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:
Thanks again for sharing this, Kimsia.
Another great post, Sebastian.
I'll read the paper in a bit, but you're basically describing the law of diminishing returns, which brings up two more points. At first, you gain a high return for effort expended. Eventually, the return will equal the effort. Finally, the effort will be higher than the return merits.
The second point is how to sidestep this law. Let's say you're learning about programming in Java. After a few years of only programming in Java, you aren't learning anything new from it (until the next release). Maybe you start programming in Python. Each language has its own philosophy of programming, so learning another language gives you a different point of view. You're also getting large returns for a smaller effort again. The point, though, is that your Java skills will also improve without extending a lot of effort for little gain.
This basically matches my idea of cross training the mind. A biologist who also learns to think like a mathematician will be a better biologist. By learning a completely different skill, you bypass the law of diminishing returns in your primary field. As long as you apply your new knowledge to your old field, of course.
I'm interested in the subject and can recommend two book on the it:
"Mastery: The Keys to Success and Long-Term Fulfillment" by George Leonard
"The Art of Learning: An Inner Journey to Optimal Performance" by Josh Waitzkin
A few questions from a reader today -
I've been in a slump recently where I have gotten very little done, and i was trying to figure out how to stop it. I could clearly see I was slacking off, falling into a pattern (probably an old one) of using my time more or less pointlessly and getting only the essentials done (which i was greatful for). I was able to turn a good portion of the wasted time toward something productive, but the time itself I still consider a waste, things I was doing without an intension to use the experience.
So I have two question here. Whats the best way to pull yourself out of a slump, to re-engage yourself and bring yourself back up to the projected level of prductivity (or at least a realistic level) ?
Fundamentals. Fundamentals are the only way out of slumps. A little exercise, a little eating well, enough sleep, some time in nature or breathing, some time with people you like, setting goals at the beginning of the day for the day, starting work on those right away, and sleeping on a decent schedule.
That's the only way I've found. There's no magic. When in a rut, work on fundamentals to get out. While that's not always easy, that seems to be the only way. Also, celebrate the small victories. If you're off-track and doing things even a little right, have a little celebration.
This site is for people who want to grow exponentially; to improve their ability to improve themselves. Is this even possible?
Here's an exponential curve:
Making one positive change makes it easier to make more positive changes in future. So at first glance, it looks as though your rate of growth should keep growing, and that exponential improvements are possible.
But clearly you can't grow exponentially forever. We don't encounter people who've reached a "productivity singularity" where they can complete their daily tasks in five minutes, and spend the rest of their time reading time-management books (while jogging on a treadmill) to become even more efficient.