Spaced Repetition: The Forgetting Curve, Hacked

In 1885, a German psychologist named Hermann Ebbinghaus published a slim monograph called Über das Gedächtnis — On Memory — built almost entirely on experiments he had run on himself. Ebbinghaus had constructed a list of about 2,300 trigram nonsense syllables, three-letter combinations like ZOK and BIF, designed to be free of any prior associations. He memorised them in fixed-length lists, waited a controlled interval, and then measured how many trials it took to relearn the list to perfect recall. The savings — the difference between original and relearning trials — gave him a quantitative measure of forgetting. The curve he plotted, with retention falling sharply within the first hour and then more gradually for days, became known as the forgetting curve, and it remains one of the most replicable findings in experimental psychology. Ebbinghaus also noticed, almost in passing, that lists studied across multiple sessions separated by hours or days were retained far better than lists studied in one massed sitting of equivalent total time. He had identified what would later be called the spacing effect, decades before anyone had a use for it.

The first explicit recommendation to apply the spacing effect to study came in a 1932 book by the British philosopher and psychologist Cecil Alec Mace, titled Psychology of Study. "Acts of revision," Mace wrote, "should be spaced in gradually increasing intervals, roughly intervals of one day, two days, four days, eight days, and so on." The advice sat unread for most of a decade. In 1939, the Iowa educational psychologist H.F. Spitzer ran what is still one of the largest applied tests, using more than 3,600 sixth-grade students learning science facts under different review schedules. Spitzer's results clearly favoured spaced review over massed cramming, and the paper was promptly forgotten outside of a small circle of educational researchers. The technique sat on the shelf, again, for another thirty years.

The popular breakthrough came not from a laboratory but from a German science journalist named Sebastian Leitner, who in 1972 published a book called So Lernt Man Lernen — How to Learn to Learn. Leitner described a deceptively simple system using physical flashcards and a wooden box divided into compartments of increasing size: 1, 2, 5, 8, and 14 centimeters wide. New cards went into the smallest compartment. Cards answered correctly were promoted one compartment to the right; cards answered wrong were demoted back to the first. Each compartment was reviewed when it filled — automatically producing longer intervals for material that was sticking and shorter intervals for material that wasn't. The Leitner system spread through European language-learning classrooms in the 1970s, and the same logic showed up almost simultaneously in the audio Pimsleur language courses, where the linguist Paul Pimsleur had laid out a graduated-interval recall schedule in a 1967 paper: 5 seconds, 25 seconds, 2 minutes, 10 minutes, 1 hour, 5 hours, 1 day, 5 days, 25 days, 4 months, 2 years.

The leap to software came from a Polish student named Piotr Wozniak, who built a paper-and-pencil prototype he called SM-0 in 1985 while preparing for his university English exam. Wozniak measured his own recall of thousands of word pairs, fit a power-law curve to his forgetting, and worked out an interval-prediction formula. He coded the result for an Atari ST in 1987 and shipped it as SuperMemo, the first commercial spaced-repetition program. The successive algorithms — SM-2, SM-5, SM-15, SM-18 — became progressively more sophisticated, but it was SM-2, the 1990 version, that mattered most for the world, because Wozniak had published it openly. In 2006, an Australian computer-science student named Damien Elmes adapted SM-2 into a free, open-source, cross-platform tool he called Anki — Japanese for "memorisation." Anki spread first through medical-school study groups, where students used it to drill thousands of cards on pharmacology, anatomy, and pathology, and then through every other discipline that requires memorising large bodies of facts. By the late 2010s, surveys at U.S. medical schools were finding that more than half of students used Anki daily.

The algorithm under Anki has now been replaced. In 2022, a team led by Junyao Ye at the Harbin Institute of Technology published what they called the Stochastic Shortest Path Minimize Memorization Cost approach, modelling the user's memory as a stochastic process and the spacing schedule as an optimal-control problem. The applied version, the Free Spaced Repetition Scheduler, fits a three-parameter memory model — difficulty, stability, retrievability — to each individual user's review log and optimises future intervals from there. Damien Elmes ported FSRS into Anki release 23.10 in October 2023, where it now sits as the default scheduler. Where SM-2 used a one-size-fits-all forgetting curve, FSRS adapts to each user's specific decay constants, and benchmarks on millions of public Anki review logs have shown roughly 30 percent fewer reviews for the same retention target. The training data, paradoxically, comes from the users themselves: every "again," "hard," "good," and "easy" press feeds back into the global model, which then re-fits each user's personal three-parameter curve from their own history of correct and incorrect recalls. Ebbinghaus, in 1885, sat alone in a room reciting nonsense syllables and tracked the rate at which his own memory leaked. The same curve, now multiplied by tens of millions of users and continuously refit by gradient descent, schedules every flashcard review on every phone running the world's most-installed study app.