ebbinghaus memory experiment conclusion

Hermann Ebbinghaus and the Experimental Study of Memory

Hermann Ebbinghaus (1850 – 1909)

On January 24, 1850, German psychologist Hermann Ebbinghaus was born. Ebbinghaus pioneered the experimental study of memory, and is known for his discovery of the forgetting curve and the spacing effect .

“When we read how one mediæval saint stood erect in his cell for a week without sleep or food, merely chewing a plantain-leaf out of humility, so as not to be too perfect; how another remained all night up to his neck in a pond that was freezing over; and how others still performed for the glory of God feats no less tasking to their energies, we are inclined to think, that, with the gods of yore, the men, too, have departed, and that the earth is handed over to a race whose will has become as feeble as its faith.” – Hermann Ebbinghaus (1885) [8]

Hermann Ebbinghaus – Early Years

Hermann Ebbinghaus was born in Barmen , in the Rhine Province of the Kingdom of Prussia and attended the University of Bonn where he intended to study history and philology. In 1870, his studies were interrupted when he served with the Prussian Army in the Franco-Prussian War. Ebbinghaus evolved a great interest in philosophy and finished his dissertation on Eduard von Hartmann ‘s Philosophie des Unbewussten ( Philosophy of the Unconscious ). After earning his doctorate degree in 1873, Ebbinghaus spent much time in Halle and Berlin and also traveled through England and France. It is assumed that Ebbinghaus took teachers positions while on travel and apparently he discovered Gustav Fechner ‘s book Elemente der Psychophysik ( Elements of Psychophysics ) while in London.[ 4 ] The book highly inspired the young scientist to start his own research on memory studies.

Experimental Psychology

Ebbinghaus’ famous work, Memory: A Contribution to Experimental Psychology was already published in 1885 and was so successful that he was appointed professor at the University of Berlin. Ebbinghaus and Arthur König founded the Psychological journal Zeitschrift für Physiologie und Psychologie der Sinnesorgane in 1890. Ebbinghaus joined the University of Breslau, Poland and studied how children’s mental ability declined during the school day. He also founded a psychological testing laboratory there. Die Grundzüge der Psychologie where published in 1902, which was an instant success. Two years later, Ebbinghaus moved to Halle. His last and quite successful work Abriss der Psychologie ( Outline of Psychology ) was published in 1908.

Prior Knowledge, Understanding, and Learning

Contrary to most scientists studying higher mental processes, Ebbinghaus believed that research could be conducted through experiments. He developed a system recognizing the fact that learning is always affected by prior knowledge and understanding. Ebbinghaus figured that he would need something that would be memorized easily but without prior cognitive associations. The scientist created the so called “ nonsense syllables “. This can be understood as a consonant-vowel-consonant combination, where the consonant does not repeat and the syllable does not have prior meaning, like DAX, BOK, and YAT. After creating the collection of syllables, Ebbinghaus pulled out a number of random syllables from a box and then write them down in a notebook. Then, to the regular sound of a metronome, and with the same voice inflection, he would read out the syllables, and attempt to recall them at the end of the procedure. One investigation alone required 15,000 recitations.

The Forgetting Curve

However, there were also some limitations in Ebbinghaus’ work on memory. For instance, he was the only subject in the study and therefore it was not generalizability to the population. Also, a large bias is to be expected when a subject is a participant in the experiment as well as the researcher. Still, Ebbinghaus managed to contribute significantly to the research on memory. His most famous finding is probably the forgetting curve , which describes the exponential loss of information that one has learned. His results roughly state that just 20 minutes after learning, we can only recall 60% of what we have learned. After one hour, only 45% of what has been learned is still in our memory, and after one day only 34%. Six days after learning, the memory has already shrunk to 23%; only 15% of what has been learned is permanently stored.

The Ebbinghaus Illusion – The two orange circles in the middle are the same size.

The Ebbinghaus Illusion

In the most famous version of this illusion, two circles of identical size are placed close to each other and one is surrounded by large circles while the other is surrounded by smaller circles; the first central circle appears smaller than the second central circle. This illusion has been used extensively in research in cognitive psychology to learn more about the different perceptual pathways in our brain. In the English-speaking world, the circles were published by Edward Bradford Titchener in a book on experimental psychology in 1901, hence their alternative name Titchener circles .

Shortly after the publication of  Abriss der Psychologie , on February 26, 1909, Ebbinghaus died from pneumonia at the age of 59.

References and Further Reading:

• [1]  Hermann Ebbinghaus at the Human Intelligence
• [2]  Hermann Ebbinghaus at Famous Psychologists
• [3]  Hermann Ebbinghaus at Britannica
• [4]  Gustav Fechner and Psychophysics , SciHi Blog, April 19, 2016.
• [5]  Works by or about Hermann Ebbinghaus  at  Internet Archive
• [6]  Hermann Ebbinghaus at the Human Intelligence website
• [7]  Ebbinghaus, H. (1885).  Memory: A contribution to experimental psychology .  New York: Dover.
• [8]  Ebbinghaus, H.  “ Experiments in Memory ,” in   Science   Vol. 6, 1885, p. 198
• [9] Hermann Ebbinghaus at Wikidata
• [10]  Chris Dula,  Memory: Forgetting Curve and Serial Position Effect , 2014, East Tennessee State University @ youtube
• [11] Ebbinghaus, H. (1908).   Psychology: An elementary textbook.   New York: Arno Press.
• [12] Timeline of German Psychologists , via DBpedia and Wikidata

Tabea Tietz

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Replication and Analysis of Ebbinghaus’ Forgetting Curve

Jaap m. j. murre.

University of Amsterdam, Amsterdam, The Netherlands

Conceived and designed the experiments: JMJM JD. Performed the experiments: JD. Analyzed the data: JMJM JD. Contributed reagents/materials/analysis tools: JMJM JD. Wrote the paper: JMJM JD.

Associated Data

Data are available from the Open Science Framework at DOI: osf.io/6kfrp .

We present a successful replication of Ebbinghaus’ classic forgetting curve from 1880 based on the method of savings. One subject spent 70 hours learning lists and relearning them after 20 min, 1 hour, 9 hours, 1 day, 2 days, or 31 days. The results are similar to Ebbinghaus' original data. We analyze the effects of serial position on forgetting and investigate what mathematical equations present a good fit to the Ebbinghaus forgetting curve and its replications. We conclude that the Ebbinghaus forgetting curve has indeed been replicated and that it is not completely smooth but most probably shows a jump upwards starting at the 24 hour data point.

Introduction

This paper describes a replication of one of the most important early experiments in psychology, namely Ebbinghaus' classic experiment on forgetting from 1880 and 1885. We replicated the experiment that yielded the famous forgetting curve describing forgetting over intervals ranging from 20 minutes to 31 days. Ebbinghaus' goal was to find the lawful relation between retention and time-since-learning. This is why he fitted the data to two different functions (a power function, 1880, and a logarithmic function, 1885), as have many theorists since (e.g., [ 1 , 2 – 4 ]). This papers also includes an analysis—including one with a new model—of the shape of the Ebbinghaus' forgetting curve and its replications. Do the replicated forgetting curves have the same shape, or must we conclude that Ebbinghaus' forgetting curve was idiosyncratic and that quite different shapes may occur?

There is currently an increasing interest in replication studies in psychology, motivated by a growing uneasiness in the community about unreliable findings in psychology. It seems particularly important to try to replicate classic studies that are included in every textbook on cognitive psychology and may also be known by the general public. A good example of this is the classic study by Bartlett [ 5 ], which until 1999 had only had unsuccessful replication attempts, until finally Bergman and Roediger [ 6 ] succeeded in replicating the basic findings. One of the reasons earlier replications may have failed is because not all details were well-documented in the original study from 1932. The exact instructions, for example, were not included. This may explain why Wynn and Logie [ 7 ] had found the forgetting gradient in their experiment to be quite different from the one in Bartlett's experiment. Bergman and Roediger [ 6 ] also argue that this may have been caused by certain differences in the study design. Replication of classic experiments, thus, serves the dual purpose of verifying the reliability of the original results and uncovering more precisely how the original experiment was conducted.

It is hard to overestimate the importance of Hermann Ebbinghaus' contribution to experimental psychology. Influenced by the work of the German philosopher Herbart, he was the first to carry out a series of rigorous experiments on the shape of forgetting, which he completed in 1880. The experiment itself was preceded by a period in which he tried out a variety of materials and methods. After having tested himself with tones, numbers, and poem stanzas, he decided that none of these served his purposes. Tones were too cumbersome to handle and too difficult to reproduce for him, he did not find digits zero to nine suitable as basic units for the long-running experiments he envisioned, and the poem fragments he tried to learn (from Byron’s Don Juan) were deemed too variable in the meanings they evoked and therefore likely to cause measurement error [ 8 ] (p. 14–17). He, therefore, introduced nonsense syllables, which had more uniform characteristics than existing words or other verbal material. In his later experiments on learning, however, he did verify his results with the Don Juan verses, confirming both his main results on learning and his intuition that the latter stimuli did indeed yield much more variance in the data [ 9 ]. Since his introduction of nonsense syllables, a large number of experiments in experimental psychology has been based on highly controlled, artificial stimuli.

In all experiments reported by Ebbinghaus [ 9 ], he used only himself as a subject. Single-subject designs are not unusual in memory psychology. Especially in the study of autobiographical memory we find several diary studies based on one person’s personal memories (e.g., [ 10 , 11 , 12 ]). They have the advantage that there is no inter-subject variability, although they still require hundreds of trials to reduce the variance due to differences in stimuli and other factors. This places a great burden on the subject. Indeed, Ebbinghaus’ forgetting curve is based on seven months of experimenting, often up to three sessions per day. Wagenaar [ 13 ] meticulously recorded one daily memory during six years and spent several months recalling these.

A disadvantage of a single-subject design is that it remains unclear what the shape of forgetting would be with other subjects. Are the results universal or did the subject happen to have a memory that was exceptional in some way [ 14 , 15 ]. The generality of the results can be assessed with a faithful replication. There have been a number of—mostly early—replications of Ebbinghaus’s forgetting curve, notably by Radossawljewitsch [ 16 ] and Finkenbinder [ 17 ], but these authors used a much slower presentation rate of the stimuli of 2 s per stimulus, where Ebbinghaus learned at 0.4 s per stimulus. This was partially the result of the development of devices for mechanical presentation by Müller and colleagues [ 18 , 19 ], who presented materials at a rate one stimulus per second. Slowing down the presentation this much alters the nature of the processing with more time to generate meaningful associations to otherwise meaningless syllables. Though the resulting forgetting curves are clearly of interest to the field, we feel that the slow method of presentation form a large departure from Ebbinghaus’ original study. Also, Finkenbinder’s [ 17 ] longest retention interval is 3 days, instead of 31 days and though in the experiment by Radossawljewitsch [ 16 ] the retention interval range extends up to 120 days, his design suffers from an uneven distribution of intervals throughout time and time-of-day. Stimuli were learned in order: in the first few days of the study all 5 min intervals were learned, then the 20 min intervals, and so on. Because he did not use a pre-experimental practice phase, the early intervals took longer to learn while the subjects were still getting used to the materials and the procedure; it is likely that this has affected the shape of the forgetting curve reported by him. There are other differences between these two studies and Ebbinghaus’, for example, the degree to which was learned and whether the subjects were allowed to pause between lists.

