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History of research on spaced repetition has been plagued by the following factors:
- guesses and heuristics used in place of mathematical optimization
- poor interaction between theory and practice with science focused on simple experiments and practice focused on simple tools
- terminological inconsistency that leads to cycles of forgetting and re-discovery!
The above agrees with my ranking of factors of failure. Until the arrival of personal computing and the web, it was hard to escape the vicious cycle.
关于间隔重复的研究历史一直受到以下因素的困扰:
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用于代替数学优化的猜测和启发式
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理论和实践的之间缺乏互动，科学侧重于简单的实验，实践侧重于简单的工具
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术语不一致，导致遗忘和重新发现的循环
以上与我对失败因素的排名一致。在个人电脑和网络出现之前，人们很难逃脱这种恶性循环。
When we asked teenagers a set of questions about how their memory works, a large proportion could come with pretty good guesses about repetition spacing without ever making any measurements. In particular, they often correctly guess that the first optimum inter-repetition interval might be 1-7 days long and that successive intervals will increase. Moreover, many could guess that the second interval might be a month long and that successive intervals might double. In other words, spaced repetition is a common intuition.
当我们问青少年一组关于他们的记忆是如何工作的问题时，很大一部分人可以很好地猜测出重复间隔，而不做任何测量。特别是，他们经常正确地猜测第一个最佳间隔可能是 1-7 天，并且连续的间隔会增加。此外，许多人可能会猜测第二个间隔可能是一个月，而连续的间隔可能是两倍。换句话说，间隔重复是一种常见的直觉。
In 1885, Hermann Ebbinghaus made a major contribution to the science of memory. He experimented on himself and came up with the first outline of the forgetting curve. He was also aware of the spacing effect. He never worked on spaced repetition. I do not credit Hermann for an inspiration in my work over spaced repetition as I simply had no idea who Hermann was and what he accomplished. I designed my own measurement that led to spaced repetition. In an unrelated and forgotten exercise, I also produced my own forgetting curve that might have influenced my thinking. Hermann's curve was much steeper and might have actually discouraged further work (see: Error of Ebbinghaus forgetting curve). Our Adam Mickiewicz University library was well stocked up with "ancient" pre-WW2 German literature, however, I knew no German. Mine was an ignorant solo effort. I read about Ebbinghaus later, and mentioned his forgetting curve in my Master's Thesis.
1885年，赫尔曼·艾宾浩斯对记忆科学做出了重大贡献。他在自己身上做了实验，提出了遗忘曲线的第一个轮廓。他也知道间隔效应。他从未研究过间隔重复。我不认为赫尔曼在我的间隔重复研究中给了我灵感，因为我根本不知道赫尔曼是谁，他完成了什么。我设计了自己的测量方法得出间隔重复。在一个无关的和被遗忘的练习中，我也产生了我自己的遗忘曲线，这可能影响了我的思考。赫尔曼的曲线要陡峭得多，实际上可能会阻碍进一步的研究(参见:艾宾浩斯遗忘曲线的错误)。我们亚当·米基维奇大学的图书馆里有大量二战前的“古代”德国文学，但我不懂德语。我是在不了解的情况下做出的努力。后来我读了关于艾宾浩斯的文章，并在我的硕士论文中提到了他的遗忘曲线。
By 1901, in texts written by William James, the superiority of spaced review seemed clear and it seemed like a matter of time before it would permeate the learning theory with optimization of spacing taken as the next obvious step. It was not to be. For another 8 decades.
到 1901 年，在威廉·詹姆斯所写的文章中，间隔复习的优越性显而易见，它将渗透到学习理论中，并将间隔优化作为下一步，似乎是迟早的事。但结果却并非如此。又过了 80 年。
In his popular book of 1932, C.A. Mace has suggested a simple spaced repetition schedule: 1 day, 2 days, 4 days, 8 days, etc. Good guess! Mace's effort was forgotten though because spaced repetition on "postcards in a pocket" before the era of the Internet must have hardly been appealing. For a good start, Mace would have to shine with his own good example to encourage others. He described his excellent ideas about efficient learning as a theory. He never mentioned his own experience. Promoting a new idea in those days was probably not easy. Herr Hitler dominated the news. Perhaps the progress in spaced repetition theory was yet another victim of the Nazi?
