Zarathustra reflects that in all one's journeys, one ultimately experiences only oneself; all discovery is self-discovery. Now he prepares for his most difficult journey yet.
Courage helps us overcome everything, even death, by helping us look lightly at what would otherwise seem serious. Zarathustra suggests that courage can teach us to say to death, "Was that life? Well then! Once more!" Thus, courage can also lead us to confront the eternal recurrence of the same events. If the past stretches back infinitely, then anything that could have happened must have happened already at some time in the past. By that logic, this very instant must have occurred at some time in the past. And similarly, if the future is infinite, everything—including this moment—must recur again sometime in the future. Zarathustra ends by recounting a vision where he saw a shepherd gagging on a snake in nausea, who then bit off the head of the snake, and spat it out, erupting with laughter.
Zarathustra still feels unable to confront the thought of the eternal recurrence. He waits for the pain of this thought to come upon him, but he remains happy.
Zarathustra praises the heavens, as being above all reason and above all purpose. Ultimately, the universe is not directed by reason and purpose, but by chance and accident.
Zarathustra returns among people and finds that they have grown smaller while he was away, so that he must now stoop to be among them. Their desire for contentment and above all their desire not to be hurt by anyone have made them small. They call this cowardice "virtue," which they express through a constant aim to please and to gratify. Zarathustra has no respect for people who are unable to assert their own will.
Zarathustra takes malicious pleasure in the winter and in the difficulties it imposes. If people could only see his boundless depth and happiness, they would resent him, but if they see him suffer, they will no longer feel jealous.
At the entrance to a large city, Zarathustra encounters a foaming fool called "Zarathustra's ape," who has learned to copy much of what Zarathustra says. He warns Zarathustra not to enter the city because it is full of small people and small minds. Zarathustra stops his tirade, saying that the ape despises these people for all the wrong reasons. He despises because he resents the people for not flattering him enough, whereas Zarathustra despises out of love for what these people could be. Zarathustra suggests that this fool should leave the city if he hates it so much: "where one can no longer love, there one should pass by."
Zarathustra finds to his dismay that many of his disciples have turned to God. They found it more comforting to have faith than to struggle forward alone. Zarathustra suggests that when the old gods died, they died from laughter at the God who said, "There is one God. Thou shalt have no other God before me!"
Zarathustra returns to his home in the mountains and delights in his solitude. He remarks on how peculiar humans are, that they talk but say nothing, and that the "good" among them are the most spiteful.
We first encounter the eternal recurrence in the chapter "On the Vision and the Riddle," and the rest of Part III deals with Zarathustra's failed attempt to come to terms with the full consequences of this doctrine. On a very basic level, the doctrine of the eternal recurrence is simple. Events do not happen once; they recur an infinite number of times, so that every event in the present has already happened an infinite number of times in the past and will recur an infinite number of times in the future. However, placing this doctrine in the context of Nietzsche's philosophy and explaining its importance might prove a little trickier.
First, we might want to question the scientific validity of this doctrine, and also ask whether scientific validity has anything to do with it. As presented in "On the Vision and the Riddle," the doctrine of the eternal recurrence seems to be based on the claim that if time is infinite, all events must recur at some time. This claim is mathematically unsound. To follow an example by Georg Simmel, we can imagine three wheels lined up together on an axis, with a mark at the top of each wheel to show that they are lined up. If the three wheels start rotating, the first at one revolution per second, the second at two revolutions per second, and the third at one/¹ revolutions per second, the three marks on the three wheels will never again line up with one another, even given an infinite amount of time.
While Walter Kaufmann provides evidence that Nietzsche sought some kind of scientific validation for this doctrine, Gilles Deleuze suggests that the eternal recurrence goes deeper than a simple mathematical assertion. One of Nietzsche's fundamental claims is that the universe is in a state of flux and that there are no absolutes, no constants. Nothing is permanent. If everything is governed by the will to power, and the will to power drives everything to change itself and to overcome itself, nothing will remain fixed. According to Deleuze, the eternal recurrence is the full expression of what he calls "the being of becoming." Everything, in Deleuze's reading, is in a state of becoming, and it always has been. If there were a final state of being that things were moving toward, they would have reached it long ago, and if there were an initial state of being that things were moving from, they would never have left it. The only constant in the universe is becoming, or change.
In Deleuze's reading, then, the eternal recurrence does not imply the recurrence of fixed states of being, like the lining up of marks on wheels. It is precisely the being of such states that Deleuze wants to deny. In a universe of constant becoming, the notion of being is replaced by the notion of returning, or recurrence: "Returning is the being of that which becomes," Deleuze writes. Thus, in Nietzsche's conception of the universe, there are no fixed things, like a one true God or one fixed morality or the like. All things change, but these changes recur eternally.
The eternal recurrence is mostly significant to Nietzsche in how we might confront the fact of recurrence. We would have to abandon the notions that there is some reason or purpose driving the universe, and accept the fact that chance governs these changes as much as anything else. We would also have to accept that everything we have done and everything that we will do will be repeated an infinite number of times. While it might seem delightful that our happiest moments might be repeated infinitely, we must also confront the fact that our worst moments and our mediocrity must always be repeated and never improved upon. Zarathustra cannot confront the thought of eternal recurrence, largely because he would have to recognize that the mediocrity of humanity that he so despises will never be fully overcome, but rather will be repeated over and over again.