[I. ETERNAL RECURRENCE]
1. THE DOCTRINE EXPOUNDED AND SUBSTANTIATED.
1.
The extent of universal energy is limited; it is not “infinite”: we should beware of such excesses in our concepts! Consequently the number of states, changes, combinations, and evolutions of this energy, although it may be enormous and practically incalculable, is at any rate definite and not unlimited. The time, however, in which this universal energy works its changes is infinite—that is to say, energy remains eternally the same and is eternally active:—at this moment an infinity has already elapsed, that is to say, every possible evolution must already have taken place. Consequently the present process of evolution must be a repetition, as was also the one before it, as will also be the one which will follow. And so on forwards and backwards! Inasmuch as the entire state of all forces continually returns, everything has existed an infinite number of times. Whether, apart from this, anything exactly like something that formerly existed has ever appeared, is completely beyond proof. It would seem that each complete state of energy forms all qualities afresh even to the smallest degree, so that two different complete states could have nothing in common. Is it to be supposed that in one and the same complete states two precisely similar things could appear—for instance two leaves? I doubt it: it would take for granted that they had both had an absolutely similar origin, and in that case we should have to assume that right back in infinity two similar things had also existed despite all the changes in the complete states and their creation of new qualities—an impossible assumption.
2
Formerly it was thought that unlimited energy was a necessary corollary to unlimited activity in time, and that this energy could be exhausted by no form of consumption. Now it is thought that energy remains constant and docs not require to be infinite. It is eternally active but it is no longer able eternally to create new forms, it must repeat itself: that is my conclusion.
3
An incalculable number of complete states of energy have existed, but these have not been infinitely different: for if they had been, unlimited energy would have been necessary. The energy of the universe can only have a given number of possible qualities.
4