Implications for Alternative Accounts of Information Processing

In light of the information and ideas that have been presented, it is important to reconsider alternative accounts of information processing and the question of their continued viability and plausibility.

4.3.1. The magical number seven plus or minus two. Although Miller (1956) offered his magical number only as a rhetorical device, the number did serve to characterize performance in many tasks. It has been taken more literally as a memory limit by many researchers (e.g., Lisman & Idiart, 1995). The present stance is that the number seven estimates a commonly obtained, compound capacity limit, rather than a pure capacity limit in which chunking has been eliminated. It occurs in circumstances in which the stimuli are individually attended at the time of encoding and steps have not been taken to eliminate chunking. What is needed, however, is an explanation of why this particular compound limit crops up fairly often when rehearsal is not prevented. One possibility is that this number reflects a certain reasonable degree of chunking. Most adults might be able to learn at most three chunks of information rapidly, each with perhaps three units, leading to a span of 9. The slightly lower estimates that are often obtained could result from the inability to learn the chunks quickly enough. However, these speculations are intended only to provoke further research into the basis of commonly obtained compound capacity limits. What is essential to point out for the present account is that these compound limits are too high to describe performance in the situations in which it can be assumed that the combination of items into higher-order chunks was severely limited or prevented.

4.3.2. The time-limitation account. The view that working memory is limited by the duration of unrehearsed information in various short-term buffers is exemplified by the model of Baddeley (1986). The research reviewed in the present article leaves open the question of whether time limitations exist (as explained in Section 1). However, whereas some have assumed that time limits can take the place of capacity limits, the evidence described in this article cannot be explained in this manner. In Baddeley's theory, memory span was said to be limited to the number of items that could be rehearsed in a repeating loop before their representations decay from the storage buffer in which they are held (in about 2 sec in the absence of rehearsal). If rehearsal is always articulatory in nature, though, this notion is inconsistent with findings that the memory span for idioms would imply a much longer rehearsal time than the memory span for individual characters (e.g., see Glanzer & Razel, 1974). Something other than just the memory's duration and the rate of articulatory rehearsal must limit recall.

The time-based account might be revived if a different means of rehearsal could be employed for idioms than for words. For example, subjects might be able to scan semantic nodes, each representing an idiom, and quickly reactivate them in that way without articulatory rehearsal of the idioms. According to a modified version of Baddeley's account, this scanning would have to be completed in about 2 sec to prevent decay of the original memory traces. However, even that modified time-based theory seems inadequate to account for situations in which the material to be recalled is presented in an array so quickly that rehearsal of any kind can contribute little to performance (e.g., Luck & Vogel, 1997). Also, any strictly time-based account has difficulty explaining why there is an asymptotic level of recall in partial report approximating 4 items with both auditory and visual presentation of characters, even though it takes much longer to reach that asymptote in audition (at least 4 s: Darwin et al., 1972) than in vision (at most 1 s: Sperling, 1960). The only way to preserve a time-based account would be to assume that the rate of extraction of information from sensory storage in the two modalities is a limiting factor and is, for some mysterious reason, inversely proportional to the duration of sensory storage, resulting in an asymptotic limit that does not depend on the duration of storage. It seems far simpler to assume a capacity limit.

4.3.3. The unitary storage account. Some theorists (e.g., Crowder, 1993) have assumed that there is no special short-term memory mechanism and that all memory may be explained according to a common set of rules. In one sense the present analysis is compatible with this view, in that the capacity limit applies not only to the recall of recently presented stimuli, but also to the recall of information from long-term memory (see Section 3.4.2). However, any successful account must distinguish between the vast information potentially obtainable from an individual, on one hand, and the small amount of information that can be obtained from that individual, or registered with the individual, in a short segment of time; the capacity limit. The focus of attention, which serves as the proposed basis of the capacity limit in the present approach, has not played a major role in unitary accounts that have been put forward to date, though it could be added without contradiction.

Given a unitary memory view expanded to consider the focus of attention, one could account for the 4-chunk limit on the grounds that every chunk added to the focus diminishes the distinctiveness of all of the chunks. Such a mechanism of indistinctiveness would be analogous to the one that has been used previously to account for the recency effect in serial recall (e.g., Bjork & Whitten, 1974); except that the dimension of similarity between chunks would be their concurrent presence in the focus of attention, not their adjacent serial locations within a list. One article written from a unitary memory view (Brown, Preece, & Hulme, in press) does attempt to account for the number of chunks available in one situation. Specifically, their account, based on oscillatory rhythms that become associated with items and contexts, correctly predicted that the serial recall of a nine-item list with overt rehearsal is optimal when the list is rehearsed in groups of three items. The explanation offered was that "This represents the point at which the optimal balance between across-group errors and within-group errors is reached in the model." The account of the 4-chunk limit offered earlier in this target article on the basis of neural oscillatory rhythms (4.1.2) is similar (albeit on a neural level of analysis). It states that, with the neural representation of too many chunks simultaneously, the representations begin to become confusable (e.g., Luck & Vogel, 1998). The critical difference between explanations is that the neural account offered by Luck and Vogel and the present article refers to particular frequencies of neural oscillation, whereas Brown et al. allowed various oscillators and did not make predictions constrained to particular frequencies of oscillation.

4.3.4. The scheduling account. It has been proposed that supposed capacity limits might be attributable to limits in the rate at which subjects can produce responses in a multi-task situation without risking making responses in the incorrect order (Meyer & Kieras, 1997). That theory appears more applicable to some situations than to others. In situations in which the limit occurs during reception of materials and fast responding is not required (e.g., Luck & Vogel, 1997), the theory seems inappropriate. That seems to be the case with most of the types of phenomena examined in the present article. It is unclear how a scheduling account could explain these phenomena without invoking a capacity notion.

