Moore's Law is one big idea (Feynman's "There is plenty of room at the bottom") filtered through the conservative engineering practice of not doing too much in one go. Much of engineering proceeds in 20% or 50% increments. Steam trains get more powerful, bridges longer, mines deeper, ships larger, all in percentage increments over the previous record holder.
Technological advances affect GDP as they become mainstream. This requires knowledge propagation in which teachers teach a students, some students become teachers and teach more students,... They say that Faraday discovered electromagnetic induction on 29th August 1831, but by the time this hit the GDP figures with the electrification of American industry in the 1920's and 1930's it had been smeared out an exponential take up on a decades time-scale determined by human factors.
Hmm, my observations don't actually lead to a prediction of a steady rate of growth.
One the other hand, the attention to human factors hints that there might be a fairly low maximum rate of growth of around 3.5% a year, set by the proportion of good students in a population. One notices how steam railway trains stagnated from err, 1910 (not too sure) but they got to 4% thermal efficiency and then all the bright young engineers went into automobiles and aviation, and steam trains remained crap until diesel -electrics came along.
I was reading a post on the economy from the political statistics blog FiveThirtyEight, and the following graph shocked me:
This, according to Nate Silver, is a log-scaled graph of the GDP of the United States since the Civil War, adjusted for inflation. What amazes me is how nearly perfect the linear approximation is (representing exponential growth of approximately 3.5% per year), despite all the technological and geopolitical changes of the past 134 years. (The Great Depression knocks it off pace, but WWII and the postwar recovery set it neatly back on track.) I would have expected a much more meandering rate of growth.
It reminds me of Moore's Law, which would be amazing enough as a predicted exponential lower bound of technological advance, but is staggering as an actual approximation:
I don't want to sound like Kurzweil here, but something demands explanation: is there a good reason why processes like these, with so many changing exogenous variables, seem to keep right on a particular pace of exponential growth, as opposed to wandering between phases with different exponents?
EDIT: As I commented below, not all graphs of exponentially growing quantities exhibit this phenomenon- there still seems to be something rather special about these two graphs.