670 



would behave as non-Euclidean solids. We might have two double 

 pyramids oabcdefgh and o a V c <f e' f g h', and two triangles a ft y 

 and a ft' y. The first double pyramid would be rectilinear, and the 

 second curvilinear. The triangle afty would consist of undilatable 

 matter, and the other of very dilatable matter. We might therefore 

 make our first observations with the double pyramid o' a h' and the 

 triangle a ft' y. 



And then the experiment would seem to show first, that Eucli- 

 dean geometry is true, and then that it is false. Hence, experiments 

 have reference not to space but to bodies. 



8. To round the matter off, I ought to speak of a very delicate 

 question, which will require considerable development; but I shall 

 confine myself to summing up what I have written in the Revue de 

 Metaphysique et de Morale and in the Monist. When we say that 

 space has three dimensions, what do we mean? We have seen the im- 

 portance of these " internal changes " which are revealed to us by 

 our muscular sensations. They may serve to characterize the different 

 attitudes of our body. Let us take arbitrarily as our origin one of 

 these attitudes, A. When we pass from this initial attitude to another 

 attitude B we experience a series of muscular sensations, and this series 

 S of muscular sensations will define B. Observe, however, that we 

 shall often look upon two series S and S' as defining the same attitude 

 B (since the initial and final attitudes A and B remaining the same, 

 the intermediary attitudes of the corresponding sensations may differ). 

 How then can we recognize the equivalence of these two series? Be- 

 cause they may serve to compensate for the same external change, or 

 more generally, because when it is a question of compen- 

 sation for an external change, one of the series may be replaced 

 by the other. Among these series we have distinguished those which 

 can alone compensate for an external change, and which we have 

 called " displacements." As we cannot distinguish two displacements 

 which are very close together, the aggregate of these displacements 

 presents the characteristics of a physical continuum. Experience 

 teaches us that they are the characteristics of a physical continuum of 

 six dimensions; but we do not know as yet how many dimensions 

 space itself possesses, so we must first of all answer another question. 

 What is a point in space ? Every one thinks he knows, but that is an 

 illusion. What we see when we try to represent to ourselves a point 

 in space is a black spot on white paper, a spot of chalk on a blackboard, 

 always an object. The question should therefore be understood as 

 follows : What do I mean when I say the object B is at the point 

 which a moment before was occupied by the object A? Again, what 

 criterion will enable me to recognize it ? I mean that although I have 

 not moved (my muscular sense tells me this), my finger, which just 

 now touched the object A, is now touching the object B. I might have 



