This came up at work (a highly productive conversation it was, too) today:
Presently, females are born at a higer rate than males (like 51% or so, give or take).
If we continue to use the present patricarchal naming convention, how long would it be before everyone in the country had the same last name? I mean, every day, families lose their surnames with all-daughters families marrying away their last name (happened in my wife’s family, her and her sister both took their husbands’ names). That should, in theory, drop the total number of available last names in the next generation.
There must be some sort of mathematical way to determine this, but my counting ability stops with my toes.