Dan Gillmor quotes Ray Kurzweil as saying that:

The rate of change … is accelerating exponentially. We are “doubling the paradigm shift rate” on a constant basis. This century will be the equivalent to 20,000 years of progress at today’s rate, and people don’t appreciate the implications of this.

I have to admit that this 20,000-years-of-progress claim sounded roughly plausible to me at first. Ted Shelton had the same reaction. But even a little bit of number-crunching shows that Kurzweil must be wildly wrong.

I’m not precisely sure what Kurzweil means by “progress,” but in light of the talk about paradigm shifts, it seems reasonable to assume that “progress” has something to do with the advancement of human knowledge, understanding, or well-being.

Kurzweil says that progress advances exponentially, which seems to be a reasonable assumption. But how fast does the exponential rise? Kurzweil’s “20,000 years” claim turns out, through the magic of logarithms, to imply a 7% annual growth rate, that is, 7% more progress each year than the year before, with the increases compounding over time. That translates to a doubling in human progress every ten years.

That just can’t be right. For one thing, it implies that the amount of human progress between 1,000,000 B.C. and 1992 A.D. is equal to the amount of progress between 1992 and 2002. By any reasonable definition of human progress, things can’t be advancing nearly as fast as Kurzweil claims.

It’s surprising that a guy as smart as Kurzweil made this kind of mistake. In retrospect, I’m surprised that the claim sounded plausible to me and Gillmor and Shelton. I guess people are not very good at thinking about exponentials.