Over 5000 years, the world population has grown from 10 million to 8 billion. This has taken place in two distinct phases that begin with steeper-than-exponential growth due to the population–technology interaction but later came to a halt, blocked by limits in Earth’s carrying capacity. These two phases stand out when data are graphed in a novel way, with time as well as population on logarithmic scales. Each phase can be fitted using a novel “tamed quasi-hyperbolic” T-function. The ancient phase reached a population of 220 million by year 1, dropping to 190 million by year 400. The present phase slowly picked up speed, reaching its maximal relative (percent) growth rate around 1970 and absolute (in million) around 2010. It projects to a population maximum of 11 billion. The entire process conforms to a “PCT model”: population–carrying capacity–technology interaction. Population growth comes from population itself, as long as population is smaller than capacity. Capacity growth comes from increase in technology, as long as capacity falls short of an ultimate carrying capacity. Technology growth comes from technology itself but also from population.

The world population growth curve shows a kink from 100 BCE to 200 CE. It occurs in all major populated regions: China, Mesopotamia, Mediterranean, and (least of all) in India. Graphing of population doubling times over time shows utter discontinuity. It looks as if Earth’s carrying capacity for humans reached a limit that no increase in technology could overcome, but by 400 CE a unique breakthrough occurred. An exponent value in “T-function” fits to population data before and after the kink shifts in a way that suggests a crucial change in innovation practices. From isolated innovators, humankind shifted to moderate interaction over space and time, due to literacy. A sudden increase around 400 CE in ability to make use of written records is implausible, yet it remains the only conceivable way to explain the kink in world population growth curve.