Error of Ebbinghaus forgetting curve
This text is part of: "I would never send my kids to school" by Piotr Wozniak (2017)
Hermann Ebbinghaus was a pioneer of memory research. He was also a pioneer of systematic self-investigations in the field. His forgetting curve has informed the science of memory for over a century. However, today, we need to correct our thinking about the forgetting curve and its impact on learning. What Ebbinghaus demonstrated may sound depressing, but the power of human brain goes well beyond those rudimentary findings.
Ebbinghaus chose nonsense syllables to investigate forgetting. He tried to detach the syllables from real life and prior knowledge, however, even nonsense words may produce associations that are easier or harder to remember.
Choosing nonsense syllables had the following implications:
- little impact of prior knowledge on forgetting
- little interference from knowledge in "real life" interactions
- minimum coherence of the memorized knowledge (low coherence accelerates forgetting)
- no differentiation between difficult and easy syllables (heterogeneous material is forgotten and re-learned differently)
Pure forgetting curve is exponential in nature. Due to the fact that Ebbinghaus used the saving on re-learning rather than recall, his curve was best described by a fast-decay power function:
b=100k/((log(t)^c+k)
where:
- b - saving on relearning in percent
- t - time in minutes
- c and k - constants (1.25 and 1.84)
This function is not universally applicable as it refers to a specific person, a specific learning material, and a specific learning procedure.
Today, we know that forgetting is exponential in nature (see: forgetting curve). It is very similar to radioactive decay. It is governed by similar principles. To see the exponential nature of forgetting, we need to select the learning material for the same level of complexity (as it is done in SuperMemo). Heterogeneous material will inevitably lead to a superposition of different forgetting curves with different decay constants.
There are many misconceptions that have roots in the misinterpretation of the research undertaken by Ebbinghaus.
Here are the most important facts to remember:
- forgetting is exponential (see: forgetting curves collected with SuperMemo)
- speed of forgetting depends on the complexity of knowledge
- speed of forgetting depends on the stability of memory (see: two component model of memory)
- in the practice of learning, speed of forgetting is by orders of magnitude slower than in Ebbinghaus experiments (years instead of minutes)
- knowledge coherence is the prime weapon against forgetting
The emphasis on knowledge coherence might be the most important of the above observations. There is a world of difference between nonsensical syllables and well-organized knowledge.
For more on knowledge coherence see: 20 rules.
Here is an exemplary forgetting curve from SuperMemo based on over 80,000 recall samples:
Figure: The first review forgetting curve for newly learned knowledge collected with SuperMemo. Power approximation is used in this case due to the heterogeneity of the learning material freshly introduced in the learning process. Lack of separation by memory complexity results in superposition of exponential forgetting with different decay constants. On a semi-log graph, the power regression curve is logarithmic (in yellow), and appearing almost straight. The curve shows that in the presented case recall drops merely to 58% in four years, which can be explained by a high reuse of memorized knowledge in real life. The first optimum review interval for retrievability of 90% is 3.96 days. The forgetting curve can be described with the formula R=0.9907*power(interval,-0.07), where 0.9907 is the recall after one day, while -0.07 is the decay constant. In this is case, the formula yields 90% recall after 4 days. 80,399 repetition cases were used to plot the presented graph. Steeper drop in recall will occur if the material contains a higher proportion of difficult knowledge (esp. poorly formulated knowledge), or in new students with lesser mnemonic skills. Curve irregularity at intervals 15-20 comes from a smaller sample of repetitions (later interval categories on a log scale encompass a wider range of intervals)
Where meaningful knowledge can be retained for years (as above), nonsense syllables from Ebbinghaus experiments lasted for hours (as below).
Figure: Forgetting curve adapted from Hermann Ebbinghaus (1885). The curve has been rendered from original tabular data published by Ebbinghaus (Piotr Wozniak, 2017).