While we suppose this kind of singularity might one day occur, we don't think it is near. In fact, we think it will be a very long time coming. Kurzweil disagrees, based on his extrapolations about the rate of relevant scientific and technical progress. He reasons that the rate of progress toward the singularity isn't just a progression of steadily increasing capability, but is in fact exponentially accelerating—what Kurzweil calls the "Law of Accelerating Returns." He writes that:
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. Within a few decades, machine intelligence will surpass human intelligence, leading to The Singularity ... 
By working through a set of models and historical data, Kurzweil famously calculates that the singularity will arrive around 2045.
This prediction seems to us quite far-fetched. Of course, we are aware that the history of science and technology is littered with people who confidently assert that some event can't happen, only to be later proven wrong—often in spectacular fashion. We acknowledge that it is possible but highly unlikely that Kurzweil will eventually be vindicated. An adult brain is a finite thing, so its basic workings can ultimately be known through sustained human effort. But if the singularity is to arrive by 2045, it will take unforeseeable and fundamentally unpredictable breakthroughs, and not because the Law of Accelerating Returns made it the inevitable result of a specific exponential rate of progress.