What is Spaced Repetition?

To learn and retain information, it has to be encountered periodically. For example, you hear one day that the capitol of Vermont is Montpelier. If you don't do anything with this piece of information, you will likely remember it for only a short period of time and then forget it. But if you were to periodically encounter this fact you would retain the information for much longer.

This could happen in many ways. You could be reviewing this fact on purpose because you have a test on the state capitols. Or maybe you're reading a book about an event that took place in Vermont. Or maybe you occasionally read a Vermont newspaper or website. Or maybe knowing the state capitols is important to your job in some way, so you frequently deal with them.

It turns out (and research has shown) that the more familiar you are with a piece of information, the less often you need to encounter it to continue to retain it. However, after a very long period without encountering even very familiar information, it can be lost.

We probably all have experienced this. For four years I worked in the returns department of a large chain of retail computer stores. While I was there I knew how to decode the part and serial numbers on hundreds of computer parts from many different manufactures because I dealt with them for hours everyday. When I first started the job, this information came slowly, but eventually it was second nature. Years after leaving that job, I continued to recall much of this information but from disuse its slowly trickled away and now I can hardly recall any of it.

Spaced repetition is a learning technique that takes advantage of these facts. It means reviewing information you wish to learn at gradually increasing intervals.

Flashcards

Using flash cards is another learning technique. It's one way stimulate artificial encounters with a piece of information for the purpose of review. It is also particularly suited to spaced repetition.

From what I hear, flashcards aren't very popular outside of the US and England. So for those who don't know, a flashcard is basically a note card with a question on one side and the answer on the other. You can quiz yourself by looking at the question on the front side, stating what you think the answer is, then turning the card over to check yourself.

For example, the front of the of the card could say "Vermont" and the back "Montpelier". Here the "question" is only one word for brevity, but it also allows you to quiz the cards in reverse: you can look at the capitol city and try to recall the state.

Sebastian Leitner did a series of research experiments with flash cards and spaced repetition in the 1970s. His research is the basis for many products based on spaced repetition and flash cards, including the Pimsleur Approach (a series of audio-based language learning programs), jMemorize (a Java-based flash card program), Memorati™ and many others.

The Leitner System consists of keeping your flash cards in several groups, which get reviewed at different frequencies. For example, the cards in group 1 are reviewed every day, group 2 is reviewed every 2 days and group 3 every 3 days. All flash cards start in group 1. When you review the cards in any group, the ones you answer correctly are moved into the next group and incorrectly answered cards are moved back to group 1. This forces to you study cards you know less well more often.

How often?

Spaced repetition is a rather vague notion. We know that we need to review our flash cards at increasing intervals based on how well each card is known. But increasing by how much?

Let's look at why we are using spaced repetition in the first place. There are two main factors: retention and efficiency.

• Retention: Do you recall the information? Here we are concerned with whether the information has stuck with you, how well and for how long. Obviously, you want to maximize your familiarity with the information and have it last as long as possible.
• Efficiency: How much time/effort was put into gaining your level of retention? You can review the state capitols every day or even every hour. But how effectively has each minute of review translated into level of retention? Clearly you want to spend your time most efficiently, only doing review that increases your retention, not just busy work.

We want the repetition to happen often enough that our memory is jogged before the information is forgotten. But we want to review as infrequently as is possible, to avoid wasting time reviewing information that we already know well enough.

Determining the time between reviews is done by a spaced repetition algorithm. There are countless algorithms but many use a Leitner System notion of "groups" to measure how well a word is known.

In terms of the algorithm, this means the amount of time before a word needs to be reviewed again -- the interval -- is a function of the number of the group its in -- which is refered to as its level.

Possible Algorithms

A more in depth discussion of this topic is coming soon in its own article. But here we will describe some simplistic algorithms as currently used by Memorati™.

The simplest algorithm is linear. This means for each level, we increase the interval by a fixed period of time, for example, one day. Cards at level 1 are quizzed one day after they are learned, level 2 in 2 days, level 3 in 3 days and so on.

This can be described mathematically as: interval = level * 1 day

The next simplest algorithm is exponential. Described mathematically it would be: interval = base ^ (level - 1) * 1 day

Below is a comparison of a linear algorithm and a couple exponential algorithms with bases 2 and 3:

View chart as a chart...

You can see that the exponential algorithms are much more agressive that linear, meaning that as a card's level increases, the interval increases very quickly.

In my experience, an aggressive algorithm works much better if you are doing a lot of cards, adding more constantly and expect to be working on them over a very long period of time (months or years). However, linear seems to work best for a small number of cards, that doesn't grow much, which you only intend to focus on for a short period of time (1-4 weeks).

The unexpected factor with regard to an aggressive algorithm, is that you are able to increase the interval quickly because each time you get a card incorrect, it goes back to the beginning. When first learning a card, you will answer it incorrectly several times. So, a new card will initially cycle between levels 1 and 3 a few times. But once you get it right 4 times in a row, it gets put into a maintenance mode, where you will only be occasionally reminded.

However, the ideal algorithm is not yet clear. This is an area that still needs much exploration.

Artificial vs. Natural

Something that needs to be discussed at some point, is the difference between reviewing something artificially and naturally.

The best way to review a piece of information is by actually using it. Flash cards are a way to artificially get you to use a piece of information. And while they can be a very useful tool, they can never replace natural use of information.

For example, you can make flash cards that contain all the information on the periodic table. After much review, you may even get to a point where you can instantly recall anything about any element. But you still won't be as intimately acquainted with knowledge as a chemist who uses it every day in his work.

This is mainly because the chemist is truly involved with this information. Atomic mass isn't just a number that can be easily confused with another number. It directly impacts experiments that can have direct observable effects both in terms of the experiment itself, but also can directly and indirectly impact his life. It may be a stretch, but you could connect this knowledge to his success at his job and his relationships with his colleagues.

But learning tools, such as flash cards and spaced repetition, can definitely be used to jump start the learning process. They are very effective when first learning a thing, which can then be turned to more intimate knowledge later, through more involved use -- or to occasionally remind you of knowledge you don't want to lose.