Exact and approximate judgements of visual and auditory numerosity: An fMRI study

Abstract

Human adults can assess the number of objects in a set (numerosity) by approximate estimation or by exact counting. There is evidence suggesting that numerosity estimation depends on a dedicated mechanism that is a-modal and non-verbal. By contrast, counting requires the coordination between the pre-existing numerosity estimation abilities with language and one-to-one correspondence principles. In this paper we investigate with fMRI the neural correlates of numerosity estimation and counting in human adults, using both visual and auditory stimuli. Results show that attending to approximate numerosity correlates with increased activity of a right lateralized fronto-parietal cortical network, and that this activity is independent of the stimuli presentation's modality. Counting activates additional left prefrontal, parietal, and bilateral premotor areas, again independently from stimulus modality. These results dissociate two neuronal systems that underlie different numerosity judgements.

Introduction

The human understanding of numbers is rooted in our ability to make judgements about numerosity. Numerosity is an abstract property of a set, since it is independent of the sensory attributes of its members and of the physical parameters of the set, such as shape, luminance, density, duration or frequency, even if it often co-varies with these parameters. Despite its abstractness, the ability to make approximate judgements on numerosity (estimation) does not depend on learning a symbolic system, as it spontaneously emerges in pre-linguistic infants (Antell and Keating, 1983, Starkey and Cooper, 1980, Xu and Spelke, 2000), and is observable in non-human species (Brannon and Terrace, 2000, Church and Meck, 1984, Davis and Pérusse, 1988).¹ When a symbolic system – such as counting words – becomes available, exact numerosity judgements can extend to numerosities larger than those correctly estimated by infants and other species. It is held that counting develops initially by mapping the pre-verbal representations of numbers to a set of number words, according to certain rules (Gallistel and Gelman, 2000, Gelman and Gallistel, 1978). This mapping from numerosities to number words produces the symmetric mapping from number words to numerosities, which allows the meaning of words as symbols for numerosity to emerge (Butterworth, 1999, Gallistel and Gelman, 1992, Wynn, 1996, Wynn, 1998). Numerosity estimation and counting are therefore highly interdependent in the numerate adult and constitute the two most basic quantification processes that appear to ground all symbolic numerical thinking (however, see Simon, 1997, and Carey, 1998, for a different view on the development of counting). Nevertheless, while the neural correlates of symbolic numerical thinking such as calculation have been extensively explored, the functional neuroanatomy of quantification processes has seldom been previously investigated.

In this paper we present a functional imaging study that attempts to answer the following questions: which cerebral structures are involved in number estimation and which in counting? To what extent are these structures specific to certain physical attributes of stimuli such as the modality of presentation?

Models of the cognitive processes involved in comparative numerosity estimation are inspired by the scalar timing theory first proposed to account for time estimation (Gibbon and Church, 1981). These models hypothesize the existence of an internal numerosity-accumulator system (Dehaene and Changeux, 1993, Meck and Church, 1983), which transforms objects and/or events into “abstract” items to be accumulated, irrespective of modality (visual, auditory, motor), mode (simultaneous or sequential), and physical characteristics (shape, position in space, duration, etc). The outputs of the accumulator are magnitudes that represent numerosity. While these models are successful in predicting behavior, they do not provide information with respect to the implementation of these mechanisms in the human (or animal) brain. However, recent electrophysiological studies have considerably improved our understanding of the neural bases of number sense, demonstrating the existence of cells that show preferential responses to a given numerosity (number coding cells) located both in the fundus of the intraparietal sulcus and in the lateral pre-frontal cortex between inferior arcuate sulcus and the principal sulcus (Nieder et al., 2002, Sawamura et al., 2002, Thompson et al., 1970). In particular, Nieder and Miller (2004) showed that neurons in the intraparietal sulcus responded to and conveyed numerosity information earlier than prefrontal neurons, suggesting that numerosity information is primarily extracted in the posterior cortex and only successively transmitted to the frontal cortex.