1932 年出版的畅销书中，C.A.梅斯提出了一个简单的间隔重复时间表：1天，2天，4天，8天，等等。很好的猜测！然而，梅斯的努力被人遗忘了，因为在互联网时代到来之前，“口袋里的明信片”上的间隔重复肯定没什么吸引力。为了有一个好的开始，梅斯必须用自己的好榜样来鼓励别人。他把他关于有效学习的优秀思想描述为一种理论。他从未提及自己的经历。在那个时候推广一个新想法可能并不容易。希特勒成了新闻的主角。也许间隔重复记忆理论的进步是纳粹的又一个受害者？
In 1966, Herbert Simon had a peek at Jost's Law derived around 1897 from Ebbinghaus's work. Simon noticed that exponential nature of forgetting necessitates the existence of a memory property that today we call memory stability. Simon wrote a short paper explaining his idea, and moved on to hundreds of other projects he had on his mind. His text was largely forgotten.
1966年，赫伯特·西蒙瞥见了1897年左右从艾宾浩斯的著作中衍生出来的约斯特定律。西蒙注意到，遗忘的指数性质必然存在一个记忆属性，今天我们称之为记忆稳定性。西蒙写了一篇简短的论文来解释他的想法，然后开始着手于他脑海中成百上千的其他项目。他的文章基本上被遗忘了。
At roughly the same time, Robert Bjork had a great deal of innovative ideas in reference to learning and memory. As it often happens, he was ahead of his time. Teachers hardly ever listen to psychologists. Students do not even know their names. If Bjork was a programmer, we might have had the first popular application of spaced repetition a decade earlier. I think he would just not let a great idea off the hook. It was Bjork who seems to have been first to clearly separate retrieval strength and storage strength in a model analogous to our two component model of memory.
大约在同一时期，罗伯特·比约克在学习和记忆方面有很多创新的想法。正如经常发生的那样，他走在了时代的前面。老师们几乎从不听心理学家的话。学生们甚至不知道他们的名字。如果比约克是一个程序员，我们可能早在十年前就有了第一个流行的间隔重复应用程序。我想他不会放过任何一个好主意。比约克似乎是第一个在一个类似于我们的记忆双变量模型的模型中明确区分检索强度和存储强度的人。
In 1967, Paul Pimsleur could clearly see that spaced repetition could be a great tool for learning word-pairs in language learning. Like SuperMemo, he struggled with terminology and used the term "graduated-interval recall". In our "serrated forgetting curve" challenge, Pimsleur came closest with the earliest known serrated curves graph as in the picture:
1967年，保罗·皮姆斯勒清楚地看到间隔重复可能是学习语言学习中单词对的一个伟大工具。就像 SuperMemo 一样，他在术语上遇到了困难，使用了“渐进间隔回忆”这个术语。在我们的“锯齿状遗忘曲线”挑战中，皮姆斯勒与图中所示的最早的锯齿曲线曲线最为接近：
Perhaps we will discover earlier sketches of the idea, however, for technical reasons, the older the print, the less rich it is in graphs, which we today generate en masse in Excel.
也许我们会发现这个想法的早期草图，然而，由于技术原因，打印的时间越早，图形的内容就越少，而我们今天在 Excel 中生成了大量图形。
Pimsleur's intervals extended into periods of hours, minutes and even seconds. It was a reflection of an intuition, not measurement. He extended his reasoning from declarative knowledge that can easily be measured (e.g. word pairs) to procedural knowledge and audio-pattern recognition, as in learning pronunciation. SuperMemo solves this problem by separating word-pair learning from pronunciation, spelling, recognition, synonyms, and the like. As a result, e.g. in Advanced English, we never need to reduce intervals beyond user's standard startup stability, which rarely drops down below a day. For practical reason and due to the role of sleep, SuperMemo never uses intervals shorter than 1 day. Sleep is also the main reason why the algorithm uses 1-day resolution in the length of intervals. SuperMemo makes it possible to review multiple times in a day, but this is part of a subset review that, on occasion, may appear useful (e.g. when cramming for an exam). Pimsleur's interval recommendations were different than those of Mace or SuperMemo on paper (Algorithm SM-0). They were not a result of a measurement, but a result of a speculation, which ranged from solid to poor. Pimsleur thought of ensuring recall of 60%, which is very low by SuperMemo standards. He bet on startup stability of 5 seconds, while SuperMemo uses 1-15 days, which is just fine for 90% recall of well-formulated knowledge. Pimsleur's base of interval exponentiation (E-Factor) was 5, which should be 1.4-2.5 in most cases. As a result, Pimsleur's spacing differs dramatically from SuperMemo's, and should not be used as a benchmark in algorithmic metric. In his original paper (1967), Pimsleur proposed intervals of 5 sec., 25 sec., 2 min., 10 min., 1 hour, 5 hours, 1 day, 5 days, 25 days, 4 months, and 2 years. The differences came mostly from the practise based on materials of different character (equivalent to high complexity in SuperMemo). The use of seconds, minutes and hours is tantamount to cramming and is strongly discouraged in SuperMemo. Instead, optimization of knowledge representation is advised.
