  Bernoulli’s result enables us to infer from the complexion of a population to the complexion of most reasonably-sized samples taken from it, since the complexion of most samples closely resembles the complexion of the population. Williams’s originality was this: he noticed that resemblance is symmetrical. If we can prove, as Bernoulli did, that most samples resemble the population from which they are drawn, then conversely the population’s complexion resembles the complexion of most of the samples.