Spaced Repetition

There is an exact time when you should revise a concept after you’ve learned it. Revising at the moment your brain is about to forget ensures recall probability increases, extending the next forgetting-gap interval.

I was trying to figure out the right time to revise the DSA algorithms I’d been learning. Which led me here.

This is a case study from the foundational papers to the state-of-the-art algorithms that comprise spaced repetition.

Ebbinghaus (1885), Memory: A Contribution to Experimental Psychology

Ebbinghaus describes memory as the persistence of mental states (sensations, feelings, ideas) which were once present in consciousness and then disappeared, but “have not absolutely ceased to exist.”

These states are stored and revealed through various effects, even when not directly observable.

Voluntary recollection. We can call back seemingly lost states by an exertion of will. The will discovers rather than creates.

Involuntary reproduction. Mental states return spontaneously, often after years without effort. These reproductions follow “laws of association,” triggered by current mental images.

Facilitation effects. Even without direct recall, prior experience facilitates similar thought processes later. More than pattern recognition: there’s a latent structure being accessed.

A certain range of thought facilitates under certain conditions the employment of a similar range of thought, even if the former does not come before the mind directly in any form.

What memory depends on

1. Individual differences. People vary; the same person varies across time.
2. Content type. Melodies stick more stubbornly than forms or colors. Emotions resist vivid re-experience.
3. Attention and interest. A single vivid experience (a burn, a humiliation) can create lasting avoidance. Casual encounters slip.
4. Repetitions. Multiple exposures build mastery. Additional repetitions build assurance beyond mastery.
5. Time and decay. Retention weakens over time without review; even deeply rooted knowledge can fade after disuse.

What Ebbinghaus actually did

He made 2,300 nonsense syllables (“ZOF,” “WID”) and formed lists of 12 to 36. He memorized each by reading aloud at fixed rhythm, tested himself after varying intervals (minutes to weeks), then relearned and noted savings. He controlled for time of day and fatigue across multiple years of self-experimentation.

The result: the forgetting curve. Retention drops sharply at first, then flattens. Relearning costs less than first learning. Each relearning raises the curve.

The main paper for FSRS

(Coming soon.)