SuperMemo-one-for-DOS.md

1987: SuperMemo 1.0 for DOS

1987：DOS 上的 SuperMemo 1.0

[TOC=2,5]

SuperMemo 1.0: day by day (1987)

SuperMemo 1.0: 日志 (1987)

SuperMemo history page at supermemo.com says that "Wozniak wrote his first SuperMemo in 16 evenings". The reality was a bit more complex. Let me describe it in detail using the notes from the day.

SuperMemo 的历史页面上写着：“Wozniak 用 16 个晚上写了他的第一版 SuperMemo”。实际情况要复杂一些。让我用当天的笔记来详细描述一下。

Building up for the idea

为这个想法做准备

I cannot figure out what I meant writing on Jul 3, 1987 that "I have an idea for a revolutionary program arranging my work and scientific experiments in SMTests" (SMTests stands for SuperMemo on paper here). A transition from paper to a computer seems like an obvious step. There must have been some mental obstacle on the way that required "thinking out of the box". Unfortunately, I did not write down details. Today it only matters in that it illustrates how excruciatingly slow a seemingly obvious idea may creep into the mind.

我不明白我在 1987 年 7 月 3 日写的“我有一个革命性的计划，在 SMTests (SMTests在这里代表 SuperMemo on paper)中安排我的工作和科学实验”是什么意思。从纸张到计算机的过渡似乎是显而易见的一步。在这条路上一定有一些思维上的障碍，需要“跳出框框思考”。不幸的是，我没有写下细节。今天，它唯一重要的是，它说明了一个看似显而易见的想法可能会缓慢得令人痛苦。

On Sep 8, 1987, my first PC arrived from Germany (Amstrad PC 1512). My enthusiasm was unmatched! I could not sleep. I worked all night. The first program I planned to write was to be used for mathematical approximations. SuperMemo was second in the pipeline.

1987 年 9 月 8 日，我的第一台个人电脑从德国运来(Amstrad PC 1512)。我的热情无与伦比！我睡不着。我工作了一整夜。我计划编写的第一个程序是用于数学近似。SuperMemo 是第二个。

Figure: Amstrad PC-1512 DD. My version had only one diskette drive. Operating system MS-DOS had to be loaded from one diskette, Turbo Pascal 3.0 from another diskette, SuperMemo from yet another. Until I had my first hard drive in 1991, my English collection had to be split into 3000-item portions. My 39,000 items had to be kept on 13 diskettes. I had many more for other areas of knowledge. On Jan 21, 1997, SuperMemo World has tracked down that original PC and bought it back from its owner: Jarek Kantecki. The PC was fully functional for the whole decade. It is now buried somewhere in dusty archives of the company. Perhaps we will publish its picture at some point. The presented picture comes from Wikipedia

图： 我的版本只有一个磁盘驱动器。操作系统 MS-DOS 必须从一个磁盘加载，Turbo Pascal 3.0 必须从另一个磁盘加载，SuperMemo 必须从又一个磁盘加载。直到 1991 年我有了自己的第一个硬盘前，我的英语集合不得不分成 3000 个部分。我的 39000 条项目被保存在 13 个磁盘上。我有很多其他领域的知识。1997 年 1 月 21 日，SuperMemo World 找到了那台最初的个人电脑，并从它的主人 Jarek Kantecki 手中买了回来。这台个人电脑在整整十年里功能齐全。现在它被埋在公司尘封的档案中。也许我们会在某个时候发布它的照片。图片来自维基百科

Oct 16, 1987, Fri, in 12 hours I wrote my first SuperMemo in GW-Basic (719 minutes of non-stop programming). It was slow like a snail and buggy. I did not like it much. I did not start learning. Could this be the end of SuperMemo? Wrong choice of a programming language? Busy days at school kept me occupied with a million unimportant things. Typical school effect: learn nothing about everything. No time for creativity and your own learning. Luckily, I never stopped using SuperMemo on paper. The idea of SuperMemo could not have died. It had to be automated sooner or later.

