The ten thousand Kims

In Korean culture, the names of family members are recorded in special family books. This makes it possible to follow the distribution of Korean family names far back in history. It is shown here that these name distributions are well described by a simple null model, the random group formation (RGF) model. This model makes it possible to predict how the name distributions change and these predictions are shown to be borne out. In particular, the RGF model predicts that for married women entering a collection of family books in a certain year, the occurrence of the most common family name 'Kim' should be directly proportional to the total number of married women with the same proportionality constant for all the years. This prediction is also borne out to a high degree. We speculate that it reflects some inherent social stability in the Korean culture. In addition, we obtain an estimate of the total population of the Korean culture down to the year 500 AD, based on the RGF model, and find about ten thousand Kims.