The Magical Number 4 in Short-Term Memory: a Reconsideration of Mental Storage Capacity
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BEHAVIORAL AND BRAIN SCIENCES (2000) 24, 87–185 Printed in the United States of America The magical number 4 in short-term memory: A reconsideration of mental storage capacity Nelson Cowan Department of Psychological Sciences, University of Missouri, Columbia, MO 65211 [email protected] www.missouri.edu/~psycowan Abstract: Miller (1956) summarized evidence that people can remember about seven chunks in short-term memory (STM) tasks. How- ever, that number was meant more as a rough estimate and a rhetorical device than as a real capacity limit. Others have since suggested that there is a more precise capacity limit, but that it is only three to five chunks. The present target article brings together a wide vari- ety of data on capacity limits suggesting that the smaller capacity limit is real. Capacity limits will be useful in analyses of information processing only if the boundary conditions for observing them can be carefully described. Four basic conditions in which chunks can be identified and capacity limits can accordingly be observed are: (1) when information overload limits chunks to individual stimulus items, (2) when other steps are taken specifically to block the recoding of stimulus items into larger chunks, (3) in performance discontinuities caused by the capacity limit, and (4) in various indirect effects of the capacity limit. Under these conditions, rehearsal and long-term memory cannot be used to combine stimulus items into chunks of an unknown size; nor can storage mechanisms that are not capacity- limited, such as sensory memory, allow the capacity-limited storage mechanism to be refilled during recall. A single, central capacity limit averaging about four chunks is implicated along with other, noncapacity-limited sources. The pure STM capacity limit expressed in chunks is distinguished from compound STM limits obtained when the number of separately held chunks is unclear. Reasons why pure capacity estimates fall within a narrow range are discussed and a capacity limit for the focus of attention is proposed. Keywords: attention; enumeration; information chunks; memory capacity; processing capacity; processing channels; serial recall; short- term memory; storage capacity; verbal recall; working memory capacity 1. Introduction to the problem of mental Hulme 1995). One possible resolution is that the focus of storage capacity attention is capacity-limited, whereas various supplemen- tary storage mechanisms, which can persist temporarily One of the central contributions of cognitive psychology has without attention, are time-limited rather than capacity- been to explore limitations in the human capacity to store limited (Cowan 1988; 1995). Other investigators, however, and process information. Although the distinction between have long questioned whether temporary storage concepts a limited-capacity primary memory and an unlimited- are necessary at all, and have suggested that the rules of capacity secondary memory was described by James (1890), learning and memory could be identical in both the short Miller’s (1956) theoretical review of a “magical number and long term (Crowder 1993; McGeoch 1932; Melton seven, plus or minus two” is probably the most seminal pa- 1963; Nairne 1992; Neath 1998). per in the literature for investigations of limits in short-term At present, the basis for believing that there is a time memory (STM) storage capacity. It was, in fact, heralded as one of the most influential Psychological Review papers ever, in a 1994 centennial issue of the journal. Miller’s ref- Nelson Cowan (Ph.D. 1980, University of Wiscon- erence to a magical number, however, was probably a sin–Madison) is Professor in the Department of Psy- rhetorical device. A more central focus of his article was the chological Sciences at the University of Missouri– ability to increase the effective storage capacity through the Columbia. He has written one book (Cowan, N. 1995. use of intelligent grouping or “chunking” of items. He ulti- Attention and memory: An integrated framework. Ox- mately suggested that the specific limit of seven probably ford University Press) and edited another (1997. The emerged as a coincidence. development of memory in childhood. Psychology Press), Over 40 years later, we are still uncertain as to the nature and has 100 other publications on working memory, and of storage capacity limits. According to some current theo- its relation to attention. He is former Associate Editor of the Journal of Experimental Psychology: Learning, ries there is no limit in storage capacity per se, but a limit Memory, and Cognition (1995–1999) and current As- in the duration for which an item can remain active in STM sociate Editor of the Quarterly Journal of Experimental without rehearsal (e.g., Baddeley 1986; Richman et al. Psychology (section A). He won the 1998 University of 1995). This has led to a debate about whether the limitation Missouri Chancellor’s Award for Research and Creative is a “magic number or magic spell” (Schweickert & Boruff Activities. 