Number in the human subcortex

Abstract

Certain numerical abilities appear to be relatively ubiquitous in the animal kingdom, including the ability to recognize and differen-tiate relative quantities. This skill is present in human adults and children, as well as in nonhuman primates and, perhaps surpris-ingly, is also demonstrated by lower species such as mosquitofish and spiders, despite the absence of cortical computation available to primates. This ubiquity of numerical competence suggests that representations that connect to numerical tasks are likely sub-served by evolutionarily conserved regions of the nervous system. Here, we test the hypothesis that the evaluation of relative numerical quantities is subserved by lower-order brain structures in humans. Using a monocular/binocular paradigm, across four experiments, we show that the discrimination of displays, consisting of both large (5–80) and small (1–4) numbers of dots, is facilitated in the monocular, subcortical portions of the visual system. This is only the case, however, when observers evaluate larger ratios of 3:1 or 4:1, but not smaller ratios, closer to 1:1. This profile of competence matches closely the skill with which newborn infants and other species can discriminate numerical quantity. These findings suggest conservation of ontogenetically and phylogenetically lower-order systems in adults' numerical abilities. The involvement of subcortical structures in representing numerical quantities provokes a reconsid-eration of current theories of the neural basis of numerical cogni-tion, inasmuch as it bolsters the cross-species continuity of the biological system for numerical abilities. subcortex | numerical cognition | vision | development | phylogeny H umans exhibit remarkable mathematical abilities. Many of today's students readily master difficult mathematical con-structs, the knowledge of which is based on the very early de-veloping appreciation of numerosity. In the adult human brain, the parietal cortex plays a central role in the representation and processing of number. More specifically, in many neuroimaging studies, bilateral intraparietal sulcus has been implicated in nu-merical tasks such as exact calculation and arithmetic problem solving (1–6), and additional evidence for the necessary role of parietal cortex comes from patients who exhibit selective num-ber-processing deficits following a parietal lesion (7, 8). A finer division between the hemispheres suggests that the left and right parietal cortices themselves exhibit relative specialization; the right parietal cortex appears to be engaged to a greater extent in more intuitive numerical approximation (2, 9, 10), whereas the left parietal cortex is engaged to a great degree in more precise arithmetic or symbolic mathematical tasks (1, 3, 11). Further-more, the connectivity between the two hemispheres is corre-lated with performance on nonsymbolic arithmetic tasks (12). Thus, areas of the parietal cortex appear to play a critical role in mathematical abilities. The cortex, however, is far from mature at birth and follows a developmental trajectory that coincides with developing number skills in growing children (13). The ontogenetic emergence of numerical skills follows a rea-sonably well-established trajectory with an initial ability to ap-proximate numerical quantity nonverbally, followed over the course of early childhood, with the development of increasingly precise representations of numerical values, including a symbolic number system that allows children to conceive of numerical information as Arabic numerals or number words (14–16). The early ability to distinguish two nonsymbolic quantities, for ex-ample, in the context of a display of varying numbers of dots potentially forms the foundation for developing math abilities akin to the " number sense " (17). This suggests that our analog number system is best described as one that tracks relative quantities, and that it can be bootstrapped during schooling when more discrete mathematical abilities are acquired (but see ref. 18). In the earlier stages of development, the number system is thought to operate with rather coarse representations, and differentiation of nonsymbolic quantities is largely dependent on ratios (19). As development proceeds, however, the system becomes more finely tuned to smaller differences in quantities. Consistent with this, infants as young as 48 h are able to differ-entiate ratios of 3:1 but not 2:1 (20), and, as they age, children show increasingly precise abilities: at 6 mo, they can distinguish ratios of 2:1, and by 9 mo, ratios of 3:2 (21, 22). They eventually reach competencies for ratios 4:3 by 3 y, 6:5 by 6 y, and 8:7 and more difficult ratios by adulthood (23–26). Furthermore, the ability to discriminate nonsymbolic number in childhood is pre-dictive of later numerical discrimination abilities (27, 28). There has been long-standing debate regarding the origins of these numerical abilities. Some have suggested that the endow-ment of a number system is innate and present from birth (29). Evidence to support this claim comes from studies showing that young children (22, 30–32) and adults in cultures without any training in mathematics (33–35) perform many numerical tasks with ratios of sufficiently large numbers independent of con-trolled nonnumeric properties such as size or density. Similar abilities have been noted in nonhuman primates (36, 37), and the presence of age-and species-invariant number ability suggests