There are several unanswered questions about Ebbinghaus’ results that formed part of the motivation for us to undertake this replication. His basic stimulus was a ‘row’ of thirteen nonsense syllables, which he studied until he could correctly recall it in the correct order twice in succession. A question that seems pertinent is how stimuli at different serial positions were learned and how these were forgotten over time. Another question is how his measure of choice, namely savings (see below) is related to the nowadays more common measure of percentage correct. Finally, we were interested in the role of interference or fatigue in the course of the experiment.

To help answer these questions, we consulted not only the widely published text of 1885 [ 9 ], which was translated into English in 1913 [ 20 ], but also an earlier report of 1880 [ 8 ]. This is a handwritten manuscript that he submitted for his Habilitation , which in Germany is a requirement to be considered for a full professorship. This text (the so called Urmanuscript or original manuscript) has been typeset and republished in German in 1983. Even with this additional source, however, we still could not answer the questions above.

For these reasons, we decided to replicate Ebbinghaus’ forgetting experiment. If our replication yielded similar results, this would support the generality of Ebbinghaus’ curve and through a more detailed analysis of our data, we would be able to address the issues above. In the course of preparing for our study, we found that there has been at least one other replication study, namely by Heller, Mack, and Seitz [ 21 ]. This study has been published only in German, without an English abstract, and is not easily accessible; at the time of writing, it is not available in electronic format (i.e., it is not available online) and it has never been cited in international journals in English. It is, however, a thorough study and an excellent replication attempt. Where the Ebbinghaus [ 8 , 9 ] texts are unclear about certain details, we have mostly followed Heller et al. [ 21 ] as a guideline so that we can also compare our results with theirs. Because we feel this is an important study that has not received the readership it deserves, we will mention more of its details here than we would have had it been more accessible at this point in time.

In 1885, Ebbinghaus introduces the savings measure of learning and memory (it does not appear in this form in his earlier text from 1880). Savings is defined as the relative amount of time saved on the second learning trial as a result of having had the first. Suppose, one has to repeat a list for 25 times in order to reach twice perfect recollection and that after one day, one needs 20 repetitions to relearn it. This is 5 less than the original 25; we can say that on relearning we saved 20% with respect to the original 25 rehearsals (5/25 = 0.2 or 20%). If it takes just as long to relearn the list as it took to learn it originally, then savings is 0. If the list is still completely known at the second trial (i.e., no forgetting at all), then savings is 1 or 100%. Ebbinghaus prefers to express savings in terms of time spent learning and relearning but the principle remains the same. After Ebbinghaus’ publication in 1885, the savings measure remained popular for several decades [ 16 – 19 , 22 – 24 ]. Eventually, researchers found the savings method too unreliable compared with other methods of measuring memory [ 24 ] and in the following decades it was used much less with some exceptions (e.g., [ 25 ]). Later, an important improvement was suggested [ 26 , 27 ], where learning is not to the 100% criterion but to a much lower one, such as 50% correct. These improved versions of the method are used nowadays, for example, when studying forgetting of foreign languages [ 28 – 30 ].

In the following, we will first report our replication experiment. Then, in the Discussion section we will revisit the shape of forgetting, analyze the effects of serial position on forgetting, and investigate what mathematical equations present a good fit to the Ebbinghaus forgetting curve and its replications. Finally, we will study whether there is evidence for a jump at 24 hours in these curves, which some authors have attributed to the effect of sleep.

The Replication Experiment

The current study was set up to replicate the findings by Ebbinghaus [ 8 , 9 ]. Despite a quite detailed account of his experiment, we found some information to be lacking and we had to estimate or guess these details, as outlined below. Also, we did not have the seven months available that Ebbinghaus invested in the experiment, but we had to accommodate our design to a 75 day period. We nonetheless believe that our experiment is close enough to his to be still called a replication.

There were a few differences between Ebbinghaus’ study, Heller et al.’s [ 21 ] replication, and ours. (i) Because we were limited in time, like Heller et al. [ 21 ], we ran only 10 replications per time interval, instead of the 12 to 45 by Ebbinghaus. This means the variance in our data is larger than in Ebbinghaus’ especially at the longest time intervals; apart from that no systematic differences were introduced. (ii) We were not able to experiment at a fixed time of day. Ebbinghaus (1880), who started experimenting in the morning at (A) 10:00, and then sometimes also at (B) 12:00 and usually at (C) 19:00 to 20:00, noticed that there was a difference between these times of the day in his ability to acquire a list. He subtracted 5% for B and 13% for C from the learning times at these hours to normalize the data with respect to time A. Heller et al. [ 21 ] were also able to conduct experimental sessions at specific times throughout the day, but they did not find such a time-of-day effect and hence did not implement a correction. (iii) Our stimulus material conformed to the phonotactics of the Dutch language and thus differs from both Ebbinghaus and Heller et al. Also, in contrast to both Ebbinghaus and Heller et al. we removed syllables that had too much meaning in order to further balance the level of difficulty of the stimuli. (iv) Our subject, J. Dros, was younger than H. Ebbinghaus, who was 29 during his experiments in 1879–1880. The ages of the two subjects in Heller et al. [ 21 ] are not given. (v) Ebbinghaus [ 8 ] gives exact testing dates for each of the short time-intervals but not for the longer ones (24 hours and up). Hence, we do not know exactly when he learned and relearned the lists for the longer intervals. This makes it impossible to calculate the number of interfering lists between learning and relearning. It also makes it nearly certain that our schedule differed from his (and from that of Heller et al. [ 21 ] who also do not supply such a schedule).

The second author, J. Dros, (22 years, male) was the only subject in the experiment. This experiment was reviewed and approved by the Review Board of the Psychology Department of the University of Amsterdam (see www.lab.uva.nl ). The project is filed with case number 2014-BC-3879 (contact is Dr. R.H. Phaf). Consent was implicit as the second author of the paper was also the only subject on which we report. This was also approved by the Review Board. The subject's native language is Dutch, making this the first non-German replication of Ebbinghaus’ forgetting experiment.

The learning material consisted of 70 lists. Each list consisted of 104 nonsense syllables, which in turn consisted of 8 ‘rows’ of 13 syllables.

Nonsense syllables

Each syllable consisted of 3 or 4 lower-case letters. The structure of a syllable was a lower-case consonant-vowel-consonant (CVC) structure. The consonant of the syllable was always one of b, d, f, g, h, j, k, l, m, n, p, r, s, t, or w. The vowel could be one of e, i, o, u, aa, uu, ee, ei, eu, oe, ie, oo or ui. The double-letters stand for standard Dutch vowels. The last consonant of the syllable was one of f, g, k, l, m, n, p, r, s, or t.

The number of different possible consonant-vowel-consonant combinations on the basis of these letter combinations is 2100 (15 × 14 × 10). Not every possible consonant-vowel-consonant combination was included in the learning material; we removed words that had too much meaning in Dutch, in order to further balance the difficulty of the stimuli. Syllables with meanings in other languages spoken by the subject, such as English and German, were not excluded.

Row and list construction

Using the pseudo-random generator of Excel 2010, rows of 13 syllables were constructed. Within a row we did not allow two syllables with the same vowel in direct succession. We also did not allow two identical syllables within one row, but we did allow them in different rows within a single list. When syllables needed to be adjusted we first tried changing only the first or second letter of a syllable until the criteria were met. If this did not suffice, additional letters were changed. The adjustment process was not purely random but was carried out by hand during stimulus preparation by the authors.

The only independent variable in this experiment was the time-interval, which started at the end of learning a list for the first time. The time-interval ended at the beginning of learning a list for the second time. The time-intervals between learning and relearning were the same as Ebbinghaus [ 8 ]: 20 minutes, 1 hour, 9 hours, 1 day, 2 days, 6 days and 31 days. For each time interval, 10 lists were learned and relearned (for the 9 hour interval only 9 lists were learned due to unforeseen circumstances).

We need to elaborate on the choice of these time intervals as there is some confusion about the exact length of the shorter retention intervals used by Ebbinghaus. He mentions both 15 min (in 1880 [ 8 ]) and 19 min (in 1885 [ 9 ]) for the shortest interval, and 63 min and 8.75 hours (525 min) for the longer intervals. He also states that relearning took place “after about one third of an hour, after 1 hour, after 9 hours, one day, two days, six days, or 31 days.” ([ 20 ], p. 66). Heller et al. [ 21 ] followed the latter intervals, using 20 min, 60 min and 9 hours, etc. We have also used these, given that this seems to have been the intended lengths of Ebbinghaus’ retention intervals. The deviations these values by Ebbinghaus are based on corrections after the experiment.

Ebbinghaus’ shortest interval (‘20 minutes’) is based on almost immediately relearning a list of eight rows and hence the interval depends on how long it took to learn the eight lists. When relearning the lists so soon it takes much less time to relearning them, than the original learning, so that the intervals between learning and relearning of lists is not constant, with List 8 being relearned earliest (e.g., 20 min) and List 1 latest (e.g., 10 min). Ebbinghaus [ 8 ] (p. 50) states that the average time is about 15 min and argues that that whereas he does not know exactly how to correct for these variable learning times, the error will be small. We recalculated the average of the times stated on page 51 of the 1880 text and find it to be 1010 s or 16.8 min. Ebbinghaus keeps using the value of 15 min throughout his text from 1880, including for fitting his ‘power function’ equation (see below). The learning and relearning times given in his 1885/1913 volume [ 20 ] are the same as in 1880 [ 8 ], but to each interval he has now added 88 s for reasons that are not made clear. The average of these learning intervals then becomes 18.3 min. Given that he also remarks that for the shortest interval “relearning of the first series of a test followed almost immediately or after an interval of one or two minutes upon the learning of the last series of the same test” ([ 20 ], p. 66) may explain rounding 18.3 min to 19 min, the value used throughout the text from 1885. In general, it seems he made more or less intuitive corrections for the variable learning times and changed his mind from 1880 to 1885 about the most appropriate method to approach this. We have used 19 min, 63 min, and 8.75 hours in the graphs and tables (and fits), for Ebbinghaus’ data. For the other data sets, we use 20 min, 1 hour, and 9 hours.

Measurement of repetitions and time

The main measurement was the number of repetitions needed to correctly reproduce the syllables in a row in the correct order.

For the forgetting curve experiment, Ebbinghaus [ 8 ] learned until twice correct, but in later experiments switched to once correct [ 9 ], because he found there to be no essential difference in the outcomes. We chose to also learn to once correct. Heller et al. [ 21 ] (p. 8) seem to be using the once-correct criterion as well but this is not made entirely clear.

