34 CREATIVE EVOLUTION 



ness, all considerations of motion may be eliminated 

 from mathematical processes ; but the introduction of 

 motion into the genesis of figures is nevertheless the 

 origin of modern mathematics. We believe that if 

 biology could ever get as close to its object as mathe 

 matics does to its own, it would become, to the physics 

 and chemistry of organized bodies, what the mathematics 

 of the moderns has proved to be in relation to ancient 

 geometry. The wholly superficial displacements of 

 masses and molecules studied in physics and chemistry 

 would become, by relation to that inner vital move 

 ment (which is transformation and not translation) what 

 the position of a moving object is to the movement 

 of that object in space. And, so far as we can see, the 

 procedure by which we should then pass from the 

 definition of a certain vital action to the system of 

 physico-chemical facts which it implies would be like 

 passing from the function to its derivative, from the 

 equation of the curve (i.e. the law of the continuous 

 movement by which the curve is generated) to the 

 equation of the tangent giving its instantaneous 

 direction. Such a science would be a mechanics of 

 transformation, of which our mechanics of translation 

 would become a particular case, a simplification, a pro 

 jection on the plane of pure quantity. And just as an 

 infinity of functions have the same differential, these 

 functions differing from each other by a constant, so 

 perhaps the integration of the physico-chemical elements 

 of properly vital action might determine that action only 

 i n p ar t a part would be left to indetermination. But 

 such an integration can be no more than dreamed of; 

 we do not pretend that the dream will ever be realised. 

 We are only trying, by carrying a certain comparison as 

 far as possible, to show up to what point our theory 



