Friday, March 20, 2009

About Points of Inflection

Mathematically, a "point of inflection" is where a curve starts to turn over.

Think about a colony of bacteria growing in a petri dish, and graph the population as a function of time.

At first the population doubles every twenty minutes, maybe. That is the classic exponential growth of a population with essentially unlimited resources.

As the colony expands, however, eventually energy supplies run short. Waste products start to build up. The population starts growing more slowly. It may level off towards a plateau, or it may overshoot and crash, its resources severely depleted.

The "point of inflection" marks the change from a regime where the model of unlimited resources is appropriate, to a regime where that model is completely misleading.

Is humanity about to pass through a point of inflection?