THE VALUE OF SCIENCE 549 



that we have some means of recognizing that these two sensations, 

 qualitatively different, have something in common. Now, according 

 to the considerations expounded in the preceding paragraph, we have 

 been able to recognize this only by the movements of the eye and the 

 observations to which they have given rise. If the eye were immovable, 

 or if we were unconscious of its movements, we should not have been 

 able to recognize that these two sensations, of different quality, had 

 something in common ; we should not have been able to disengage from 

 them what gives them a geometric character. The visual sensations, 

 without the muscular sensations, would have nothing geometric, so that 

 it may be said there is no pure visual space. 



To do away with this difficulty, consider only sensations of the 

 same nature, red sensations for instance, differing one from another 

 only as regards the point of the retina that they affect. It is clear 

 that I have no reason for making such an arbitrary choice among all 

 the possible visual sensations, for the purpose of uniting in the same 

 class all the sensations of the same color, whatever may be the point 

 of the retina affected. I should never have dreamt of it, had I not 

 before learned, by the means we have just seen, to distinguish changes 

 of state from changes of position, that is, if my eye were immovable. 

 Two sensations of the same color affecting two different parts of the 

 retina would have appeared to me as qualitatively distinct, just as two 

 sensations of different color. 



In restricting myself to red sensations, I therefore impose upon 

 myself an artificial limitation and I neglect systematically one whole 

 side of the question; but it is only by this artifice that I am able to 

 analyze visual space without mingling any motor sensation. 



Imagine a line traced on the retina and dividing in two its surface ; 

 and set apart the red sensations affecting a point of this line, or those 

 differing from them too little to be distinguished from them. The 

 aggregate of these sensations will form a sort of cut that I shall call C, 

 and it is clear that this cut suffices to divide the manifold of possible 

 red sensations, and that if I take two red sensations affecting two points 

 situated on one side and the other of the line, I can not pass from one 

 of these sensations to the other in a continuous way without passing 

 at a certain moment through a sensation belonging to the cut. 



If, therefore, the cut has n dimensions, the total manifold of my 

 red sensations, or, if you wish, the whole visual space, will have n-\-l. 



Now, I distinguish the red sensations affecting a point of the cut C. 

 The assemblage of these sensations will form a new cut C. It is clear 

 that this will divide the cut C , always giving to the word divide the 

 same meaning. 



If, therefore, the cut C has n dimensions, the cut C will have 

 n -\- 1 and the whole of visual space n -f- 2. 



If all the red sensations affecting the same point of the retina were 



