Over a decade ago, Ray Kurzweil argued that Singularity – the melding of mind with machine – was just around the corner. He also coined the "Law of Accelerating Returns":
So we won't experience 100 years of progress in the 21st century—it will be more like 20,000 years of progress (at today's rate). The "returns," such as chip speed and cost-effectiveness, also increase exponentially. There's even exponential growth in the rate of exponential growth.
Paul Allen and Mark Greaves counter with their idea of the "complexity brake":
The closer we look at the brain, the greater the degree of neural variation we find. Understanding the neural structure of the human brain is getting harder as we learn more. Put another way, the more we learn, the more we realize there is to know, and the more we have to go back and revise our earlier understandings. We believe that one day this steady increase in complexity will end—the brain is, after all, a finite set of neurons and operates according to physical principles. But for the foreseeable future, it is the complexity brake and arrival of powerful new theories, rather than the Law of Accelerating Returns, that will govern the pace of scientific progress required to achieve the singularity.
The Dish 