皮姆斯勒的间隔时间延长到数小时、数分钟甚至数秒。这是直觉的反映，而不是衡量。他将他的推理从容易测量的陈述性知识(如单词对)扩展到程序性知识和声音模式识别，如学习发音。SuperMemo 解决了这个问题，它将单词对学习从发音、拼写、识别、同义词等方面分离出来。因此，在 Advanced English 中，我们从不需要减少超出用户标准启动稳定性的时间间隔，它很少下降到一天以下。由于实际原因和睡眠的作用， SuperMemo 从不使用短于 1 天的间隔。睡眠也是该算法在时间间隔长度上使用 1 天分辨率的主要原因。SuperMemo 可以让你在一天内复习很多次，但是这是一个子集复习的一部分。与梅斯和纸上的 SuperMemo（算法 SM-0）的推荐间隔不同。它们不是测量的结果，而是推测的结果，从可靠到不可靠。皮姆斯勒想确保 60% 的保留率，这在 SuperMemo 的标准下是非常低的。他打赌启动稳定性是 5 秒，而 SuperMemo 使用 1-15 天，这对于 90% 的良好的知识回忆来说是可以的。皮姆斯勒的区间指数基数(E-Factor)是5，在大多数情况下应该是1.4-2.5。因此，皮姆斯勒的间隔与 SuperMemo 的间隔有很大的不同，不应该用作算法度量的基准。在他的原始论文(1967)中，皮姆斯勒建议间隔 5 秒、25 秒、2 分钟、10 分钟、1 小时、5 小时、1 天、 5 天、25 天、4 个月和2 年。差异主要来自于基于不同性质材料的实践(相当于 SuperMemo 中的高复杂性)。秒、分和小时的使用相当于死记硬背，在 SuperMemo 中强烈不鼓励使用。相反，建议优化知识表示。
In 1969, Alfred Maksymowicz wrote "Read and think". You will not find his book in your library. It was written in Polish and for a narrow circle of students of technical universities. It mentioned spaced repetition, forgetting curves, and even how the forgetting index might determine the optimum interval. Maksymowicz proposed the first optimum interval to be 3 days. As many efforts before and after, this good advice remained largely ignored. Students rush to pass an exam and then forget. Cram and dump is a principle by which the pressure of schooling destroys the prospects of good long-term learning. I know of Maksymowicz's book only because I studied at a technical university in Poland, and I was pretty loud of my own spaced repetition method. I can only imagine that there have been dozens other similar texts where intuitions were formulated as a good advice that then remained ignored by the masses. Without the coincidence of time and space, future texts on spaced repetition might never notice Maksymowicz ever existed. Maksymowicz might have been inspired by Pimsleur, Mace, his own intuition, or other potential texts of which I have no knowledge. Maksymowicz gives credence to the words of Szafraniec, skeptical of SuperMemo: "all has occurred before".
