The following chart has one dot for every country on the planet. The vertical axis shows how productive a country’s citizens are. For example, people in Peru produce around $1000 per year. The countries are ordered from left to right, in rank order, so the most productive country Switzerland is first. The least is just off the graph on the right. The chart is a log log graph! There are lots of poor countries; some are frighteningly poor.

These straight lines on log-log graphs of ranking in populations appear in lots of situations. For example in the distribution of wealth, the popularity of words in languages, or the sizes of cities. These go by different names; power-law, zipf’s law, Pareto’s law because it was noticed in different situations.

What do these things have in common?

The simple awnser is that this happens in systems where, over time, the rich get richer. If the system’s evolution gives some advantage to the better off then curves like this will settle out of the random processes that grow the system. Consider a city; if it’s got people those people will tend to breed and it’s population will grow; if there is something attractive about that crowd of people more people will be attracted; if we have few such positive reenforcements that and time is all we need.

Of course if these are systems created by human goverments then we somebody maybe tinkering with the rules. That can make the rich get richer faster or slower. I suspect that the top of that curve illustrates how the top few countries aren’t such separate countries when it comes to this measure productivity.