Ray Kurzweil has a new book out, called "The Singularity is Near" or something like that. I don't have to bother reading it (and I won't, because it wouldn't be good for my blood pressure) because I already know exactly what fundamental mistake he made.

The "Singularity" is a popular term for the idea that the pace of technology is advancing at an exponentially faster rate, and that some time in the not-too-distant future (before 2050 according to Kurzweil), technology will reach a "tipping point" where the acceleration becomes driven by ever more advanced machine intelligence. The result is sort of a geek version of The Rapture, complete with semi-religious overtones and visions of techno-heaven and/or techno-hell.

A lot of very smart people (mostly techno-geeks) agree with him. The evidence cited is that (a) major technological advances are becoming ever more frequent, and (b) advances in semiconductor technology follow an exponential curve (Moore's Law).

But they're all wrong.

Kurzweil and other believers in the Singularity have made the A-number-one mistake in data analysis I used to teach in the first week of freshman Physics: Never ever extrapolate an exponential curve indefinitely into the future. In fact, be extremely wary of extrapolating exponential curves at all.

The problem is that exponential curves grow really really fast over time, but everything in the real world has some sort of limit. When you're far away from that limit, the temptation is to assume that there is no limit at all, but the exponential growth will stop very quickly once the limit starts to approach.

For example, over the past 40 or so years, semiconductor performance has followed Moore's Law very nicely. But this can't go on forever, or else someday we'd have computers which violate the Planck limit for information density. The actual limit is certainly much closer, but we don't know where it is.

Now think about some other technology. Rockets, for example. If you draw a graph of maximum rocket payload from the earliest German missiles in WWII up to the Saturn V in the 1960's, you'd get something which looks like a fairly neat exponential growth curve. A sort of Moore's Law for rocket payload.

But what happened since the 1960's? Not much. The Saturn V and contemporary Soviet heavy lift vehicles were pretty much the last rockets to follow this exponential growth in payload. Subsequent advances (to the extent that there have been any at all) have been smaller and much less frequent. While it is possible to build bigger rockets, the technology hit a wall of cost and practicality.

Another big mistake that Singularity believers make is a very strong recency bias. One graph from Kurzweil's book (reproduced here) purports to show paradigm shifting technological changes from the beginning of life to the invention of the wheel up through the personal computer. The argument is that the advances are happening faster and faster over time.

But that argument only holds water if each shift is of equal importance. Would a historian 1,000 years in the future consider the invention of the computer and the invention of the personal computer to be equally important? Probably not. Would a future historian even view the invention of the telephone, the Internet, and the computer as separate events (even though they occur across a span of a century), or as part of a single "communications revolution" the same way Kurzweil lumps the invention of steam power, the automated loom, and the electric motor into a single "industrial revolution"?

For that matter, would a future historian even view the Industrial Revolution as distinct from the Communications Revolution, or would they all get tied together as part of a single period, much as the Renaissance is generally seen as a distinct historical period even though it covered several centuries?

But if you want to believe in the Singularity, go ahead. Just excuse me if I remain skeptical.