Discontinuity in the enumeration of sequentially presented auditory and visual stimuli

Abstract

The seeking of discontinuity in enumeration was recently renewed because Cowan [Cowan, N. (2001). The magical number 4 in short-term memory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences, 24, 87–185; Cowan, N. (2005). Working memory capacity. Hove: Psychology Press] suggested that it allows evaluating the limit of the focus of attention, currently estimated at four items. A strong argument in favour of a general constraint of the cognitive system is that similar discontinuities should be observed in modalities different from the classic simultaneous presentation of visual objects. Recently, data were provided on tactile stimuli, but the authors diverged in their conclusion about the existence of such discontinuity [Gallace, A., Tan, H. Z., & Spence, C. (2006). Numerosity judgments for tactile stimuli distributed over the body surface. Perception, 35(2), 247–266; Riggs, K. J., Ferrand, L., Lancelin, D., Fryziel, L., Dumur, G., & Simpson, A. (2006). Subitizing in tactile perception. Psychological Science, 17(4), 271–272]. Following a similar rationale, our study aimed at evaluating discontinuity in the enumeration of auditory and visual stimuli presented sequentially. The clear and similar discontinuity observed in error rates, response times and given responses for both modalities favours the general capacity limit view, but also questions the size of this capacity, because the discontinuity occurred here at size 2. However, the masking of stimuli in sensory memory could not be entirely discarded.

Introduction

Since more than a century, studies on enumeration of visual objects have shown a discontinuity between fast and accurate performance for small collections, whereas larger arrays are slowly and erroneously quantified (Jevons, 1871). In the latter, the serial counting of objects lead to a linear increase of error rates and response times (RTs) with size, whereas in the former (referred to as the subitizing range), no such increase is observed and the slope of RTs being very small (around 40 ms/item; Kaufman et al., 1949, Trick and Pylyshyn, 1994).

Recently, Cowan, 2001, Cowan, 2005 suggested that the capacity limit of the focus of attention could be estimated by examining performance discontinuities such as in enumeration. The lack of increase of error rates and RTs with the number of objects would reveal the number of objects that can be conjointly held within the focus of attention. When this number of objects overcomes the capacity limit, the focus of attention needs to be moved sequentially among the objects, which induces an increase of error rates and RTs. This theoretical view predicts similar discontinuity patterns in modalities other than the simultaneously presented visual stimuli used in previous enumeration studies (Mandler and Shebo, 1982, Trick and Pylyshyn, 1994). Recently, two papers evaluated enumeration in tactile perception (Gallace et al., 2006, Riggs et al., 2006), but they led to opposite conclusions about the existence of a discontinuity in this modality. The former observed a linear relationship between the number of tactile stimulations and both mean RTs and error rates, whereas the latter showed a discontinuity between 1–3 and 4–6 stimulations on accuracy and RTs. It might be that the rather uncommon use of tactile information to evaluate numerosity obscured the results. Thus, our study tested the auditory modality, in which numerosity processing is used more frequently (e.g., the number of sounds of bells indicates the time; Garner, 1951, John, 1972, Massaro, 1976).

Numerosity processing for auditory material can concern both simultaneous and sequential presentations of sounds. However, simultaneous processing of sounds requires processes of fusion and stream segregation (Bregman, 1990), and these processes might veil the perceived number of separated sources. To avoid acoustical ambiguity, we adapted a sequential stimulus presentation in the auditory modality and, for sake of comparison, in the visual modality. However, to prevent the sequential processing of the stimuli, i.e., their counting, they were presented rapidly (Stimulus Onset Asynchrony = 80 ms); the enumeration of the French numberline taking around 160 ms per item (Camos, Barrouillet, & Fayol, 2001). Albeit this sequential presentation, the stimuli have to be simultaneously maintained in the focus of attention to evaluate their numerosity. As the capacity limit of the focus of attention is not exceeded, the representations of the stimuli would not suffer from a time decay of their activation and could then be enumerated. In our present study, the auditory stimuli were pure tones at different pitch heights without tonal relationships and the visual stimuli were colour dots presented sequentially at the centre of the screen. These material and presentation forms excluded any pattern recognition, a mechanism that is often mentioned to account for the performance observed in small size collections (Mandler and Shebo, 1982, Peterson and Simon, 2000). Our study aimed at seeking for the discontinuity in the enumeration of auditory and visual modalities presented sequentially. The hypothesis of a domain-general limit of processing predicts a similar discontinuity in performance for both modalities. However, if enumeration relies even partly on some modality-specific processes, its limit should differ between the two modalities.