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.

nthesis of these findings, the tension between the discrete and the continuous, which has been central to the historical development of mathematical thought, is rooted in the non-verbal foundations of numerical thinking, which, it is argued, are common to humans and non-verbal animals. In this view, the non-verbal representatives of number are mental magnitudes (real numbers) with scalar variability. Scalar variability means that the signals encoding these magnitudes are "noisy;" they vary from trial to trial, with the width of the signal distribution increasing in proportion to (scaled to) its mean. In short, the greater the magnitude, the noisier its representation. These noisy mental magnitudes are arithmetically processed--added, subtracted, multiplied, divided and ordered. Recognition of the importance of arithmetically processed mental magnitudes in the non-verbal representation of number has emerged from a convergence of results from human and animal studies. This is comparative

Abstract not found

Abstract not found

In two experiments, a manual search task explored 12- to 14-month-old infants' representations of small sets of objects. In this paradigm, patterns of searching revealed the number of objects infants represented as hidden in an opaque box. In Experiment 1, we obtained the set-size signature of object-file representations: infants succeeded at representing precisely 1, precisely 2, and precisely 3 objects in the box, but failed at representing 4 (or even that 4 is greater than 2). In Experiment 2, we showed that infants' expectations about the contents of the box were based on number of individual objects, and not on a continuous property such as total object volume. These findings support the hypothesis that infants maintained representations of individuals, that object-files were the underlying means of representing these individuals, and that object-file models can be compared via one-to-one correspondence to establish numerical equivalence.

Dehaene (this volume) articulates a naturalistic approach to the cognitive foundations of mathematics. Further, he argues that the `number line' (analog magnitude) system of representation is the evolutionary and ontogenetic foundation of numerical concepts. Here I endorse Dehaene's naturalistic stance and also his characterization of analog magnitude number representations. Although analog magnitude representations are part of the evolutionary foundations of numerical concepts, I argue that they are unlikely to be part of the ontogenetic foundations of the capacity to represent natural number. Rather, the developmental source of explicit integer list representations of number are more likely to be systems such as the object--file representations that articulate mid--level object based attention, systems that build parallel representations of small sets of individuals.

Although much evidenceindicates that younginfants perceive unitaryobjects by analyzingpatterns of motion,infants #abilities to perceive object unity by analyzing Geslyz properties and by integratingdisegra views of an object over time are indispute.Toaddres thes controvers--6z fourexperiments invesments adults # and infants perception of the unity of a center-occluded, moving rod withmis)6)--(z viss) edges Both alignment information and depth information a#ectedadults # perception of object unity inszU)41 ways andinfants perceived object unity by integrating information about objectfeatures over time. However,infants perceived a moving,misg,z(6U( three-dimensH(4/ objectas indeterminate inits connectednesz whereas adults perceived itas connected behind the occluder.Thes findings indicate that thee#ectivenes of common motion insU:6U4zH( unifiedsifiedz) acros an occluderis reduced bymis())zH((1 ofedges Alignment information enhances perception of object unity either byszU4(( directlyas information for unity or by optimizing the detectability of motion-carried information for unity. In addition, younginfants are able to retain information about edge orientation over serz intervals in determining connectednes via aproces ofsU/1/6zH--UU)z integration.

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