4.3.5. The multiple-capacity account. Some theorists have suggested that there is not a single capacity limit, but rather limits in separate capacities (e.g., visual and auditory or spatial and verbal; see Wickens, 1984). I would suggest that, although there may well be various types of distinct processes and storage facilities in the human brain, there is no evidence that they are limited by capacity per se (as opposed to other limitations such as those imposed by decay and interference). Sections 1 and 3 of the present paper should illustrate that strict conditions must apply in order for chunk capacity limits to be clearly observed at all, free of other factors. Moreover, the finding of Sirevaag et al. (1989) of a tradeoff between tasks in the the P300 response magnitude in event-related potentials (discussed in Section 4.2) seems to indicate that very disparate types of processes still tap a common resource. Even the left and right hemispheres do not appear to operate independently. Holtzman and Gazzaniga (1992) found that split brain patients are impeded in responses made with one hemisphere when a concurrent load is imposed on the other hemisphere, despite the breakdown in informational transmission between the hemispheres through the corpus collosum. There thus appears to be some central resource that is used in disparate tasks, and by both hemispheres.

4.3.6. The storage versus processing capacities account. Daneman and Carpenter (1980), like many other investigators, have noted that a working memory storage load does not interfere with processing nearly as much as would be expected if storage and processing relied upon a common workspace. Halford et al. (1998) noted the storage limit of about 4 items but also proposed, parallel to that limit but separate from it, a processing limit in which the complexity of relations between items being processed is limited to 4 dimensions in adults (and to fewer dimensions in children). Thus, within processing, "complexity is defined as the number of related dimensions or sources of variation" (p. 803). For example, transitive inference is said to be a ternary relation because it can be reduced to such terms: "the premises 'Tom is smarter than John, John is smarter than Stan' can be integrated into the ternary relational instance monotonically-smarter (Tom, John, Stan)" (p. 821), an argument with three fillers. The parallel between processing and storage was said to be that "both attributes on dimensions [in processing] and chunks [in storage] are independent units of arbitrary size" (p. 803). However, the model did not explain why there was the coincidental similarity in the processing and storage limits, to about 4 units each.

According to the present view, both processing and storage would be assumed to rely on a common capacity limit. The reason is that, ultimately, what we take to be stored chunks in short-term memory (and what I have, for simplicity, described as such up to this point) actually are relations between chunks. It is not chunks per se that have to be held in short-term memory (as they in fact are part of long-term memory), but rather chunks in relation to some concept. For example, "in-present-array (x, q, r, b)" could describe the quaternary relation leading to a whole report response in Sternberg's (1960) procedure. "Monotonically-later (3-7, x, 2, 4-8)" could describe a quaternary relation leading to partially correct serial recall of an attended list of digits for which 3-7 is a memorized initial chunk; x represents a placemarker for a digit that cannot be recalled; 2 represents an unchunked digit; and 4-8 represents another memorized chunk.

If this analysis is correct, there is no reason to expect a separation between processing and storage. The reason why a storage load does not much interfere with processing is that the storage load and the process do not have to be expanded in the focus of attention at the same time. Although both are activated at the same time, there is no capacity limit on this activation, only with its use (cf. Schneider & Detweiler, 1987). The subject might only hold in the focus of attention a pointer to the activated, stored information while carrying out the processing, and then the subject could shift the focus to the stored information when necessary to recall the memory load.

4.3.7. The task-specific capacities account. A skeptic might simply assume that although there are capacity limits, they vary from situation to situation for reasons that we cannot yet understand. This type of view probably cannot be answered through reasoned discourse as it depends on a different judgment of the presented evidence. Further assessment of the view that there is a fixed underlying capacity could be strengthened by subsequent research in which new conditions are tested and found to conform to or violate the capacity limit. Numerous examples of novel conditions leading to the predicted limit can be given, but two of them are as follows. First, in the research by Cowan et al. (1999), a capacity limit for ignored speech was expected to be similar to those that have been obtained for attended visual arrays (Luck & Vogel, 1997; Sperling, 1960) on the grounds that the task demands were logically analogous, even though the materials were very different. That expectation was met. Second, it was expected that one could observe the capacity limit by limiting rehearsal for spoken lists, and that expectation provided a very similar limit in numerous published experiments (as shown in Table 2). A third example has yet to be tested. Specifically, it was predicted (in Section 1.2.1) that the capacity limit could be observed in a modified n-back task in which subjects must only indicate, as rapidly as possible, if a particular item has been included in the stimulus set previously, and in which some items would be repeated in the set but other, novel items also would be introduced.

4.4. Boundaries of the central-capacity-limit account. The boundaries of the present type of analysis have yet to be examined. For example, Miller (1956) indicated that absolute judgments in perception are limited in a way that is not clear; apparently not in chunks as for other types of phenomena. For unidimensional stimuli the limit appears to be up to about 7 categories that can be used consistently, but the limit in the number of total categories is considerably higher for multidimensional stimuli (e.g., judgments of tones differing in both intensity and pitch). One possibility is that the subject need only retain, in short-term memory, pointers to the dimensions while accessing category divisions one dimension at a time. Because faculties that are not specifically capacity-limited, such as sensory memory, can be used for supplementary storage, the focus of attention is free to shift to allow the sequential use of the capacity limit to judge the stimulus on different dimensions, one at a time. This analysis might be tested with absolute judgments for backward-masked stimuli, as backward masking would prevent sensory storage from holding information while the focus of attention is shifted from one dimension to another. Thus, as in this example, the capacity concept potentially might have a broad scope of application indeed.