The Eternal Return is one of Nietzsche's most important thoughts. Nietzsche was not the first to write on the subject, but he did expand the idea of recurrence greatly. He first encountered the idea in his reading of Heinrich Heine, whom Nietzsche admired. Here is a selection from Heine's writing:
For time is infinite, but the things in time, the concrete bodies are finite.... Now, however long a time may pass, according to the eternal laws governing the combinations of this eternal play of repetition, all configurations that have previously existed on this earth must yet meet, attract, repulse, kiss, and corrupt each other again.... And thus it will happen one day that a man will be born again, just like me, and a woman will be born, just like Mary (citation from Kaufmann's Translator's Introduction to The Gay Science, p. 16).
The Eternal Return
The Eternal Return is for Nietzsche the most weighty thought. In Nietzsche's mind the Eternal Return was a horrifying thought, almost paralyzing. Here is a selection from The Gay Science:
The greatest weight. -- What, if some day or night a demon were to steal after you into your loneliest loneliness and say to you: "This life as you now live it and have lived it, you will have to live once more and innumerable times more; and there will be nothing new in it, but every pain and every joy and every thought and sigh and everything unutterably small or great in your life will have to return to you, all in the same succession and sequence -- even this spider and this moonlight between the trees, and even this moment and I myself. The eternal hourglass of existence is turned upside down again and again, and you with it, speck of dust!" Would you not throw yourself down and gnash your teeth and curse the demon who spoke thus? Or have you once experienced a tremendous moment when you would have answered him: "You are a god and never have I heard anything more divine"? If this thought gained possession of you, it would change you as you are, or perhaps crush you. (GS 341)
Also in The Will To Power Nietzsche writes "Duration 'in vain' without end or aim is the most paralyzing idea...." (WP 55)
The Eternal Return is basically the theory that there is infinite time and a finite number of events, and eventually the events will recur again and again infinitely. Consider the world as a super-complex chess game. If games of chess are played one after another forever, eventually a game will be repeated since there is only a finite number of possible games. It is the same with the world; eventually events will recur in the same order. The world is an eternal process of coming to be and passing away. The process, however, has no beginning or end. Eventually every combination of matter and energy will be realized and repeated an infinite number of times. Here is a selection from The Will To Power:
If the world may be thought of as a certain definite quantity of force and as a certain definite number of centers of force -- and every other representation remains indefinite and therefore useless -- it follows that, in the great dice game of existence, it must pass through a calculable number of combinations. In infinite time, every possible combination would at some time or another be realized; more: it would be realized an infinite number of times. And since between every combination and its next recurrence all other possible combinations would have to take place, and each of these combinations conditions the entire sequence of combinations in the same series, a circular movement of absolutely identical series is thus demonstrated: the world as a circular movement that has already repeated itself infinitely often and plays its game ad infinitum. (WP 1066)
Nietzsche believed that there is no final state of the universe; that the world is in a constant state of flux, always changing and becoming: "If the world had a goal it must have been reached." (WP 1063) There is no permanence, no duration, no "once-and-for-all": "That a state of equilibrium is never reached proves that it is not possible." (WP 1064) The world never reaches a final state. There is no finality of time; time is infinite. There is also no beginning to time. Nietzsche's time is like a cyclic time, non-linear, bent round in to a circle.
Means for Enduring the Eternal Return
In order to endure this horrifying thought of Eternal Return Nietzsche says we must gain freedom from morality. There must be a revaluation of all values. "To endure the idea of the recurrence one needs: freedom from morality; new means against the fact of pain (pain conceived as a tool, as the father of pleasure; there is no cumulative consciousness of displeasure); the enjoyment of all kinds of uncertainty, experimentalism, as a counterweight to this extreme fatalism; abolition of the concept of necessity; abolition of the 'will'; abolition of 'knowledge-in-itself.'" (WP 1060)
Nietzsche's world is a "Dionysian world of the eternally self-creating, the eternally self-destroying, this mystery world of the twofold voluptuous delight, my "beyond good and evil," without goal, unless the joy of the circle is itself a goal." (WP 1067)
I leave you with a question: Do you desire recurrence eternally once more and again?