In order to put our finger on this vital difference, let us assume for a moment that some mischievous illustration genius, more powerful still than the mischievous genius conjured up by Descartes decreed that all the movements of the universe should go twice as fast. There would be no change in astronomical phenomena, or at any rate in the equations which enable us to foresee them, for in these equations the symbol _t_ does not stand for a duration, but for a relation between two durations, for a certain number of units of time, in short, for a certain number of _simultaneities:_ these simultaneities, these coincidences would still take place in equal number: only the intervals which separate them would have diminished, but these intervals never make their appearance in our calculations. Now these intervals are just duration _lived,_ duration which our consciousness perceives, and our consciousness would soon inform us of a shortening of the day if we had not experienced the usual amount of duration between sunrise and sunset. No doubt it would not measure this shortening, and perhaps it would not even perceive it immediately as a change of quantity; but it would realize in some way or other a decline in the usual storing up of experience, a change in the progress usually accomplished between sunrise and sunset. [Sidenote: Astronomical prophecy such as acceleration.] Now, when an astronomer foretells e.g. a lunar eclipse, he merely exercises in his own way the power which we have ascribed to our mischievous genius. He decrees that time shall go ten times, a hundred times, a thousand times as fast, and he has a right to do so, since all that he thus changes is the nature of the conscious intervals, and since these intervals, by hypothesis, do not enter into the calculations. Therefore, into a psychological duration of a few seconds he may put several years, even several centuries of astronomical time: that is his procedure when he traces in advance the path of a heavenly body or represents it by an equation. What he does is nothing but establishing a series of relations of position between this body and other given bodies, a series of simultaneities and coincidences, a series of numerical relations: as for duration properly so called, it remains outside the calculation and could only be perceived by a consciousness capable of living through the intervals and, in fact, living the intervals themselves, instead of merely perceiving their extremities. Indeed it is even conceivable that this consciousness could live so slow and lazy a life as to take in the whole path of the heavenly body in a single perception, just as we do when we perceive the successive positions of a shooting star as one line of fire. Such a consciousness would find itself really in the same conditions in which the astronomer places himself ideally; it would see in the present what the astronomer perceives in the future. In truth, if the latter