Two explanations of Nietzsche's Concept of Eternal Recurrence

“Those who criticize without creating are the plague of philosophy.” - Gilles Deleuze

1.  A transcript of Michael Sugrue's Youtube video about Nietzsche:

Nietzsche, unlike the other intellectuals in the late 19th century, sees the implications of the collapse of religion. Rather than thinking that we could be sustained by naive, Darwinian belief in progress, he says “there's no progress to have.” Whatever we do, happens next – it doesn't mean that it's progressing. It's not going in any direction – it's all random. “The world is in all eternity Chaos. All hymns have sung to the teeming Chaos.”

Chaos in the Greek tradition is compared to Cosmos.  A Cosmos is an ordered universe; Chaos is a disordered universe. Cosmos is knowable; Chaos is not.

Once we've killed God, we've also destroyed knowledge, which means science is dead, philosophy is dead – our whole intellectual tradition has suffered an earthquake-like disaster. Nietzsche asks, what do we do now? How would we be big enough? How will we be strong enough to create a culture? To create a an intellectual life, when everything that we depended on, is now gone for good? ...

...Nietzsche’s madman is the one who announces that “God is dead.” He goes to the churches and he sees the people are going through the motions, but don't believe this anymore.
He talks to other people who have given up on religion, and the madman says “don't you realize how catastrophic this is?” “That everything is now tumbling down around our heads?”
He describes it as falling in every direction at once – imagine being in inter-stellar space – no up, no down, no front, no back. Where are we? What are we? All of this is up for grabs now. That's what the death of God is.

Since the Christian God is now dead, he's not kidding when he thinks "I can replace that."  If Christianity was a human construction, and if we need something to fill in the gap, Nietzsche is willing to step up and give us his best shot.
This is what he does when he says “Dionysus versus the Crucified.” The Greek god Dionysus – the god of wine, the god of drama, the god of intoxication, the god of sexual desire, the god of irrationality – is Nietzsche’s Nom de Plume. It's the mask that he uses to say “I have a new religion for you.” “I'm going to revive the religion of Dionysus,” because the status that Rationality previously held, can no longer hold. He thinks Christianity is dead, so he's trying to offer us some way out of this Labyrinth.

Hegel said that the highest achievements of human beings are three things: art, religion, and philosophy. Nietzsche believes that he has shown quite conclusively that religion and philosophy are gone. They're dead, and that leaves only art. Nietzsche is going to create a philosophy of culture which says art is the only way out of the Labyrinth; we must construct life-giving illusions that will connect art to religion–art to our longing for coherence–and which will prevent us from being destroyed and torn apart by the vacuum of meaning that emerges after God dies. 
Christians used to call someone the Antichrist as a kind of ultimate insult. Nietzsche says “No, we really need an Antichrist now!” and “I'm the only one that could do it, because I'm the only one who really understands how deep our problems run.” 

So Dionysus is going to be a religious and artistic alternative to both science and to Christianity. For example, he says look in the past. Judges who believed in witchcraft accused ‘witches’ and condemned them to death on that basis. Nietzsche says, “Now, not only is there no witchcraft, but now there's no Justice either." The guilt that both the witches and the their accusers thought they were bearing doesn't exist, because there aren't any moral or immoral boundaries anymore. Witchcraft and the belief in moral guilt are equally superstitious.

The only way to renew our culture is to find some solace in art. It's art that is going to take up the redemptive qualities that religion used to offer us. Nietzsche says that he is an artist, and that's the only way the philosophy can be done now–artistically.

Instead of writing long treatises like Kant’s Critique of Pure Reason, Nietzsche writes small, poetic aphorisms. The lack of systematic wholeness of his works reflects the lack of systematic wholeness in the universe. Cosmos, you can write a treatise about; but Chaos, you can only have this idea about, that idea about, try this on, and see how this works. Everything is tentative; everything is provisional... In other words, Knowledge is done. What do we do in the absence of knowledge? We find some way of reconciling ourselves to a completely meaningless world. That's what “The world is in all eternity, Chaos” means. He is the philosopher of Chaos, he is the prophet of Chaos, he speaks on behalf of Chaos.

