In chapter 2 I mentioned that in an infinite universe there can exist an infinite number of extraterrestrial human beings, and in fact an infinite number of beings identical to myself. In this appendix I shall derive this result in a rather more precise form. The treatment is based on an argument of G.F.R. Ellis and G.B. Brundrit of the University of Cape Town.
First, it is an elementary result of probability theory that if (i) there exists an ensemble of identical systems with an infinite number of members, (ii) each member can. exist in a finite number of states, (iii) a given state A. occurs with a finite probability for a finite duration, then. at any given time there will exist, with expectation probability 1 (i.e., a prediction of certainty), an infinite number of members in state A. This is a formal statement of the informal dictum "In an infinite universe anything that can happen will happen, and happen infinitely often."
The issue that then faces us is whether this result can be applied to the problem of the existence of sentient beings in the real universe. In particular, can we apply the conclusions of the theorem to the case where state A is "my body" or something similar? Given that the conclusions of the theorem, when applied in this way, may seem