Ebbinghaus [ 8 ] uses elapsed time to calculate the number of repetitions, because he finds keeping count too distracting. Heller et al. [ 21 ] use a chain with wooden, colored beads, much like a rosary to keep count. We found that word processing software (Microsoft Word) was handy to keep track of the number of repetitions. During learning, each single repetition of a row was counted by pressing the button ‘1’ on the keyboard at the beginning of every single repetition of a row. At the end of learning a list, the total number of 1’s for each row was counted and entered into the database.

We also measured the time in seconds needed to learn a list. A clock was shown on the computer screen during the task and we recorded the begin times and end times of learning a list. Subtracted from the time were the pauses of 15 s between two rows (cf. [ 8 ], p. 19). When relearning a list, the extra time (15 s) introduced by the voice recording of the first retrieval attempt was subtracted from the total relearning time.

The practice phase and experimental phase

Following Ebbinghaus, we preceded the experimental phase of the experiment with a practice phase to prevent as much as possible general learning effects due to growing experience with the task and materials. The practice phase took place between 08-11-2011 and 29-11-2011. A total of 14 lists was learned and relearned after 20 minutes (Heller et al. [ 21 ] relearned lists after one hour). After these, a further 19 lists were learned only (i.e., not relearned later) for additional familiarization with the task.

In the experimental phase, which took place between 01-12-2011 and 13-02-2012, a total of 69 lists was learned and relearned (9 for the 9 hour interval). The total time spent on data collection in the experimental phase amounted to about 70 hours. We distributed the ten lists for each time interval as much as possible over the whole experimental period. Due to the limited time available to run the whole experiment, we were not able to achieve this for the 31 days time interval condition, so that we decided to learn these lists near the beginning of this experimental period.

List learning phase

All lists were printed on paper (black ink, font ‘Calibri’, 11 points) (eight rows per page; a row was actually printed in a column format for easier studying). The non-studied rows were covered by sheets of paper. The subject was seated behind a desk in a quiet room. The main goal was to learn a list as quickly as possible, to learn each row until it could be reproduced correctly once.

Following Ebbinghaus [ 8 ] (p.18), the syllables were softly spoken from the first syllable to the 13 th syllable at a constant speed of 150 beats per minute. The repetition of a row took 5.2 s on average. Our subject preferred to speak the syllables in a jambus-like manner, where syllables were paired so that the emphasis always was on the second syllable (i.e. wes-hóm, niem-hág, etc…). The last syllable (13 th syllable) was not paired to another syllable and was not spoken with an emphasis. Here, we use an approach similar to Heller et al. [ 21 ] and not to Ebbinghaus, who prefers a ¾ rhythm, stressing the first syllable in each group of three (this is in fact the reason he gives for his preference for rows of length 10, 13, or 16 syllables, see Ebbinghaus [ 8 ], p. 19).

During the learning phase, the subject had a continuous choice to either read or reproduce the syllables. Towards the end of the learning process, occasional attempts were made to produce an entire row by heart. When there was a moment of hesitation during such ‘blind’ reproduction, the rest of the list was read (i.e., not blind) to the end. Blind reproduction always started with the first syllable of a row. Rows were not learned in parts. Each time the 13 th syllable had been reached and the row still contained errors, it was read again from the beginning. After having learned one row and before starting the next one, there was an interval of 15 sec. The interval served as a moment of rest and pause. All of this was aimed at following Ebbinghaus as closely as possible. Each row was thus learned to a 100% correct criterion before moving to learning the next row.

During the pre-pretraining phase, a metronome was used at first to achieve a recitation rate of 150 beats, but this was found to be too intrusive and distracting. Eventually, the rhythm was internalized and the metronome was only used for occasional rate checks. During the experimental phase, it was not used. After each rehearsal of a row, there was a little transition-pause of about 3 beats to take a breath before the next repetition of the row.

Learning of a list was considered complete, if all rows had thus been learned in order. The retention interval was started at the time a list had been learned. On most days two or three lists were learned or relearned with a maximum of four. The full learning schedule is given in Fig 1 .

Relearning times are not shown but can be derived by adding the retention interval (e.g., 6 days).

Relearning phase

We added one additional measurement to Ebbinghaus’ procedure: the number of correct syllables at first reproduction of a row at relearning, not necessarily at the right location. We recorded the recall of the first time a row was relearned with an Olympus WS-450s voice-recorder. After the last relearning session of the experimental phase, the sound files were transcribed and scored.

Rows were relearned in the same order as during original learning. During relearning, the subject was seated at a desk with a computer. A word processing program was opened on the computer and a clock was visible on the screen. A sheet of paper with a list printed on it was laid in front of the subject with only the syllables from the row to be learned visible. The other rows were covered by a piece of paper. During learning, the subject used the ‘1’ button on the keyboard to count the number of repetitions. Following Ebbinghaus [ 8 ] (p. 19), after successful relearning there was a 15 second pause. Then, the row learned last was covered, a next row uncovered and the procedure was repeated.

Relearning of a row started with turning on the voice recorder. Then the row was read once as described above. Twenty seconds after turning the voice recorder on, the subject stopped recall attempts and turned the voice recorder off. After that, relearning continued in the usual fashion. This procedure was repeated for every row in the list. After a list had been relearned, the audio file of the recording was saved on a computer.

The forgetting curve

The main objective was to replicate Ebbinghaus’ famous forgetting curve. The average number of repetitions is given in Table 1 and the number of seconds spent on learning and relearning each list, with the calculated savings scores, is given in Table 2 . The raw data of this experiment are freely available online at the website of the Open Science Foundation (URL: https://osf.io/6kfrp/ ). To see whether there were differences between the time-intervals in the average number of repetitions at first learning, a one-way independent ANOVA with the average number of repetitions per list as the dependent variable and the time-interval as the independent variable. There was no significant effect for the time-interval, F(6, 69) = 0.691, p = 0.658. This means that the average number of repetitions per list did not differ significantly per time interval, indicating there were no randomization confounds.

Savings scores (based on time in s) are compared with those of Ebbinghaus [ 8 ], and Mack and Seitz [ 21 ] in Table 3 and plotted with error bars in Fig 2 using loglog coordinates and in Fig 3 using log coordinates only for the time axis. Despite the fact that the original experiment dates from 1880 and replications were done over a century later, and despite the fact that our replication was carried out in a Dutch language context, the four forgetting curves share many characteristics. To facilitate a direct comparison we have overlaid the four curves in Fig 4 where we have normalized the savings scores such that the first data point (at 20 min) was always equal to 1.0. Given expected individual differences, we find the resemblance of the four graphs remarkable. The greatest deviation is by Dros at 31 days; his savings score is much lower that any of the other three. We can only speculate at the reason for this. It may be that this subject simply has more long-term forgetting. Another explanation bears on the fact that the lists for the 31 day interval were all learned early in the experiment (see Fig 1 ) and learning times were shorter at the beginning, due to greater initial enthusiasm, less pro-active interference, or yet another reason. It is also possible that the low savings score on the 31 day point is an effect of the relatively short time period in which initial learning took place for the 31-day data point (i.e., massed learning); learning for other intervals was more widely spaced. We were forced to place the learning sessions at the beginning because of the limited time available by the subject for data collection. Ebbinghaus could spread his sessions of a seven-month interval, though we do not know the exact schedule for the intervals past 9 hours, nor do we know anything about the schedule followed by Mack and Seitz. Finally, we considered where the number of intervening lists had influenced retention at the 31-day-point. For this time point, the number of intervening lists varied from 23 to 33. Our analysis, however, revealed virtually no relationship with savings score as a function of intervening lists ( R 2 was about 8.4%). Our data did not allow us to further disentangle the effect of number of intervening lists versus time because list number and time were too strongly confounded in our design.

We found a gradual increase in learning time throughout the course of the experiment as can be seen in Fig 5 , where averaged learning time in s has been plotted for consecutive ten-day periods (‘bins’). In the course of the 75 days of the experimental phase there was an average increase in learning time of 2.67 s per day for a list (this linear regression explained 56.18% of the variance). If we correct for this steady increase, which mostly affects the 31 day interval, the corrected savings measure would be 0.137 for the 31 day interval instead of 0.0410. This, however, is still well below the values for the three others, which are in the 0.20 range. This steady increase in learning time may be due to pro-active interference or fatigue. Ebbinghaus [ 8 ] and Heller et al. [ 21 ] do not report or analyze this.

We also analyzed the false alarms and correct answers measured on first relearning. We did a one-way independent ANOVA with the number of false alarms per row as the dependent variable and the retention interval as the independent variable. There was no significant effect for the time interval, F(6 , 512) = 0 . 753 , p > 0 . 608 , indicating that the number of false alarms was not significantly different for the time-intervals. A one-way independent ANOVA with the number of hits per row as the dependent variable and retention interval as the independent variable, however, yielded a significant effect for the time-interval, F(6 , 512) = 3 . 85 , p < 0 . 01 , which we will analyze further in the next section.

Serial position effects

In Fig 6 , we have plotted the average serial position curves for each retention interval and for the grand average. Even if a correct syllable was not mentioned at the correct position, it was still scored as correct for its intended position (this was rare and had only a small effect on the data). Fig 6 shows clear serial position curves for all retention intervals.

In Fig 6 , it also seems that there is more forgetting with time in the middle positions. In Fig 7A , overall forgetting is shown, where the average of all positions is shown for each retention interval. Though there is forgetting, these curves are much shallower than the savings curves, which are shown as well for comparison. In Fig 7B , forgetting is shown for four groups of serial positions, indicating that indeed there is virtually no forgetting in the final positions 11 to 13. A regression line is nearly horizontal for positions 11–13 (slope -0.000183) and 1–2 (slope is -0.000112) with the largest decrease over time found in positions 3–8 (slope is -0.0114) and 9–10 (slope is -0.0119). The averaged curve has a slope of -0.00930, with all slopes calculated over the untransformed scores (i.e., not on a logarithmic scale).

(a) Proportion correct, averaged over all serial positions, shown with Dros’ savings scores for comparison. (b) Proportion correct curves for different groups of serial positions and for the average over all 13 positions.

We believe that we may conclude that our attempt to replicate Ebbinghaus’ classic forgetting was successful. We were able to follow his method quite closely and the resulting curve is very similar to both that of Ebbinghaus and that of the two subjects in an earlier German replication [ 21 ], with the exception of the savings value at 31 days, which in our case is much lower than the others. The latter difference remains even if we correct for increased learning time over the course of the experiment. It is possible that with Ebbinghaus and Heller et al. there were far fewer intermediary lists learned between learning and relearning and hence much less interference. Unfortunately, this information is not available, so this must remain speculation.