1987 年 10 月 16 日，星期五，在 12 个小时内，我用 GW-Basic 写了我的第一个 SuperMemo(719 分钟的不间断编程)。它像蜗牛一样慢，而且很笨重。我不太喜欢它。我没有开始学习。这会是 SuperMemo 的终结吗？错误的编程语言选择？在学校忙碌的日子让我忙于无数不重要的事情。典型的学校影响：什么都不学。没有时间去创造和学习。幸运的是，我从未停止使用 SuperMemo on paper。SuperMemo 的想法不可能消亡。它迟早要自动化。

On Nov 14, 1987, Sat, SuperMemo on paper got its first user: Mike Kubiak. He was very enthusiastic. The fire kept burning. On Nov 18, I learned about Turbo Pascal. It did not work on my computer. In those days, if you had a wrong graphics card, you might struggle. Instead of Hercules, I had a text-mode monochrome (black-and-white) CGA. I managed to solve the problem by editing programs in the RPED text editor rather than in the Turbo Pascal environment. Later I got the right version of Turbo Pascal for my display card. Incidentally, old SuperMemos show in colors. I was programming it in shades of gray, and never knew how it really looked in the color mode.

1987 年 11 月 14 日，纸上的 SuperMemo 迎来了它的第一个用户：Mike Kubiak。他非常热情。热情之火一直在燃烧。11 月 18 日，我了解了 Turbo Pascal。它不能在我的电脑上工作。在那些日子里，如果你有一个有问题的显卡，你可能会非常艰难。我没有使用 Hercules，而是使用了文本单色模式(黑白)CGA。我设法通过在 RPED 文本编辑器而不是在 Turbo Pascal 环境中编辑程序来解决这个问题。后来我得到了正确版本的 Turbo Pascal 适配我的显卡。顺便提一下，旧的 SuperMemo 是有颜色的。我用深浅不一的灰色来编程，但从来不知道它在颜色模式下到底是什么样子。

Writing SuperMemo 1.0

编写 SuperMemo 1.0

SuperMemo 1.0 chronology:

