THE VALUE OF SCIENCE 



79 



I B R t 





THE VALUE OF SCIENCE 



By M. H. POINCARE 



MEMBER OF THE INSTITUTE OF FRANCE 



§ 3. Tactile Space 

 1 1 THUS I know how to recognize the identity of two points, the point 

 -*- occupied by A at the instant a and the point occupied by B at the 

 instant /?, but only on one condition, namely, that I have not budged 

 between the instants a and /?. That does not suffice for our object. 

 Suppose, therefore, that I have moved in any manner in the interval 

 between these two instants, how shall I know whether the point oc- 

 cupied by A at the instant a is identical with the point occupied by B 

 at the instant (3? I suppose that at the instant a, the object A was in 

 contact with my first finger and that in the same way, at the instant /?, 

 the object B touches this first finger; but at the same time, my muscular 

 sense has told me that in the interval my body has moved. I have 

 considered above two series of muscular sensations S and S', and I have 

 said it sometimes happens that we are led to consider two such series 

 S and S' as inverse one of the other, because we have often observed that 

 when these two series succeed one another our primitive impressions 

 are reestablished. 



If then my muscular sense tells me that I have moved between the 

 two instants a and /?, but so as to feel successively the two series of 

 muscular sensations S and S' that I consider inverses, I shall still con- 

 clude, just as if I had not budged, that the points occupied by A at 

 the instant a and by B at the instant /? are identical, if I ascertain that 

 my first finger touches A at the instant a and B at the instant /?. 



This solution is not yet completely satisfactory, as one will see. 

 Let us see, in fact, how many dimensions it would make us attribute to 

 space. I wish to compare the two points occupied by A and B at the 

 instants a and /?, or (what amounts to the same thing since I suppose 

 that my finger touches A at the instant a and B at the instant /?) I 

 wish to compare the two points occupied by my finger at the two 

 instants a and /?. The sole means I use for this comparison is the 

 series 2 of muscular sensations which have accompanied the movements 

 of my body between these two instants. The different imaginable 

 series 2 form evidently a physical continuum of which the number of 

 dimensions is very great. Let us agree, as I have done, not to consider 

 as distinct the two series 2 and 2 -f- s -f- s', when s and s' are inverses 

 one of the other in the sense above given to this word; in spite of this 