Effects of serial position on forgetting

Ebbinghaus does not say anything about serial position curves or indeed about the order in which he acquired the syllables. Our data allow us to say a little more about this. When interpreting the serial position scores in Fig 6 , one has to bear in mind the nature of the savings methods with lists of nonsense syllables. With Ebbinghaus-type relearning, a row is always first studied before it is relearned. Savings experiments are very different from normal memory retention experiments where the subject learns something at after some time interval is tested for retention. With savings, the retention measurement itself consists of relearning the original material in repeated recall trials each of which is preceded by prior exposure to the stimulus materials. In theory it is, therefore, possible in extreme cases that there are subjects who can learn a row of 13 syllables in a single learn-recall trial but who subsequently always forget the learned materials in say 10 min. By conventional (non-savings) retention tests, these subjects would be reported as have 0% retention past 10 min, but these same subjects would show 100% savings for all retention intervals past 10 min because when testing their savings performance they would go through the exposure-learn sequence, always (re)learning the materials immediately: at t = 0, they take 1 trial to learn the material and at t = 1 day they also take 1 trial, showing perfect savings (i.e., seemingly no forgetting). Thus, when stimuli are very easy to learn true forgetting becomes impossible to measure with the savings method, because original learning will be at ceiling (one-trial learning) as will be relearning after a time-interval (again: one-trial learning), no matter how long the interval.

Here, it seems that the first two and the last three syllables were very easily learned (and relearned), probably because of primacy and recency effects. This effect was also noticed by other early researchers who adapted Ebbinghaus’ method (e.g., [ 17 ]). Relearning the harder parts of a list, in particular the middle syllables, benefits most from recently having learned these sometime before (i.e., before the relearning phase of the savings experiment), as is evident from the savings scores. The discrepancy between savings and recall or recognition has also been found by other authors (e.g.,[ 24 , 31 , 32 , 33 ]) and appears here as a function of serial position.

The fairly evident primacy and recency effects also suggest that the despite Ebbinghaus’ efforts to construct equivalent stimuli, there is a great variation in how well they eventually were learned: During the first phase (t = 0), stimuli in the first and last positions were very easily and hence very well learned, while those in the middle were learned much less. The effect seems quite constant, however, so that it need not affect the validity of the shape of the forgetting curve, but we should be aware that its shape is based on a combination of very well learned items and just barely learned items. In that sense, the forgetting curve by Ebbinghaus is an average over different forgetting curves of items in various serial positions, which have been learned to varying degrees. This in itself may explain part of the characteristic shape of the curve, which we will explore in the next section.

Curve fitting

Hermann Ebbinghaus [ 8 ] was the first to try to find a mathematical equation that describes the shape of forgetting. Many researchers who used his method have followed suit, also trying to summarize the forgetting curve in a concise equation. In his first manuscript, from 1880, Ebbinghaus proposes the equation x = [1 − (2/ t ) 0.099 ] 0.51 , where x equals 1 minus savings at time t (in min). It is of some interest that Ebbinghaus [ 8 ] (p. 57–63) puts the entire section in which he fits this equation to the data between square brackets, making it an aside: something that is also interesting but not belonging to the main text. Nonetheless, he gives a well-motivated derivation based on a differential equation of a gradually slowing forgetting process. Interesting is that in the write-up of the experiment in 1885 [ 9 ], the equation has been changed to the very different one, which has been become generally known as the ‘Ebbinghaus Forgetting Equation’, rather than the first one, namely Q ( t ) = 1.84 / ((log t ) 1.25 + 1.84), where the log is taken with base 10. This equation is lacking a derivation and Ebbinghaus remarks on it: “Of course this statement and the formula upon which it rests have here no other value than that of a shorthand statement of the above results which have been found but once and under the circumstances described. Whether they possess a more general significance so that, under other circumstances or with other individuals, they might find expression in other constants I cannot at the present time say.” [ 20 ]

We are now in a better position to verify Ebbinghaus’ question about the general significance of his equation by fitting his equations to the other data. The results are given in Table 4 and were obtained with a nonlinear fitting procedure in Mathematica 9 (the Mathematica code is available from the author). We calculated several goodness-of-fit measures including the Akaike Information Criterion or AIC [ 49 , 58 ], which contrary to, for example, variance explained ( R 2 ) or sum of squared differences ( SSD ), takes into account (and penalizes for) the number of free parameters. It also allows a comparison of the goodness-of-fit of different models, even if they have different numbers of parameters. Lower values indicate better fit, where a difference of more than 2 is seen as a meaningful difference in goodness-of-fit [ 49 ].

See text for the meaning of the parameters. SSD is the sum of squared differences between data and fitted curve, R 2 is proportion variance explained, and AIC is the Akaike Information Criterion. To stay close to Ebbinghaus’ own estimates, the parameters are fitted for time expressed in minutes.

In the table, we see that in the case of his power function from 1880 [ 8 ], Ebbinghaus' calculations, carried out by hand, were quite close the computer-optimized parameter values: he found values 0.51 and 0.099 for the parameters, whereas we found 0.523 and 0.101, respectively. For the logarithmic function from 1885 [ 9 ], we also found similar parameters to those parameters Ebbinghaus reported: 1.8 and 1.21 for his values of 1.85 and 1.25 respectively.

The goodness-of-fit of his functions is quite good, in both cases explaining 98.8% of the variance ( R 2 ) for his own data. The equation from 1885 has a slightly smaller SSD value (i.e., fits better), which in fact is the lowest value for an individually fitted curve we obtained (also see below and Table 5 ). Though the equations found by Ebbinghaus fit his own data very well, they do not always fit the other curves well, with especially Mack and Dros showing a relatively bad fit on these ‘classic’ equations. This is perhaps not concluded from the variance explained ( R 2 ), which is very high for all studies, but if we base our judgment on the AIC we observe large differences where the AIC for the Ebbinghaus data is almost twice as low as on the Dros data. This suggests that the general applicability of Ebbinghaus equations may be lacking. We further investigate this by comparing Ebbinghaus’ functions with some other functions that have been proposed in the literature.

See text for the meaning of the parameters. SSD is the sum of squared differences between data and fitted curve, R 2 is proportion variance explained, and AIC is the Akaike Information Criterion. The parameters are fitted for time expressed in seconds.

Ebbinghaus function from 1880 is a type of double power function. A normal power function is described by the equation Q ( t ) = (1+ μ 1 t) − a 1 , where Q ( t ) is savings at time t and μ 1 and a 1 are parameters. The latter equation has been proposed by several authors to describe the time-course of forgetting (e.g., [ 1 , 3 , 4 , 34 ]). The forgetting mechanism typically associated with a power function is a constant slowing down of the forgetting rate with time (cf. Ebbinghaus' account from 1880 mentioned above). Whereas this is certainly a viable mechanism of forgetting, it can be proven mathematically that (spurious) power functions may emerge from averaging over different subjects or items [ 35 , 36 ]. This has also been shown in simulations considering a wide range of circumstances [ 37 , 38 ]. As argued in the previous section, the forgetting curve (also) averages over items that have been learned to various degrees, due to their serial position. There are, therefore, several reasons to expect and consider the power function.

The goodness-of-fit of the simple power function to our data is given in Table 5 . As can be seen, the fit to Ebbinghaus’ data is still impressive, though somewhat less good than either of his own equations. The goodness-of-fit of the power function, as expressed by the SSD , averaged over all four subjects’ is comparable to the Ebbinghaus 1885 ‘logarithmic’ function and it is somewhat worse than his 1880 ‘power’ function. The AIC is slightly worse, but probably not meaningfully so as the difference in AIC measures is only 1.

Heller et al. [ 21 ] also fitted the Ebbinghaus 1885 ‘logarithmic’ equation to the Mack and Seitz data and noticed that it did not fit the Mack and Seitz data well. They therefore proposed a different equation, the sum of two exponentials: Q ( t ) =  μ 1 e − a 1 +  μ 2 e − a 2 A similar function has independently been proposed by Rubin, Hinton and Wenzel [ 39 ] to successfully fit a forgetting curve with very large numbers of observations per data point, which could not be fitted satisfactorily with any of the more than hundred functions studied in Rubin and Wenzel [ 2 ]. None of these authors gave a forgetting mechanism associated with these functions.

Though providing us with a superior fit, a disadvantage of the summed exponential is that there are no memory models that explain why forgetting might have this shape. As remarked by several authors investigating the shape of learning and forgetting [ 35 , 38 , 40 ], simply fitting sums of exponentials is expected to yield progressively better fits for the simple reasons that any function may be approximated by such a sum, which is related to the Laplace transformation.

A model of forgetting and amnesia developed by our group also yields a summed exponential function, but with a different parameterization [ 41 ]. This so called Memory Chain Model assumes that a memory passes through several neural processes or stores, from short-term to very long-term memory. While a memory is (exponentially) declining in intensity in Store 1 (e.g., the hippocampus), its contents is steadily transferred to a Store 2 (e.g., the neocortex) from which it will decline at a lower rate. We still have two exponentially declining stores, as in the summed exponential function above, but they are linked by a memory consolidation process. The decay rates in Store 1 and Store 2 are given by a 1 and a 2 , respectively. The initial strength of the memory traces in Store 1 are given by μ 1 and the rate of consolidating the contents of Store 1 to Store 2 is given by μ 2 . In experiments with dementia patients and experimental animals, Store 1 may typically be identified with the hippocampus and Store 2 with the neocortex. Lesioning Store 1, will produce a retrograde amnesia gradient that can be modeled by the Memory Chain Model simultaneously with the forgetting gradient of healthy controls [ 42 ].

The Memory Chain Model (MCM) equation for type of savings studied here is given by

The MCM function has the same number of parameters but they are arranged differently. The proof that this equation is a mathematical formalization of the memory consolidation process can be found elsewhere [ 42 ]. As can be seen in Table 5 , the summed exponential and the MCM function give exactly the same fits, though the parameters differ. The gain of using the MCM function lies primarily in the fact that its parameters can be interpreted more clearly, that it is associated with a type of consolidation mechanism, and that also explains other types of data than the savings function [ 41 – 43 ]. The MCM function assumes a neural system consolidation mechanism [ 44 , 45 ] that has been dubbed the 'Standard Consolidation Theory' [ 46 , 47 ], where the latter authors propose a different theory, the so called Multiple Trace Theory of consolidation. It is here not our goal to evaluate the merits of these theories; we have reviewed these and other theories of consolidation elsewhere [ 48 ]. We merely want to apply the MCM equation to these four savings curves and evaluate the goodness-of-fit, viewing it as a conceptual improvement of the summed exponential.

If we compare the MCM equation or summed exponential function to the other functions, this only makes sense if we rely on the AIC , which takes into account the varying number of parameters. The MCM function (or double exponential function) fits two of the four curves (Mack and Dros) better than Ebbinghaus’ own equations from 1880 and 1885, it gives about the same fit on the Seitz data, and it does much worse on Ebbinghaus' own data. The average AIC is 0.5 less than the average AIC for the classic Ebbinghaus functions, which—though it indicates a better fit—may not be considered a meaningful difference; a difference of 2 is considered 'meaningful' [ 49 ]. We also fitted a single exponential with only two parameters but this fared far much worse on all data sets, including Ebbinghaus’ data (also see [ 3 ]).

