# The Forgetting Curve

Your brain is programmed to throw away useless memories in order to optimize the availability of useful ones. You can think of the equation for the forgetting curve as an attempt to mathematically replicate the algorithm that the brain uses in order to determine what memories should get thrown away at what times. The equation for the forgetting curve says that there are three main factors that determine when a memory will be forgotten: retrievability, stability, and time. Time is pretty straightforward, so let’s talk about the other two.

The retrievability of a memory is the probability that you will be able to successfully recall that memory at a specific point in time1. If I asked you what your name is, we can assume that there is a 99.99% chance that you will be able to successfully recall your name and tell me what it is. Therefore, for you, the retrievability of your name is 99.99%. If I told you that my middle name is Lawrence, and then just 30 seconds later, asked you to tell me what my middle name is, we can assume that you would be able to tell me. So, 30 seconds after initially learning my middle name, the retrievability is also around 99%. If the retrievability of your own name, which you know extremely well, and the retrievability of my middle name, which you just learned and are likely to soon forget, are both around 99%, then clearly we need some other sort of metric in order to talk about how deeply/strongly a memory is lodged into our brain. This is stability.

The stability of a memory is the rate at which retrievability drops over time. Because you know your own name so well (or in other words, because the memory is so stable), hypothetically, you might be able to go years without recalling it and still have the retrievability stay above 99%. On the other hand, after a week, the retrievability of my middle name will likely drop to around 20% (there will only be a 20% probability that you would be able to successfully recall it).

If a memory is successfully recalled before it is forgotten, AKA reviewed, the retrievability of the memory will be reset to 100%, and the stability of the memory will increase. The amount that stability increases with each review depends on how low retrievability is at the time of recall: the lower the retrievability at the time of recall, the larger the increase in stability. This is what is known as the spacing effect: the best time to review something is right before you forget it. So less review can actually create stronger memories. But you have to be careful, because if you wait too long and a memory is actually forgotten, it will have to be relearned, and the stability will actually decrease. I will also note here that relearning is distinctly different from initial learning; once relearned, although stability will have decreased, a majority of the previous stability will still have been retained.

The standard formulation of the equation for the forgetting curve is set up to allow one to find the retrievability of a memory at a specific point in time, given the stability. But if we want to be able to track how the stability of memories grow as we continue to review them over time, there is actually a third factor that we need to take into account: the difficulty of the information. Different kinds of information can be inherently harder or easier to remember. For example, remembering a new word in a language you are fluent in is easy, while remembering a new word in a language you just started to learn is more difficult. This is what SuperMemo calls the “absolute factor” of memories, and what I like to call the intrinsic difficulty. The more intrinsically difficult a piece of information is, the more often it will have to be reviewed in order to keep it in your memory (the slower that stability will increase over time).

In Anki, retention rate accounts for retrievability, intervals account for stability, and ease factors account for intrinsic difficulty. I will talk more about retention rate later, but for now, let’s focus on interval and ease factor. The interval of a card is simply how often you review it; if you review a card once a month, it has an interval of one month. The ease factor of a card represents how quickly the interval of that card will grow; the larger the ease factor, the more quickly that card’s interval will grow.