How many repetitions for long term retention?

Some students ask how many repetitions are required to memorize something. Long ago I was told that seven repetitions make us remember almost anything. But now I am ready to add some science to it. Basically, I follow the logic of this article.

Our neurons are hard-wired to forget something with roughly exponential speed. We can fight this phenomenon via various techniques.
Most of our techniques work simply because neurons work as groups, and any new knowledge is supported by other neurons within the group. We trick the brain into including new pieces of knowledge with older and established knowledge and ensure we will not forget anything important. Eventually, we are left only with things that simply cannot be connected to strongly connected established neural groups: numbers, new words, names, and whole new areas of knowledge. Then we need to activate the spaced repetition approach.

We can try to check what we forget and learn it again and again until we succeed. This method is labor intensive and involves checking the recall again and again. If we fail we will check it more often, but if we succeed we will need to check it much less often, until we do not need to check any more. In this approach, the frequency of repetition is governed by the amount of new data we need to learn. Computers make the job easy (using Anki or equivalent). All we need to do is create the cards with the pieces of knowledge we need to retain.

Alternatively, we may assume that all the pieces of knowledge are equally complex, like words of a new language. Then we can calculate and time the next recall. In his work, Pimsleur used 5 seconds, 25 seconds, 2 minutes, 10 minutes, 1 hour, 5 hours, 1 day, 5 days, 25 days, 4 months, and 2 years.
This is slightly more than the rule of seven, but the effect of each following repetition is reduced. Please notice that the words need to be presented in random order for the method to work.

At this point, I will refer to the original study of the learning and forgetting curves:

“In 1885 Ebbinghaus published his groundbreaking Über das Gedächtnis (“On Memory”, later translated to English as Memory. A Contribution to Experimental Psychology) in which he described experiments he conducted on himself to describe the processes of learning and forgetting. Ebbinghaus made several findings that are still relevant and supported to this day. First, arguably his most famous finding, the forgetting curve. The forgetting curve describes the exponential loss of information that one has learned. The sharpest decline occurs in the first twenty minutes and the decay is significant through the first hour. The curve levels off after about one day. The learning curve described by Ebbinghaus refers to how fast one learns information. The sharpest increase occurs after the first try and then gradually evens out, meaning that less and less new information is retained after each repetition. Like the forgetting curve, the learning curve is exponential. Ebbinghaus had also documented the serial position effect, which describes how the position of an item affects recall. The two main concepts in the serial position effect are recency and primacy. The recency effect describes the increased recall of the most recent information because it is still in the short-term memory. The primacy effect better memory of the first items in a list due to increased rehearsal and commitment to long-term memory. Ebbinghaus also described the difference between involuntary and voluntary memory, the former occurring “with apparent spontaneity and without any act of the will” and the latter being brought “into consciousness by an exertion of the will”.

It is interesting to note that Ebbinghaus used to learn meaningless syllables and he remembered the syllables that had meaning by mere chance much more than others. Moreover, even if he forgot something, he learned it easier the next time he had to re-learn it. Finally, he applied a great deal of effort to eliminate any dual coding or memorization technique from his study to preserve statistical purity. You are not studying memory curves, so you should do just the opposite: add dual coding, add meaning, and add memorization techniques.

I will summarize the subject as follows:

1. If you learn simple facts in the area you are familiar with you may retain them without spaced repetition.
2. If you encode the information in many forms (associations, audio, image, the way the word looks) you may need a few repetitions.
3. For new language or other unstructured data, you may need seven repetitions or more with each repetition contributing less than the previous.
4. If you do need spaced repetitions, it is best to use computer programs with flash cards.

To train the technique, you can for example work with certification examination dumps. Here is a link to certification dumps.