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.

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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...

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Numeracy is regarded as an emergent property of the human brain, suggesting that neural network based simulations may provide some insight into the “cerebral substrate” used in operations related to numeracy. Two operations, subitization – the so-called phenomenon of the discrimination of visual number – and counting – a recurrent operation – have been studied within a multi-net framework. A multi-net architecture comprising unsupervised networks has been developed which successfully simulates aspects of subitization, especially when compared to similar work using supervised learning algorithms. Another multi-net architecture comprising unsupervised networks, and a recurrent backpropagation network, appears to learn numerosity and successfully simulates errors children make when they are learning to count. The systems for subitizing and counting were incorporated into a gated multi-net system for simulating the dual existence of both subitization and counting. Multi-net architectures provide a good basis for studying the emergent properties of an intelligent system in that a single monolithic network may be used to fit almost any data available.

this article, we test the hypothesis that at least part of the abnormal activation and symptom association of the cingulate gyrus observed in patients with schizophrenia may, in fact, be attributed to disrupted white matter connections of this region with other limbic structures. To date, white matter findings in schizophrenia have been equivocal. Most of the studies investigating volumetric differences between schizophrenia and control subjects have detected gray but not white matter volume reductions (see review by Shenton et al 2001). Two recent studies, however, both report white matter volume deficits, within the temporal and frontal regions on the left side (Sigmudsson et al 2001), and within the frontal lobes bilaterally (Paillere-Martinot et al 2001). Lack of compelling evidence for white matter abnormalities in schizophrenia is not surprising, given that white matter appears fairly uniform and homogeneous on conventional MR scans, where the orientation, density, and asymmetry of the fiber tracts cannot be visualized or quantified

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ABSTRACT—Subitizing is the rapid and accurate enumeration of small sets (up to 3–4 items). Although subitizing has been studied extensively since its first description about 100 years ago, its underlying mechanisms remain debated. One hypothesis proposes that subitizing results from numerical estimation mechanisms that, according to Weber’s law, operate with high precision for small numbers. Alternatively, subitizing might rely on a distinct process dedicated to small numerosities. In this study, we tested the hypothesis that there is a shared estimation system for small and large quantities in human adults, using a masked forced-choice paradigm in which participants named the numerosity of displays taken from sets matched for discrimination difficulty; one set ranged from 1 through 8 items, and the other ranged from 10 through 80 items.

Neurologists ’ knowledge of number processing impairments is often limited to the notion that acalculia is part of Gerstmann’s syndrome (Benton, 1992; Gerstmann, 1940). It may extend to the classical typology proposed by Hécaen, who distinguished aphasic, spatial, and anarithmetic acalculia (Hécaen et al., 1961). Actually, modern research on acalculia (a term