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Galton describes the first procedure he used to cue memories as follows. "I walked leisurely along Pall Mall, a distance of 450 yards, during which time I scrutinised with attention every successive object that caught my eyes, and I allowed my attention to rest on it until one or two thoughts had arisen through direct association____Samples of my whole life passed before me'' (1879, p. 151). He then moved from the "real world'' into the "laboratory." Galton produced sheets of paper, each with one word on it, waited a few days, placed a sheet with a word on it partially under a book so that it was blocked from view until he would lean forward to see it. He recorded his associations and his reaction times to 75 words on four occasions. "It was a most repugnant and laborious work'' (1879, p. 153). Of the 124 different associations he obtained, 48 were from "boyhood and youth,'' 57 were from "subsequent manhood,'' and 19 were from "quite recent events.''

Crovitz and Schiffman (1974) revived Galton's technique. About the same time Robinson (1976) independently came upon the same procedure. People were asked to think of an autobiographical memory in response to each word presented to them. They were then asked to return to their memories and date each one as accurately as possible.

The distribution of memories over the lifespan of the undergraduate can be described as a power function of the time since the event occurred (Crovitz & Schiffman, 1974). Figure 1 is of a typical plot. The power function (i.e., y = at~b) is a simple two parameter curve that has often been used in psychology (Newell & Rosenbloom, 1981; Stevens, 1975).

Figure 1

The relative number of autobiographical memories per hour reported by undergraduates as a function of the age of those memories. Both axes are logarithmic, so a straight line is a power function. (Adapted from Rubin, 1982, figure 2.)

Figure 1

The relative number of autobiographical memories per hour reported by undergraduates as a function of the age of those memories. Both axes are logarithmic, so a straight line is a power function. (Adapted from Rubin, 1982, figure 2.)

When both axes are plotted as logarithmic scales, as they are in figure 1, the power function becomes a straight line (i.e., log(y) =—b log(t) + log(a)). The fits to the curve are surprisingly good, with correlations usually over .95. If we assume that undergraduates encode an equal number of events each day of their lives, then the plot shown in figure 1 is a retention function. Because the power function is a common choice for a retention function (Anderson & Schooler, 1991; see Rubin & Wenzel, 1996, for a review), as a first approximation it appears that laboratory and autobiographical memory have similar patterns of forgetting (but see Rubin, Hinton & Wenzel, 1999).

A recurring theme can now be introduced (Rubin, 1989). Figure 1 presents some of the most regular data in memory research. Correlations over .95 are not all that common in cognitive psychology, especially when a two-parameter function is fit to over a dozen points and the function is a reasonable choice in terms of the existing literature. But figure 1 is of data that was collected with one of the least controlled experimental procedures in cognitive psychology. There are no restrictions or controls over the learning of the material or over which autobiographical mem ories people are to report. The function is not dependent on how the dating of memories is done; it does not change whether participants report the age of the memory with an estimate of the actual date in term of its month, day, and year or whether they use phrases of the form n hours, days, weeks, months, or years ago. The shape of the function does not depend on the cue words used, as it occurs when people respond to a single cue word, when they respond to different numbers of cue words, when odors are used instead of cue words, and when no cues are used at all—they respond to just a request for 50 autobiographical memories (Rubin, 1982; Rubin, Groth & Goldsmith, 1984). One reason for the regularity may be that the retention interval is large (from either 1 hour or 1 day ago to about 20 years ago) and the range of the dependent measure is large (often four orders of magnitude). Such large ranges on scales can be more easily obtained outside the laboratory.

Scott Wetzler, then a graduate student in clinical psychology, wondered what would happen if older adults were tested. After all, the undergraduates had only about 20 years of life on which to report. Would the retention function remain the same or perhaps just change its slope or intercept parameter? Would the whole shape of the function change? Robert Nebes, who was then at Duke, had data, and Scott wrote to other people for their data. They were all generous in their cooperation (their original articles were published as Fitzgerald & Lawrence, 1984; Franklin & Holding, 1977; Zola-Morgan, Cohen & Squire, 1983).

