View source for Forgetting curve

== Formula ==
'''Forgetting curve''' describes the decline in the probability of [[recall]] over time <small>(source: [http://www.super-memory.com/english/2vm.htm Wozniak, Gorzelanczyk, Murakowski, 1995])</small>:

:<font size="5"><strong>R=exp<sup>(-t/S)</sup></strong></font>

where:
* '''R''' - probability of recall ([[retrievability]] of memory)
* '''S''' - ''strength'' of a memory trace ([[stability]] of memory)
* t - time

__NOTOC__

== Explanation ==

In a mass of remembered details, the shape of the forgetting curve will depend on (1) [[memory complexity]] (i.e. how difficult it is to uniformly bring individual knowledge details from memory), and (2) [[stability|memory stability]] (i.e. how well individual details have been established in memory). For example, a set of easy French words, memorized on the same day, may align into a curve that meets the above formula. Those French words will have low complexity (because they are easy), and low stability (because they have just been learned). Those French words will be lost to memory, one by one, at equal probability over time. The chance of recalling a given word will be R ([[retrievability]]) after time t. With time going to infinity, the [[recall]] will approach zero. However, if all words are reviewed again, their stability will increase and [[retention]] time will be extended. This is used in [[spaced repetition]] to minimize the cost of an indefinite retention of memories.

== Power or Exponential? ==

Forgetting is exponential, however, superposition of forgetting rates for different [[stability|stabilities]] will make forgetting follow the power law. In other words, when memories of different [[memory complexity|complexity]] are mixed, the forgetting curve will change its shape, and may be better approximated with a negative power function (as originally [[Error of Ebbinghaus forgetting curve|discovered by Hermann Ebbinghaus in 1885]]). Plotting the forgetting curve for memories of different stability is of less interest. It can be compared to establishing a single expiration date for products of different shelf life produced at different times. Power approximations face the problem of t=0 point. On the other hand, exponential forgetting may seem devastating in its power. Luckily, for [[20 rules|well-formulated material]], decay constants are very low due to high [[stability|memory stabilities]] developed after just a few reviews.

{{Important note|'''Forgetting is exponential''' due to the random nature of memory [[interference]]}}

For more see: [[Exponential nature of forgetting]]

== Data ==

[[Spaced repetition]] software [[SuperMemo]] routinely collects data and displays a set of forgetting curves that depend on memory [[stability]] and [[memory complexity|knowledge complexity]]. Each user and each knowledge [[collection]] are assigned a set of 400 forgetting curves for different combinations of [[stability]] and [[complexity]] levels. In addition, newer SuperMemos keep 400 curves where time is expressed by memory [[retrievability]] estimate. This rich dataset helps [[SuperMemo]] keep an accurate model of each student's memory.

Examples of curves collected with SuperMemo:

* [http://help.supermemo.org/wiki/File:First_forgetting_curve.jpg Power curve for the first review of heterogeneous knowledge]
* [http://help.supermemo.org/wiki/File:Forgetting_curves.jpg Exponential curve for the second review of homogeneous knowledge]
* [http://help.supermemo.org/wiki/File:Cumulative_forgetting_curve.jpg Cumulative normalized curve for different levels of stability and memory complexity] (over 214,000 data points taken from over 380,000 repetitions)
* [http://help.supermemo.org/wiki/File:Recall.jpg 3D curve for various levels of stability] ([[retrievability]] log axis reversed in reference to time)

See also: 
* [[Error of Ebbinghaus forgetting curve]]
* [[Stabilization curve]]
* [[Two component model of long-term memory]]<noinclude>

{{:ArticleSuperMemo}}</noinclude>

== Examples ==
[[File:Forgettingcurve.jpg|600px|thumb|center|Forgetting curve collected with SuperMemo 17]]
{{:Image:Forgettingcurve.jpg}}

[[File:Exponential_forgetting_curve.jpg|600px|thumb|center|Exponential forgetting curve collected with SuperMemo 17]]
{{:Image:Exponential_forgetting_curve.jpg}}

[[File:Cumulative_forgetting_curve.jpg|600px|thumb|center|Cumulative forgetting curve collected with SuperMemo 17]]
{{:Image:Cumulative_forgetting_curve.jpg}}

[[File:Forgetting curve from preschoolers SuperMemo collection.jpg|600px|center|A forgetting curve from a preschooler's SuperMemo collection]]
{{:File:Forgetting curve from preschoolers SuperMemo collection.jpg}}

[[File:Forgetting curve in coercive learning.png|600px|center]]
{{File:Forgetting curve in coercive learning.png}}