Brad Templeton has a post suggesting a new law on semiconductor growth. Basically, Moore’s “Law” isn’t really a law at all, since it’s been slowing down. Brad suggests a new law, in which the period of doubling doubles every 40 years. I commented:
I’ve always thought that the weight placed on Moore’s Law (and the ensuing hystrionics when it’s discovered to have “slowed down”) was pretty silly. It’s clearly not reasonable to expect exponential growth to continue indefinitely. Resource limitations will put pressure on growth. In this case, we’re talking about physical limits, as well as limits on the resources needed to construct chip fabs capable of making the denser chips.
A more reasonable “law” would model the growth as a logistic function, the way population growth is modeled in biology/ecology. A logistic is (essentially) an exponential that “slows down”. (sound familiar?) In fact, your characterization of an exponential whose rate is cut in half every 40 years may in fact be a logistic. Anyway, if I had the data, I’d love to regress a logistic curve onto it and see what comes out. Since the logistic eventually levels off, the model would give a prediction of the limit of semiconductor growth.
You can read about the logistic curve at MathWorld. Curves like the logistic show up in other bounded-growth analyses, like the Hubbert curve for oil production, in which the amount of production at any particular time is essentially the derivative of a logistic-like sigmoid function, and can probably be nicely modeled using the logistic.
If anyone has data on the maximum chip transistor density over time since the 60’s, I’d take a crack at regressing a logistic onto it in MatLab, or whatever. Another interesting set of data to use would be Hans Moravec’s data on computing power per unit cost. The data goes back to 1892. The Moravec paper I linked has the raw data in the appendix. I’ll take a crack at it, when/if I get time (probably not for a couple weeks.