Ebbinghaus's experiment and quantitative psychology of memory
In 1879, Hermann Ebbinghaus, a German philosopher who had turned to experimental psychology, began a series of experiments in which he served as both researcher and subject. The material consisted of nonsense syllables—three-letter combinations like zof, bik, lut, deliberately stripped of semantic connections to exclude the influence of existing knowledge. Ebbinghaus memorized lists of these syllables to perfect recall, then measured at various intervals how much effort was required to bring the list back to its original level. The difference between the initial learning time and the time spent on relearning—the so-called savings method—became the foundation for a quantitative approach to memory.
The results, published in 1885 in the work Über das Gedächtnis, showed the characteristic shape of the forgetting curve: the steepest drop in retention occurs in the first hours after learning, then the process slows, and after several days the level of retained material levels off. But another observation proved more important. Each subsequent repetition not only restored what was lost but also made the curve itself increasingly shallow—material was forgotten more slowly with each repetition. This effect—that memory improves more with spaced repetitions than with an equal amount of massed learning concentrated in one session—is called the spacing effect in modern cognitive psychology.
From spacing effect to algorithmic implementation
Throughout the twentieth century, the spacing effect was confirmed by hundreds of experiments but remained primarily academic knowledge: ordinary learners needed a practical system that would decide when exactly to return to specific material. The answer to this need came from the work of Polish researcher Piotr Wozniak. While still a student in the early 1980s, he kept detailed records of his own intervals for repeating foreign words, and by 1987 had formalized his observations in the SM-2 algorithm, which became the foundation of the SuperMemo program. The 1990 publication Optimization of learning made the algorithm available to a broad audience; its direct descendants power Anki, Mnemosyne, and dozens of other spaced repetition systems today.
The SM-2 idea is simpler than its reputation suggests. For each card, the algorithm stores just three parameters: the current repetition number, the current interval in days, and the so-called easiness factor (EF)—a dimensionless coefficient starting at 2.5. After each showing, the user rates their own recall on a scale from 0 to 5, where 5 is instant and confident response, 3 is recall with noticeable effort, and 0 is complete lack of recognition. Ratings of 3 and above mean the card was recalled successfully; the first two intervals are fixed—1 day and 6 days—and each subsequent one equals the previous one multiplied by EF. The EF itself is adjusted after each rating: a confident answer slightly increases it, an uncertain one decreases it, with a hard minimum of 1.3 so that even the most "difficult" card will eventually return. A rating below 3 resets progress: the interval drops to minimum, and the card returns to the next session.
Why this works better than cramming
The fundamental difference between spaced repetition and massed learning lies not in the amount of time invested but in its distribution. A meta-analysis by Cepeda and colleagues (Cepeda et al., 2006), summarizing data from over 800 experiments, shows that with equal total time, spaced repetitions yield retention averaging 10-30% higher than massed sessions, and over longer horizons—months—the gap only increases. This effect is explained by two complementary mechanisms. The first is retrieval practice theory: the effort of remembering strengthens memory traces more than passive rereading. The second is Robert Bjork's concept of desirable difficulties: recalling at the edge of forgetting requires greater cognitive investment and therefore produces a more durable result.
SM-2 builds both these ideas into daily practice. A card is shown exactly when it's almost forgotten but still recoverable. Showing too early—repeating what you already remember—does little work; showing too late returns the learner to the starting point. The algorithm seeks balance empirically, adjusting the interval to the individual difficulty of the card: a rare character that the user consistently rates 3 will return to the queue more often than an easy word confidently recognized with a 5.
Practice: three scenarios from real work
Chinese character. An HSK 3 student adds a card to Tomyo with the character 复杂 (fùzá, "complex"). First showing—the next day: the user recalls the meaning with difficulty and gives it a 3. Second showing—after 6 days; this time recognition happens faster, rating 4. SM-2 calculates the third interval based on EF, slightly adjusted downward after the first three—about 13-14 days. If the next rating is again 4, the interval will expand to about a month; if the user makes a mistake, the card returns the next day. Eventually, after six months, the student returns to 复杂 only a few times—exactly as many as needed to keep the character in their active vocabulary.
Quote from a book read. A user saves a phrase from Sun Tzu's Art of War: "All warfare is based on deception." The card contains the quote on one side and context—chapter, author, personal note—on the other. After a day, after a week, after two weeks, the system brings it up from the bottom of the stack. The quote isn't memorized mechanically; each return becomes a brief reflection during which the user re-integrates the phrase into their own conceptual framework. After a few months, the quote becomes available for citation in conversation or writing—not because it was crammed, but because it was repeatedly worked with.
Term from notes. A student saves a definition from a cognitive psychology lecture: "generation effect—better memory for material produced independently compared to material read or heard." Five or six returns to this card over six months make the term part of their working vocabulary rather than a one-time note in their notebook—without any special time allocated "for reviewing flashcards."
SM-2 limitations and modern developments
SM-2 is a 1987 algorithm, and it would be naive to consider it the final word. Its main weaknesses are known. First, it relies on subjective user assessment: the same person on different days might rate equally confident recall differently. Second, it uses a single formula for all types of material—from characters to legal definitions—though their actual forgetting curves differ. Third, it's based on a relatively crude model of memory where intervals grow geometrically and EF is assumed to be a global property of the card.
Modern implementations refine this model. The FSRS algorithm (Free Spaced Repetition Scheduler), built into Anki since 2023, replaces fixed formulas with a model trained on data from millions of repetitions; it explicitly optimizes showings for a given recall probability (e.g., 90%) and accounts for different cards aging differently. Nevertheless, SM-2 remains a reference point: it's simple enough to be transparent and effective enough to prove its worth in practice over nearly four decades. For Tomyo's tasks—retaining words, quotes, notes—its behavior is predictable, and its mathematics allows auditing: any user wanting to understand why a card appeared today rather than tomorrow can do so.
What this means for users
Spaced repetition is not a trick or a product innovation of recent years. It's a direct engineering implementation of an effect first documented in 1885, and its effectiveness has been repeatedly measured in rigorous experiments building on Ebbinghaus's original observations. Tomyo doesn't promise effortless memorization—on the contrary, the effort in recall is precisely the mechanism that makes memory durable. What Tomyo actually does is remove from users the task of deciding when exactly to return to a specific word or quote, delegating this decision to an algorithm with known lineage and transparent mathematics.
If your collection has accumulated quotes, characters, or notes that you'd like to actually remember rather than just store—this is exactly what Tomyo's card mode is for: it returns material at the moment when that return provides the greatest benefit.