SuperMemo 1.0 大事记：

• Nov 21, 1987 was an important day. It was a Saturday. Days free from school are days of creativity. I hoped to get up at 9 am but I overslept by 72 minutes. This is bad for the plan, but this is usually great for the brain and the productivity. I started the day from learning with SuperMemo on paper (reviewing English, human biology, computer science, etc.). Later in the day, I read my Amstrad PC manual, learned about Pascal and Prolog, spent some time thinking about how the human cortex might work, did some exercise, and in the late evening, in a slightly tired state of mind, in afterthought, decided to write SuperMemo for DOS. This would be my second attempt. However, this time I chose Turbo Pascal 3.0 and never regretted. To this day, as a direct consequence, SuperMemo 17 code is written in Pascal (Delphi XE3). The name SuperMemo was proposed much later. In those days, I called my program: SMTOP for Super-Memorization Test Optimization Program. In 1988, Tomasz Kuehn insisted we call it CALOM for Computer-Aided Learning Optimization Method.
• 1987 年 11 月 21 日是一个重要的日子。那是一个星期六。不用上学的日子是充满创造力的日子。我本希望早上 9 点起床，但我睡过头了 72 分钟。这不利于计划，但这通常对大脑和生产力有好处。我用 SuperMemo on paper(复习英语、人类生物学、计算机科学等)开始新的一天。当天晚些时候，我读我的连电脑手册，了解 Pascal 和 Prolog，花了一些时间思考人类的皮层如何工作，做了一些锻炼，晚上，略显疲惫的精神状态，然后决定写 SuperMemo for DOS。这将是我第二次尝试。然而，这次我选择了 Turbo Pascal 3.0，并没有后悔。直到今天，直接的结果是，SuperMemo 17 的代码是用 Pascal (Delphi XE3)编写的。SuperMemo 的名字是在很久以后才提出来的。在那些日子里，我把我的程序命名为：SMTOP for 超级记忆测试优化程序 *。1988 年，Tomasz Kuehn 坚持称其为 CALOM for 计算机辅助学习优化方法。
• Nov 22, 1987 was a mirror copy of Nov 21. I concluded that I know how the brain cortex worksm and that one day it would be nice to build a computer using similar principles (check Jeff Hawkins's work). The fact that I returned to programming SuperMemo in the late evening, i.e. very bad time for creative work, seems to indicate that the passion has not kicked in yet.
• 1987 年 11 月 22 日是 11 月 21 日的翻版。我的结论是，我知道大脑皮层是如何工作的，有一天，用类似的原理来建造一台电脑将是件好事(参见 Jeff Hawkins 的工作)。事实上，我在深夜回到编程 SuperMemo，也就是非常不适合做创造性工作的时候，似乎表明我的热情还没有开始。
• Nov 23, 1987 looked identical. I am not sure why I did not have any school obligations on Monday, but this might have saved SuperMemo. On Nov 24, 1987, the excitement kicked in and I worked for 8 hours straight (in the evening again). The program had a simple menu and could add new items to the database.
• 1987 年 11 月 23 日看起来一模一样。我不知道为什么我周一没有任何学校的义务，但这可能会拯救 SuperMemo。1987 年 11 月 24 日，我开始兴奋起来，连续工作了 8 个小时(又是晚上)。该程序有一个简单的菜单，可以向数据库添加新项目。
• Nov 25, 1987 was wasted: I had to go to school, I was tired and sleepy. We had excruciatingly boring classes in computer architecture, probably a decade behind the status quo in the west.
• 1987 年 11 月 25 日被浪费了：我必须去上学，我又累又困。我们上的计算机架构课非常无聊，可能比西方的现状落后了 10 年。
• Nov 26 was free again and again I was able to catch up with SuperMemo work. The program grew to be 15,400 bytes "huge". I concluded the program might be "very usefull" (sic!).
• 11 月 26 日是自由的，我一次又一次地赶上了 SuperMemo 的工作。程序增长到 15400 字节“巨大”。我的结论是，这个程序可能“非常有用”(原文如此！)
• On Nov 27, I added 3 more hours of work after school.
• 11 月 27 日，我放学后又增加了 3 个小时的工作时间。
• Nov 28 was Saturday and I could add 12 enthusiastic hours of non-stop programming. SuperMemo now looked like almost ready for use.
• 11 月 28 日是周六，我可以增加 12 个小时不间断的热情编程。SuperMemo 现在看起来差不多可以使用了。
• On Nov 29, Sunday, I voted for economic reforms and democratization in Poland. In the evening, I did not make much progress. I had to prepare an essay for my English class. The essay described the day when I experimented with alcohol one day in 1982. I was a teetotaller, but as a biologist, I concluded I need to know how alcohol affects the mind.
• 11 月 29 日，星期天，我投票赞成波兰的经济改革和民主化。晚上，我没有取得多大的进步。我必须为英语课准备一篇作文。这篇文章描述了 1982 年的一天，我尝试喝酒。我是个滴酒不沾的人，但作为一名生物学家，我的结论是，我需要知道酒精是如何影响大脑的。
