  Objections to Darwinian evolution are often based on the time required to
carry out the necessary mutations. Seemingly, exponential numbers of mutations
are needed. We show that such estimates ignore the effects of natural
selection, and that the numbers of necessary mutations are thereby reduced to
about $K\log{L}$, rather than $K^L$, where $L$ is the length of the genomic
"word", and $K$ is the number of possible "letters" that can occupy any
position in the word. The required theory makes contact with the theory of
radix-exchange sorting in theoretical computer science, and the asymptotic
analysis of certain sums that occur there.
