TEE VALUE OF SCIENCE . 87 



ically subsequent to space, since we can represent it to ourselves only 

 under the form of a straight line; as well say that time is logically 

 subsequent to the cultivation of the prairies, since it is usually repre- 

 sented armed with a scythe. That one can not represent to himself 

 simultaneously the different parts of time, goes without saying, since 

 the essential character of these parts is precisely not to be simultaneous. 

 That does not mean that we have not the intuition of time. So far as 

 that goes, no more should we have that of space, because neither can 

 we represent it, in the proper sense of the word, for the reasons 1 have 

 mentioned. What we represent to ourselves under the name of straight 

 is a crude image which as ill resembles the geometric straight as it 

 does time itself. 



Why has it been said that every attempt to give a fourth dimension 

 to space always carries this one back to one of the other three? It is 

 easy to understand. Consider our muscular sensations and the ' series ' 

 they may form. In consequence of numerous experiences, the ideas 

 of these series are associated together in a very complex woof, our 

 series are classed. Allow me, for convenience of language, to express 

 my thought in a way altogether crude and even inexact by saying that 

 our series of muscular sensations are classed in three classes correspond- 

 ing to the three dimensions of space. Of course this classification is 

 much more complicated than that, but that will suffice to make my 

 reasoning understood. If I wish to imagine a fourth dimension, I 

 shall suppose another series of muscular sensations, making part of a 

 fourth class. But as all my muscular sensations have already been 

 classed in one of the three preexistent classes, I can only represent to 

 myself a series belonging to one of these three classes, so that my fourth 

 dimension is carried back to one of the other three. 



What does that prove ? This : that it would have been necessary 

 first to destroy the old classification and replace it by a new one in 

 which the series of muscular sensations should have been distributed 

 into four classes. The difficulty would have disappeared. 



It is presented sometimes under a more striking form. Suppose I 

 am enclosed in a chamber between the six impassable boundaries formed 

 by the four walls, the floor and the ceiling; it will be impossible for me 

 to get out and to imagine my getting out. Pardon, can you not 

 imagine that the door opens, or that two of these walls separate ? But 

 of course, you answer, one must suppose that these walls remain im- 

 movable. Yes, but it is evident that I have the right to move; and 

 then the walls that we suppose absolutely at rest will be in motion 

 with regard to me. Yes, but such a relative motion can not be any- 

 thing; when objects are at rest, their relative motion with regard to 

 any axes is that of a rigid solid; now, the apparent motions that you 

 imagine are not in conformity with the laws of motion of a rigid solid. 