• Nov 30 was wasted at school, but we had a nice walk home with Biedalak. We had a long conversation in English about our future. That future was mostly to be about science, probably in the US.
• 11 月 30 日在学校被浪费了，但是我们和 Biedalak 一起很愉快地走回家。我们用英语就我们的未来进行了长时间的交谈。那个未来主要是关于科学的，可能在美国。
• Dec 1-4 were wasted at school again. No time for programming. In a conversation with some Russian professor, I realized that I completely forgot Russian in short 6 years. I used to be proudly fluent! I had to channel my programming time into some boring software for designing electronic circuits. I had to do it to credit a class in electronics. I had a deal with the teacher that I would not attend lectures, just write this piece of software. I did not learn anything and to this day I mourn the waste of time. If I was free, I could have invested this energy in SuperMemo.
• 12 月 1 日至 4 日在学校又浪费了。没有时间编程。在与一位俄罗斯教授的交谈中，我意识到我在短短的 6 年时间里完全忘记了俄语。我曾经骄傲地说一口流利的英语！我不得不把我的编程时间用在一些设计电子电路的无聊软件上。我必须这样做才能获得电子学的学分。我和老师说好了我不去上课，只写这款软件。我什么也没学到，直到今天我还在为浪费时间而悲哀。如果我有时间，我可以把这些精力投入到 SuperMemo 中。
• Dec 5 was a Saturday. Free from school. Hurray! However, I had to start from wasting 4 hours on some "keycode procedure". In those days, even decoding the key pressed might become a challenge. And then another hour wasted on changing some screen attributes. In addition, I added 6 hours for writing "item editor". This way, I could conveniently edit items in SuperMemo. The effortless things you take for granted today: cursor left, cursor right, delete, up, new line, etc. needed a day of programming back then.
• 12 月 5 日是星期六。从学校中解放。万岁！然而，我不得不从浪费 4 个小时在一些“关键代码过程”开始。在那些日子里，甚至破译按键也可能成为一项挑战。然后又浪费了一个小时来更改一些屏幕属性。此外，我还增加了 6 个小时的时间来编写“项目编辑器”。这样，我可以方便地在 SuperMemo 中编辑条目。今天您认为理所当然的事情：左、右、删除、上、回车等，都需要一天的编程。
• Dec 6 was a lovely Sunday. I spent 7 hours debugging SuperMemo, adding "final drill", etc. The excitement kept growing. In a week, I might start using my new breakthrough speed-learning software.
• 12 月 6 日是一个可爱的星期天。我花了 7 个小时调试 SuperMemo，添加了“结束练习”等。兴奋之情与日俱增。一周后，我可能会开始使用我的新突破性的快速学习软件。
• On Monday, Dec 7, after school, I added a procedure for deleting items.
• 12 月 7 日星期一放学后，我添加了一个删除项目的程序。
• On Dec 8, while Reagan and Gorbachev signed their nuclear deal, I added a procedure for searching items and displaying some item statistics. SuperMemo "bloated" to 43,800 bytes.
• 12 月 8 日，里根和戈尔巴乔夫签署了他们的[核协议](https://en.wikipedia.org/wiki/middle - range_nuclear _forces - treaty)，我添加了一个搜索项目和显示某些项目统计数据的程序。SuperMemo “膨胀”到 43,800 字节。
• Dec 9 was marred by school and programming for the electronics class.
• 12 月 9 日被学校和电子学课程的编程给毁了。
• On Dec 10, I celebrated power cuts at school. Instead of boring classes, I could do some extra programming.
• 12 月 10 日，我在学校庆祝停电。我可以做一些额外的编程，而不是上无聊的课。
• On Dec 11, we had a lovely lecture with one of the biggest brains at the university: Prof. Jan Weglarz. He insisted that he could do more in Poland than abroad. This was a powerful message. However, in 2018, his Wikipedia entry says that his two-phase method discovery was ignored, and later duplicated in the west because he opted for publishing in Polish. Weglarz created a formidable team of best operations research brains in Poznan indeed. If I did not sway in the direction of SuperMemo, I would sure come with a begging hat to look for an employment opportunity. In the evening, I added a procedure for inspecting the number of items to review each day. This is today's Calendar (or Workload in older versions).
• 12 月 11 日，我们和大学里最有头脑的人之一 Jan Weglarz 教授进行了一次愉快的讲座。他坚持认为他在波兰能做的比在国外更多。这是一个强有力的信息。然而，在 2018 年，他在维基百科上的条目说，他的两阶段方法发现被忽视了，后来在西方被重复了，因为他选择用波兰语出版。Weglarz 教授在 Poznan 创造了一个强大的团队，拥有最优秀的运筹学人才。如果我不转向 SuperMemo，我肯定会带着一顶乞求的帽子来找工作。晚上，我添加了一个程序来检查每天要检查的项目的数量。这是今天的 Calendar(或者旧版本的 Workload)。

