THE RELATIVITY OF SPACE. 115 



the former, but not of it alone ; it required to be 

 fertilized by the faculty we have of constructing 

 mathematical concepts, such, for instance, as that of 

 the group. It was necessary to find among these 

 pure concepts the one that was best adapted to 

 this rough space, whose genesis I have tried to 

 explain in the preceding pages, the space which is 

 common to us and the higher animals. 



The evidence of certain geometrical postulates is 

 only, as I have said, our unwillingness to give up 

 very old habits. But these postulates are infinitely 

 precise, while the habits have about them some- 

 thing essentially fluid. As soon as we wish to think, 

 we are bound to have infinitely precise postulates, 

 since this is the only means of avoiding contradic- 

 tion. But among all the possible systems of postu- 

 lates, there are some that we shall be unwilling to 

 choose, because they do not accord sufficiently with 

 our habits. However fluid and elastic these may be, 

 they have a limit of elasticity. 



It will be seen that though geometry is not an 

 experimental science, it is a science born in con- 

 nexion with experience ; that we have created the 

 space it studies, but adapting it to the world in 

 which we live. We have chosen the most con- 

 venient space, but experience guided our choice. 

 As the choice was unconscious, it appears to be 

 imposed upon us. Some say that it is imposed by 

 experience, and others that we are born with our 

 space ready-made. After the preceding considera- 

 tions, it will be seen what proportion of truth and 

 of error there is in these two opinions. 



In this progressive education which has resulted 



