THE RELATIVITY OF SPACE. 99 



I mean to say that the former will be for its inhab- 

 itants what the second is for its own. This would 

 be true so long as the two universes remained foreign 

 to one another. Suppose we are inhabitants of the 

 universe A ; we have constructed our science and 

 particularly our geometry. During this time the in- 

 habitants of the universe B have constructed a science, 

 and as their world is the image of ours, their geometry 

 will also be the image of ours, or, more accurately, 

 it will be the same. But if one day a window were to 

 open for us upon the universe B, we should feel 

 contempt for them, and we should say, " These 

 wretched people imagine that they have made a 

 geometry, but what they so name is only a grotesque 

 image of ours ; their straight lines are all twisted, 

 their circles are hunchbacked, and their spheres have 

 capricious inequalities." We should have no suspicion 

 that they were saying the same of us, and that no 

 one will ever know which is right. 



We see in how large a sense we must understand 

 the relativity of space. Space is in reality amorphous, 

 and it is only the things that are in it that give it 

 a form. What are we to think, then, of that direct 

 intuition we have of a straight line or of distance ? 

 We have .so little the intuition of distance in itself 

 that, in a single night, as we have said, a distance 

 could become a thousand times greater without our 

 being able to perceive it, if all other distances had 

 undergone the same alteration. And in a night the 

 universe B might even be substituted for the universe 

 A without our having any means of knowing it, and 

 then the straight lines of yesterday would have ceased 

 to be straight, and we should not be aware of anything. 



