"Comment les nombres se répartissent dans l'espace ? Une intuition originelle logarithmique"

Des branches entières des mathématiques sont fondées sur des liens posés entre les nombres et l'espace : mesure de longueurs, définition de repères et de coordonnées, projection des nombres complexes sur le plan, etc. Loin d'être fortuits, ces liens entre les nombres et l'espace reflètent une intuition fondamentale logaithmique, façonnée au cours des millénaires par la sélection naturelle, et qui aurait servi de guide et d'inspiration aux mathématiciens

Geometric categories in cognition.

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Cartographie successive des entreprises métallurgiques dans les Pyrénées nord-catalanes : support préliminaire à l'étude éco-historique des forêts charbonnées

The historic approach of the mountain environment, and this of the dynamic evolution of theforest settlements, which are characterized by the charcoal metallurgy, is included in a combined research project. The successive cartography of the geographic implantation of the iron and steel industry, constitutes a preliminary source document necessary for the study of paleosettlements in the Catalan Pyrénées. The forest, long considered as an inexhaustible energy source, has been in the heart of the protoindustrial economy. Victim of the "charcoal-burners axe", it still shows the scars of a centuries old exploitation, the marks of which are to befound everywhere in the landscape. Through this study, the spreading of the iron and steel industry, arises quite clearly, both in space and in time, and its repercussions of the environement also appear. It shows a coherent image of the " iron-landscapes ", integral part of the Catalan patrimony.L'approche historique de l'environnement montagnard et de la dynamique des peuplements forestiers marqués par la métallurgie au bois s'inscrit dans une démarche interdisciplinaire. La cartographie successive de l'implantation géographique de la sidérurgie est un support préliminaire indispensable à l'étude des paléo-peuplements dans les Pyrénées-catalanes. La forêt, longtemps considérée comme source d'énergie inépuisable, a été au cœur de l'économie proto-industrielle. Victime de la "hache du charbonnier", elle porte aujourd'hui encore les cicatrices d'une exploitation multiséculaire dont les empreintes se retrouvent partout dans le paysage. A travers cette étude apparaissent nettement l'extension de la pression métallurgique, tant dans l'espace que dans le temps, et ses répercussions sur l'environnement. Elle offre une image cohérente " des paysages du fer", partie intégrante du patrimoine catalan.Izard Véronique. Cartographie successive des entreprises métallurgiques dans les Pyrénées nord-catalanes ; support préliminaire à l'étude éco-historique des forêts charbonnées. In: Archéologie du Midi médiéval. Tome 12, 1994. pp. 115-129

Exact and Approximate Arithmetic in an Amazonian Indigene Group

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Reading Angles in Maps

Preschool children can navigate by simple geometric maps of the environment, but the nature of the geometric relations they use in map reading remains unclear. Here, children were tested specifically on their sensitivity to angle. Forty-eight children (age 47:15–53:30 months) were presented with fragments of geometric maps, in which angle sections appeared without any relevant length or distance information. Children were able to read these map fragments and compare two-dimensional to three-dimensional angles. However, this ability appeared both variable and fragile among the youngest children of the sample. These findings suggest that 4-year-old children begin to form an abstract concept of angle that applies both to two-dimsional and threedimensional displays and that serves to interpret novel spatial symbols. Geometry defines abstract concepts that apply to various types of spatial entities. For example, we may find angles in two-dimensional line drawings, in the contours of three-dimensional objects, in the arrangement of the walls surrounding us, or even in the projections of star patterns in the sky. Similarly, in geometry the length of an object and the distance between two landmarks or walls are captured by the same abstract concept of metric distance. Comparing shapes of different entities is challenging, because one must abstract away from the particular medium in which these shapes appear. In young children, this ability might take time to develop: For example, 1-year-old toddlers still fail to recognize the matching shapes of blocks and holes or flat patterns (Shutts, € Ornkloo, von Hofsten, Keen, & Spelke, 2009), and even in adults, the presence of convex or concave segments induce different descriptions of interlocking shapes (Cohen & Singh, 2007). In an effort to understand children’s developing sensitivity to abstract geometry, here we focus on angle, a central concept in Euclidean geometry. We ask whether preschool children possess an abstract representation of angle that applies The authors thank Danielle Hinchey and Christine Size for their help with recruiting participants and constructing stimuli

Archéologie de la forêt charbonnée : questions et méthodes, illustrées par I'exemple du site de Lercoul (Ariège)

International audienceL'archéologie des forets charbonnées que nous pratiquons a pour objectif de restituer la dynamique des peuplements sur le long terme. La question principale concerne la représenta­tivité des charbonnières étudiées, notamment en fonction des pratiques des charbonniers

Are numbers special? An overview of chronometric, neuroimaging, developmental and comparative studies of magnitude representation

There is a current debate whether the human brain possesses a shared representation for various types of magnitude such as numerical quantities, physical size, or loudness. Here, we critically review evidence from chronometric, neuroimaging, developmental and comparative fields, and supplement it with a meta-analysis of the neuroimaging data. Together, based on such an integrative overview, we discuss limitations inherent in each approach, and the possibility whether shared, or distinct magnitude representation, or both representations exist

"Exact Equality and Successor Function : Two Keys Concepts on the Path towards Understanding Exact Numbers"

International audienceHuman possess two nonverbal systems of representing numbers : the first represents numbers in an approximate fashion, and the second one conveys information about small numbers. Conception of exact large numbers has therefore been thought to arise from the manipulation of exact numerical symbols. We focuss on two fundamental properties of exact numbers as prerequesites to the concept of EXACT NUMBERS : The fact that all numbers can be generated by a successor function and the fact that equality between numbers can defined in an exact fashion

"Response to Nuñez": "Reading between the Number lines"

International audienceWe agree with Nuñez that the Mundurucu do not master the formal propreties of number lines and logarithms, but as the term "intuition" implies, they spontaneously experience a logarithmic mapping of number to space as natural and "feeling right.

"Examining Knowledge of Geometry : Response to Wulff and Delson"

http://www.sciencemag.org/cgi/content/summary/312/5778/1309a?maxtoshow=&HITS=10&hits=10&RESULTFORMAT=&fulltext=pica+pierre&searchid=1&FIRSTINDEX=0&resourcetype=HWCITInternational audienceLa connaissances noyau de la géométrie euclidienne est liée au raisonnement déductif et non à la reconnaissance de motifs perceptuel