Memory and Forgetting (Hermann Ebbinghaus – 1885)

As generally accepted methods of inquiry transitioned from philosophical reasoning to quantitative scientific inquiry in the latter half of the 19th century, Hermann Ebbinghaus built on Aristotle’s foundation of the association of ideas by conducting the first recorded experimental studies of memory.[1] His desire was “to go a step farther into the workings of the mind and to submit to an experimental and quantitative treatment the manifestations of memory” (1913, p. v). The experiments were conducted from 1879 to 1880 and from 1883 to 1884. In his study he explored “the rapidity of learning series of syllables as a function of their length,” “the increase in rapidity of learning in the case of meaningful material,” “retention as a function of the number of repetitions,” “the effect of a decided increase in the number of repetitions,” “retention and obliviscence as a function of time,” “retention as a function of repeated learning,” and” retention as a function of the order of succession of the members of the series.”

Though his experiments were conducted using himself as the only subject of experimentation, and though he acknowledged and qualified many times in his writing, that the results of the tests are of limited individual significance, his findings are nevertheless very interesting, and have been applied quite broadly.

In the process of conducting his experiments, one of the first things he noticed is that, for him at least, a series of seven[2] or fewer syllables required only a single reading in order to recite it perfectly (Ebbinghaus, 1913, p. 48). Multiple readings were required before the first unaided reproduction was possible for lists of length greater than seven. The significance of this observation is that the capacity of immediate memory is clearly limited to active retention of a rather small number of items, and that learning generally happens through repeated experience:

Under ordinary circumstances, indeed, frequent repetitions are indispensable in order to make possible the reproduction of a given content. Vocabularies, discourses, and poems of any length cannot be learned by a single repetition even with the greatest concentration of attention on the part of an individual of very great ability. By a sufficient number of repetitions their final mastery is ensured, and by additional later reproductions gain in assurance and ease is secured. (Ebbinghaus, 1913, p. 4)

He found that neither an excess nor an insufficiency of repetition was harmful to learning, or entirely wasteful:

What will happen, it may be asked, if the number of repetitions actually given to a certain series is less than is required for memorization or if the number exceeds the necessary minimum?

The general nature of what happens has already been described. Naturally the surplus repetitions of the latter alternative do not go to waste. Even though the immediate effect, the smooth and errorless reproduction, is not affected by them, yet they are not without significance in that they serve to make other such reproductions possible at a more or less distant time. The longer a person studies, the longer he retains. And, even in the first case, something evidently occurs even if the repetitions do not suffice for a free reproduction. By them a way is at least opened for the first errorless reproduction, and the disconnected, hesitating, and faulty reproductions keep approximating more and more to it. (Ebbinghaus, 1913, p. 52)

This phenomenon he described metaphorically, as a process of engraving and fading:

These relations can be described figuratively by speaking of the series as being more or less deeply engraved in some mental substratum. To carry out this figure: as the number of repetitions increases, the series are engraved more and more deeply and indelibly; if the number of repetitions is small, the inscription is but surface deep and only fleeting glimpses of the tracery can be caught; with a somewhat greater number the inscription can, for a time at least, be read at will; as the number of repetitions is still further increased, the deeply cut picture of the series fades out only after ever longer intervals. (Ebbinghaus, 1913, pp. 52-53)

He found that increased repetition during a period of study provided a savings in relearning at a later period. Specifically, he found that for each three additional repetitions that he spent on a given day on the study of a series, he saved, in learning that series 24 hours later, on the average, approximately one repetition (Ebbinghaus, 1913, p. 57). But he also learned that this was of limited effect. The savings of relearning did not continue to increase proportionally with an increased number of repetitions above a certain limit:

I have made some trial tests partly with shorter series, and partly with familiar series, all of which confirmed the result that the proportion in question gradually ceases to hold with a further increase of repetitions. Measured by the saving of work after 24 hours the effect of the later repetitions gradually decreases. (pp. 59-60)

The effect of increasing the number of repetitions of series of syllables on their inner fixedness in the above defined sense grew at first approximately in proportion to the number of repetitions, then that effect decreased gradually, and finally became very slight when the series were so deeply impressed that they could be repeated after 24 hours, almost spontaneously. (p. 61)