Nietzsche says maybe we can get a foothold on the world by imagining that everything repeats itself. He calls this the Eternal Recurrence.
Possibly, we can give some meaning and some stability to the choices we make in life, on the basis that “Whatever we choose, we choose forever.” “We will be reconstituted at some infinitely distant time from now, and we will be forced to live the same life.” If you choose an inferior life, then you will live in that inferior condition forever–you are stuck in an endless repetition. 

2. A transcript of Plastic Pill's (subscriber only) video "Deleuze on Nietzsche: Video Supplement" 

[Nietzsche’s character] Zarathustra plays dice with the gods. The dice throw is seen as an analogy for Deleuze, as the affirmation of becoming. So you see what number comes up, and this is immediately anti-Hegelian, because it includes pure chance and the affirmation of pure chance.

…

The whole point of pure difference is that there are not really superiors and lessers.  Because if you're if you take an affirmative view, if you affirm everything, if you roll the dice and you affirm all becoming, then you can't you can't put yourself in a position outside of difference in order to judge it. You don't get to be the judge; you don't get to be the moralizer; you don't get to be the arbiter. That's not what philosophy is.

…

The eternal return is fantastic in Deleuze’s interpretation. People do not understand it. Like in the movie True Detective, “time is a flat circle and everything comes back”–this is so misunderstood.  The eternal return is not just a thought experiment first of all, and it's not that the same state of affairs keeps coming back. 

Do you know the snake eating its own tail, the ouroboros? That's the symbol of this eternal return. But it's not that you keep living the same life over and over again, it's not the things that return. Everything is a river, and the river's never the same. You can't have the same river more than once. Nietzsche says this actually twice in Zarathustra. He says “imagine willing the same thing over and over again.” The thing that is willed is Return. Not the state of affairs returning, but the Return itself–the dice roll. So the Eternal Return is just to continually affirm returning–that the dice roll happens over and over… The thing that is most individual about processes, is the Eternal Return of that process. So it's not just that thought experiment in Zarathustra:

And there will be nothing new in it, but every pain and every joy and every thought and every sigh must return to you all in the same succession and sequence. The eternal hourglass of existence is turned over 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 experienced a tremendous moment when you have answered him “You are a god, and never have i heard anything more divine.”

So the point of this is not that the state of affairs itself repeats, but that the Return repeats. In Deleuze’s interpretation, there’s a double selection: first there's the selection of willing, when the demon asks “do you want this again?” If you will the Return, then only that which becomes is the thing that can return.  “There will be nothing new in it, but every pain and every joy and every thought and every sigh must return to you.” So do you affirm existence? Every roll of the dice that has ever happened. Or do you say, “no, I can't live this life anymore.” 

Because if you want it to end, the denial, you can have that. You have that with your Christianity–“a little poison now and then makes for pleasant dreams.” You have that with your philosophy–saying “no I know what ‘the Right’ is, and that ‘Right’ will stop changing.” You can see this even in like leftist politics “If we only got there.” But there is no ‘there’. If you think there's a purposive end, then you're not living the eternal return. The eternal return is the affirmation of the return of everything, always–even the stuff that's painful. Nietzsche says twice in Zarathustra, it's not the same state of affairs that returns. Becoming is eternal. Becoming–not history. Becoming is the part that's eternal, not the history, not the states of events. You will the returning of becoming–temporality without ends in it. 

The negation destroys the returning. It represents the returning as having been destroyed, because there's a finishing point–we can be done with it. “If we only had this!” 

The over man in nature the superman is the one who just says “Yes, everything will return; I am that! I am that returning.” 

…

So for Deleuze, the will to power is not wanting, coveting, or seeking power, but only creating–and creation has to always happen over and over again. You can't defend the vanished concept, not even your own concept, not even your self conception. 

“To cast the dice is to remove from thought the questions of truth and falsity.”