ARE SPACE AND TIME INFINITE? 83 



greater than the distance of the furthest known nebulae. 

 But the boundlessness has nothing to do with the 

 bigness. Space is boundless by re-entrant form not by 

 great extension. That which is is a shell floating in the 

 infinitude of that which is not. We say with Hamlet, 

 "I could be bounded in a nutshell and count myself a 

 king of infinite space". 



But the nightmare of infinity still arises in regard to 

 time. The world is closed in its space dimensions like 

 a sphere, but it is open at both ends in the time dimen- 

 sion. There is a bending round by which East ulti- 

 mately becomes West, but no bending by which Before 

 ultimately becomes After. 



I am not sure that I am logical but I cannot feel the 

 difficulty of an infinite future time very seriously. The 

 difficulty about A.D. co will not happen until we reach 

 A.D. 00, and presumably in order to reach A.D. 00 the 

 difficulty must first have been surmounted. It should 

 also be noted that according to the second law of thermo- 

 dynamics the whole universe will reach thermodynamical 

 equilibrium at a not infinitely remote date in the future. 

 Time's arrow will then be lost altogether and the whole 

 conception of progress towards a future fades away. 



But the difficulty of an infinite past is appalling. It 

 is inconceivable that we are the heirs of an infinite time 

 of preparation; it is not less inconceivable that there was 

 once a moment with no moment preceding it. 



This dilemma of the beginning of time would worry 

 us more were it not shut out by another overwhelming 

 difficulty lying between us and the infinite past. We 

 have been studying the running-down of the universe; 

 if our views are right, somewhere between the beginning 

 of time and the present day we must place the winding 

 up of the universe. 



