On the extinction paradox, the finiteness of resources, and the nature of probability

A talk by Lewins is discussed. Lewins addressed the subject of randomness in nature, and some implications for nuclear reactors. In particular, Lewins described the extinction paradox: a critical ''reactor is self-sustaining in the mean, nevertheless it will shut down with certainty!'' According to Lewins, the paradox arises because the idealized chain process leaves out the fact that resources are always finite (ie, the number of initial neutrons is finite, and the amount of fissile atoms in a reactor depends upon Avogadro's number). This explanation, however, only implies that the model used to reach the paradox is too naive to represent a real reactor (indeed, Lewins immediately explains more realistic models), but the paradox still remains in the context of the idealized chain reaction. Two ways of explaining the paradox are considered. (author)