One story for exponential growth that I don’t see you address (though I didn’t read the whole post, so forgive me if I’m wrong) is the possibility of multiplicative costs. For example, perhaps genetic sequencing would be a good case study? There seem to be a lot of multiplicative factors there: amount of coverage, time to get one round of coverage, amount of DNA you need to get one round of coverage, ease of extracting/preparing DNA, error probability… With enough such multiplicative factors, you’ll get exponential growth in megabases per dollar by applying the same amount of improvement to each factor sequentially (whereas if the factors were additive you’d get linear improvement).
I’m actually writing another (long) post on exponential growth and the different phenomena that could lead to it. Multiplicative costs are on the list of plausible explanations. I’ve discussed these multiplicative stories with Jonah and Luke before.
One story for exponential growth that I don’t see you address (though I didn’t read the whole post, so forgive me if I’m wrong) is the possibility of multiplicative costs. For example, perhaps genetic sequencing would be a good case study? There seem to be a lot of multiplicative factors there: amount of coverage, time to get one round of coverage, amount of DNA you need to get one round of coverage, ease of extracting/preparing DNA, error probability… With enough such multiplicative factors, you’ll get exponential growth in megabases per dollar by applying the same amount of improvement to each factor sequentially (whereas if the factors were additive you’d get linear improvement).
I’m actually writing another (long) post on exponential growth and the different phenomena that could lead to it. Multiplicative costs are on the list of plausible explanations. I’ve discussed these multiplicative stories with Jonah and Luke before.
I think that multiplicative costs is a major part of the story for the exponential-ish improvements in linear programming algorithms, as far as I could make out based on a reading of this paper: http://web.njit.edu/~bxd1947/OR_za_Anu/linprog_history.pdf
More in my upcoming post :).
UPDATE: Here’s the post: http://lesswrong.com/lw/k1s/stories_for_exponential_growth/