SPACE AND TIME 



/ J 



tinuous boundary between the open page of this book and 

 the air above it ? Would it be possible to say at any 

 distinct step of the passage from air to paper, here air 

 ends and paper begins ? At this point we reach one of 

 the most important problems of science. Are we to 

 consider the groups of sense-impressions which we term 

 bodies continuous or not? If bodies are not continuous, 

 then it is clear that boundaries are only mental symbols 

 of separation, and on deeper analysis correspond to no 

 exact reality in the sphere of sense-impression. 



Would every element of the surface of a body still 

 appear to us a continuous boundary, however small the 

 element and however much we magnified it up ? If I 

 could take the hundredth part of a square inch of this 

 page and magnify it to a billion times its present size, 

 would there still appear a continuous boundary between 

 air and paper ? 



Consider the boundary of still water. It furnishes us 

 with the impression of a continuous surface. On the 

 other hand, examine a heap of sand closely, and it 

 appears to have no continuous boundary at all. Are 

 there any reasons which would lead us to suppose that, if 

 we could sufficiently magnify a small element of this page 

 of paper, it would produce in us sense-impressions not of 

 continuity but of discontinuity ? Would it look, sup- 

 posing it were still visible, like the surface of water, or 

 rather like a heap of sand, a pile of small shot, or, better 

 still, like a starry patch of the heavens on a clear night ? 

 No group of stars is in perception separated from another 

 by a line or surface. We can imagine such boundaries 

 drawn across the heavens, but we do not perceive them. 



of tlie sea, the surface of a sheet of paper. Although in some cases the idea 

 of the thickness or the depth of the thing spoken of may be present in the 

 speaker's mind, yet as a rule no stress is laid on depth or thickness. Wlien 

 we speak of a geometrical surface., we put aside the idea of depth and thickness 

 altogether" (H. M. Taylor, /'/// Press Euclid, i.-ii. p. 3). It seems to me 

 that in ordinary language there is something more than lengtli and breadtli 

 involved — there is an idea of coiitiinious boundary. It is difficult to say how 

 far this idea is really involved in the word extension. A veil may have 

 extension in two directions, but it fails to fulfil our idea of surface because it 

 is not a continuous boundary. 