Summarizing, Ebbinghaus' data fit his own equations and the power function best. The AIC indicates that on average the MCM equation (or summed exponential function) is on average better than all equations considered thus far, where the difference with the power function is 1.5. The difference with Ebbinghaus' own equations is only 0.5 but this is partially because his own data have an exceptionally good fit on his own equations, with a very low AIC of about -30.5 (and an extremely high 99.8% variance explained). It is likely, however, that Ebbinghaus actively searched for an equation that achieves such an exceptional fit, which in his eyes was no more than a 'summary' of the forgetting curve (see citation above). This also explains why he has no problems substituting a 'logarithmic' equations for the earlier 'power' equation: it shows a slightly better fit.

Fitting data is always done with a purpose. Ebbinghaus achieved a concise summary of his forgetting data, the power function is a parsimonious description of the forgetting function that shows a good or at least adequate fit in many types of forgetting experiments, and the MCM equation attempts to capture the shape of a hypothetical consolidation process in the brain albeit at the expense of additional parameters. Taking into account these extra parameters, however, does not give a worse fit on the AIC and approaches a meaningful improvement over the power function.

The 24-hour point in Ebbinghaus' forgetting curve

When looking at the shapes of the four curves in Fig 2 , savings after 1 day (or 2 days) seems higher than expected. Ebbinghaus [ 8 ] notices this as well but merely writes it off as a discrepancy from his fitted curve (see above) that still falls within the error bars ([ 8 ], p. 62). He clearly did not trust this data point because in his text from 1885 [ 9 ] he reports that he later had replicated this 24 hour data point. The replicated data for this point gave a very similar score, so we must consider it a valid measurement. Jenkins and Dallenbach [ 50 ], however, interpreted the discrepancy as an effect of sleep, which motivated them to investigate this closer in an experiment on the effect of sleep on forgetting. They also refer to the forgetting curve by Radossawljewitsch [ 16 ], who also found higher savings after both 1 and 2 days (0.689 and 0.609, resp.) compared with after 8 hours (0.474). To them, this is suggestive of a very strong effect of sleep, but Finkenbinder [ 17 ] points out that Radossawljewitsch's 8-hour data point may not be reliable, because these lists were all relearned during the afternoon, when there was less rapid learning resulting in fewer savings. He, therefore, suggests using a corrected savings score at 8 hours of 0.66, which is not unreasonable given that Ebbinghaus also corrected his savings scores for time-of-day effects, in some cases up to 13%. Even if savings would be 0.66 at 8 hours, however, the 1 day savings score is still higher than the 8 hour score and the 2 day savings is still higher than what one would expect.

Using free recall and retention up to 8 hours, the seminal study by Jenkins and Dallenbach [ 50 ] yielded a positive effect of sleep on recall. This effect has since been replicated many times, for example in recent studies on the effects of different sleep stages on both procedural and declarative memory (e.g., [ 51 , 52 – 56 ]). Whereas the older studies from the 1970s and before typically confound the sleep manipulation with time-of-day effects or fatigue, this is no longer the case in the recent studies, so that there is now very strong evidence that sleep does indeed have an effect on memory independent of the effects of, say, rest or lack of interference. In some of the sleep-memory experiments cited above, we even see a temporary increase in the forgetting curve, where subjects score better than after learning in the days following sleep, but not if they skipped the night of sleep after learning (e.g., [ 53 ]). This result—and other studies—suggests that the first night of sleep after learning has a particularly important effect on memory that may continue to evolve for several days afterwards. Such an effect may also be observed in savings curve by Mack and to some extent in the Seitz curve, both show a tendency to increase in savings score for two days following learning.

Given that we can trace the history of research on the effects of sleep on memory to the 24 hour point of Ebbinghaus' forgetting curve, we think it is interesting to evaluate this data point more formally. If we can establish the jump in the curve more formally, it will make a stronger case that the 'true shape' of the long-term forgetting curve has a jump in at 24 hours (or perhaps right after the subject has slept), although we may not conclude from this that the local increase is due to sleep per se, which would require more research is necessary for that.

If we first informally inspect the data points shown in Fig 2 and compare them with the fitted power function, we see relatively less forgetting at either day 1, day 2, or both. In all four panels, at least one of these points is above the fitted power function curve at a distance of at least one standard error. The same is true for the fitted curves of the summed exponential, Ebbinghaus’ 1880 ‘power’ function and his 1885 ‘logarithmic’ function (not shown here). We also see this effect for the Memory Chain Model curve in Fig 3 , though somewhat less pronounced (in the Seitz panel, the fitted curve crosses the error bars at 1 and 2 days). The reason for this is that the Memory Chain Model already incorporates the effects of a hypothetical consolidation process. In short, we observe that there is seems to be a memory ‘boost’ in the classic Ebbinghaus’ forgetting curve and its replications. The current body of research on sleep and memory would predict such a boost after one or two nights and attribute it to sleep, though for this particular type of experiments this has to established more firmly in further experiments. Whatever its cause, we can better quantify the visually observed boost by including it in the equations fitted. We, therefore, made a variant of the power function that differs only in the addition of a constant boost factor to the savings of the retention intervals of 1 day and higher. This power function with boost is also plotted in Fig 2 .

The results are mixed, though on average they suggest a trend towards improvement with a boost parameter. The original power function had a average AIC of -22, a sum-of-squared-differences ( SSD ) of 0.00932 and explained 98.7% of the variance (see Table 5 ), whereas adding the boost reduces the AIC to -23.6, the SSD to 0.00628 and increases the average variance explained to 99.1%, putting its goodness-of-fit on a par with the MCM (or summed exponential) function. A difference in average AIC of 1.6 may perhaps be called a trend towards a meaningful difference, though there were large differences between the individual subjects. The boost parameter in Table 5 shows the size of the upward jump after 24 hours. We see that for Ebbinghaus, this jump is small (0.030), whereas for Mack it is quite substantial (0.131). The Dros data show no evidence for a boost but these fits are probably influenced strongly by the very low 31 day data point.

Concluding Remark

In 1880, Ebbinghaus [ 8 ] set new standards for psychology experiments, already incorporating such ‘modern’ concepts as controlled stimulus materials, counter-balancing of time-of-day effects, guarding against optional stopping, statistical data analysis, and modeling to find a concise mathematical description and further verify his results. The result was a high-quality forgetting curve that has rightfully remained a classic in the field. Replications, including ours, testify to the soundness of his results.

His method can also be seen as a precursor to implicit memory tests in that certain inaccessible representations, seemingly forgotten, can still be relearned faster compared with others that do not show such an advantage. This is evidence of implicit memory because the subjects may not be consciously aware they still possess traces of the memory representations, which cannot be recalled or recognized but that do show savings. The savings method is still used today as a sensitive method to study the decline of foreign languages in order to assess the true extent of linguistic knowledge retained over a long time [ 57 ].

Ebbinghaus [ 8 ] also emphasizes the importance of sleep for memory, but these remarks are limited to how low-quality or insufficient sleep may have inflated his own learning times at certain dates ([ 8 ], p. 66) and as an explanation for the observed time-of-day effects; he learns faster in the morning than at other times. In other words, he acknowledges the effects of previous sleep on current learning, but he does not admit to the role of sleep in slowing down long-term forgetting. The formal analysis above suggests that the classic forgetting curve is not completely smooth but does show a jump at the 1 day retention interval. Current research on the effects of sleep on memory would predict such a jump, but for this particular type of experiment this remains to be established.

Acknowledgments

We would like to thank Annette de Groot and Jeroen Raaijmakers for helpful suggestions when writing this.

Funding Statement

This experiment was conducted as an employee (JM) and student (JD) of the University of Amsterdam. The authors received no specific funding for this work.

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Hermann Ebbinghaus

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• Hermann Ebbinghaus - Student Encyclopedia (Ages 11 and up)

Hermann Ebbinghaus (born January 24, 1850, Barmen, Rhenish Prussia [Germany]—died February 26, 1909, Halle , Germany) was a German psychologist who pioneered in the development of experimental methods for the measurement of rote learning and memory.

Ebbinghaus received a Ph.D. degree from the University of Bonn in 1873. Shortly thereafter he became assistant professor at the Friedrich-Wilhelm University, Berlin, a post he held until 1894, when he was appointed professor at the University of Breslau.

Using himself as a subject for observation, Ebbinghaus devised 2,300 three-letter nonsense syllables for measuring the formation of mental associations. This learning invention, together with the stringent control factors that he developed and his meticulous treatment of data, brought him to the conclusion that memory is orderly. His findings, which included the well-known “forgetting curve” that relates forgetting to the passage of time, were reported in Über das Gedächtnis (1885; Memory ).

After completing his work on memory, Ebbinghaus turned to research on colour vision and in 1890, with the physicist Arthur König, founded the periodical Zeitschrift für Psychologie und Physiologie der Sinnesorgane (“Journal of the Psychology and Physiology of the Sense Organs”). In conjunction with a study of the mental capacities of Breslau schoolchildren (1897), he created a word-completion test. That same year the first part of another work on which his reputation rests, Grundzüge der Psychologie (1902; “Principles of Psychology”), was published. In 1905 he left Breslau for the University of Halle, where he wrote a still more popular work, Abriss der Psychologie (1908; “Summary of Psychology”). Ebbinghaus’ research showed that, contrary to prevailing beliefs, scientific methods could be applied to the study of the higher thought processes.

Recalling Psychology’s Past: The Memory Drum

• History of Psychology

In 1885, Hermann Ebbinghaus (1850-1909) published Memory: A Contribution to Experimental Psychology . The work has stood the test of time and earned Ebbinghaus a place of distinction in the study of memory.

In order to study memory free from the effects of prior learning, Ebbinghaus constructed his now famous “nonsense syllables.” All together, he created about 2,300 nonsense syllables that he grouped into and subsequently tried to memorize. Using a metronome to pace himself, he would measure how long memorization took.

Ebbinghaus’ work inspired a new generation of early psychologists intent on researching memory. Among these were Georg Elias Mueller (1850-1934) and Friedrich Schumann (1862-1940). Although they recognized the value of Ebbinghaus’ work, they also saw limitations.

First, Ebbinghaus used himself as both subject and experimenter, creating multiple roles that could have impacted his findings. Secondly, his use of lists of syllables meant that even though he was only supposed to be viewing one stimulus at a time, his visual range could perceive other syllables occurring above and below on the list. Thirdly, Ebbinghaus’ use of the metronome to pace himself was a step in the right direction of equalizing exposure to each syllable; but it was not the most precise method. What was needed was a new piece of laboratory apparatus that could address and improve upon these issues.

Mueller and Schumann discovered a new function for an already ubiquitous piece of lab equipment: the kymograph, a rotating metal drum that would revolve paper against a stylus in order to record physiological responses. The kymograph was particularly useful since its rotation was timed and would be constant. James McKeen Cattell had used a similar device for presenting color patches and words when he was a student with Wilhelm Wundt at Leipzig (Haupt, 2001).

