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.

Would you 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.

That is Nietzsche, The Gay Science §341, and the section is titled "The greatest weight". The doctrine of eternal recurrence is that passage, and everything else written about it is commentary on a question that works by being asked.

Why the test is so hard to pass

Ordinary life-affirmation is cheap. Asked whether your life has been worthwhile on the whole, most people say yes, and the answer costs nothing — "on the whole" is doing all the work, quietly averaging the bad years away.

The demon removes the averaging. The recurrence is of everything, in the same order, with no negotiation. You cannot keep the good parts and drop the humiliation, the wasted decade, the thing you did that you have never told anybody. It returns entire or the question has not been answered.

That is what makes it a test rather than a rhetorical flourish. Almost any life can be affirmed in summary. Very few can be affirmed in full detail, and the gap between those two is exactly what Nietzsche is measuring.

Note also what is not being asked. It is not whether you would enjoy living it again. Enjoyment is passive and beside the point; the question is whether you would will it. A person can want something they did not like, and the capacity to do that about your own life is the thing being tested. What passing would amount to is treated under amor fati.

The cosmological reading

There is a second version, and it should be kept in proportion.

Some passages in the unpublished notebooks suggest Nietzsche thought recurrence was literally true: matter and energy are finite, time is infinite, so every configuration must repeat infinitely often, including this one. He never published the argument.

It has obvious problems — finite energy in the relevant sense is not established, and infinite time does not by itself guarantee that every possible arrangement occurs. Whether Nietzsche believed it is disputed and probably undecidable.

What matters is that the test does not depend on it. The demon's question works as a hypothetical. If the answer to a merely possible recurrence is no, that answer has told you something, and no cosmology is required to make it sting.

Why Zarathustra cannot say it

Thus Spoke Zarathustra handles the doctrine strangely, and the strangeness is deliberate.

Zarathustra knows it and cannot get it out. When he tries he collapses and spends a week ill — the chapter is called "The Convalescent" — and when affirmation finally comes it arrives as song rather than argument.

The form is the point. A doctrine of this kind cannot be transmitted by being explained, because understanding it and being able to affirm it are different achievements, and only the second is what Nietzsche is after. That is why the demon appears in a thought experiment rather than a proof, and why the whole thing is staged as a question somebody asks you when you are alone.

Not reincarnation

The commonest misreading, and it inverts the doctrine.

Reincarnation offers another life — a further chance, possibly better, possibly earned. Eternal recurrence offers exactly this one, again, unchanged, forever. There is no progress in it and no accumulation of wisdom across cycles, because each cycle is identical.

Which is why it can function as a test of affirmation and reincarnation cannot. A second chance is a consolation. The same chance repeated is a verdict on the first one.