Something I don't understand from Ray Kurzweil's arguments about the “Singularity”: he says that we're in the “knee” of the growth curve:
... exponential growth is seductive, starting out slowly and virtually unnoticable, but beyond the knee of the curve it turns explosive and profoundly transformative.
There's a big problem with this idea.
Exponential curves do not have knees.
Exponential curves are scale-free. If you replot them at a different scale, the knee will appear to be in a different place. Furthermore, the knee will always appear to be near the right edge of the curve, so you'll always think the knee just occurred recently.
I searched Google to find any page on how to define the “knee” of an exponential curve, but did not find one. I only found one page that even mentions the issue. Why aren't people pointing this out? Am I missing something? Only Steve Jurvetson, in a comment on his own blog, says:
For almost any issue, the “knee in the curve” occurred in the recent past, and history before that seemed pretty flat. But, of course, there is no knee or inflection point or “hockey stick” in an exponential curve (when plotted on log paper, this more obvious). Roll the clock forward 5 years, plot again, and the perceived “knee” on a linear graph will have moved forward 5 years.
I'm only on page 10 in Kurzweil's new book, The Singularity is Near (which I received at the Accelerating Change 2005 conference), and his opening argument is suspect. This is going to leave a bad taste in my mouth as I read the rest of the book.