Arguments Against Eternal Return
Nietzsche scholar Walter Kaufmann has described an argument originally put forward by Georg Simmel, which rebuts the claim that a finite number of states must repeat within an infinite amount of time:
Even if there were exceedingly few things in a finite space in an infinite time, they would not have to repeat in the same configurations. Suppose there were three wheels of equal size, rotating on the same axis, one point marked on the circumference of each wheel, and these three points lined up in one straight line. If the second wheel rotated twice as fast as the first, and if the speed of the third wheel was 1/π of the speed of the first, the initial line-up would never recur.
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“And thus we rust Life’s iron chain
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“It is the secret of the world that all things subsist and do not die, but only retire from sight and afterwards return again.”
—Ralph Waldo Emerson (1803–1882)