The results for older adults with a mean age of 70 are shown in figure 2. They were a surprise. No one had plotted the data this way before, and so we could find no earlier empirical demonstration of the nonmonotonic plot. The shape of the curve also appeared replicable, because it appeared in the plots of the data from 70-year-old participants from each of the three laboratories that were summed to provide figure 2 and also in the plots from three laboratories for adults who were 50 years old (Rubin, Wetzler & Nebes, 1986). For figure 2, about one half of the memories were dated as occurring within the last year and were not plotted because they would make all decades but the last have very low values; they are, however, considered in detail when retention functions for the most recent decade are plotted. The large number of memories from the recent past also shows that older adults are not "living in the

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Figure 2

The distribution of autobiographical memories over the lifespan for older adults. Events dated as occurring in the most recent year are excluded. (Data from Rubin et al., 1986.)

past.'' From the shape of the plot and the retention-function fit for undergraduates, we assumed that the curve had three components: retention, childhood amnesia, and a bump or increase in the number of memories recalled from adolescence and early adulthood. Because the topic of this chapter, the increase in memories from ages 10 to 30, is defined empirically by what is left after the retention and childhood amnesia components are removed, these two components are considered briefly before concentrating on the nonmonotonic component.

The first component is a retention function that covers the whole lifespan, but that has most of its memories distributed over the most recent two decades of life; for periods more than two decades ago, it is too small to produce a measurable number of memories. If one assumes that the retention function of figure 1 holds for people of all ages without systematic age changes in the slope (an assumption supported by considerable data, e.g., Rubin et al., 1986; Rubin & Schulkind, 1997a, 1997b), then for a typical slope of —.8, the number of memories per hour decreases by a factor of .57 every time the retention interval doubles. If from a month that occurred three months ago an older adult recalled 10

memories, from months that occurred 2, 1, 2, 4, 8, 16, 32, and 64 years ago that adult would recall 6, 3, 2, 1, .6, .4, .3, .2, and .1 memories. Thus, without some modification of the function, older adults would recall little from their youth.

The second component is childhood amnesia. When undergraduates were tested, there was an inflection in the power-function curve (Wetzler & Sweeney, 1986), but it is hard to argue that some other curve would not naturally fit this inflection. However, when adults of different ages were tested, it became clear that a function was needed that went to zero at or near the birth of the person no matter whether their birth was 20, 50, or 70 years before the date of testing. Thus a childhood-amnesia component based on age at the time of the event rather than time since the event had to be added to ensure that the curves of people of different ages all went to zero at birth. In mathematical terms, there had to be a function in terms of age at the time or the event (or equivalently, retention interval — current age) in addition to a function in terms of retention interval (i.e., f (t — age) as well as f (t), where t is the time since the event). This component is very stable over numerous studies, having the same basic shape no matter what method is used to produce the data, as long as the participants come from the United States (Rubin, 2000). Thus, as with the retention component, the data are remarkably regular, though the experimental procedure has minimal control. The childhood-amnesia component is, however, affected by culture, and within some cultures by gender (Mullen, 1994; MacDonald, Uesiliana & Hayne, 2000). Figure 3 provides a sample plot.

The third component is the increase in memories from when older adults were between 10 and 30 years old compared to what would be expected from the other two components or from any monotonically decreasing function. We termed it "the bump'' to emphasize our lack of theoretical understanding, a lack due to the paucity of an organized existing literature. Our later searches of the literature, however, found a multitude of possible theoretical explanations that could have predicted the bump, but that somehow did not lead to empirical tests.

The initial description of the bump was based on data from several laboratories. Since that time there have been consistent findings using the word-cue technique with older adults (Hyland & Ackerman, 1988;

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Figure 3

The distributions of 10,118 memories dated as occurring before age 8 from published studies. (Data from Rubin, 2000.)

Jansari & Parkin, 1996; Rubin & Schulkind, 1997a, 1997c; see Rubin, 1999, and Rybash, 1999, and the articles that follow in his special issue of the Journal of Adult Development for reviews). Minor differences exist in the shape of the distribution with changes in procedure and subject population, but the bump appears repeatedly, even for individuals (Rubin & Schulkind, 1997c). This literature indicates that the bump occurs when as few as 10 to 20 and as many as 900 word cues are given to each person; so the bump is not caused by just a few highly available memories.

The word-cue technique is useful to help people produce memories. It helps ensure that each memory is not cued mainly by the memories recalled previously, and thus provides a wider sampling of memories. But this is only one way to access autobiographical memories and not the one most commonly used in everyday life. A series of studies from Denmark first demonstrated that the bump occurs even when a life narrative is obtained from older adults and the distribution of experimenter-defined events from that life study is plotted (Fromholt & Larsen, 1991; Fromholt, Larsen & Larsen 1995; see Schrauf & Rubin, 2000, for a replication).

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