The law of accelerating returns

Kurzweil, R. (2001)

This is the law of accelerating returns, more or less (I think) as it appears in 'The Singularity is Near':

An analysis of the history of technology shows that technological change is exponential, contrary to the common-sense "intuitive linear" view.
There's even exponential growth in the rate of exponential growth.
Within a few decades, machine intelligence will surpass human intelligence, leading to The Singularity - technological change so rapid and profound it represents a rupture in the fabric of human history.

Kurzweil, R. (2004)

This is a later update. The case made for "evolutionary processes", biological as well as technical. I've selected the technical case.

Technology, like any evolutionary process, builds on itself. This aspect will continue to accelerate when the technology itself takes full control of its own progression.
The resources underlying the exponential growth of an evolutionary process are relatively unbounded.
One resource is the (ever-growing) order of the evolutionary process itself.
The other required resource is the "chaos" of the environment in which the evolutionary process takes place and which provides the options for further diversity.
In technological evolution, human ingenuity combined with ever-changing market conditions keep the process of innovation going.

This is the law of accelerating returns, now Kurzweil's law, again:

In an evolutionary process, positive feedback increases order exponentially. A correlate is that the “returns” of an evolutionary process (such as the speed, cost-effectiveness, or overall “power” of a process) increase exponentially over time — both for biology and technology.

Argument map

argument map for the law of accelerating returns