First repetitions in SuperMemo

第一次在 SuperMemo 中重复

Dec 12, 1987 was a Saturday. I expanded SuperMemo by a pending queue editor, and seemed ready to start learning, however, … on Dec 13, I was hit by a bombshell: "Out of memory". Turbo Pascal refused to compile my program for it grew too large. In those days, memory in DOS was split in 64KB segments and I was probably limited to using just a single segment. I somehow managed to fix the problem by optimizing the code.

1987 年 12 月 12 日是星期六。我通过一个等待处理的队列编辑器扩展了 SuperMemo，似乎准备开始学习，然而，……12 月 13 日，我被一个炸弹击中：“内存不足”。Turbo Pascal 拒绝编译我的程序，因为它太大了。在那些日子里，DOS 中的内存被分割成 64KB 的段，我可能只能使用一个段。我设法通过优化代码来解决这个问题。

The last option I needed to add to SuperMemo was for the program to read the date. Reading the date was a big deal hack in those days. Without it, I would need to type in the current date at every day at the start of the work with SuperMemo.

我需要添加到 SuperMemo 中的最后一个选项是程序读取日期。在那些日子里，阅读日期是一件大事。如果没有它，我将需要在每天开始使用 SuperMemo 时输入当前日期。

Finally, at long last, in the afternoon, on Dec 13, 1987, I was able to add my first items to my human biology collection: questions about the autonomic nervous system. As much as July 31, 1985 could be considered the birthday of spaced repetition. Dec 13, 1987 could be named the birthday of spaced repetition software.

终于，在 1987 年 12 月 13 日的下午，我终于能够将我的第一个项目添加到我的人类生物学收藏中：关于自主神经系统的问题。早在 1985 年 7 月 31 日就被认为是间隔重复的生日。1987 年 12 月 13 日是间隔重复软件诞生的日子。

Spaced repetition software was born on Dec 13, 1987

间隔重复软件诞生于 1987 年 12 月 13 日

By Dec 23, 1987, my combined paper and computer databases included 3795 questions on human biology (of which almost 10% were already stored in my new SuperMemo program database). Sadly, I had to remove the possibility of storing full repetition histories from SuperMemo on that day. There wasn't enough space on 360K diskettes. Spaced repetition research would need to wait a few more years. Only in 1996, SuperMemo resumed collecting the full record of repetitions.

到了 1987 年 12 月 23 日，我的论文和计算机数据库包含了 3795 个关于人类生物学的问题(其中近 10% 已经存储在我新的 SuperMemo 程序数据库中)。遗憾的是，那天我不得不从 SuperMemo 中删除存储完整重复历史的可能性。在 360K 的磁盘上没有足够的空间。间隔重复研究需要再等几年。直到 1996 年，SuperMemo 才重新开始收集重复次数的完整记录。

Figure: SuperMemo 1.0 for DOS (1987) was the first computer application of spaced repetition. It introduced Algorithm SM-2 that remains popular three decades later

图： SuperMemo 1.0 for DOS(1987)是第一个使用间隔重复的计算机。它引入的算法 SM-2 在 30 年后仍然很流行

Algorithm SM-2

算法 SM-2

Here is the description of the algorithm used in SuperMemo 1.0 for DOS (1987). The description was taken from my Master's Thesis written 2.5 years later (1990). SuperMemo 1.0 was soon replaced by a better-looking SuperMemo 2.0 that I would give away to friends at the university. There were insignificant updates to the repetition spacing algorithm that was named Algorithm SM-2 after the version of SuperMemo. This means there has never been Algorithm SM-1.

下面是在 SuperMemo 1.0 for DOS(1987)中使用的算法的描述。这个描述取自我 2.5 年后(1990 年)写的[硕士论文](https://supermemo.guru/wiki/Master's _thesis)。SuperMemo 1.0 很快就被一个更好看的 SuperMemo 2.0 所取代，我把它送给了大学里的朋友们。重复间隔算法在 SuperMemo 版本之后被命名为算法 SM-2。这意味着从来没有算法 SM-1。

I mastered 1000 questions in biology in the first 8 months of use. Even better, I memorized exactly 10,000 items of English word pairs in the first 365 days. I worked an average of 40 minutes per day. This speed of learning was used as a benchmark in advertising SuperMemo in its first commercial days. Even today, 40 minutes is the daily investment recommended to master Advanced English in 4 years (40,000+ items).

在使用的头 8 个月里，我掌握了 1000 道生物题。更棒的是，在最初的 365 天里，我准确地记住了一万对英语单词。我平均每天工作 40 分钟。这种学习速度在 SuperMemo 最初的商业时代被用作广告的基准。即使在今天，每天花 40 分钟来掌握高级英语也是值得的。

Algorithm SM-2 remains popular and is still used by applications such as Anki, Mnemosyne, and more. 算法 SM-2 依然流行，仍然被一些程序使用，比如Anki、Mnemosyne。

Archive warning: Why use literal archives?

