration. X-rays impinge on the atoms and toss the electrons into higher orbits. We see these electrons falling back again, sometimes by steps, sometimes with a rush, caught in a cul-de-sac of metastability, hesitating before “forbidden passages”. Behind it all the quantum regulates each change with mathematical precision. This is the sort of picture that appeals to our understanding—no insubstantial pageant to fade like a dream.