  Data describing the growth of the world population in the past 12,000 years
are analysed. It is shown that, if unchecked, population does not increase
exponentially but hyperbolically. This analysis reveals three
approximately-determined episodes of hyperbolic growth: 10,000-500 BC, AD
500-1200 and AD 1400-1950, representing a total of about 89% of the past 12,000
years. It also reveals three demographic transitions: 500 BC-AD 500, AD
1200-1400 and AD 1950-present, representing the remaining 11% of the past
12,000 years. The first two transitions were between sustained hyperbolic
trajectories. The current transition is to an unknown trajectory. There was
never any form of dramatic transition from stagnation to growth, described
often as a takeoff, because there was no stagnation in the growth of the world
population. Correct understanding of the historical growth of human population
is essential in the correct interpretation of the historical growth of income
per capita.