In 1887, Mueller and Schumann literally turned the kymograph on its side and put the material to be memorized around it. A screen was placed in front of the rotating drum so that only one item was visible at any time. Through several revisions using different types of kymographs, Mueller and Schumann finally found one that suited their needs. Their 1894 article was the first to explain the use of a new laboratory apparatus: the memory drum.

A drawback of Mueller and Schumann’s memory drum was that its constant movement always had the stimulus in motion upwards or downwards. Otto Lipmann (1880-1933), a student of Ebbinghaus, devised a way of moving the drum a certain amount in a stepping action so that the stimulus was held still for a fixed amount of time and then stepped out of sight. (Lipmann, 1904). It was Lipmann’s device that Ralph Gerbrands at Harvard used as the basis for his memory drum, illustrated in Robert Woodworth’s influential Experimental Psychology (Woodworth, 1938). This drum would be the design used for virtually all the memory drums to come later.

Soon to become a staple in psychology laboratories across the world, memory drums would continue to yield to innovation. Variations of this first apparatus have come and gone in the century since its invention, and many interesting examples can be found at the Archives of the History of American Psychology in Akron, Ohio.

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About the Authors

Nick Joyce is a graduate assistant at the Archives of the History of American Psychology and a doctoral student in counseling psychology at the University of Akron. David Baker is the Margaret Clark Morgan Director of the Archives of the History of American Psychology and Professor of Psychology at the University of Akron. Rand Evans, Emeritus Professor of Psychology, East Carolina University, is the editor of this series.

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Hermann Ebbinghaus and the Scientific Study of Memory

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Hermann Ebbinghaus was a pivotal figure in psychology, renowned for his groundbreaking research on memory. His experiments with over 2,300 nonsensical syllables led to the discovery of the forgetting curve and insights into the learning curve and spaced repetition. Ebbinghaus's work on memory retention, relearning, and the serial position effect has significantly influenced cognitive psychology and learning theories.

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Early Life and Inspiration

Birth and background.

Hermann Ebbinghaus was born on January 24, 1850, in Barmen, Germany and was inspired by the works of Gustav Fechner

Influence of Gustav Fechner

Elements of Psychophysics

Ebbinghaus was inspired by Gustav Fechner's "Elements of Psychophysics" in his pursuit of studying memory

Beginning of Memory Experiments

In 1878, Ebbinghaus began conducting systematic memory experiments on himself

Contributions to Experimental Psychology

Establishment of experimental psychology.

Ebbinghaus was instrumental in establishing experimental psychology as a scientific discipline

Co-founding of "Zeitschrift für Psychologie und Physiologie der Sinnesorgane"

Ebbinghaus co-founded the "Zeitschrift für Psychologie und Physiologie der Sinnesorgane" (Journal of Psychology and Physiology of the Sense Organs)

Academic Positions

Ebbinghaus held academic posts at the University of Berlin, the University of Breslau, and the University of Halle

Groundbreaking Memory Experiments

Use of nonsense syllables.

Ebbinghaus used over 2,300 nonsensical syllables to control for prior knowledge and semantic associations in his memory experiments

Discovery of the Forgetting Curve

Ebbinghaus's research led to the discovery of the forgetting curve, which shows the decline in memory retention over time

Learning Curve and Spaced Repetition Technique

Ebbinghaus also examined the learning curve and provided empirical support for the spaced repetition technique, which enhances memory consolidation and retention over time

Key Concepts in the Study of Memory

Savings in relearning.

Ebbinghaus introduced the concept of "savings" in relearning, indicating that previously learned information is easier to reacquire

Involuntary and Voluntary Memory

Ebbinghaus distinguished between involuntary and voluntary memory

Serial Position Effect

Ebbinghaus described the serial position effect, which explains why items at the beginning and end of a list are more likely to be remembered

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Ebbinghaus's influential book, 'On Memory,' was originally published in the year ______.

Ebbinghaus's challenge to Wundt's belief

Ebbinghaus contested Wundt's view that memory couldn't be experimentally studied.

Ebbinghaus's method for studying memory

Used over 2,300 nonsensical syllables to study memory retention and forgetting.

Ebbinghaus's experimental variables

Varied list lengths and repetition frequencies to analyze memory processes.

The equation ______ = e^(-t/S) mathematically represents the decline in memory retention, where 't' stands for time.

Forgetting Curve Concept

Ebbinghaus's theory that memory retention decreases over time without practice or review.

Learning Curve Description

Graphical representation of the rate at which new information is learned; steep at first, flattens over time.

Spaced Repetition Technique

Learning strategy involving reviewing information at gradually increasing intervals to enhance retention.

He noted the 'serial position effect,' where items at the ______ and ______ of a list are more memorable, known as the ______ and ______ effects.

beginning end primacy recency

Ebbinghaus's empirical approach

Used controlled experiments and nonsense syllables to eliminate bias and ensure objectivity in memory research.

Ebbinghaus's contribution to verbal intelligence testing

Developed sentence completion tests, a method still used in psychological assessments to measure verbal intelligence.

Ebbinghaus's influence on psychology publications

Founded a specialized psychology journal, promoting academic discourse and research in the field of psychology.

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Hermann Ebbinghaus: A Trailblazer in Memory Studies

The Methodology of Ebbinghaus's Memory Experiments

Insights into the learning curve and spaced repetition, ebbinghaus's contributions to memory and learning theories, the enduring influence of ebbinghaus in psychology.

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Memory: a contribution to experimental psychology

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• 1 Translated by Henry A. Ruger & Clara E. Bussenius (1913) (Reprinted with permission).
• PMID: 25206041
• PMCID: PMC4117135
• DOI: 10.5214/ans.0972.7531.200408

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• DOI: 10.5214/ans.0972.7531.200408
• Corpus ID: 62151260

Memory: a contribution to experimental psychology.

• H. Ebbinghaus
• Published in Annals of Neurosciences 1 September 1987

668 Citations

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Hermann Ebbinghaus

1850-1909 German psychologist whose work resulted in the development of scientifically reliable experimental methods for the quantitative measurement of rote learning and memory.

Hermann Ebbinghaus ( Corbis-Bettmann . Reproduced with permission.)

Born in Germany, Hermann Ebbinghaus received his formal education at the universities of Halle, Berlin, and Bonn, where he earned degrees in philosophy and history. After obtaining his philosophy degree in 1873, Ebbinghaus served in the Franco-Prussian War. For the next seven years following the war, he tutored and studied independently in Berlin, France, and England. In the late 1870s, Ebbinghaus became interested in the workings of human memory . In spite of Wilhelm Wundt 's assertion in his newly published Physiological Psychology that memory could not be studied experimentally, Ebbinghaus decided to attempt such a study, applying to this new field the same sort of mathematical treatment that Gustav Fechner (1801-1887) had described in Elements of Psychophysics (1860) in connection with his study of sensation and perception .

Using himself as both sole experimenter and subject, Ebbinghaus embarked on an arduous process that involved repeatedly testing his memorization of nonsense words devised to eliminate variables caused by prior familiarity with the material being memorized. He created 2,300 one-syllable consonant-vowel-consonant combinations—such as taz , bok , and lef— to facilitate his study of learning independent of meaning. He divided syllables into a series of lists that he memorized under fixed conditions. Recording the average amount of time it took him to memorize these lists perfectly, he then varied the conditions to arrive at observations about the effects of such variables as speed, list length, and number of repetitions. He also studied the factors involved in retention of the memorized material, comparing the initial memorization time with the time needed for a second memorization of the same material after a given period of time (such as 24 hours) and subsequent memorization attempts. These results showed the existence of a regular forgetting curve over time that approximated a mathematical function similar to that in Fechner's study. After a steep initial decline in learning time between the first and second memorization, the curve leveled off progressively with subsequent efforts.

Ebbinghaus also measured immediate memory, showing that a subject could generally remember between six and eight items after an initial look at one of his lists. In addition, he studied comparative learning rates for meaningful and meaningless material, concluding that meaningful items, such as words and sentences, could be learned much more efficiently than nonsense syllables. His experiments also yielded observations about the value of evenly spaced as opposed to massed memorization. A monumental amount of time and effort went into this ground-breaking research. For example, to determine the effects of number of repetitions on retention, Ebbinghaus tested himself on 420 lists of 16 syllables 340 times each, for a total of 14,280 trials. After careful accumulation and analysis of data, Ebbinghaus published the results of his research in the volume On Memory in 1885, while on the faculty of the University of Berlin. Although Wundt argued that results obtained by using nonsense syllables had limited applicability to the actual memorization of meaningful material, Ebbinghaus's work has been widely used as a model for research on human verbal learning, and Über Gedachtnis ( On Memory) has remained one of the most cited and highly respected sourcebooks in the history of psychology.

In 1894, Ebbinghaus joined the faculty of the University of Breslau. While studying the mental capacities of children in 1897, he began developing a sentence completion test that is still widely used in the measurement of intelligence . This test, which he worked on until 1905, was probably the first successful test of mental ability . Ebbinghaus also served on the faculties of the Friedrich Wilhelm University and the University of Halle. He was a cofounder of the first German psychology journal, the Journal of Psychology and Physiology of the Sense Organs, in 1890, and also wrote two successful textbooks, The Principles of Psychology (1902) and A Summary of Psychology (1908), both of which went into several editions. His achievements represented a major advance for psychology as a distinct scientific discipline and many of his methods continue to be followed in verbal learning research.

See also Forgetting curve ; Intelligence quotient

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Why Ebbinghaus’ savings method from 1885 is a very ‘pure’ measure of memory performance

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• Published: 07 September 2022
• Volume 30 , pages 303–307, ( 2023 )

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• Jaap M. J. Murre 1 &
• Antonio G. Chessa 1 , 2  

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This paper analyzes the savings measures introduced by Ebbinghaus in his monograph of 1885. He measured memory retention in terms of the learning time saved in subsequent study trials relative to the time spent on the first learning trial. We prove mathematically that Ebbinghaus’ savings measure is independent of initial encoding strength, learning time, and relearning times. This theoretical model-free result demonstrates that savings is in a sense a very ‘pure’ measure of memory. Considering savings as an old-fashioned and unwieldy measure of memory may be unwarranted given this interesting property, which hitherto seems to have been overlooked. We contrast this with often used forgetting functions based on recall probability, such as the power function, showing that we should expect a lower forgetting rate in the initial portion of the curve for material that has been learned less well.

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Introduction

It is hard to overestimate the importance of Hermann Ebbinghaus’ contribution to experimental psychology (Ebbinghaus, 1880 , 1885 , 1913/1885 ). In 1885, he published a monograph with a series of rigorous experiments on the basis of his habilitation’s thesis from 1880 on the shape of learning and forgetting. He introduced the use of nonsense syllables, which had more uniform characteristics than words or other verbal material, though verified his findings with more natural material such as poems. He was, furthermore, one of the first psychologists to make extensive use of statistics and mathematical modeling, notably fitting mathematical equations to his now famous forgetting curve.