1969年，阿尔弗雷德·马克西莫维奇写了《阅读与思考》。你在你的图书馆里找不到他的书。这本书是用波兰语写的，面向的是一小部分技术大学的学生。它提到了间隔重复，遗忘曲线，甚至遗忘指数可能决定最佳间隔。马克西莫维奇提出的第一个最佳间隔为 3 天。就像之前和之后的许多努力一样，这个好建议在很大程度上仍然被忽视。学生们急于通过考试，然后就忘记了。临时抱佛脚是一个原则，学校的压力会通过这个原则毁掉长期良好学习的前景。我之所以知道马克西莫维奇的书，是因为我在波兰的一所技术大学学习过，而且我对自己的间隔重复方法很感兴趣。我只能想象，有几十个类似的文本中，直觉被表述为一个好建议，然后仍然被大众忽视。如果没有时间和空间的巧合，将来关于间隔重复的文章可能永远不会注意到马克西莫维奇曾经存在过。马克西莫维奇的灵感可能来自皮姆斯勒、梅斯、他自己的直觉，或者其他我不知道的潜在文本。马克西莫维奇给扎弗拉涅克的话以自信，对SuperMemo表示怀疑："一切都发生过"。
The greatest practical and algorithmic success in the area of spaced review before SuperMemo can be attributed to Sebastian Leitner. In 1972, he proposed the Leitner box system. In a Leitner system, flashcards are prioritized and dumped to boxes corresponding with different stability levels. The Leitner system has one huge advantage over the theoretical advice dished prior to his proposition: it was practical. It was a system anyone could use with little introduction. Even SuperMemo on paper (1985) seems complex in comparison.
在 SuperMemo 之前，在间隔复习领域最大的实践和算法上的成功要归功于塞巴斯蒂安·莱特纳。1972年，他提出了莱特纳盒子系统。在莱特纳系统中，抽认卡被按优先级排序，并被转储到对应不同稳定性级别的盒子中。与之前提出的理论建议相比，莱特纳系统有一个巨大的优势：它是实用的。这是一个任何人都可以使用的系统，几乎不需要介绍。即使是写在纸上的 SuperMemo(1985) 相比之下也显得复杂。
Figure: An incorrect mutation of the Leitner system where failed answers are moved back by one box only (source: Wikipedia). This variant was in use in Duolingo for a while
图片：一个错误的Leitner系统的突变，失败的答案只被移回一个方框(来源:Wikipedia)。这种变体在Duolingo中使用了一段时间
The Leitner box is not a spaced repetition tool. It is a prioritization tool. There is no concept of an interval, let alone optimum interval. The name box comes from the original implementation in the form of physical flashcard boxes with not association to passing time. When the Leitner box is used regularly on a small-sized collection of flashcards, it simulates the behavior of spaced repetition. If intervals are too short, it leads to cramming. If they get too long, it leads to sub-optimum outcomes. However, in SuperMemo, low priority material may also be postponed cyclically and yield very long intervals which reduce expected stability increase, but carry a larger stability increase for items that survive longer intervals. In the 1990s and early in the new millennium, the Leitner system was used in many successful flashcard applications. As they kept tinkering and improving the review procedures, these apps might have actually evolved into a full-blown spaced repetition system. Their application declined though due to the popularity of SuperMemo's Algorithm SM-2 that turned out to be easy to implement and vastly superior.
莱特纳盒子不是一个间隔重复工具。它是一个排序工具。没有间隔的概念，更不用说最优间隔。盒子的名称来源于最初的实现，以物理闪卡盒的形式出现，与时间无关。当莱特纳盒子定期用于一个小型的抽卡片集合时，它会模拟间隔重复的行为。如果间隔太短，就会导致死记硬背。如果太长，就会导致次优结果。然而，在SuperMemo，低优先级的材料也可能周期性推迟，并产生很长的间隔，这会降低预期的稳定性增长，但对于记忆时间较长的卡片，稳定性增长会变得较大。在 20 世纪 90 年代和新千年之初，莱特纳系统被用于许多成功的闪卡应用。随着他们不断修改和改进复习程序，这些应用程序实际上可能已经发展成为一个成熟的间隔重复系统。由于 SuperMemo 的 SM-2 算法的流行，他们的应用下降了，但结果证明该算法很容易实现，而且非常优秀。
Newer software mutations of the Leitner box system may attach intervals to priority boxes, e.g. 16 days for Box #5, but this approach has flaws tantamount to cramming: (1) failure still leads to the regression of intervals, while it should lead to resumed learning, (2) five repetitions in the first month does not compare well to well-formulated knowledge that may reduce the cost of learning in SuperMemo in the first month alone by 60-80%, and (3) more boxes would be needed. We have seen intervals well beyond maximum human lifespan in SuperMemo. The needs for lifetime applications are 200 thousand percent higher. This is the difference between a permastore interval and 16 days. 11 extra boxes would be needed to cover the lifetime at E-factor of 2.
