SPACE, TIME 285 



absence of first and last points in the temporal series. Tech- 

 nically a series is infinite when, given any element, there is 

 available a principle by which another element may be 

 found. It is clear that the only argument for the infinity 

 of space and time is of the rational type similar to that 

 employed a moment ago when space and time were shown 

 to be without gaps. It is obviously impossible to ask "When 

 did time begin?" or "Where does space end?" since the 

 very use of the words 'when" and ' where " implies a 

 temporal and spatial background. Thus the question, 

 "When did time begin?' means "At what instant in (an- 

 other) time did time begin?" and the question, "Where does 

 space end?" means "At what point in (another) space does 

 space end?" 



Homogeneity. To assert that space and time are, respec- 

 tively, homogeneous is to say simply that they are every- 

 where alike. No point in space, and no instant in time bears 

 any qualitative feature by virtue of which the general en- 

 vironment of space or of time from which it has been selected 

 could be ascertained. Space and time do not exhibit any 

 hummocks or irregularities, any compressions or expansions, 

 any twis tings or deformations. A mile selected from the 

 line joining Chicago and New York would be indistinguish- 

 able from a mile selected from the line joining Paris and 

 London; a ten-minute section drawn from the hours of the 

 morning would be indistinguishable from a ten-minute sec- 

 tion drawn from the afternoon. Neither the 'here'' nor 

 the "now" is unique; no physical law describing the change 

 in state of a system prescribes the time of day or the time 

 of year when the law holds. The equations of the pendulum, 

 for example, "c/o not contain t explicitly. The state of the 

 system varies at any stage in a way dependent only on the 

 instantaneous state itself, but not on the date of this state, 

 not on the indication of the clock." 1 "Now" points and 

 "here" points are determined by observers; but observers 

 are of no importance so far as abstract time and space are 



1 L. Silberstein, Causality (New York: Macmillan, 1933), p. 129. 