1986) or whether rehearsal really plays a role (Brown & © 2000 Cambridge University Press 0140-525X/00 $12.50 87 Cowan: The magical number 4 limit to STM is controversial and unsettled (Cowan et al. pacity limits but they are in line with Miller’s 7 6 2 (e.g., 1997a; 1997b; Crowder 1993; Neath & Nairne 1995; Ser- still taken at face value by Lisman & Idiart 1995). (View 2) vice 1998). The question is nearly intractable because any Short-term memory is limited by the amount of time that putative effect of the passage of time on memory for a par- has elapsed rather than by the number of items that can be ticular stimulus could instead be explained by a combination held simultaneously (e.g., Baddeley 1986). (View 3) There of various types of proactive and retroactive interference is no special short-term memory faculty at all; all memory from other stimuli. In any particular situation, what looks results obey the same rules of mutual interference, distinc- like decay could instead be displacement of items from a tiveness, and so on (e.g., Crowder 1993). (View 4) There limited-capacity store over time. If the general question of may be no capacity limits per se but only constraints such whether there is a specialized STM mechanism is to be an- as scheduling conflicts in performance and strategies for swered in the near future then, given the apparent unre- dealing with them (e.g., Meyer & Kieras 1997). (View 5) solvability of the decay issue, general STM questions seem There are multiple, separate capacity limits for different more likely to hinge on evidence for or against a chunk- types of material (e.g., Wickens 1984). (View 6) There are based capacity limit. separate capacity limits for storage versus processing The evidence regarding this capacity limit also has been (Daneman & Carpenter 1980; Halford et al. 1998). (View controversial. According to one view (Wickens 1984) there 7) Capacity limits exist, but they are completely task-spe- is not a single capacity limit, but several specialized capac- cific, with no way to extract a general estimate. (This may ity limits. Meyer and Kieras (1997) questioned the need for be the “default” view today.) Even among those who agree capacity limits to explain cognitive task performance; they with the 4-chunk thesis, moreover, a remaining possible instead proposed that performance scheduling concerns ground of contention concerns whether all of the various (and the need to carry out tasks in the required order) ac- phenomena that I will discuss are legitimate examples of count for apparent capacity limits. The goal of this target ar- this capacity limit. ticle is to provide a coherent account of the evidence to date These seven competing views will be re-evaluated in sec- on storage capacity limits . tion 4 (sects. 4.3.1–4.3.7). The importance of identifying One reason why a resolution may be needed is that, as the chunk limit in capacity is not only to know what that mentioned above, the theoretical manifesto announcing limit is, but more fundamentally to know whether there is the existence of a capacity limit (Miller 1956) did so with such a limit at all. Without evidence that a consistent limit considerable ambivalence toward the hypothesis. Although exists, the concepts of chunking and capacity limits are Miller’s ambivalence was, at the time, a sophisticated and themselves open to question. cautious response to available evidence, a wealth of subse- quent information suggests that there is a relatively con- 1.1. Pure capacity-based and compound STM estimates stant limit in the number of items that can be stored in a wide variety of tasks; but that limit is only three to five I will call the maximum number of chunks that can be re- items as the population average. Henderson (1972, p. 486) called in a particular situation the memory storage capac- cited various studies on the recall of spatial locations or of ity, and valid, empirically obtained estimates of this num- items in those locations, conducted by Sperling (1960), ber of chunks will be called estimates of capacity-based Sanders (1968), Posner (1969), and Scarborough (1971), to STM. Although that chunk limit presumably always exists, make the point that there is a “new magic number 4 6 1.” it is sometimes not feasible to identify the chunks inasmuch Broadbent (1975) proposed a similar limit of three items on as long-term memory information can be used to create the basis of more varied sources of information including, larger chunks out of smaller ones (Miller 1956), and inas- for example, studies showing that people form clusters of much as time- and interference-limited sources of infor- no more than three or four items in recall. A similar limit in mation that are not strictly capacity-limited may be used capacity was discussed, with various theoretical interpreta- along with capacity-limited storage to recall information.