莱特纳盒系统的较新的软件版本可能会将间隔附加到优先级盒上，例如第 5 盒需要 16 天，但是这种方法的缺陷无异于死记硬背：（1）失败仍会导致间隔的回归，但这应导致重新学习；（2）第一个月重复5次，不能很好地与组织良好的知识相配，组织良好的知识可以在第一个月减少 60-80% 的学习成本。（3）需要更多的盒子。在SuperMemo中，我们看到间隔时间远远超过了人类的最长寿命。对应用程序的使用寿命需求增加了 200%。这是永久记忆间隔与16天之间的差异。 需要额外的 11 个盒子来覆盖 EF 为 2 的使用寿命。
Today, one of the most popular systems for learning languages is Duolingo. For a long while, it used the Leitner system. Today they employ their own new algorithm based on retrievability predictions. However, they still used the Leitner system as a benchmark. To make matters worse, their benchmark used the reverse transfer of flashcard in priority boxes (where the post-lapse stability is overestimated). Normalized Leitner might be used as a benchmark, however, simple normalization equivalent to using E-factor of 2, may produce different results than the choice of E-factor 1.6. In the future, all algorithms should switch to a universal metric proposed by SuperMemo, and Algorithm SM-2 might become a useful metric benchmark that can be implemented in parallel with proprietary solutions. I hope users will demand clarity, statistics, metrics, and full openness in that respect. Incidentally, if you happen to use SuperMemo 17 version 17.4, you can compare Algorithm SM-17 with the Leitner system, Pimsleur and Algorithm SM-2. Needless to say, if your collection is sizeable enough, the differences are pretty stunning.
如今，最流行的语言学习系统之一是 Duolingo。很长一段时间，它都使用莱特纳系统。如今，他们采用了基于可提取性预测的新算法。然而，他们仍然使用莱特纳系统作为基准。更糟糕的是，他们的基准使用了优先级盒中的抽认卡的反向传输(在这里，遗忘后的稳定性被高估了)。归一化莱特纳可以作为一个基准，然而，简单的归一化相当于使用 EF 为 2，可能会产生与选择 EF 为 1.6 不同的结果。在未来，所有的算法都应该转换到一个由 SuperMemo 提出的通用度量，并且 SM-2 可能成为一个有用的度量基准，可以与专用解决方案并行实现。我希望用户在这方面要求清楚、统计、度量和完全开放。顺便说一句，如果您碰巧使用了SuperMemo 17 版本 17.4，您可以将 SM-17 与莱特纳系统、皮姆斯勒和 SM-2 进行比较。不用说，如果您的集合足够大，差异相当惊人。
In the 1970s, Tony Buzan would focus on structured knowledge with his mind-mapping innovations. Mind maps and SuperMemo would, paradoxically, stand in conflict due to a lack of a good unifying theory. In short, we need good models to understand the world, and we need the spaced review to retain the components of the model in the long term. Buzan also had his own ideas how the review should be spaced. When he first met SuperMemo in the early 1990s, he instantly agreed with the concept, however, he always preferred to focus on knowledge structure rather than a mere review.
在 20 世纪 70 年代，托尼·布赞通过思维导图创新专注于结构化知识。矛盾的是，思维导图和 SuperMemo 会因为缺乏统一的理论而产生冲突。简而言之，我们需要好的模型来理解这个世界，我们需要间隔重复来长期保留模型的组成部分。布赞也有他自己的想法，那就是如何将复习间隔开。当他在 20 世纪 90 年代初第一次见到 SuperMemo 时，他立刻同意了这个概念，然而，他总是更喜欢关注知识结构而不是简单的回顾。
My own work entered the picture in 1982 when I really got fed up with a never-ending process of forgetting. I wanted to learn biochemistry and physiology. I would read books, make notes and it would all be for nothing due to the process of forgetting. Even the most important facts could slip the memory at the most unfortunate moment (e.g. exam). I decided to employ active recall. Instead of just making notes, I would make notes as questions and answers. I could cover answers and respond using active recall. This would dramatically improve learning. This is how it is done in SuperMemo to this day. This new approach had a lovely impact on boosting my love of learning.
