Towards a Quantitative Theory of Civilizations

A mathematical theory of civilizations is described that is based on the analysis of Toynbee and others. A detailed successful comparison is made with historical events for all known civilizations. We quantitatively describe: its application to sequences of affiliated civilizations, the effects of catastrophes on civilizations, the interaction of barbarians and civilizations, the interaction of two civilizations, and the impact of technology on civilizations. We suggest the existence of 15 previously unidentified civilizations. Defining progress mathematically, as a sum over the world’s civilizations, we show that progress has been increasing linearly with time over the past 5,500 years.