>that if particles and their configurations are finite, then moments in lived experience necessarily repeat themselves
I don't know much about Nietzsche, but this statement does not seem correct. One can have infinite configurations of a finite number of particles. The only way a finite number of particles would imply finite configurations would be (a) space is finite, and (b) space is not continuous. That is, if you imagine the universe as composed of discrete slots in which particles must exist, and the number of slots is finite, then his idea makes sense. But, is there a reason to think this?
I don't know much about Nietzsche, but this statement does not seem correct. One can have infinite configurations of a finite number of particles. The only way a finite number of particles would imply finite configurations would be (a) space is finite, and (b) space is not continuous. That is, if you imagine the universe as composed of discrete slots in which particles must exist, and the number of slots is finite, then his idea makes sense. But, is there a reason to think this?