1982 年，我自己的作品进入了人们的视野，那时我真的受够了没完没了的遗忘过程。我想学生物化学和生理学。我会读书，做笔记，因为遗忘的过程，一切都是徒劳的。即使是最重要的事实也可能在最不幸的时刻(如考试)被遗忘。我决定采用主动回忆。我不只是做笔记，而是把笔记当成问题和答案。我可以覆盖答案，并使用主动回忆来回应。这将极大地改善学习。这就是 SuperMemo 直到今天的做法。这个新方法对我提高我对学习的热爱产生了很好的影响。
By 1984, I was fluent enough with my active recall approach to know that complex questions don't work. If you pack too much stuff into the answer, e.g. make a long list of it, you will keep forgetting. This would be futile learning. I later called that quest for simplicity "minimum information principle". Today, this principle is one of the first mentioned among 20 rules of knowledge formulation.
到 1984 年，我已经熟练地掌握了主动回忆法，知道复杂的问题是行不通的。如果你在答案中填了太多东西，例如，列一张长长的清单，你就会一直忘记。这将是徒劳的学习。我后来把这种对简单性的追求称为“最小信息原则”。今天，这一原则是最早提到的组织知识 20 条规则之一。
The real breakthrough came in 1985, i.e. exactly 100 years after the publication of Ebbinghaus' dissertation on memory. I wanted to check how the spacing of review affects recall. I needed to figure out the length of optimum intervals between repetitions. Obviously, those intervals exist. I only needed to measure them. The experiment is described here. The experiment was simple, rough, lazy, and hurried. Instead of taking a patient few years to find out all details, after 6 months I formulated the first SuperMemo algorithm. You can call it the first case of somewhat scientific spaced repetition. My research was based on one person, and one type of learning material, but it was universal enough to have many faithful users years later. On Jul 31, 1985, I started learning biochemistry using the new method. This is the birthday of computational spaced repetition. The computer program, SuperMemo for DOS came in 1987, and the name SuperMemo was proposed in 1988.
真正的突破出现在 1985 年，即艾宾浩斯关于记忆的论文发表 100 年后。我想检查一下间隔是如何影响回忆的。我需要找出重复之间的最佳间隔的长度。显然，这些间隔是存在的。我只需要测量它们。实验过程在这。这个实验简单、粗糙、懒惰、仓促。6 个月后，我制定了第一个 SuperMemo 算法，而不是花几年时间让耐心找出所有的细节。你可以称它为第一个有点科学的间隔重复。我的研究是基于个人和一种学习材料，但它足够普遍，多年后有许多忠实的用户。在 1985 年 7 月 31 日，我开始使用新的方法学习生物化学。这是使用计算机的间隔重复的生日。计算机程序 SuperMemo for DOS 出现于 1987 年，SuperMemo 这个名字提出于 1988 年。
In the 1980s, Jaap Murre's Memory Chain Model was one of the early models of memory that might have led to a solid spaced repetition algorithm. It even had its own early application, Captain Mnemo, that might have competed with SuperMemo for priority in the field. Captain Mnemo and OptiLearn are examples of why, in academic environments, great theories are often not followed by practical implementations that could gain wider appeal.
在 20 世纪 80 年代，贾普·穆尔的记忆链模型是可能会得出一个固定的间隔重复算法的最早的记忆模型之一。它甚至有自己的早期应用——《尼莫船长》(Captain Mnemo)——可能与 SuperMemo 在这一领域展开竞争。Captain Mnemo 和 OptiLearn 就是这样的例子，它们说明了为什么在学术环境中，伟大的理论往往不能得到更广泛的应用。
In 1991, SuperMemo World was formed and its beginnings are described here. As of that point, expansion of spaced repetition has been exponential. By 1999, we started using the term "spaced repetition" instead of the "SuperMemo method". For recent developments at SuperMemo World see here.
在 1991 年，SuperMemo World 成立，并描述了它的起源。从那时起，间隔重复的发展已经呈指数级增长。到 1999 年，我们开始使用“间隔重复”这个术语来代替“SuperMemo 方法”。有关 SuperMemo World 的最新进展，请参见此处。