114 SCIENCE AND METHOD. 



between the alarm Ai and the parry Bi, that is, a 

 property residing in our intelh'gence. But why is 

 there this connexion? It is because the parry Bi 

 enables us effectively to defend ourselves against the 

 danger Ai, and that is a fact exterior to us, a 

 property of the exterior world. Our distribution 

 board, then, is only the translation of an assemblage 

 of exterior facts ; if it has three dimensions, it is 

 because it has adapted itself to a world having 

 certain properties, and the most important of these 

 properties is that there exist natural solids which 

 are clearly displaced in accordance with the laws 

 we call laws of motion of unvarying solids. If, then, 

 the language of three dimensions is that which 

 enables us most easily to describe our world, we 

 must not be surprised. This language is founded 

 on our distribution board, and it is in order to 

 enable us to live in this world that this board has 

 been established. 



I have said that we could conceive of thinking 

 beings, living in our world, whose distribution board 

 would have four dimensions, who would, consequently, 

 think in hyperspace. It is not certain, however, that 

 such beings, admitting that they were born, would 

 be able to live and defend themselves against the 

 thousand dangers by which they would be assailed. 



VI. 



A few remarks in conclusion. There is a striking 

 contrast between the roughness of this primitive 

 geometry which is reduced to what I call a distribu- 

 tion board, and the infinite precision of the geometry 

 of geometricians. And yet the latter is the child of 



