THE RELATIVITY OF SPACE. 113 



tions of ideas, would be sufficient to give us a dif- 

 ferent distribution board, and that might be enough 

 to endow space with a fourth dimension. 



Some people will be astonished at such a result. 

 The exterior world, they think, must surely count 

 for something. If the number of dimensions comes 

 from the way in which we are made, there might 

 be thinking beings living in our world, but made 

 differently from us, who would think that space has 

 more or less than three dimensions. Has not M. 

 de Cyon said that Japanese mice, having only two 

 pairs of semicircular canals, think that space has 

 two dimensions ? Then will not this thinking being, 

 if he is capable of constructing a physical system, 

 make a system of two or four dimensions, which 

 yet, in a sense, will be the same as ours, since it will 

 be the description of the same world in another 

 language? 



It quite seems, indeed, that it would be possible to 

 translate our physics into the language of geometry 

 of four dimensions. Attempting such a translation 

 would be giving oneself a great deal of trouble for 

 little profit, and I will content myself with men- 

 tioning Hertz's mechanics, in which something of 

 the kind may be seen. Yet it seems that the 

 translation would always be less simple than the 

 text, and that it would never lose the appearance of 

 a translation, for the language of three dimensions 

 seems the best suited to the description of our 

 world, even though that description may be made, 

 in case of necessity, in another idiom. 



Besides, it is not by chance that our distribution 

 board has been formed. There is a connexion 



(1,"7) 8 



