SPACE AND GEOMETRY 31 



beads to form a wall. But now the individual ; 



blocks are not trapped ; two blocks may be slid : 



about so that they exchange places. If two ends 

 of the wall are brought together then a block 

 may be trapped inside the wall. It cannot escape 

 by sliding, without breaking through the wall 

 itself. If you lift the block over the wall the 

 child cries, "That is not fair," for he is playing 

 the game of two-dimensional space. Finally, if i 



the blocks are nailed together to form a closed 

 box, then one block left inside the box is com- ! 



pletely trapped and neither you nor the child I 



can find any way of getting it out without 

 breaking the box. It is such facts that lead to i 



the idea that space is limited to three dimen- 

 sions, i 



Let us glance for an instant at the problem 

 of empty space. We pour water out of a jug, I 



but if we say that the jug is then empty it is 

 because we have forgotten that the water has 

 been replaced by air. But the air, in its turn, ] 



may be withdrawn by means of a pump, and 

 though we cannot obtain a perfect vacuum we 

 are coming nearer to it year by year. In any i 



case we can imagine the air all withdrawn. Some I 



years ago it would have been said that there still j 



remains the ether, but this, as we shall see in the j 



