There were some very good comments on, "Is Exponential Growth Possible?." Kimsia linked to this interesting academic paper on learning - http://acs.ist.psu.edu/papers/ritterS01.pdf

It's fairly intuitive and not groundbreaking, but there's a few really interesting points in there.

The basic idea behind the paper is that the more you practice a skill, the faster you get at it - but the gains slow down and flatten out over time.

The pattern is a rapid improvement followed by ever lesser improvements with further practice. Such negatively accelerated learning curves are typically described well by power functions, thus, learning is often said to follow the "power law of practice". Not shown on the graph, but occurring concurrently, is a decrease in variance in performance as the behavior reaches an apparent plateau on a linear plot. This plateau masks continuous small improvements with extensive practice that may only be visible on a log-log plot where months or years of practice can be seen. The longest measurements suggests that for some tasks improvement continues for over 100,000 trials.

I found that whole paragraph to be fascinating:

First, their main point - rapid improvement is followed by gradually less and less improvement per time practicing. Makes sense, we've all experienced it.

Second point is really interesting - "a decrease in variance in performance" as you reach the flat part of the curve... that means you'll tend to have less days where you perform much better than average (because you're performing consistently high) and less days where you slip up and make mistakes. Again, it jives with reality, but I hadn't thought through that before. More practice = less variance. Obvious when put that way, but a good insight none the less.

Thirdly - you might keep improving up to 100,000 trials and beyond. That also jives, but - wow. That's a wow thing for me to hear.

This part of the piece stood out the most to me -

The power law of practice is ubiquitous. From short perceptual tasks to team-based longer term tasks of building ships, the breadth and length of human behavior, the rate that people improve with practice appears to follow a similar pattern. It has been seen in pressing buttons, reading inverted text, rolling cigars, generating geometry proofs and manufacturing machine tools (cited in Newell and Rosenbloom, 1981), performing mental arithmetic on both large and small tasks (Delaney, Reder, Staszewski, & Ritter, 1998), performing a scheduling task (Nerb, Ritter, & Krems, 1999), and writing books (Ohlsson, 1992). Further examples are noted in reviews (e.g., Heathcote, Brown, & Mewhort, in press). In manufacturing this curve is called a progress function. You can see it for yourself by taking a task, nearly any task, and timing how long it takes to complete over 10 trials, or better over a hundred trials.

Interesting that such a wide variety of skills follow the same pattern.

Interesting paper. It's academic-ish, so it's not beach reading, but it's fairly short and there's some good insights in there. Might be worth a read if the topic piques your interest:

http://acs.ist.psu.edu/papers/ritterS01.pdf

Thanks again for sharing this, Kimsia.