  In the Korean culture the 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 here shown 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 the total number of married women with the same proportionality
constant for all the years. This prediction is also borne out to 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 year 500 AD, based on the RGF model and find about ten
thousand Kims.
