What if some day or night a demon were to steal 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 again and innumerable times again; and there will be nothing new in it, but every pain and every joy and every thought and sigh and everything unspeakably small or great in your life must 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 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 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 power over you, as you are it would transform and possibly crush you; the question in each and every thing, 'Do you want this again and innumerable times again?' would lie on your actions as the heaviest weight! (341)
Unless one has already read Thus Spoke Zarathustra and consequently had the understanding that Nietzsche's idea of the eternal recurrence is a cosmology, there is no way one would read Nietzsche as suggesting anything cosmological here. What Nietzsche presents here is, as Bernard Williams puts it, "an entirely hypothetical question, a thought-experiment" ('Introduction' to the Cambridge edition of The Gay Science). Our responses to the thought-experiment reflect our attitudes towards our lives. The thought-experiment can thus be seen as a test of whether one affirms one's life: if one answers 'yes' to Nietzsche's question ('Do you want this again and innumerable times again?'), then one passes the test of the eternal recurrence, that is, one affirms one's life. The answer 'no' may not be outright nihilistic, but it is at least unsettled and dubious.
However, even understood merely as a thought-experiment rather than a cosmological doctrine, the idea of the eternal recurrence still invites a host of questions. Will I remember 'my' past lives? The answer is presumably 'no', for otherwise the lives in the eternal recurrence will not be identical ("all in the same succession and sequence") because of the ever-increasing extra knowledge in later lives. But if I don't remember those prior lives, what makes them my lives? Or, to put it reversely, if the later person will not remember my life, what makes his life a recurrence of mine?
Even if I can put these questions aside and understand the recurring lives as all mine, I may not have reason to care about any of them except this one. Since my recurring lives have to be identical, in each of them I do not know that it is a repetition of prior lives. The lack of such knowledge in each life logically follows from the fact that in the very first life of the series I do not have such knowledge. But if in each life I do not know that it is a repetition, then what reason do I now have for minding that my life will be repeated? If my later selves won't mind, why should I mind for them? And if I don't, and won't, mind the repetitions, how can the eternal recurrence be a good test for the affirmation of life? (Note that for the thought-experiment to be coherent, if I ask the demon whether my life is already a repetition, the demon will have to either always answer 'no' or erase my memory of having met him.)
None of the above questions should be dismissed lightly, because what the test of the eternal recurrence requires is not our hasty judgments or knee-jerk psychological responses but our considering Nietzsche's question, in Williams's words, "seriously and in the fullest consciousness". Hasty judgments or knee-jerk psychological responses are not sufficient for the affirmation of life.