档案警告：为什么使用文本存档？

This text was part of: "Optimization of learning" by Piotr Wozniak (1990)

这篇文章是：“改进学习” Piotr Wozniak (1990) 的一部分

3.2. Application of a computer to improve the results obtained in working with the SuperMemo method

3.2. 应用计算机对SuperMemo方法的计算结果进行改进

I wrote the first SuperMemo program in December 1987 (Turbo Pascal 3.0, IBM PC). It was intended to enhance the SuperMemo method in two basic ways:

我在 1987 年 12 月编写了第一个 SuperMemo 程序(Turbo Pascal 3.0, IBM PC)。它旨在以两种基本方式增强 SuperMemo 方法:

• apply the optimization procedures to smallest possible items (in the paper-based SuperMemo items were grouped in pages),
• 将优化过程应用到尽可能小的项目（在基于纸张的 SuperMemo 中被组织为页面）
• differentiate between the items on the base of their different difficulty.
• 根据不同的难度来区分项目。

Having observed that subsequent inter-repetition intervals are increasing by an approximately constant factor (e.g. two in the case of the SM-0 algorithm for English vocabulary), I decided to apply the following formula to calculate inter-repetition intervals:

观察到后续的重复间隔增加了一个近似常数的因子(例如英语词汇量的 SM-0 算法增加了两个)，我决定用下面的公式来计算重复间隔：

I(1):=1

I(2):=6

for n>2 I(n):=I(n-1)*EF

where:

• I(n) - inter-repetition interval after the n-th repetition (in days)
• EF - easiness factor reflecting the easiness of memorizing and retaining a given item in memory (later called the E-Factor).

I(1) = 1

I(2) = 2

当 n > 2 时 I(n) = I(n-1) * EF

上式中：

• I(n) - 重复 n 次后的重复间隔(以天为单位)
• EF - 简易因子反映了记忆和记忆一个给定的项目的轻松程度(后来称为简易度)。

E-Factors were allowed to vary between 1.1 for the most difficult items and 2.5 for the easiest ones. At the moment of introducing an item into a SuperMemo database, its E-Factor was assumed to equal 2.5. In the course of repetitions, this value was gradually decreased in case of recall problems. Thus the greater problems an item caused in recall the more significant was the decrease of its E-Factor.

简易度允许在最困难的 1.1 和最简单的 2.5 之间变化。在将一个项目引入 SuperMemo 数据库时，它的简易度被假定为 2.5。在重复的过程中，这个值会随着回忆问题的出现而逐渐降低。因此，一个项目在回忆中引起的问题越大，其简易度的降低就越显著。

Shortly after the first SuperMemo program had been implemented, I noticed that E-Factors should not fall below the value of 1.3. Items having E-Factors lower than 1.3 were repeated annoyingly often and always seemed to have inherent flaws in their formulation (usually they did not conform to the minimum information principle). Thus not letting E-Factors fall below 1.3 substantially improved the throughput of the process and provided an indicator of items that should be reformulated. The formula used in calculating new E-Factors for items was constructed heuristically and did not change much in the following 3.5 years of using the computer-based SuperMemo method.

在第一个 SuperMemo 程序实现后不久，我注意到简易度不应该低于 1.3。简易度低于 1.3 的项目经常被重复使用，而且似乎总是存在固有的缺陷(通常它们不符合最小信息原则)。因此，不让简易度降至 1.3 以下大大提高了流程的吞吐量，并为需要重新制定的项目提供了一个指标。计算项目新简易度的公式是启发式构造的，在接下来的 3.5 年里，使用基于计算机的 SuperMemo 方法并没有太大的变化。

In order to calculate the new value of an E-Factor, the student has to assess the quality of his response to the question asked during the repetition of an item (my SuperMemo programs use the 0-5 grade scale - the range determined by the ergonomics of using the numeric key-pad). The general form of the formula used was:

为了计算一个简易度的新值，学生必须评估他在重复一个项目时回答问题的质量(我的 SuperMemo 程序使用 0-5 级量表——使用数字键盘的人机工程学决定的范围)。公式的一般形式为：

EF':=f(EF,q)

where:

• EF' - new value of the E-Factor
• EF - old value of the E-Factor
• q - quality of the response
• f - function used in calculating EF'.

EF':=f(EF,q)

上式中：

• EF' - 简易度的新值
• EF - 简易度的旧值
• q - 回答的质量
• f - 用于计算 EF' 的函数。

The function f had initially multiplicative character and was in later versions of SuperMemo program, when the interpretation of E-Factors changed substantially, converted into an additive one without significant alteration of dependencies between EF', EF and q. To simplify further considerations only the function f in its latest shape is taken into account:

函数 f 最初具有乘法特性，在 SuperMemo 程序的后续版本中，当简易度的解释发生重大变化时，将其转换为加法因子，而不会显著改变 EF'、EF 和 q 之间的相关性。为简化进一步考虑，仅考虑最新形状的函数 f：

EF':=EF-0.8+0.28*q-0.02*q*q

which is a reduced form of:

这是以下形式的简化形式:

EF':=EF+(0.1-(5-q)*(0.08+(5-q)*0.02))

Note, that for q=4 the E-Factor does not change.

