Wikipedia actually has a pretty good introductory article on the concept of the learning curve. Because I can’t put it any more succinctly, I’ll quote from the article:
The learning curve effect and the closely related experience curve effect express the relationship between experience and efficiency. As individuals and/or organizations get more experienced at a task, they usually become more efficient at them. Both concepts originate in the old adage, “practice makes perfect”.
So, an experience vs. efficiency curve generally looks somewhat logrithmic; a little bit of experience doesn’t produce a proportional gain in efficiency over base neophyte (the tangent is very “steep”–over unity–initially), but once you get to a certain level of experience the curve “breaks over” (where the tangent becomes fractional) and you become more adept at figuring out how to anticipate and solve problems and where to find data.
In manufacturing, the notion of a learning curve has been used for a long time–Robert McNamara, later Secretary of Defense, introduced it to Ford Motor Company when he became part of their nascient quality department–to quantify the process of “getting the kinks out”. It is often incorrectly conflated with efficiencies of scale (which come about due to cost/labor reductions of bulk purchasing and automation).
Here’s[sup]*[/sup] a funny example of “learning curve”: When physicist Richard Feynman started doing research on the properties and behavior of superfluid helium (He II) in the early Fifties, he spent a lot of time looking in journals, talking to experimentalists, and otherwise becoming acquainted with the state of knowledge regarding that substance. He came up with a novel theory of its behavior, but despite extensive efforts couldn’t figure out the details of the thermodynamic functions at the phase transition. He presented a paper on his theory at a conference in Japan in 1951, apologizing for his inability to address this particular detail. Another, more experienced researcher in the field. Lars Onsager, spoke up and said, “Mr. Feynman is new in our field, and there is evidently something he doesn’t know about it, and we ought to educate him.” Feynman was mortified and was prepared for a scathing attack on his ignornance, but Onsager continued, “so I think we should tell him that the exact behavior of the thermodynamic functions near a transition is not yet adequately understood for any real transition in any substance whatsoever.”
In other words, if Feynman had known what other physicists involved in thermodynamic research of material phase transitions all knew he wouldn’t have spent much time or felt the need to apologize. Heh.
Stranger
I’m currently reading Perfectly Reasonable Deviations From the Beaten Track, a collection of correspondence from and to Feynman, and he brings this up in a letter to Onsager’s biographer. He appears to have later retooled this passage for one of his own autobiographical collections of anecdotees (“Surely You’re Joking, Mr. Feynman?”* I believe).