Why Do Diffusion Data not Fit the Logistic Model? A Note on Network Discreteness, Heterogeneity & Anisotropy

"The original publication is available at www.springerlink.com"Diffusion of innovations and knowledge is in most cases accounted for by the logistic model. Fieldwork research however constantly report that empirical data utterly deviate from this mathematical function. This chapter scrutinizes network forcing of diffusion process. The departure of empirical data from the logistic function is explained by social network discreteness, heterogeneity and anisotropy. New indices are proposed. Results are illustrated by empirical data from an original study of knowledge diffusion in the medieval academic network

As redes universitárias de difusão das ciências matemáticas como fator de desenvolvimento da perspectiva. Uma agenda de pesquisa para o historiador da perspectiva no Brasil

Neste capítulo, vou apresentar os resultados de um estudo recente, relativo à difusão da óptica nas universidades europeias dos séculos XIII e XIV. O assunto pode parecer fora dos temas discutidos neste evento – ou seja a pintura quadraturista colonial e o barroco dos séculos XVII e XVIII. No entanto, os resultados deste estudo são dependentes de um método geral que pode ser transferido para outras regiões e épocas. Em primeiro lugar, vou introduzir o tema da relação entre óptica e perspectiva. Em segundo lugar, vou explicar o método utilizado para estudar a mobilidade acadêmica dos professores na Idade Média. Enfim, vou discutir a possível aplicação deste método ao contexto brasileiro

Geometric and Arithmetical Methods in Early Medieval Perspective

International audienceThis paper examines the hypothesis that early perspective paintings were drawn arithmetically, without vanishing points. The best argument for this hypothesis is that the division of two parallel lines by straight lines intersecting each other at the vanishing point (geometrical method) is equivalent to the division of those parallel lines in proportional parts (arithmetical method). If arithmetical method had been used, then the vanishing points exhibited ex post should be purely fortuitous. But the lack of multiples and submultiples of measurement units, the absence of proportionality ratios, the length of the operating series, and the correspondence of vanishing points to visible loci of the picture offer sound objections for this hypothesis. The use of optics and geometrical method is more probative—though it does not mean that painters were using concepts of linear perspective, which would be an anachronism

Schema as an architectural design operator. The case of the transformation of the morphological model

Theme: Architecturolog

La perspective aérienne de Léonard de Vinci et ses origines dans l'optique d'Ibn al-Haytham (De aspectibus, III, 7)

International audienceThe concept of aerial perspective has been used for the first time by Leonardo da Vinci (1452-1519). This article studies its dependence on Ptolemy's Optica and overall on the optical tradition inaugurated by Ibn al-Haytham's Kitâb al-Manâzir (d. after 1040). This treatise, that was accessible through several Latin and Italian manuscripts, and was the source of many Medieval commentaries, offers a general theory of visual perception emancipated from the case of the moon illusion, in which physical and psychological factors are closely combined. Atmospheric extinction (not refraction, which it is sometimes confused with) affects the conjectured size of remote objects. This phenomenon is also the core source for a pictorial rendering of depth, that is based onto a principle different from the diminution of size.Le concept de perspective aérienne a été introduit par Léonard de Vinci (1452-1519). L'article étudie sa dépendance vis-à-vis de l'Optique de Ptolémée et surtout de la tradition optique inaugurée par le Kitâb al-manâzir d'Ibn al-Haytham (m. après 1040). Ce traité, accessible par plusieurs manuscrits latins et italien, qui a fait l'objet de nombreux commentaires médiévaux, offre une théorie générale de la perception visuelle émancipée du seul cas de l'illusion lunaire, dans laquelle les facteurs physiques et psychologiques sont étroitement associés. L'extinction atmosphérique (et non la réfraction, avec laquelle elle est parfois confondue) influence la perception de la taille des objets éloignés. Elle est aussi à l'origine d'une restitution picturale de la profondeur, fondée sur un principe autre que celui de la diminution des grandeurs

Le schème, opérateur de la conception architecturale, II : le cas de la conservation du modèle morphologique

This paper is a study of architectural design process. The explanation of an elementary change of state of the project is faced with two cases: (i) change of state transforms the morphological model, in which case schema operator is needed to describe the design operation (Raynaud, 1999); (ii) change of state does not involve such a transformation and just consists in a size adjustment. The present paper examines the second case onto several examples (Gio Ponti, Sebastiano Serlio, Villard de Honnecourt). It is shown that schema operator is also required to describe the design operation in its entirety. But, since scale is regarded as a design operator by architecturology, the connection between schema and scale must be clarified. The reasons leading to the characterization of scale and schema as design cooperators are reviewed. Keywords: architectural design process, operations, operators, schema, scale.Deux cas sont à distinguer pour expliquer le passage d’un état à un autre du projet architectural : (i) le changement d’état introduit une transformation du modèle morphologique, auquel cas il faut introduire l’opérateur schème pour décrire l’opération de conception (Raynaud, 1999) ; (ii) le changement d’état consiste seulement en un ajustement dimensionnel. L’article étudie ce dernier cas sur plusieurs projets (Gio Ponti, Sebastiano Serlio, Villard de Honnecourt) et montre qu’il faut encore recourir à l’opérateur schème pour décrire l’opération de conception. L’architecturologie considérant l’échelle comme un opérateur de conception, la relation entre schème et échelle doit être clarifiée. L’article examine les raisons conduisant à qualifier l’échelle et le schème comme co-opérateurs de la conception architecturale. Mots-clefs: conception architecturale, opérations, opérateurs, schème, échelle

Le schème, opérateur de la conception architecturale, II : le cas de la conservation du modèle morphologique

This paper is a study of architectural design process. The explanation of an elementary change of state of the project is faced with two cases: (i) change of state transforms the morphological model, in which case schema operator is needed to describe the design operation (Raynaud, 1999); (ii) change of state does not involve such a transformation and just consists in a size adjustment. The present paper examines the second case onto several examples (Gio Ponti, Sebastiano Serlio, Villard de Honnecourt). It is shown that schema operator is also required to describe the design operation in its entirety. But, since scale is regarded as a design operator by architecturology, the connection between schema and scale must be clarified. The reasons leading to the characterization of scale and schema as design cooperators are reviewed. Keywords: architectural design process, operations, operators, schema, scale.Deux cas sont à distinguer pour expliquer le passage d’un état à un autre du projet architectural : (i) le changement d’état introduit une transformation du modèle morphologique, auquel cas il faut introduire l’opérateur schème pour décrire l’opération de conception (Raynaud, 1999) ; (ii) le changement d’état consiste seulement en un ajustement dimensionnel. L’article étudie ce dernier cas sur plusieurs projets (Gio Ponti, Sebastiano Serlio, Villard de Honnecourt) et montre qu’il faut encore recourir à l’opérateur schème pour décrire l’opération de conception. L’architecturologie considérant l’échelle comme un opérateur de conception, la relation entre schème et échelle doit être clarifiée. L’article examine les raisons conduisant à qualifier l’échelle et le schème comme co-opérateurs de la conception architecturale. Mots-clefs: conception architecturale, opérations, opérateurs, schème, échelle