Exponentiation
Exponentiation is a mathematical operation, written as , involving two numbers, the "base" and the "exponent" . When is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, is the product of multiplying bases:
The Singularity Is Near
Kurzweil explains that evolutionary progress is exponential because of positive feedback; the results of one stage are used to create the next stage. Exponential growth is deceptive, nearly flat at first until it hits what Kurzweil calls "the knee in the curve" then rises almost vertically. In fact Kurzweil believes evolutionary progress is super-exponential because more resources are deployed to the winning process. As an example of super-exponential growth Kurzweil cites the computer chip business. The overall budget for the whole industry increases over time, since the fruits of exponential growth make it an attractive investment; meanwhile the additional budget fuels more innovation which makes the industry grow even faster, effectively an example of "double" exponential growth.