In humans much more data are available on the neural basis of number cognition, and it points to a crucial role for the parietal regions. However, the majority of the studies have been concerned with mental arithmetic or other tasks that depend on interpreting conventional symbols for numbers (numerals or number words) (Dehaene et al., 2003 for a review), while investigations into numerosity estimation are very sparse. Initially, neuropsychological studies showed that impairments in numerosity estimation are more likely to occur after right than left hemisphere damage (Kimura, 1996, McFie et al., 1950). Later it was shown that the right parietal lobe was the only locus relevant for estimation performance (Warrington and James, 1967), since, out of a pool of subjects with lesions in the three lobes of the two hemispheres, only the group with lesions in the right parietal were impaired at numerosity estimation. Indeed, a right hemisphere superiority in quantity estimation was replicated using unilateral tachistoscopic presentation of stimuli to normal subjects (Kosslyn et al., 1989a, McGlone and Davidson, 1973, Young and Bion, 1979).

However, in all the aforementioned experiments stimuli consisted of simultaneous, very brief, visually presented items; no other modality (auditory, or motor) or mode (sequential) of presentation was tested. This prevents any conclusion being drawn that numerosity estimation is a modality independent process. Second, tasks involved the production of a number word. This could be problematic for investigations of non-verbal estimation because it is possible that subjects, having to generate an exact numerical result, may have used arithmetical strategies that depended on number symbols (such as counting by groups). In this sense, this procedure is not comparable with other studies in animals and infants in which no symbolic output is required, and where estimation is often tested by means of comparison between numerosities. Using fMRI, recently, two groups have independently demonstrated that certain regions in the intraparietal sulci of both hemispheres respond to approximate visual numerosity while subjects are simply passively exposed to arrays of stimuli (Ansari et al., 2006, Piazza et al., 2004, recently replicated by Cantlon et al., 2006). This suggests that both hemispheres possess approximate representations of numerosity. Even if these studies have the merit of not requiring the production of a number word, they do not directly investigate the cerebral correlates of explicit numerosity estimation, on which we are particularly interested here. Moreover, no other modality (auditory, or motor) or mode (sequential) of presentation was tested.

Cognitive models of counting (Gelman and Gallistel, 1978) propose that it relies on three crucial mechanisms: the individuation² of every single element of the set, the attribution of attentional “indexes” to already counted items to keep track of the previously explored spatial location and to avoid counting items twice (this only applies when items are simultaneously presented), and the use of articulatory and phonological codes in order to update the running total in the verbal short term storage (Logie and Baddeley, 1987).

Investigations of the neural implementation of this multi-stage attentional and linguistic process have shown a crucial role of both posterior parietal and prefrontal regions (Piazza et al., 2002, Piazza et al., 2003, Sathian et al., 1999). However, as in the case of estimation, most studies on counting used simultaneously presented visual items, and this prevents interpretation in terms of a modality independent mechanism.

In the present study, we used fMRI to investigate and directly compare brain responses to a numerosity estimation task, and to an exact counting task, using both visual and auditory stimuli. First, we wanted to segregate the functional structures involved in estimation and counting. While the counting task required an exact answer, we used a comparative estimation task (like the one used in infant or animal studies), in order to prevent subjects from counting and/or using arithmetical strategies. Moreover, we kept the stimuli constant across tasks in order to make sure that differences in cerebral activation were not due to differences in the sensory stimulation. The second goal was to investigate to what extent the brain structures involved in estimation and counting are specific to the modality of stimuli presentation, and therefore we used both visual and auditory stimuli.

Stimuli consisted of temporal sequences of alternating items (presented at a high rate of approximately 1 every 3 s) (see Fig. 1 and Experimental procedures). There were two different categories per modality: red and green lights for the visual presentation, and high and low tones for the auditory presentation. The numerosity estimation task consisted of deciding which category contained more items, and the counting task consisted of reporting the number of alternations between the two categories (e.g., the number of switches from a high tone to a low tone, and vice-versa). We also introduced a baseline perceptual task which consisted of deciding if the last item in the sequence was identical to the first one. This was included in order to control for attention to the whole stimulus sequence, holding some information in working memory for the whole stimulus sequence, and a final two-choice button-press response.