注意，对于 q=4，简易度没有变化。

Let us now consider the final form of the SM-2 algorithm that with minor changes was used in the SuperMemo programs, versions 1.0-3.0 between December 13, 1987 and March 9, 1989 (the name SM-2 was chosen because of the fact that SuperMemo 2.0 was by far the most popular version implementing this algorithm).

现在让我们考虑在 1987 年 12 月 13 日和 1989 年 3 月 9 日之间的 SuperMemo 程序中使用的 SM-2 算法的最终形式，版本 1.0-3.0 (选择 SM-2 是因为 SuperMemo 2.0 是目前实现该算法的最流行的版本)。

Algorithm SM-2 used in the computer-based variant of the SuperMemo method and involving the calculation of easiness factors for particular items:

基于计算机的 SuperMemo 方法的变体所用的算法 SM-2，涉及对特定项目的简易度的计算：

1. Split the knowledge into smallest possible items.

2. With all items associate an E-Factor equal to 2.5.

3. Repeat items using the following intervals:

4. After each repetition assess the quality of repetition response in 0-5 grade scale:

5. After each repetition modify the E-Factor of the recently repeated item according to the formula:

6. If the quality response was lower than 3 then start repetitions for the item from the beginning without changing the E-Factor (i.e. use intervals I(1), I(2) etc. as if the item was memorized anew).

7. After each repetition session of a given day repeat again all items that scored below four in the quality assessment. Continue the repetitions until all of these items score at least four.

8. 把知识分成尽可能小的部分。

9. 所有项的简易度都等于 2.5。

10. 使用以下间隔重复项目：

11. 每次重复后用 0-5 级量表评定重复的反馈质量：

12. 每次重复后，根据公式修改最近重复项的简易度。

13. 如果反馈的质量低于 3，那么重复就重新开始，不要改变简易度(即使用间隔 I(1)，I(2) 等，就像重新记忆一样)。

14. 在某一天的所有重复训练之后，重复所有在质量评估中得分低于 4 分的项目。继续重复，直到所有项目至少 4 分。

During the first year of using the SM-2 algorithm (learning English vocabulary), I memorized 10,255 items. The time required for creating the database and for repetitions amounted to 41 minutes per day. This corresponds to the acquisition rate of 270 items/year/min. The overall retention was 89.3%, but after excluding the recently memorized items (intervals below 3 weeks) which do not exhibit properly determined E-Factors the retention amounted to 92%. Comparing the SM-0 and SM-2 algorithms one must consider the fact that in the former case the retention was artificially high because of hints the student is given while repeating items of a given page. Items preceding the one in question can easily suggest the correct answer.

在使用 SM-2 算法(学习英语词汇)的第一年，我记住了 10255 个单词。创建数据库和重复所需要的时间为每天 41 分钟。这相当于 270 个项目/年/分钟的学习率。整体保留率为 89.3%，但剔除近期记忆(间隔在 3 周以下)没有正确确定简易度后，保留率为 92%。比较 SM-0 和 SM-2 算法，我们必须考虑这样一个事实：在前一种情况下，由于学生在重复给定页面的项目时得到了提示，所以保留率被人为地提高了。问题前面的项目可以很容易地给出正确答案。

Therefore the Algorithm SM-2, though not stunning in terms of quantitative comparisons, marked the second major improvement of the SuperMemo method after the introduction of the concept of optimal intervals back in 1985. Separating items previously grouped in pages and introducing E-Factors were the two major components of the improved algorithm. Constructed by means of the trial-and-error approach, the SM-2 algorithm proved in practice the correctness of nearly all basic assumptions that led to its conception

因此，算法 SM-2 虽然在定量比较方面并不令人惊叹，但它标志着 SuperMemo 方法在 1985 年引入最佳区间概念后的第二次重大改进。将先前分组在页面中的项目分离和引入简易度是改进算法的两个主要组成部分。SM-2 算法是通过试错法构建的，它在实践中证明了导向其概念的几乎所有基本假设的正确性