One, two, three, many – Subitizing in active touch

Abstract

‘Subitizing’ refers to rapid and accurate judgement of small numbers of items, while response times and error rates increase rapidly for larger set-sizes. Most enumeration studies have been done in vision. Enumeration studies in touch have mostly involved ‘passive touch’, i.e. touch without active exploration. In daily life a much more common situation is that of ‘active touch’, e.g. when we count the number of coins in our pocket. To investigate numerosity judgement in active touch, we let subjects haptically explore varying numbers of spheres. Our results show that enumeration for up to 3 items is more efficient than for larger numbers of items. We also show that enumeration in this regime was not performed through estimation. Furthermore, it is shown that numerosity information was accessed directly and not through mass or volume cues. Not only do our results show that a haptic version of subitizing exists in active touch, they also suggest similar underlying enumeration mechanisms across different modalities.

Introduction

From visual studies it is known that people judge the numbers of items on a display rapidly, accurately and almost effortlessly up to a certain number. This phenomenon is known as subitizing (Kaufman, Lord, Reese, & Volkmann, 1949). With increasing set-sizes, enumeration becomes error prone and response times (RT) increase markedly. Consequently, subitizing is characterised by a sharp upward bend in the slope of the RTs and error rates as a function of set-size. The location of the bend depends on the stimulus, but in vision it is generally at about four items (e.g. Atkinson et al., 1976, Mandler and Shebo, 1982). A total of three processes for numerosity judgement can be distinguished. First, for small numerosities there is the efficient and accurate process labelled ‘subitizing’ as described above. Secondly, for larger numerosities a more time-consuming and error-prone process is used which is referred to as ‘counting’. Finally, there is the efficient process of ‘estimation’ for approximate numerosity judgement. The term ‘enumeration’ refers to numerosity judgement in general through any of these processes.

Outside the visual modality, numerosity judgement experiments in audition have also reported evidence for subitizing (Camos and Tillmann, 2008, Ten Hoopen and Vos, 1979). In this case items are usually presented sequentially and not simultaneously as is often done in vision. There has been much debate on whether two separate mechanisms are involved for subitizing and counting. Recently several brain imaging studies have focussed on this question. Pasini and Tessari (2001) suggested left hemispherical specialisation for subitizing and right hemispherical specialisation for counting. A study by Piazza, Mechelli, Price, and Butterworth (2006) reported left hemispherical specialisation for approximate numerosity judgement in both vision and audition. If a similar or even a single mechanism underlies both visual and auditory numerosity judgement, it is likely that this mechanism also extends to the haptic modality.

In touch, enumeration studies have been mostly restricted to ‘passive touch’, i.e. touch without active exploration. One study in which subjects had to judge the number of fingers stimulated with pins reported subitizing (Riggs et al., 2006), but no subitizing was found in a study where subjects had to report how many vibrators were distributed over the body surface (Gallace, Tan, & Spence, 2006). This raises the question whether subitizing only occurs in touch when stimuli are presented to the separate fingers. In a follow-up study where vibrators were presented to the subjects’ fingers, Gallace, Tan, and Spence (2008) again reported no indication for subitizing. However, for both presentation to the separate fingers and presentation distributed over the body surface, error rates were extremely high (up to 90% ). These results show that stimulation of the separate fingers does not necessarily lead to subitizing, but it is also possible that vibrators are not a suitable stimulus for investigating tactile numerosity judgement. It is still not unlikely that stimulation of the separate fingers represents a special case in haptic numerosity judgement for which subitizing can occur. Recent studies have shown that there are interactions between spatial and number representations in the parietal cortex (see Hubbard, Piazza, Pinel, & Dehaene (2005) for an overview). It has been shown that areas involved in number processing partially overlap with those involved in finger movements (Pesenti, Thioux, Seron, & De Volder, 2000). Furthermore, finger motor circuits are activated during cognitive tasks such as enumeration and can facilitate cognitive processing (Andres et al., 2007, Carlson et al., 2007). Since motor circuits are activated during number processing, an even more important question than that of the importance of stimulating separate fingers is whether subitizing also occurs in active touch.

In daily life, we usually explore objects through active touch. Allowing to actively explore enables the subjects to adopt the most efficient exploration strategy (Lederman & Klatzky, 1987). When exploratory movements are restricted, haptic information processing can be impaired (e.g. Lederman & Klatzky, 2004). Therefore, experiments using active or passive touch do not necessarily yield similar results. We investigated whether subitizing occurs in active touch by letting subjects enumerate varying numbers of spheres grasped in the hand. Response time and error rates were then recorded as a function of the numbers of items. First a numerosity judgement experiment was carried out to investigate whether two regimes exist in this type of numerosity judgement task. A second experiment was performed to investigate the role of relative discriminability between the presented numbers of items. In the last experiment the role of volume and mass cues was investigated. Finally, we introduce a model to predict response times for numerosity estimation and determine whether this model can describe the data from the second and third experiments.