I first learned of the learning curve when I was a newly hired analyst at a defense think-tank. A learning curve

is a graphical representation of how an increase in learning (measured on the vertical axis) comes from greater experience (the horizontal axis); or how the more someone (or something) performs a task, the better they [sic] get at it.

In my line of work, the learning curve figured importantly in the estimation of aircraft procurement costs. There was a robust statistical relationship between the cost of making a particular model of aircraft and the cumulative number of such aircraft produced. Armed with the learning-curve equation and the initial production cost of an aircraft, it was easy to estimate of the cost of producing any number of the same aircraft.

The learning curve figures prominently in tests that purport to measure intelligence. Two factors that may explain the Flynn effect — a secular rise in average IQ scores — are aspects of learning: schooling and test familiarity and a generally more stimulating environment in which one learns more. The Flynn effect doesn’t measure changes in intelligence, it measures changes in IQ scores resulting from learning. There is an essential difference between ignorance and stupidity. The Flynn effect is about the former, not the latter.

Here’s a personal example of the Flynn effect in action. I’ve been doing The New York Times crossword puzzle online since February 18, 2019. I have completed all 365 puzzles published by TNYT from that date through the puzzle for February 17, 2020, with generally increasing ease:

The fitted curve is a decaying exponential, which means that progress continues but at an increasingly slower rate, which is typical of a learning curve.

The difficulty of the puzzle varies from day to day, with Monday puzzles being the easiest and Sunday puzzles being the hardest (as measured by time to complete):

For each day of the week, my best time is more recent than my worst time, and the trend of time to complete is downward for every day of the week (as reflected in the first graph above). In fact:

• My worst times were all recorded in March through June of last year.

• Today I tied my best time for a Monday puzzle.

• I set or tied my best time for the Wednesday, Friday, and Sunday puzzles in the last three weeks.

• In the same three weeks, my times for the Tuesday puzzle have twice been only a minute higher than my best.

I know that that I haven’t become more intelligent in the last 52 weeks. And being several decades past the peak of my intelligence, I am certain that it diminishes steadily, though in tiny increments (I hope). I have simply become more practiced at doing the crossword puzzle because I have learned a lot about it. For example, certain clues recur with some frequency, and they always have the same answers. Clues often have double meanings, which are hard to decipher at first, but which become easier to decipher with practice. There are other subtleties, all of which reflect the advantages of learning.

In a nutshell, I am no smarter than I was 52 weeks ago, but my ignorance of TNYT crossword puzzle has diminished significantly.

(See also “More about Intelligence“, “Selected Writings about Intelligence“, and especially “Intelligence“, in which I quote experts about the Flynn Effect.)