Nietzsche's Argument for the Eternal Return:

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 dice game in infinitum. [6]

Nietzsche's Presentation of the Eternal Return --
In modern times, the doctrine is most closely associated with Friedrich Nietzsche. Here's how Nietzsche first puts it:

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. The question in each and every thing, "Do you desire this once more and innumerable times more?" would lie upon your actions as the greatest weight. Or how well disposed would you have to become to yourself and to life to crave nothing more fervently than this ultimate eternal confirmation and seal? [3]

In another book, Thus Spoke Zarathustra, Nietzsche invents a character named Zarathustra, a wandering philosopher who has many adventures. In one adventure, Zarathustra climbs a mountain and argues with his arch-enemy, a dwarf named the Spirit of Gravity (sort of the spirit of depression and despair). Zarathustra has a vision of the eternal return:

Behold this moment!, Zarathustra said. From this gateway [called] Moment, a long, eternal lane runs back: an eternity lies behind us.

Must not all things that can run have already run along this lane? Must not all things that can happen have already happened, been done, run past?

And if all things have been here before: what do you think of this moment, dwarf? Must not this gateway, too, have been here -- before?

And are not all things bound fast together in such way that this moment draws after it all future things? Therefore -- draws itself too?

For all things that can run must also run once again forward along this long lane.

And this slow spider that creeps along in the moonlight, and this moonlight itself, and I and you at this gateway whispering together, whispering of eternal things -- must we not all have been here before?

-- and must we not return and run down that other lane out before us, down that long, terrible lane -- must we not return eternally? [4]

For the complete discussion here's the site url:
http://www.wpunj.edu/cohss/philosophy/courses/livedead/RETURN.HTM


So you see? 'Tis all a Yart/Tray, or Tray/Yart anyway!