In addition to looking at the effect of an increased number of repetitions during a given period of study, he also examined the effect of multiple periods of study on retention of what has been learned. He found that each subsequent relearning of a series strengthens its retention:

The series are gradually forgotten, but—as is sufficiently well known—the series which have been learned twice fade away much more slowly than those which have been learned but once. If the relearning is performed a second, a third or a greater number of times, the series are more deeply engraved and fade out less easily and finally, as one would anticipate, they become possessions of the soul… (Ebbinghaus, 1913, p. 81)

In conjunction with his investigation on the effect of repeated learning, he also asked whether it was better to study all at once, or to break the task down into multiple periods of study. He found that for the relearning of a 12-syllable series, “38 repetitions, distributed in a certain way over the three preceding days, had just as favorable an effect as 68 repetitions made on the day just previous” (p. 89). Though based on a limited data set, Ebbinghaus felt that the difference was significant enough to warrant a conclusion in favor of spaced practice:

Even if one makes very great concessions to the uncertainty of numbers based on so few researches, the difference is large enough to be significant. It makes the assumption probable that with any considerable number of repetitions a suitable distribution of them over a space of time is decidedly more advantageous than the massing of them at a single time.

With this result, found here for only very limited conditions, the method naturally employed in practice agrees. The schoolboy doesn’t force himself to learn his vocabularies and rules altogether at night, but knows that he must impress them again in the morning. A teacher distributes his class lesson not indifferently over the period at his disposal but reserves in advance a part of it for one or more reviews. (p. 89)

He also noted, however, that an important factor which affected his ability to learn was the time of day at which he studied, with morning hours being more productive than the later hours of the day:

In the later hours of the day mental vigor and receptivity are less. The series learned in the morning and then relearned at a later hour, aside from other influences, require more work for relearning than they would if the relearning were done at a time of mental vigor equal to that of the original learning. (Ebbinghaus, 1913, p. 66)

Ebbinghaus is perhaps most well known for his description of what is commonly referred to as the forgetting curve:

Left to itself every mental content gradually loses its capacity for being revived, or at least suffers loss in this regard under the influence of time. Facts crammed at examination time soon vanish, if they were not sufficiently grounded by other study and later subjected to a sufficient review. But even a thing so early and deeply founded as one’s mother tongue is noticeably impaired if not used for several years. (1913, p. 4)

He discovered that the rate of forgetting could be approximated quite accurately by a negatively accelerated, exponential logarithmic function where the amount remembered, b, is calculated as a function of time (in minutes), t, which have passed, counting from one minute before the end of learning (pp. 76-79), where the constants k and c are given values of 1.84 and 1.25, respectively:

 b = 100k/[(log t)^c + k]

In addition to repetition and forgetting, Ebbinghaus also had something to say about individual differences, content-type effects of learning, attention and interest, meaningfulness, content-length effects on learning, the influence of recollection on reproduction, capacity, and order effects on the association of ideas learned in series. In regard to individual differences, he simply noted that individuals vary in their ability to memorize, and that the capacity of a given person varies with age and time of day (1913):

How differently do different individuals behave in this respect! One retains and reproduces well; another, poorly. And not only does this comparison hold good when different individuals are compared with each other, but also when different phases of the existence of the same individual are compared: morning and evening, youth and old age, find him different in this respect. (p. 3)

He also noted that the type of content to be learned is of great influence on the amount of effort required to learn it (1913):

Melodies may become a source of torment by the undesired persistency of their return…Forms and colors are not so importunate; and if they do return, it is with noticeable loss of clearness and certainty…It is with something of a struggle that past states of feeling are realized; when realized, and this is often only through the instrumentality of the movements which accompanied them, they are but pale shadows of themselves. (p. 3)

Furthermore, the combination of content type and individual differences is the source of great variation in the work required to learn (1913):

If the two foregoing points of view are taken together—differences in individuals and differences in content—an endless number of differences come to light. One individual overflows with poetical reminiscences, another directs symphonies from memory, while numbers and formulae, which come to a third without effort, slip away from the other two as from a polished stone. (p. 3)

Additionally, he noted that the intensity of attention and interest play a significant role:

Very great is the dependence of retention and reproduction upon the intensity of the attention and interest which were attached to the mental states the first time they were present. The burnt child shuns the fire, and the dog which has been beaten runs from the whip, after a single vivid experience. People in whom we are interested we may see daily and yet not be able to recall the color of their hair or of their eyes. (pp. 3-4)