Ebbinghaus ( 1913 ; we shall mainly refer to this early English translation, which is readily available) based nearly all of his experiments on the savings measure of learning and memory, which is defined as the relative amount of time saved on the second learning trial as a result of having had the first. So, if it takes only half the time to relearn a list, savings will be 0.5 (we use proportions here instead of percentages). If it takes exactly as long to relearn the list as it took to learn it originally, then savings is 0. If the list is still completely known at the second trial (i.e., no forgetting at all), then savings is 1. If we call savings after time t as Q ( t ), this can be summarized as:

Here, L is the time (or number of repetitions) needed to learn the material to criterion at t = 0 and L t is the time needed to relearn the material at time t .

The savings measure of learning and forgetting remained popular for several decades (Ammons et al., 1958 ; Boreas, 1930 ; Finkenbinder, 1913 ; Krueger, 1929 ; Radossawljewitsch, 1907 ), but is used only sporadically today (see https://osf.io/xtfnd for a data repository with savings data and curve fits). This is remarkable because many papers use Ebbinghaus’ classic savings data to test hypothesis about the shape of learning and forgetting (e.g., Anderson & Schooler, 1991 ; Rubin & Wenzel, 1996 ; Wixted & Ebbesen, 1991 ). Nelson ( 1985 ) summarizes several reasons why the savings measure was abandoned. First, there may be a relatively large learning-to-learn effect, because it takes a lot of experience with the nonsense syllable materials and the savings procedure to get used to them. During this time, performance continues to improve, simply because the subject is still getting used to the experimental method. Ebbinghaus realized this, which is why he spent a relatively long time learning and relearning lists before he started the actual experiment; we followed him in this in our replication of his classic forgetting curve (Murre & Dros, 2015 ). Second, savings scores may be unreliable when learning to once or twice correct, which had already been observed by Luh ( 1922 ). With learning to once correct, learning proceeds until the trial on which all nonsense syllables can be produced correctly (100% correct); with learning to twice correct, learning proceeds until two successive trials are 100% correct. This can be remedied by learning to a lower criterion, such as 80% or 50% correct. Third, the savings measure can only be interpreted on an interval scale if the underlying learning process proceeds in a linear fashion with learning trials or time. If not, it is not really possible to compare different magnitudes of the savings measure (Nelson, 1985 , p. 475). This is most troubling because if the underlying learning process is nonlinear and unknown, fitting a “forgetting curve” to savings data becomes meaningless (Wixted, 1990 ). As we shall see below, assuming a linear learning process for Ebbinghaus’ data seems warranted.

In this paper, we analyze the savings measure in more detail. Our analyses demonstrate that, unexpectedly, Ebbinghaus’ savings measure is an exceptionally good measure of memory, which in many ways is to be preferred above the more usual measures such as free or cued recall. In particular, we prove analytically that under many circumstances, savings is a “pure” retention measure: the shape of forgetting as measured through the savings method does not depend on the strength of the initial memory encoding or initial length of learning.

Analysis of Ebbinghaus’ Savings Measures

Savings experiments differ from other memory retention experiments in the role of learning time. In recall experiments, subjects typically learn items for some pre-established time, during which memory encoding is hypothesized to take place. In Ebbinghaus’ classical savings experiment, learning time is a running variable where subjects continue learning until a pre-set criterion has been reached (e.g., one perfect recitation or 80% correct). One implication of the difference between the classical savings and other types of memory measures is that recall always (also) takes place immediately after a learning trial in a savings experiment. This is necessary to assess the initial level of learning. One might suspect that leaving learning time a free variable leads to less controlled testing, but as we argue here, the opposite is true: The savings measure may well suffer from fewer confounding variables than recall or recognition measures.

In our analysis, we first derive the expression for Ebbinghaus’ classical savings measure. Let L and L t denote the learning times at the first and the second trial, respectively, which are separated by a retention lag t . Without loss of generalization, we assume that learning continues on both trials until the stimulus material can be fully recalled, rather than, say, to 80% correct. Learning, thus, continues until a certain “minimum memory strength” or “intensity” has been acquired that leads to successful recall. To make our line of reasoning easier to follow, we present two versions of our analyses, where the second one makes fewer assumptions than the first: (1) This analysis is based on a specific forgetting function and serves as an example for the next version. (2) Here, we show that the analysis of Version 1 can be generalized to all viable forgetting functions.

Analysis Based on Power Function Decline

We assume that learning proceeds until the memory trace has reached a strong enough intensity to produce learned behavior that meets the criterion (e.g., perfect recall of a list of words or nonsense syllables). We often denote memory intensity as μ where 0 ≤  μ  ≤ 1. Without further addressing the theoretical implications of this here, we note that this assumes that for the purposes of our analyses it is meaningful to speak of the scalar-valued “intensity” of a memory trace. Another assumption – which we shall pursue in more detail below – is that intensity increases linearly with learning time L . After a delay of t time units (e.g., seconds or days or learning trials), the relearning time to reach the set criterion once again is denoted as L t . We assume for Version 1 of the proof that the original strength has declined with a power function to μ (1 +  t ) − a , where a ≥ 0 is the forgetting parameter. During the relearning trial, the declined strength is increased through additional learning during L t seconds, giving an additional strength of νL t , denoting the learning rate as ν . This is a formal introduction of the linear learning assumption. Keeping in mind that μ  =  νL ,we now have:

We can rearrange this as:

But this is the expression for the savings measure Q ( t ), so we have:

In other words, if we assume power function decline of the underlying strength of a memory trace, the savings method will measure exactly this function, independently of the original memory strength.

Analysis Generalized to any Decline Function

The previous analysis can easily be generalized to any decline function f( t ), assuming that the original strength of the memory trace has declined to μ f( t ). We then have

We can summarize this result as follows: If there is some function f( t ) that describes the decline of the memory strength underlying memory performance as a function of time t , the savings method will directly measure this. Moreover, the savings method is completely independent of the initial learning strength and learning criterion: the observed savings-based forgetting curves should be the same for a criterion of 30%, 80%, or 100%. In this sense, the savings method is a “pure” measure of underlying memory strength.

Varying Initial Level of Learning

Ebbinghaus ( 1913 , Ch. VI) also includes an experiment where he systematically varied the initial level of learning by increasing the number of initial learning trials on the first day. After 24 h, he relearned until once successful recall and measured the learning time on the second day. In a similar manner as that described above, we can derive the expression for the expected relation between learning time on Day 1 and Day 2, as follows.

Suppose it would take L seconds to learn a list to some criterion (e.g., once correct) corresponding with a memory intensity of μ . Now, instead of learning to criterion, we learn for fewer seconds, L 1 < L, at Time 1. That is, we stop learning before we have reached the criterion. Then at Time 2, which takes place t seconds later (in Ebbinghaus’ case, 24 h later), we do learn until the criterion has been reached, this time taking L 2 seconds.

Assuming a linear learning process and an initial learning trial of L 1 seconds, this gives an initial intensity after learning on Day 1 of μ 1  =  νL 1 , where ν is the learning rate. After t seconds have passed, the intensity will have declined as described by the forgetting function. Above, we found the forgetting function to be equivalent to the savings measure itself, Q ( t ). So, on Day 2 after t seconds have passed, we retain an intensity of νL 1 Q ( t ). This intensity must now be increased to reach the memory intensity μ corresponding to the criterion by doing additional learning trials for L 2 seconds. This gives an extra contribution to the intensity of νL 2 . We are interested in how L 2 depends on L 1 .

From this, we can derive the relationship between partial learning time L 1 and relearning time to criterion L 2 , where savings at time t is a non-free parameter :

This relationship is a simple linear one and we are able to predict this learning data without using any estimated parameters, as is shown below.

Table 1 summarizes the mean relearning time as a function of the number of initial learning trials with only relearning until successful recall, as reported by Ebbinghaus ( 1913 , Ch. VI). In the first column of this table, we see that the mean relearning time after zero initial learning trials is equal to 1,270 s, which we use as an estimate for L . Because the stimulus material used in this experiment is the same as the lists used in Ebbinghaus’ classical savings experiment, for the 24-h data point, Ebbinghaus reports that Q ( t ) = 0.337, where t = 24 h after initial learning.

Ebbinghaus ( 1913 , Ch. VI, p. 57) also reports that a repetition of a single 16-syllable series takes between 6.6 and 6.8 s. If we use an approximation of 6.7 s per list and noting there are six of such 16-syllable lists per repetition, then each repetition took about 40.2 s. The data and fit are shown in Fig. 2 . The predicted function coincides well with the data points, explaining 99.75% of the variance (sum of squared differences is 5963.64). Note that this function was not fitted to the data but based on separate values reported by Ebbinghaus. If we allow a shorter time than 6.7 s per list, we find that 6.38 s explains the same amount of variance but gives the lowest attainable sum of squared differences, namely 1,521.49. Given the excellent fit, one might argue that the assumption of a linearly increasing intensity with time is a reasonable one for Ebbinghaus’ data.

As we show above, Ebbinghaus’ classical savings function is independent of initial learning time and encoding strength and directly measures the underlying forgetting curve, assuming a learning process by which the memory intensity increases linearly with learning time. The fit of Ebbinghaus’ data relating initial learning time to relearning time in Fig. 1 further illustrates this, explaining nearly 100% of the variance without any free parameters.

Varied levels of initial learning time L 1 versus relearning time L 2 to criterion after 24 h (Ebbinghaus, 1913, Ch. VI). The data are shown as diamonds. The predicted data are shown as a solid line

We should, perhaps, point out here that other measures of memory do not have this characteristic. For example, consider the power function, using probability of recall as a measure of memory: p ( t ) =  μ (1 +  t ), − a where μ is the initial intensity of the underlying learning process, which again is assumed to increase with learning time. If we take the first derivative of the forgetting function, we obtain the predicted initial forgetting rate for various levels of initial learning μ : p ′ ( t ) =  −  a (1 +  t ) −1 −  a μ . With various levels of initial learning at t = 0, we have p ′ (0) =  −  aμ . In other words, if there is a stronger initial memory (with higher μ ), there will be relatively higher forgetting rates at t = 0 (see Fig. 2 for an illustration).

Power functions with a = 0.5 and two levels of initial intensity: μ = 1 (solid line) and μ = 0.25 (dashed line)

It can easily be shown that the same result obtains for other forms of the power function, or for the exponential function (Loftus, 1985 ). More generally, any forgetting function of shape p ( t ) =  μ f( t ), where f( t ) is a function that does not itself depend on μ , will give the same result because of the standard “constant factor rule” for finding the derivative of a product of a constant and a function: p ′ ( t ) = f ′ ( t ) μ .If f(t) is a declining function, at t = 0, f ′ (0) =  −  a , for some positive constant a , so p ′ ( t ) =  −  aμ . This means that for a large class of functions, we predict a lower forgetting rate in the initial portion of the curve for material that has been learned less well. This is also intuitively understandable from the idea that the role of the μ parameter is to shrink (or stretch, up to probability 1) the entire curve along the vertical axis; shrinking implies flattening, implying in turn lower forgetting rates. Of course, it will depend on the exact nature of a particular forgetting function f( t ) how difficult it is to disentangle the effects of intensity (e.g., Wixted & Ebbesen, 1991 ). Our analysis of the relationship between learning and forgetting here is brief and incomplete. Indeed, there is a rich literature on this topic (Kauffman & Carlsen, 1989 ; Loftus, 1985 ; Slamecka & McElree, 1983 ; Yang et al., 2016 ) with ongoing experimentation and theorizing (Fisher & Radvansky, 2019 ; Radvansky et al., 2022 ; Rivera-Lares et al., 2022 ). We merely intend to illustrate that the savings measure cannot directly be compared with other measures of memory – for example, probability correct in cued recall – but that from a theoretical perspective it is expected to behave differently. In particular, from a theoretical perspective, its shape is independent of level of initial learning.

