It replaces the names of countries ranked in size order with their ordering in terms of population.
Jason then throws out the offhand remark:
Interestingly, four countries stay in the same positions: the US, Ireland, Yemen, and Brazil.
The mathematically inclined among you will recognize those as fixed points.
I’m not sure what to make of the fact that a mapping from population to size has 4 fixed points, but Kakutani might.