Learning and the mind
The forgetting curve
Memory for new material drops fast in the first hours and then slowly; what is left after a day is most of what will be left after a month.
Hermann Ebbinghaus, Über das Gedächtnis (1885), from experiments he ran on himself in 1879 to 1880 and 1883 to 1884.
Ebbinghaus learned lists of nonsense syllables until he could recite them twice without error, waited, then relearned them and measured how much less time the second learning took. That saving is his measure of what remained. From 163 double tests run in 1879 and 1880 he found that about 58 percent of the original effort was saved after 20 minutes, 44 percent after an hour, 36 percent after nine hours, 34 percent after a day, 28 percent after two days, 25 percent after six and 21 percent after a month. Plotted, the points drop steeply and then flatten: most of the loss happens on the first day, and a memory that survives the day decays much more slowly after that. He fitted a formula in which the saving falls with a power of the logarithm of time.
The curve matters because it says when to intervene. A review placed before the steep part has done its work is nearly wasted; a review placed after the memory has gone is relearning from scratch. The gentle tail means that each successful review resets a slower curve, which is what spaced repetition exploits. In 2015 Jaap Murre and Joeri Dros repeated the experiment on one subject with 70 lists of 104 syllables, about 70 hours of work, and got the same shape: 47 percent saved at 20 minutes, 32 at a day, 4 at 31 days. Their curve also had a bump at the 24-hour point, with savings at one day higher than at nine hours, which they read as a likely sign of consolidation during the first night's sleep.
The curve describes nonsense syllables learned by rote, by one highly practised subject. Meaningful material, which attaches to what you already know, is forgotten more slowly, and the exact rates in the chart are his, not yours. The savings measure is also not recall: 21 percent saved after a month does not mean 21 percent remembered. Popular charts of the curve often carry numbers that are not in Ebbinghaus's table; check any figure against the seven he published. And Murre and Dros found the original's month-long tail far higher than their own, so treat the shape as reliable and the numbers as illustrative.
Example
Murre and Dros's replication, published in PLOS ONE in 2015, had one subject, Dros himself, aged 22, learn 70 lists of 104 nonsense syllables between 1 December 2011 and 13 February 2012, about 70 hours of work, and relearn each list after 20 minutes, one hour, nine hours, one day, two days, six days or 31 days. Savings were 47.2 percent at 20 minutes, 37.3 at an hour, 27.6 at nine hours, 31.7 at a day, 23.0 at two days, 16.8 at six days and 4.1 at 31 days, against Ebbinghaus's 58.2, 44.2, 35.8, 33.7, 27.8, 25.4 and 21.1. The shape matched. In the replication the one-day point sat above the nine-hour point, a jump the authors say most probably reflects something that happens during the first night, and the month-long tail was far lower than the original's.
Where it applies
The /flashcards scheduler and the review feature at /models/review are timed against this curve: the first review comes soon, later ones further apart. The same shape applies to a runbook you read once; by the time the pager goes off you are on the tail of the curve, so the fix is a rehearsed procedure rather than a longer document. See half-life for the same decay in the facts themselves.
Think about it
What did you learn about a week ago that you have not touched since, and how much of it could you write down now?
Applied it to something real? Log it.
Test yourselfWhat did Ebbinghaus actually measure, and what shape did he find?
Savings: how much less time relearning a list took after a delay. About 58 percent saved at 20 minutes, 34 at a day, 21 at a month, so loss is steep in the first hours and then slow.
Related models
- Half-lifeA quantity that loses a fixed fraction per period has a half-life, and after a few of them most of it is gone, whether it is carbon-14 or a fact.
- Spaced repetitionReviews spread out over time beat the same reviews crammed together, and the best gap grows with how long you need to remember.
- Sleep and memory consolidationThe brain replays and reorganises the day's memories while you sleep, so a night of sleep improves recall and skill where a day awake does not.
- Retrieval practicePulling something out of memory strengthens it more than putting it in again, so a test is a better study tool than a reread.