That which carries greater meaning for the learner is more easily acquired. In comparing the learning of series of nonsense syllables to the learning of a poem, Ebbinghaus found a very large difference between the number of repetitions required to learning nonsense material and the number of repetitions required to learn that which was meaningful:

In order to keep in mind the similarities and differences between sense and nonsense material, I occasionally made tests with the English original of Byron’s “Don Juan.” These results do not properly belong here since I did not vary the length of the amount to be learned each time but memorized on each occasion only separate stanzas. Nevertheless, it is interesting to mention the number of repetitions necessary because of their contrast with the numerical results just given.

[When learned to the point of the first possible reproduction] each stanza required hardly nine repetitions; or, if the errorless reproduction is abstracted, scarcely eight repetitions.

If it is born in mind that each stanza contains 80 syllables (each syllable, however, consisting on the average of less than three letters) and if the number of repetitions here found is compared with the results presented above, there is obtained an approximate numerical expression for the extraordinary advantage which the combined ties of meaning, rhythm, rhyme, and a common language give to material to be memorised [sic]. If the above curve is projected in imagination still further along its present course, then it must be supposed that I would have required 70 to 80 repetitions for the memorisation [sic] of a series of 80 to go nonsense syllables. When the syllables were objectively and subjectively united by the ties just mentioned this requirement was in my case reduced to about one-tenth of that amount [italics added]. (Ebbinghaus, 1913, pp. 50-51)

The curve referred to is that which resulted from plotting “the number of repetitions necessary for the memorisation [sic] of series in which the number of syllables progressively increased” (p. 48). Where the length of the series was seven or less, only one reading was necessary before the list could be recited perfectly, with lists of fewer than seven items requiring less and less attention. As the length of the series was increased, the number of repetitions required to learn the series increased non-linearly, with the ascent of the curve at first being very steep, but gradually flattening out.

The increased number of repetitions required to learn the series initially also had the side effect of establishing it more firmly in the mind:

…the effect of this need of more numerous repetitions in the cases investigated consists not merely in making the series just reproducible, but also in the firmer establishment of the longer series. After an interval of 24 hours they could be relearned to the point of being just reproducible with a saving both absolutely and relatively greater than with the shorter series.” (p. 84)

As a result of this “firmer establishment” longer lists could be more easily relearned:

On each day the average number of repetitions necessary for the committing of a given series is less than on the preceding day. With the longer series, in whose case the first output of energy is great, the decrease in the amount of work each time necessary to reach the first possible reproduction is proportionally rapid. With the shorter series, where the first output is small, the decrease is proportionally slow.  (p. 85)

Another very interesting yet subtle observation was that whether or not he could remember studying a series of lists on a previous day made no difference in the effort required to master the series (1913):

When the series were repeated 8 or 16 times they had become unfamiliar to me by the next day. Of course, indirectly, I knew quite well that they must be the same as the ones studied the day before, but I knew this only indirectly. I did not get it from the series, I did not recognise [sic] them. But with 53 or 64 repetitions I soon, if not immediately, treated them as old acquaintances, I remembered them distinctly. Nothing corresponding to this difference is evident in the times for memorisation [sic]and for savings of work respectively. They are not smaller relatively when there is no possibility of recollection nor larger relatively when recollection is sure and vivid. The regularity of the aftereffect of many repetitions does not noticeably deviate from the line that is, so to speak, marked out by a smaller number of repetitions although the occurrence of this after-effect is accompanied by recollection in the first case just as indubitably as it lacks recollection in the second case. (pp. 58-59)

In the final chapter of his book, Ebbinghaus reported his findings regarding the mental association between members of a series, measured by the savings observed when learning a new series methodically constructed from a series previously learned through the omission of 1, 2, 3 or seven intermediate members. His findings provide empirical support in favor of Aristotle’s law of contiguity. The new series formed by leaving out intermediate members from the original series were learned with a time savings that was greatest where fewer intermediate members were omitted (1913):

There seems to be an association not merely in direct but also in indirect succession. The strength of these connections decreases with the number of the intervening numbers; with a small number it was, as will be admitted, of surprising and unanticipated magnitude. (p.101)

