Boltzmann showed us that the entropy of an event is equivalent to the likelihood of said event. This seems to imply that the higher the entropy of your perception, the more occurring your perception is since perception is an event. Entropy can be thought of as dis-order. Perception requires some minimum amount of order. Perceptions that have high order, or low entropy, are outnumbered by perceptions that have low order, or high entropy. Even in Nietzsche's eternal recurrence, there is a distribution of recurring events.

As a man, my perception is very disordered, very high in entropy. Thus, my disordered perception is eternally recurring. A way to "solve" my predicament is to make my way towards higher order, lower entropy, thinking/perceiving/conceiving. It's a solution because by lowering the entropy of my thinking, I am making my self-perception ever less and less likely. If I continue this forever, I can make my self-perception infinitely rare. Even an infinite number of dice rolls can't replicate my self-perception because of how infinitely rare it is. Infinite rarity and infinite attempts cancel out.

So does the overman live only once?

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    Entropy is not equivalent to the likelihood of an event, entropy of an event does not make sense. Boltzmann's formula gives the entropy of a macrostate of a statistical physical system. Identification of entropy and disorder is misleading, it is a measure of energy dispersal, and it certainly does not apply to the "disorder" of thinking. It is also unclear what either entropy or disorder have to do with recurrence, or what thinking and self-perception have to do with the overman. – Conifold May 2 '19 at 0:33

The question is whether the overman lives only once in Nietzsche's eternal recurrence, that is, the overman can somehow escape this eternal return.

Wikipedia notes the following about the eternal recurrence:

Walter Kaufmann suggests that Nietzsche may have encountered this idea in the works of Heinrich Heine, who once wrote:

[T]ime is infinite, but the things in time, the concrete bodies, are finite. They may indeed disperse into the smallest particles; but these particles, the atoms, have their determinate numbers, and the numbers of the configurations which, all of themselves, are formed out of them is also determinate. Now, however long a time may pass, according to the eternal laws governing the combinations of this eternal play of repetition, all configurations which have previously existed on this earth must yet meet, attract, repulse, kiss, and corrupt each other again...[Kaufmann, Walter. Nietzsche; Philosopher, Psychologist, Antichrist. 1959, page 376.]

The eternal recurrence supposes that time is infinite, but the configurations of bodies are finite. Since the overman is one of these finite bodies, the overman would also be part of in this eternal recurrence. Even succeeding to make one's way"towards higher order, lower entropy" may only increase or decrease the number of distinct configurations associated with the overman in comparison to someone else. They would all eternally return.

Although there is no way for the overman to get out of this through the overman's superior abilities, perhaps there is no eternal recurrence for anyone. The eternal recurrence depends on the distinct configurations being finite. What if they, like time, are also infinite?

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.[Kaufmann, Walter. Nietzsche: Philosopher, Psychologist, Antichrist. (Fourth Edition) Princeton University Press, 1974. p327]

If that is the case then the eternal return need not apply to anyone.

Wikipedia contributors. (2019, April 16). Eternal return. In Wikipedia, The Free Encyclopedia. Retrieved 10:39, May 2, 2019, from https://en.wikipedia.org/w/index.php?title=Eternal_return&oldid=892764595

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