In conclusion, the savings measure introduced by Ebbinghaus (Ebbinghaus, 1880 , 1885 , 1913/1885 ) should not be regarded as old-fashioned and unwieldy. Among all memory retention measures proposed, it may be the purest one and worthy of renewed attention.

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Acknowledgements

This research was supported by NWO, the Netherlands Society for Scientific Research. We would like to thank Jeroen Raaijmakers for helpful comments.

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Murre, J.M.J., Chessa, A.G. Why Ebbinghaus’ savings method from 1885 is a very ‘pure’ measure of memory performance. Psychon Bull Rev 30 , 303–307 (2023). https://doi.org/10.3758/s13423-022-02172-3

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• How Memory Works

Memory is the ongoing process of information retention over time. Because it makes up the very framework through which we make sense of and take action within the present, its importance goes without saying. But how exactly does it work? And how can teachers apply a better understanding of its inner workings to their own teaching? In light of current research in cognitive science, the very, very short answer to these questions is that memory operates according to a "dual-process," where more unconscious, more routine thought processes (known as "System 1") interact with more conscious, more problem-based thought processes (known as "System 2"). At each of these two levels, in turn, there are the processes through which we "get information in" (encoding), how we hold on to it (storage), and and how we "get it back out" (retrieval or recall). With a basic understanding of how these elements of memory work together, teachers can maximize student learning by knowing how much new information to introduce, when to introduce it, and how to sequence assignments that will both reinforce the retention of facts (System 1) and build toward critical, creative thinking (System 2).

Dual-Process Theory

Think back to a time when you learned a new skill, such as driving a car, riding a bicycle, or reading. When you first learned this skill, performing it was an active process in which you analyzed and were acutely aware of every movement you made. Part of this analytical process also meant that you thought carefully about why you were doing what you were doing, to understand how these individual steps fit together as a comprehensive whole. However, as your ability improved, performing the skill stopped being a cognitively-demanding process, instead becoming more intuitive. As you continue to master the skill, you can perform other, at times more intellectually-demanding, tasks simultaneously. Due to your knowledge of this skill or process being unconscious, you could, for example, solve an unrelated complex problem or make an analytical decision while completing it.

In its simplest form, the scenario above is an example of what psychologists call dual-process theory. The term “dual-process” refers to the idea that some behaviors and cognitive processes (such as decision-making) are the products of two distinct cognitive processes, often called System 1 and System 2 (Kaufmann, 2011:443-445). While System 1 is characterized by automatic, unconscious thought, System 2 is characterized by effortful, analytical, intentional thought (Osman, 2004:989).

Dual-Process Theories and Learning

How do System 1 and System 2 thinking relate to teaching and learning? In an educational context, System 1 is associated with memorization and recall of information, while System 2 describes more analytical or critical thinking. Memory and recall, as a part of System 1 cognition, are focused on in the rest of these notes.

As mentioned above, System 1 is characterized by its fast, unconscious recall of previously-memorized information. Classroom activities that would draw heavily on System 1 include memorized multiplication tables, as well as multiple-choice exam questions that only need exact regurgitation from a source such as a textbook. These kinds of tasks do not require students to actively analyze what is being asked of them beyond reiterating memorized material. System 2 thinking becomes necessary when students are presented with activities and assignments that require them to provide a novel solution to a problem, engage in critical thinking, or apply a concept outside of the domain in which it was originally presented.  

It may be tempting to think of learning beyond the primary school level as being all about System 2, all the time. However, it’s important to keep in mind that successful System 2 thinking depends on a lot of System 1 thinking to operate. In other words, critical thinking requires a lot of memorized knowledge and intuitive, automatic judgments to be performed quickly and accurately.

How does Memory Work?

In its simplest form, memory refers to the continued process of information retention over time. It is an integral part of human cognition, since it allows individuals to recall and draw upon past events to frame their understanding of and behavior within the present. Memory also gives individuals a framework through which to make sense of the present and future. As such, memory plays a crucial role in teaching and learning. There are three main processes that characterize how memory works. These processes are encoding, storage, and retrieval (or recall).

• Encoding . Encoding refers to the process through which information is learned. That is, how information is taken in, understood, and altered to better support storage (which you will look at in Section 3.1.2). Information is usually encoded through one (or more) of four methods: (1) Visual encoding (how something looks); (2) acoustic encoding (how something sounds); (3) semantic encoding (what something means); and (4) tactile encoding (how something feels). While information typically enters the memory system through one of these modes, the form in which this information is stored may differ from its original, encoded form (Brown, Roediger, & McDaniel, 2014).

• Retrieval . As indicated above, retrieval is the process through which individuals access stored information. Due to their differences, information stored in STM and LTM are retrieved differently. While STM is retrieved in the order in which it is stored (for example, a sequential list of numbers), LTM is retrieved through association (for example, remembering where you parked your car by returning to the entrance through which you accessed a shopping mall) (Roediger & McDermott, 1995).

Improving Recall

Retrieval is subject to error, because it can reflect a reconstruction of memory. This reconstruction becomes necessary when stored information is lost over time due to decayed retention. In 1885, Hermann Ebbinghaus conducted an experiment in which he tested how well individuals remembered a list of nonsense syllables over increasingly longer periods of time. Using the results of his experiment, he created what is now known as the “Ebbinghaus Forgetting Curve” (Schaefer, 2015).

Through his research, Ebbinghaus concluded that the rate at which your memory (of recently learned information) decays depends both on the time that has elapsed following your learning experience as well as how strong your memory is. Some degree of memory decay is inevitable, so, as an educator, how do you reduce the scope of this memory loss? The following sections answer this question by looking at how to improve recall within a learning environment, through various teaching and learning techniques.

As a teacher, it is important to be aware of techniques that you can use to promote better retention and recall among your students. Three such techniques are the testing effect, spacing, and interleaving.

• The testing effect . In most traditional educational settings, tests are normally considered to be a method of periodic but infrequent assessment that can help a teacher understand how well their students have learned the material at hand. However, modern research in psychology suggests that frequent, small tests are also one of the best ways to learn in the first place. The testing effect refers to the process of actively and frequently testing memory retention when learning new information. By encouraging students to regularly recall information they have recently learned, you are helping them to retain that information in long-term memory, which they can draw upon at a later stage of the learning experience (Brown, Roediger, & McDaniel, 2014). As secondary benefits, frequent testing allows both the teacher and the student to keep track of what a student has learned about a topic, and what they need to revise for retention purposes. Frequent testing can occur at any point in the learning process. For example, at the end of a lecture or seminar, you could give your students a brief, low-stakes quiz or free-response question asking them to remember what they learned that day, or the day before. This kind of quiz will not just tell you what your students are retaining, but will help them remember more than they would have otherwise.
• Spacing.  According to the spacing effect, when a student repeatedly learns and recalls information over a prolonged time span, they are more likely to retain that information. This is compared to learning (and attempting to retain) information in a short time span (for example, studying the day before an exam). As a teacher, you can foster this approach to studying in your students by structuring your learning experiences in the same way. For example, instead of introducing a new topic and its related concepts to students in one go, you can cover the topic in segments over multiple lessons (Brown, Roediger, & McDaniel, 2014).
• Interleaving.  The interleaving technique is another teaching and learning approach that was introduced as an alternative to a technique known as “blocking”. Blocking refers to when a student practices one skill or one topic at a time. Interleaving, on the other hand, is when students practice multiple related skills in the same session. This technique has proven to be more successful than the traditional blocking technique in various fields (Brown, Roediger, & McDaniel, 2014).

As useful as it is to know which techniques you can use, as a teacher, to improve student recall of information, it is also crucial for students to be aware of techniques they can use to improve their own recall. This section looks at four of these techniques: state-dependent memory, schemas, chunking, and deliberate practice.

• State-dependent memory . State-dependent memory refers to the idea that being in the same state in which you first learned information enables you to better remember said information. In this instance, “state” refers to an individual’s surroundings, as well as their mental and physical state at the time of learning (Weissenborn & Duka, 2000). 
• Schemas.  Schemas refer to the mental frameworks an individual creates to help them understand and organize new information. Schemas act as a cognitive “shortcut” in that they allow individuals to interpret new information quicker than when not using schemas. However, schemas may also prevent individuals from learning pertinent information that falls outside the scope of the schema that has been created. It is because of this that students should be encouraged to alter or reanalyze their schemas, when necessary, when they learn important information that may not confirm or align with their existing beliefs and conceptions of a topic.
• Chunking.  Chunking is the process of grouping pieces of information together to better facilitate retention. Instead of recalling each piece individually, individuals recall the entire group, and then can retrieve each item from that group more easily (Gobet et al., 2001).
• Deliberate practice.  The final technique that students can use to improve recall is deliberate practice. Simply put, deliberate practice refers to the act of deliberately and actively practicing a skill with the intention of improving understanding of and performance in said skill. By encouraging students to practice a skill continually and deliberately (for example, writing a well-structured essay), you will ensure better retention of that skill (Brown et al., 2014).

For more information...

Brown, P.C., Roediger, H.L. & McDaniel, M.A. 2014.  Make it stick: The science of successful learning . Cambridge, MA: Harvard University Press.

Gobet, F., Lane, P.C., Croker, S., Cheng, P.C., Jones, G., Oliver, I. & Pine, J.M. 2001. Chunking mechanisms in human learning.  Trends in Cognitive Sciences . 5(6):236-243.

Kaufman, S.B. 2011. Intelligence and the cognitive unconscious. In  The Cambridge handbook of intelligence . R.J. Sternberg & S.B. Kaufman, Eds. New York, NY: Cambridge University Press.

Osman, M. 2004. An evaluation of dual-process theories of reasoning. Psychonomic Bulletin & Review . 11(6):988-1010.

Roediger, H.L. & McDermott, K.B. 1995. Creating false memories: Remembering words not presented in lists.  Journal of Experimental Psychology: Learning, Memory, and Cognition . 21(4):803.

Schaefer, P. 2015. Why Google has forever changed the forgetting curve at work.

Weissenborn, R. & Duka, T. 2000. State-dependent effects of alcohol on explicit memory: The role of semantic associations.  Psychopharmacology . 149(1):98-106.

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