In contrast to this observed savings—yet still consistent with the idea that mental concepts are associated with one another, and that the order of succession is one of the characteristics learned when learning a series—he also found that when a new series was constructed not by omitting intermediate members of the original series but by permutation of the members (i.e., changing the order) there was an increase in the expenditure of time required to learn the new series, suggesting that the ordering of the original list interfered with the learning of the new list (1913):

By derivation of the transformed series by skipping I, 2, 3, 7 intermediate syllables, the derived series were therefore learned with an average saving of 110, 79, 64, 40 seconds. On the contrary with derivation of the series by permutation of the syllables the learning required an average increase in expenditure of 5 seconds. (p. 104)

He also found that there was a present, yet weaker, reciprocal association formed between the members of a series. When the transformed series is formed by mere reversal of the syllable sequence, there is a time savings in learning of the transformed series, as compared to learning an unrelated, arbitrary series of the same length:

As a result of the learning of a series certain connections of the members are therefore actually formed in a reverse as well as in a forward direction…The strength of the predispositions thus created was again a decreasing function of the distance of the members from each other in the original series. It was, however, considerably less for the reverse connections than for the forward ones, the distances being equal. (pp. 112-113)

The studies that Ebbinghaus conducted were rooted in the ideas of association, but were clearly mentalistic, in contrast with the contemporary behavioristic S-R theories of Pavlov and Thorndike. As such, Ebbinghaus’s studies provided a precedent on which much of the cognitive learning research conducted during the 20thcentury was based.

[1] Though often cited unequivocally as the first experimental studies of memory, given the inquisitive nature of man, and evidence of man’s methodological inspection of both the external and internal realm since the time of the early Greeks, it is unlikely that it actually is the first. That said, until some predating study is identified, comparable in clarity and coherence, we accept it as such.

[2] In 1956, George A. Miller published The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information (Miller, 1956). Though he didn’t specifically cite Ebbinghaus’s study, he was not unaware of its existence (p. 94). In his article Miller cited several examples in which the unidimensional channel capacity—operationally defined based on information theory as the number of bits a person was able to take as input which varied along a single scale and then pass on as output, usually in a verbal absolute judgment or report—was found to be sufficient to represent 7 distinct elements, plus or minus two. For absolute judgments of tones it was found that listeners never confused two or three distinct tones, rarely confused four, but with five or more confusions were frequent. Psychologists “have been using seven-point rating scales for a long time, on the basis that trying to rate into finer categories does not really add much to the usefulness of the ratings” (p. 84). Channel capacity for absolute judgments of loudness average 2.3 bits, or enough to represent about five discriminable alternatives. For taste discrimination, 1.9 bits, or four distinct concentrations can be identified—less distinctive than auditory stimuli, but not far off. Visual capacity seems to have a much higher capacity, ranging from 3.2 to 3.9 bits, meaning 10 to 15 distinct positions along a linear interval can be uniquely identified. Channel capacity for the skin was found to have “about four intensities, about five durations, and about seven locations” (p. 86).

Miller’s conclusion was that “there seems to be some limitation built into us either by learning or by the design of our nervous systems, a limit that keeps our channel capacities in this general range” (p. 86). Miller also notes, however, that in everyday experience we are able to “identify accurately any one of several hundred faces, any one of several thousand words, any one of several thousand objects, etc.” (p. 87) This he attributes to our ability to make simultaneous and successive discriminations. With simultaneous discriminations “we can make relatively crude judgments of several things simultaneously” (p. 88) thereby increasing our total capacity. Language is made up of sequences of phonemes, so we are able to make several judgments successively as we process the input. Our span of immediate memory exhibits a similar trait in that it seems to be limited to about seven items in length. Miller is quick to point out that while the limits of absolute judgment and immediate memory are similar, we should not jump to the conclusion that they are rooted in the same source, although that may be the case.

In his article several years later, entitled, “The Magical Number Seven: Still Magic After All These Years?,” Baddeley (1994) concluded that:

In emphasizing the importance of recoding, Miller pointed the way ahead for the information-processing approach to cognition, and in developing the concept of chunking, he provided a concept that continues to be fruitful in the analysis of learning and memory. The article, if not the number seven, retains its magic. (p. 356)

Associationism (Aristotle – 350 B.C.E)Purposive Behaviorism (Edward Chance Tolman – 1922) >

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