The forgetting curve

Hermann Ebbinghaus published Memory: A Contribution to Experimental Psychology in 1885. The standard English translation, by Henry Ruger and Clara Bussenius, appeared in 1913.

To avoid the meanings that words carry, he built about 2,300 syllables, each with a vowel sound between two consonants. He mixed them, drew them by chance and strung them into series.

In all the experiments reported in the 1885 book he was his own and only subject.

His forgetting curve rests on about seven months of experimenting, often with up to three sessions per day.

He did not test recall directly. He measured savings: how much less time it took to relearn a series of 13 syllables than it took to learn it the first time, given as a percentage of the first learning time.

One hour after learning, half of the original effort had to be spent again before the series could be reproduced. After 8 hours, the work to be made up amounted to two thirds of the first effort.

After 24 hours about one third of the first work still counted, after 6 days about one fourth, and after a month about one fifth.

Forgetting was very rapid at first and very slow later. Ebbinghaus expected that a complete vanishing of the effect would take an indefinitely long time.

His own table gave 33.7 percent saved at 24 hours. He suspected that figure was a little too large, perhaps by 1 to 2 units, and said it was upheld by other observations.

He cautioned that the results were special, individual and uncertain: they came from one person and a 13-syllable series. He added that nobody should expect a law to be read from the numbers at once.

He fitted the data with a power function in 1880 and a logarithmic function in 1885. Both explained 98.8 percent of the variance in his own data.

In 2015 Jaap Murre and Joeri Dros of the University of Amsterdam published a replication in PLOS ONE. One subject spent about 70 hours learning lists and relearning them after 20 minutes, 1 hour, 9 hours, 1 day, 2 days or 31 days.

The sessions ran between 1 December 2011 and 13 February 2012. In all, 69 lists were learned and relearned.

The results were similar to Ebbinghaus's original data, and the authors concluded that the curve had indeed been replicated. They found the resemblance of the four curves they compared remarkable.

The curve was not perfectly smooth. It most probably shows a jump upwards starting at the 24 hour data point, which some authors have attributed to sleep.

The replication has limits. It used one subject and 10 lists per interval, against the 12 to 45 Ebbinghaus ran, and its 31-day value was much lower than in the other studies.

Ebbinghaus's equations fitted his own data well but did not always fit the other curves, so the authors questioned how generally they apply.

In another set of experiments Ebbinghaus relearned series at the same hour on successive days. Learning a 36-syllable series to the first possible reproduction saved six tenths of the effort at 24 hours, against one third for a 12-syllable series.

Researchers began to demonstrate benefits from spreading practice out in the late 1800s, with Ebbinghaus in 1885, Jost in 1897 and Thorndike in 1912 cited as early examples.

A 2006 review by Nicholas Cepeda and colleagues covered 839 assessments of distributed practice in 317 experiments reported in 184 articles.

When total study time was equal, people who studied an item at two separate times recalled a greater percentage of items than people whose study was nearly uninterrupted. This held for retention intervals from under a minute to over a month.

The gap between study sessions that gave the best retention grew as the retention interval grew.