i INDIVIDUALITY AND AGE 23 



The instant &quot; immediately before &quot; is, in reality, that 

 which is connected with the present instant by the 

 interval dt. All that you mean to say, therefore, is 

 that the present state of the system is defined by 

 equations into which differential coefficients enter, 

 such as dsjdt, dv/dt^ that is to say, at 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 /, there 

 is nothing to prevent him from supposing that the uni 

 verse vanishes from this moment till that, and suddenly 

 reappears. It is the /-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 / ; with the interval up to T 

 he is not concerned. If he divides the interval into 

 infinitely small parts by considering the differential dt y 

 he thereby expresses merely the fact that he will 

 consider accelerations and velocities that is to say, 

 numbers which denote tendencies 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 Bowing time. In short, 

 the world the mathematician deals with is a world that 

 dies and is reborn at every instant, the world which 



