While worldwide population density increased, that of the of most populous states stubbornly remained between 5 and 10 persons per square kilometer, from 3000 BCE to 500 CE. Expansion into less densely inhabited regions may not have paid off. The range has widened since. In hemmed-in India, density approaches 500 per square kilometer, while the largest empire, Russia, remains at 9, far below the world average of 60. It is not certain that imperial peace outweighs imperial taxes so as to boost population and hence, presumably, wellbeing. The evidence is mixed. Inexplicably, the population share of the most populous empire kept increasing proportional to the square root of world population from 3000 BCE to 1800 CE, but since then it has been decreasing. At the same time, the area share of the most populous empire kept increasing proportional to world population, and it also has been decreasing since 1800. In a crowded world, some five-millennia regularities are breaking down. We live in interesting times.