A number of related, and in some cases identical, mathematical models were developed in the early decades of the 20th century to explain the apparent paradox between the second law of thermodynamics and its meaning in statistical mechanics, to model the number of calls in a telephone exchange, and to verify experimentally the theory of Brownian motion. I will give a historical review of these models and then jump ahead to the end of the century when at least some of the same models and essentially the same questions reappear in the statistical foundations of gene mapping in experimental and human genetics.