[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 foresees a future phenomenon, it is only on condition of making it to a certain extent a present phenomenon, or at least of enormously reducing the interval which separates us from it. In short, the time of which we speak in astronomy is a number, and the nature of the units of this number cannot be specified in our calculations; we may therefore assume them to be as small as we please, provided that the same hypothesis is extended to the whole series of operations, and that the successive relations of position in space are thus preserved. We shall then be present in imagination at the phenomenon we wish to foretell; we shall know exactly at what point in space and after how many units of time this phenomenon takes place; if we then restore to these units their psychical nature, we shall thrust the event again into the future and say that we have foreseen it, when in reality we have seen it.