THE VALUE OF SCIENCE 545 



THE VALUE OF SCIENCE 



By M. H. POINCARE 



MKMBEK OF THE INSTITUTE OF FRANCE 



5. The Notion of Displacement 



HAA 7 E shown in ' Science and Hypothesis ' the preponderant role 

 -"- played by the movements of our body in the genesis of the notion 

 of space. For a being completely immovable there would be neither 

 space nor geometry; in vain would exterior objects be displaced about 

 him, the variations which these displacements would make in his im- 

 pressions would not be attributed by this being to changes of position, 

 but to simple changes of state; this being would have no means of 

 distinguishing these two sorts of changes, and this distinction, funda- 

 mental for us, would have no meaning for him. 



The movements that we impress upon our members have as effect 

 the varying of the impressions produced on our senses by external 

 objects; other causes may likewise make them vary; but we are led to 

 distinguish the changes produced by our own motions and we easily 

 discriminate them for two reasons : ( 1 ) because they are voluntary ; 

 (2) because they are accompanied by muscular sensations. 



So we naturally divide the changes that our impressions may under- 

 go into two categories to which perhaps I have given an inappropriate 

 designation : ( 1 ) the internal changes, which are voluntary and accom- 

 panied by muscular sensations; (2) the external changes, having the 

 opposite characteristics. 



We then observe that among the external changes are some which 

 can be corrected, thanks to an internal change which brings everything 

 back to the primitive state; others can not be corrected in this way 

 (it is thus that when an exterior object is displaced, we may then by 

 changing our own position replace ourselves as regards this object in 

 the same relative position as before, so as to reestablish the original 

 aggregate of impressions ; if this object was not displaced, but changed 

 its state, that is impossible). Thence comes a new distinction among 

 external changes: those which may be so corrected we call changes of 

 position; and the others, changes of state. 



Think, for example, of a sphere with one hemisphere blue and the 

 other red ; it first presents to us the blue hemisphere, then it so revolves 

 as to present the red hemisphere. Now think of a spherical vase con- 

 taining a blue liquid which becomes red in consequence of a chemical 

 reaction. In both cases the sensation of red has replaced that of blue; 

 our senses have experienced the same impressions which have succeeded 



