Number sense " is a short-hand for our ability to quickly understand, approximate, and manipulate numerical quantities. My hypothesis is that number sense rests on cerebral circuits that have evolved specifically for the purpose of representing basic arithmetic knowledge. Four lines of evidence suggesting that number sense constitutes a domain-specific, biologically-determined ability are reviewed: the presence of evolutionary precursors of arithmetic in animals; the early emergence of arithmetic competence in infants independently of other abilities, including language; the existence of a homology between the animal, infant, and human adult abilities for number processing ; and the existence of a dedicated cerebral substrate. In adults of all cultures, lesions to the inferior parietal region can specifically impair number sense while leaving the knowledge of other cognitive domains intact. Furthermore, this region is demonstrably activated during number processing. I postulate that higher-level cultural developments in arithmetic emerge through the establishment of linkages between this core analogical representation (the " number line ") and other verbal and visual representations of number notations. The neural and cognitive organization of those representations can explain why some mathematical concepts are intuitive, while others are so difficult to grasp. Thus, the ultimate foundations of mathematics rests on core representations that have been internalized in our brains through evolution.

Did evolution endow the human brain with a predisposition to represent and acquire knowledge about numbers? Although the parietal lobe...

We measured cerebral activation with functional magnetic resonance imaging at 3 Tesla while eight healthy volunteers performed various number processing tasks known to be dissociable in brain-lesioned patients: naming, comparing, multiplying, or subtracting single digits. The results revealed the activation of a circuit comprising bilateral intraparietal, prefrontal, and anterior cingulate components. The extension and lateralization of this circuit was modulated by task demands. The intraparietal and prefrontal activation was more important in the right hemisphere during the comparison task and in the left hemisphere during the multiplication task and was intensely bilateral during the subtraction task. Thus, partially distinct cerebral circuits with the dorsal parietal pathway underlie distinct arithmetic operations.

Four experiments investigated infants' sensitivity to large, approximate numerosities in auditory sequences. Prior studies provided evidence that 6-month-old infants discriminate large numerosities that differ by a ratio of 2.0, but not 1.5, when presented with arrays of visual forms in which many continuous variables are controlled. The present studies used a head-turn preference procedure to test for infants' numerosity discrimination with auditory sequences designed to control for element duration, sequence duration, interelement interval, and amount of acoustic energy. Six-month-old infants discriminated 16 from 8 sounds but failed to discriminate 12 from 8 sounds, providing evidence that the same 2.0 ratio limits numerosity discrimination in auditory-temporal sequences and visual-spatial arrays. Nine-month-old infants, in contrast, successfully discriminated 12 from 8 sounds, but not 10 from 8 sounds, providing evidence that numerosity discrimination increases in precision over development, prior to the emergence of language or symbolic counting.

INTRODUCTION The goal of the present work is to examine whether the semantic representations of numbers and body parts are associated with partially distinct cortical territories. Clinical and cognitive neuropsychology studies associate semantic deficits in both domains to lesions coarsely localized to the left parietal lobe (McCarthy and Warrington, 1990). Furthermore, patients with left inferior parietal lesions often exhibit simultaneous deficits for numbers and body parts (Benton, 1992; Gerstmann, 1940). Such an association of neuropsychological deficits is however notoriously ambiguous, and has been the subject of much debate. It might suggest that there is a shared substrate for numbers and body parts in the left parietal region, perhaps based on a common functional system for spatial representation and manipulation (Gerstmann, 1940) or on the crucial role that finger counting plays in numerical development (Butterworth, 1999). However, it might also reflect the existence of dis

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Neuropsychological studies have revealed different subtypes of...

Both animals and humans represent and compare numerical quantities, but only humans have evolved multi-digit place-value number systems. This article develops a Spatial Number Network, or SpaN, model to explain how these shared numerical capabilities are computed using a spatial representation of number quantities in the Where cortical processing stream, notably the inferior parietal cortex. Multi-digit numerical representations that obey a place-value principle are proposed to arise through learned interactions between categorical language representations in the What cortical processing stream and the Where spatial representation. Learned semantic categories that symbolize separate digits, as well as place markers like `ty,' `hundred,' and `thousand,' are associated through learning with the corresponding spatial locations of the Where representation. Such What-to-Where auditory-to-visual learning generates place-value numbers as an emergent property, and may be compared with other examples of multi-modal cross-modality learning, including synesthesia. The model quantitatively simulates error rates in quantification and numerical comparison tasks, and reaction times for number priming and numerical assessment and comparison tasks. In the Where cortical process, transient responses to inputs are integrated before they activate an ordered spatial map that selectively responds to the number of events in a sequence and exhibits Weber law properties. Numerical comparison arises from activity pattern changes across the spatial map that define a `directional comparison wave.' Variants of these model mechanisms have elsewhere been used to explain data about other Where stream phenomena, such as motion perception, spatial attention, and target tracking. The model is compared wi...

this report, we applied this knowledge to the surgical resection of a glioma invading the left AG, by performing under local anaesthesia an intraoperative electrostimulation mapping of the cortical areas involved in calculation processes. Our goals were first to avoid permanent postoperative calculation deficit, and to study the involvement of different left parietal regions in multiplication versus subtraction, two operations that can be doubly dissociated after parietal lesions. On the basis of these findings, the anatomo-functional organisation of the AG, its integration in calculation networks, and its interaction with language and working memory functions are discussed

We report the case of a patient suffering from a severe neologistic jargon sparing number words. Neologisms resulted from pervasive phoneme substitutions with frequent preservation of the overall syllabic structure (e.g. /revolver / ® /reveltil/). Word and nonword reading, as well as picture naming, were equally affected. No significant influence of frequency, imageability, and grammatical class was found. In striking contrast with this severe speech impairment, the patient made virtually no phonological errors when reading aloud arabic or spelled-out numerals, but made frequent word selection errors (e.g. 250 ® “four hundred and sixty”). This observation indicates that during speech planning, different categories of words are processed by separable brain systems down to the level of phoneme selection, a more peripheral level than was previously assumed. Number words may be singled out during phonological processing either because they constitute a particular semantic category, or because they benefit from special brain mechanisms devoted to the production of “automatic speech”, or because they are the elementary building blocks of speech during the production of complex numerals.