When some states are huge and some others tiny, an “effective number” widely used for parties in political science can be applied both to state areas and populations. These numbers decrease exponentially over 5000 years, pointing to a single world state around 3700 by area and 5000 by population. Combination with estimates from top state area and population points toward a single world state by 4600, if the 5000-year trends continue. But projections are not predictions!

A square root law of effective numbers of states applies: The population-based effective number of states and tribes tends to be the square root of the area-based number. The zone of variation around the average trends is wide. Thus, even when the average millennial trends keep holding, the immediate future is wide open. The zigzags in the past curves remind us of how fleeting human history has been. Often a mere hundred years has thoroughly altered the number and size of states. We can expect similar reversals in future.