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The development of socio-economic geosystems is limited by rigid invariants. The sizes of the areas of human activity are determined by the possibilities of transport. Man is viewed as a territorial animal, and territoriality as the basic instinct that prompts to development of the territory. Studies of the formation and breakdown of 20 diverse empires operating over almost 3,000 years describe this process. Territorial expansion can be represented in time by one logistic equation. 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.