Quantitative modeling of social systems shows a large component of automatic drives in the behavior of individual humans and human society. Studies of the formation and breakdown of 20 diverse empires operating over almost 3,000 years describe these processes with utmost clarity and paradigmatic simplicity. Taking territorial expansion as the basic parameter, we show that it can be represented in time by a single logistic equation in spite of the complicated sequences of events usually reported by historians. The driving forces of empire, leading to expansion and saturation at 14 days of travel from the capital, can be reduced to testosterone and progesterone.