22 CREATIVE EVOLUTION [chap. 



bottom, present velocities and present accelerations. You 

 are therefore really speaking only of the present — a present, 

 it is true, considered along with its tendency. • The systems 

 science works with are, in fact, in an instantaneous present 

 that is always being renewed; such systems are never in 

 that real, concrete duration in which the past remains 

 bound up with the present. When the mathematician 

 calculates the future state of a system at the end of a time 

 t, there is nothing to prevent him from supposing that the 

 universe vanishes from this moment till that, and suddenly 

 reappears. It is the t-th moment only that counts — 

 and that will be a mere instant. What will flow on in 

 the interval — that is to say, real time — does not count, 

 and cannot enter into the calculation. If the mathe- 

 matician says that he puts himself inside this interval, 

 he means that he is placing himself at a certain point, 

 at a particular moment, therefore at the extremity again 

 of a certain time t'; with the interval up to T f he is not 

 concerned. If he divides the interval into infinitely small 

 parts by considering the differential dt, he thereby expresses 

 merely the fact that he will consider accelerations and 

 velocities — that is to say, numbers which denote ten- 

 dencies and enable him to calculate the state of the system 

 at a given moment. But he is always speaking of a given 

 moment — a static moment, that is — and not of flowing 

 time. In short, the world the mathematician deals with is 

 a world that dies and is reborn at every instant — the world 

 which Descartes was thinking of when he spoke of continued 

 creation. But, in time thus conceived, how could evolution, 

 which is the very essence of life, ever take place? Evo- 

 lution implies a real persistence of the past in the present, 

 a duration which is, as it were, a hyphen, a connecting 

 link. In other words, to know a living being or natural 

 system is to get at the very interval of duration, while 



