Cowan's revisiting of the magic number is very timely and the case he makes for a more moderate number than seven is persuasive. It is also appropriate to frame his case within a theoretical context, since this will influence what evidence to include and how to interpret it. He presents his model however, as a contrast to the working memory model of Baddeley (1986). I suggest that this reflects a misinterpretation of our model resulting in a danger of focusing attention on pseudo-problems rather than genuine disparities between his approach and my own.

The complex relationship between attention and STM forms a core issue in the study of human cognition, and Cowan's target article attempts, quite successfully, to elucidate an important part of this relationship. However, while I agree that aspects of STM performance may reflect the action mechanisms that we normally consider to subserve “attention” I shall argue here that attention is not subject to a fixed four-object capacity limit as Cowan suggests. Rather, performance in attention tasks as well as STM may be best accounted for in terms of decay and interference.

Cowan's experimental techniques cannot constrain subject's recall of presented information to distinct independent chunks in short-term memory (STM). The encoding of associations in long-term memory contaminates recall of pure STM capacity. Even in task environments where the functional independence of chunks is convincingly demonstrated, individuals can increase the storage of independent chunks with deliberate practice – well above the magical number four.

Different hypotheses about the mechanisms underlying working memory lead to different predictions about working memory capacity when information is distributed across the two hemispheres. We present preliminary data suggesting that memory scanning time (a parameter often associated with working memory capacity) varies depending on how information is subdivided across hemispheres. The data are consistent with a distributed model of working memory.

A temporal account of the mental capacities for processing information may not be relevant in a context where the goal is to search for storage capacity expressed in chunks. However, if mental capacity and information processing is the question, the time issue can be rehabilitated. A very different temporal viewpoint on capacity limit is proposed in this commentary.

Cowan's review shows that a short-term memory limit of four items is consistent with a wide range of phenomena in the field. However, he does not explain that limit, whereas an existing theory does offer an explanation for capacity limitations. Furthermore, processing capacity limits cannot be reduced to storage limits as Cowan claims.

Future work is needed to establish that pure short-term memory is a coherent individual difference attribute that is separable from traditional compound short-term memory measures. Psychometric support for latent pure short-term memory capacity will provide an important starting point for future fine-grained analyses of the intrinsic factors that influence individual differences in math skills.

A physiological model for short-term memory (STM) based on dual theta (5–10 Hz) and gamma (20–60 Hz) oscillation was proposed by Lisman and Idiart (1995). In this model a memory is represented by groups of neurons that fire in the same gamma cycle. According to this model, capacity is determined by the number of gamma cycles that occur within the slower theta cycle. We will discuss here the implications of recent reports on theta oscillations recorded in humans performing the Sternberg task. Assuming that the oscillatory memory models are correct, these findings can help determine STM capacity.

Cowan's concept of a pure short-term memory (STM) capacity limit is equivalent to that of memory subitizing. However, a robust phenomenon well known in the Sternberg paradigm, that is, the linear increase of RT as a function of memory set size is not consistent with this concept. Cowan's STM capacity theory will remain incomplete until it can account for this phenomenon.

One of our recent studies has revealed that a numerically trained chimpanzee can memorize a correct sequence of five numbers shown on a monitor. Comparative investigations with humans show very similar patterns of errors in the two species, suggesting humans and chimpanzee share homologous memory processes. Whether or not 5 is a pure capacity limit for the chimpanzee remains an empirical question.

Computational models of learning provide an alternative technique for identifying the number and type of chunks used by a subject in a specific task. Results from applying CHREST to chess expertise support the theoretical framework of Cowan and a limit in visual short-term memory capacity of 3–4 looms. An application to learning from diagrams illustrates different identifiable forms of chunk.

Measures of retrieval speed for recently presented events show a sharp dichotomy between representations in focal attention and representations that are recently processed but no longer attended. When information is presented over time, retrieval measures show that focal attention and rapid privileged access is limited to the most recently processed unit or chunk, not the last 3–5 chunks that Cowan estimates from various recall procedures.

Cowan postulates that the capacity of short-term memory is limited to the number of items to which attention can be simultaneously directed. Unfortunately, he endows attention with unexplained properties, such as being able to locate the most recent inputs to short-term memory, so his theory does little more than restate the data.

Using explicit memory measures, Cowan predicts a new circumstance in which the central capacity limit of 4 chunks should obtain. Supporting results for such an experiment, using continuous old-new recognition, are described. With implicit memory measures, Cowan assumes that short-term repetition priming reflects the central capacity limit. I argue that this phenomenon instead reflects limits within individual perceptual processing modules.

I compare the concepts of “activation” and “storage” as foundations of short-term memory, and suggest that an attention-based view of STM does not need to posit specialized short-term stores. In particular, no compelling evidence supports the hypothesis of time-limited stores. Identifying sources of activation, examining the role of activated procedural knowledge, and studying working memory development are central issues in modelling capacity-limited focal attention.

Partial matching theory, which maintains that some memory representations of target items in immediate memory are overwritten by others, can predict both a “theoretical” and an “actual” maximum memory span provided no chunking takes place during presentation. The latter is around 4 ± 2 items, the exact number being determined by the degree of similarity between the memory representations of two immediately successive target items.

Memory and forgetting are inextricably intertwined. Any account of short-term memory (STM) should address the following question: If three, four, or five chunks are being held in STM, what happens after attention is diverted?

Cowan assumes that chunk-based capacity limits are synonymous with the essence of a “specialized STM mechanism.” In a single experiment, we measured the capacity, or span, of long-term memory and found that it, too, corresponds roughly to the magical number 4. The results imply that a chunk-based capacity limit is not a signature characteristic of remembering over the short-term.

The boundaries, the influences on, and consequences of a short-term memory (STM) capacity of 4 leads us to consider global versus local processing. We argue that in schizophrenia cognitive problems can lie partly in pre-conscious automatic selective attention and partly with the speed of processing in later controlled processes (including compound STM). The influence of automatic attentional mechanisms may be under-estimated in normal psychology and explain the loss of the magic 4 in schizophrenia.

Cowan fails to obtain a magical number of 7 because his analysis is faulty. This is revealed by an alternative analysis of Cowan's own tasks. The analysis assumes a number 7 for adults, and neoPiagetian mental- capacity values for children. Data patterns and proportions of success (reported in Cowan's Figs. 2 and 3) are thus quantitatively explained in detail for the first time.