PSYCHOLOGICAL SCIENCE Research Article REFLECTIONS OF THE ENVIRONMENT IN MEMORY John R Anderson and Lael J Schooler Department of Psychology Carnegie Mellon University Abstract Avallahility of human memories for specific items shows reliable relationships to frequency recency and pattern of prior exposures to the item These relationships have defied a systematic theoretical treatment A number of environmental sources New York Times parental speech eleetronic mail are examined to show that the probability that a memory will be needed also shows reliable relationships to frequency recency and pattern of prior exposures Moreover the environmental relationships are the same as the memory relationships ft is argued that human memory has the form it does because it is adapted to these environmental relationships Models for both the environment and human memory are described Among the memory phenomena addressed are the practice function the retention function the effect of spacing of practice and the relationship between degree of practice and retention The title of our paper is inspired by the following remark in Shepard 1990 We may look into that window on the mind as through a glass darkly but what we are beginning to discern there looks very much like a reflection of the world p 213 He was commenting on how the principles of perception are exquisitely tuned to the features of the environment in which we live Basically Shepard s thesis is that perception has been optimized through evolution to make the best possible inferences about the world given the perceptual input Recently Anderson 1989 1990 has suggested that the same might be true about human memory Many people hold the bias that human memory is anything but optimal They point to the many frustrating failures of memory However these criticisms fail to appreciate the task before human memory which is to try to manage a huge stockpile of memories In any system responsible for managing a vast data base there must be failures of retrieval It is just too expensive to maintain access to an unbounded number of items Given the initial bias against human memory it would be particularly compelling if we could show that human memory were optimal How does a system behave optimally when it is faced with a huge data base of items and cannot make all of them instantaneously available It would be behaving optimally if it made most available those items that were most likely to be needed In this paper we explore the issue of whether human memory is behaving optimally with respect to the pattern of past information presentation Each item in memory has had some history of past use For instance our memory for one person s name may not have been used in the past month but might have been used five times in the month previous to that What is the probability that the memory will be needed used during the 396 Copyright 1991 American Psychological Society current day Memory would be behaving optimally if it made this memory less available than memories that were more likely to be used but made it more available than less likely memories In this paper we examine a number of environmental sources to determine how probability of a memory being needed varies with pattern of past use However we first review how availability in human memory varies with pattern of past use Some aspects of this problem have been extensively studied in empirical studies of human memory FORM OF THE MEMORY FUNCTIONS Two of the most basic statistics we might gather about pattern of past use are how often a memory has been practiced and how long it has been since it was last practiced Learning functions and retention functions to describe these two aspects of human memory have been collected since the original experiments of Ebbinghaus 1885 1964 Figure 1 shows the retention function and practice function obtained by Ebbinghaus The Retention Function Ebbinghaus measured retention in terms of the percent savings in relearning a list of nonsense syllables The function shows the classic negative acceleration typical of such retention functions In order to be able to compare this memory function to the environment we need to decide how to characterize the forgetting function Some e g Loftus 1985 have suggested that these functions satisfy an exponential formula P Ae b T 1 where P is the performance measure T is the delay time and A and b are parameters of the model The intuitive appeal of an exponential function probably explains why it is so often suggested It implies that during each unit of time the memory loses a constant fraction of what is left This process evokes images of radioactive decay an analogy often used to describe forgetting One can investigate whether this function holds by performing a log transformation of the performance scale If the underlying relationship is exponential a linear relationship should obtain between log performance and time log P Jog A bT 2 A precondition to performing an adequate test of such a function is that we have a large manipulation of the time scale VOL 2 NO 6 NOVEMBER 1991 PSYCHOLOGICAL SCIENCE John R Anderson and Lael J Schooler 60 r 60 a Ebblnghaus s Retention data b Ebbinghaus s Practice Data 50 50 40 S 30 20 10 200 400 600 Hours of Delay BOO 2 3 4 5 Days 01 Practice Fig 1 a Ebbinghaus s 1885 1964 retention function showing percent savings as a function of delay Ebbinghaus used delays from 20 minutes to 31 days b Ebbinghaus s practice data showing total number of trails to master a set of lists as a function of number of days of practice Ebbinghaus s data certainly satisfy this precondition as he varied retention intervals from 20 minutes to 31 days Figure 2a illustrates the Ebbinghaus data with the performance scale transformed As may be observed the resulting function is anything but linear Thus despite its popularity the hypothesis of an exponential forgetting function is not supported Wickelgren 1976 using a d memory measure and delays from 2 minutes to 14 days found evidence for a power function relating delay to retention A power function has the form P AT 1 Actually Wickelgren s theory also had an exponential component that would dominate the power component at very long delays log P 3 B62 0 126 log D R V2 0 976 4 2 4 0 3 a Ebbinghaus s Retention Data with Log Transformation of the Performance Scale 4 2 b Ebbinghaus s Retention Date with i og Transformations of Both Scales 4 0 3 8 u 3 6 3 4 3 2 200 400 600 Hours of Delay 800 3
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