Dominique Raynaud

This book explores the interrelationships between optics, vision and perspective before the Classical Age, examining binocularity in particular. The author shows how binocular vision was one of the key juncture points between the three concepts and readers will see how important it is to understand the approach that scholars once took. In the Middle Ages and the Renaissance, the concept of Perspectiva – the Latin word for optics – encompassed many areas of enquiry that had been viewed since antiquity as interconnected, but which a erwards were separated: optics was incorporated into the field of physics (i.e., physical and geometrical optics), vision came to be regarded as the sum of various psycho-physiological mechanisms involved in the way the eye operates (i.e., physiological optics and psychology of vision) and the word ‘perspective’ was reserved for the mathematical representation of the external world (i.e., linear perspective). The author shows how this division, which emerged as a result of the spread of the sciences in classical Europe, turns out to be an anachronism if we confront certain facts from the immediately preceding periods. It is essential to take into account the way medieval scholars posed the problem – which included all facets of the Latin word perspectiva – when exploring the events of this period.

The idea that linear perspective arose only in the West due to the strength of an unusual process of rationalization is denied by the fact that IXth century Islamic scholars had yet a thorough knowledge of the optical and geometrical materials required in perspective. In addition, the process of rationalization was rarely so intense as in that time, because truth uniqueness and scientific communalism were core values of Medieval Islam. The puzzle is not a matter of less or more rationality, but a matter of axiological motives. First, Islamic disregard for perspective is the result of a value-set insofar painters were fearing the hadīths' prohibition, or wished to avoid pretentiousness of their name (muṣawwir). Second, Islamic art did not draw from Qurʿān and hadīth's precepts directly. Third, painters implemented axiological motives, to put iconic practice in accordance with aniconic leanings.

L'étude de la conception architecturale se trouve au carrefour de trois approches: sciences de la conception, psychologie cognitive et architecturologie. Cette dernière tente de modéliser toute la gamme des changements d'état qui apparaissent durant le processus de conception. L'architecturologie sait décrire, au moyen d'échelles, les opérations de conception par lesquelles l'architecte attribue des mesures à l'édifice. Cette modélisation paraît adéquate lorsque le modèle morphologique n'est pas transformé durant le processus de conception (comme dans certains projets de Jørn Utzon ou de Alvar Aalto). Dans d'autres cas – comme dans certains projets de Philibert de l'Orme, Ludwig Mies van der Rohe, Norman Foster – les changements d'état altèrent la structure même du modèle morphologique. De telles transformations ne peuvent plus être décrites par l'échelle. Reprenant une idée de Herbert A. Simon, l'article suggère que la description de ces nouvelles transformations appelle une autre classe d'opérateurs. Ce pourrait être des schèmes, si l'on entend par ce terme la classe des actions prototypiques qui peuvent être exprimées par des verbes fondamentaux comme ouvrir, fermer, séparer, lier, etc.

This article studies the legacy in the West of Abū al-Wafā’s Book on those Geometric Constructions which are Necessary for Craftsmen. Although two-thirds of the geometric constructions in the text also appear in Renaissance works, a joint analysis of original solutions, diagram lettering and probability leads to a robust finding of independent discovery. The analysis shows that there is little chance that the similarities between the contents of Abū al-Wafā’s Book and the works of Tartaglia, Marolois and Schwenter owe anything to historical transmission. The commentary written by Kamāl al-Dīn Ibn Yūnus seems to have had no Latin legacy either.

L'essor de la perspective linéaire a suscité de nombreuses polémiques tout au long du Quattrocento et du Cinquecento, opposant les partisans d'une géométrisation artificialiste de la vision à ceux qui vantaient les qualités du dessin d'après nature ou invoquaient des arguments de nature physiologique. Ces débats peuvent être retracés à partir des quatre alternatives qui en constituent le noyau dur : champ de vision restreint vs. large ; immobilité vs. mobilité oculaire ; tableau plan vs. curviligne ; vision monoculaire vs. binoculaire. En retenant les premiers termes de ces quatre alternatives, l'histoire de la perspective a rejeté de nombreux systèmes hétérodoxes. Du point de vue de la mathématisation, l'intérêt de ces débats tient à ce qu'ils ont succédé, et non précédé, l'adoption du dispositif perspectif comme intersection de la pyramide visuelle. L'histoire de la perspective linéaire offre ainsi un authentique cas de justification a posteriori des fondements ou, pour ainsi dire, de mathématisation à rebours

Contemporary sociology of scientific knowledge (SSK) is defined by its relativist trend. Its programme often calls for the support of philosophers, such as Duhem, Quine, and Wittgenstein. A critical re-reading of key texts shows that the main principles of relativism are only derivable with difficulty. The thesis of the underdetermination of theory doesn't forbid that Duhem, in many places, validates a correspondence-consistency theory of truth. He never said that social beliefs and interests fill the lack of underdetermination. Quine's idea of a selective revision of hypotheses, as well as the neat incompatibility between holism and conventionalism, openly challenges the principles of relativism. Wittgenstein's work, which is not presented in book-form but rather as a tree, forces us to avoid aphoristic choices that credit any text-excising. This remark allows us to tackle the passages that sociological relativism is based on.Mathematical conventions are not anthropological objects. When Wittgenstein examines the "language-games," he only speaks of the functioning of natural language, not to be confused with scientific formal languages. We then should render the formula "language-game" by "well-defined, explicit and compulsory rules of communication", which is a much less attractive formula for relativism. Consequently, there does not exist a real continuity between the epistemologies of Duhem, Quine and Wittgenstein, and the recent works of the SSK.

Why did linear perspective rise in trecento–quattrocento central Italy rather than in any other cultural context? This book provides new insight into the question of the early Italian pioneership in perspective, building on the fact that many references to optics can be found in Renaissance treatises. The fact that most of the medieval optical manuscripts were written by Franciscan masters—the best known among them being Roger Bacon and John Pecham—suggests the need for a closer look at how the medieval universities (studia generalia) operated. An in-depth study of recruitment highlights the exceptional mobility of masters and lectors throughout Europe. However, through the thirteenth and fourteenth centuries, the closer a university was to central Italy, the more cosmopolitan it was. This is a result of the topology of the academic network, since cosmopolitanism depends on the studium’s closeness centrality. This is why, through the masters’ mobility, knowledge circulating in the network preferentially flowed into central Italy.

In view of the progress made in recent decades in the fields of stemmatology and the analysis of geometric diagrams, the present article explores the possibility of establishing the stemma codicum of a handwritten tradition from geometric diagrams alone. This exploratory method is tested on Ibn al-Haytham’s Epistle on the Shape of the Eclipse, because this work has not yet been issued in a critical edition. Separate stemmata were constructed on the basis of the diagrams and the text, and a comparison showed no major differences. The greater reliability of a stemma codicum constructed on the basis of the diagrams rather than the text of a mathematical work is discussed and preliminary conclusions are drawn

The 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 Kitāb al-Manāẓir (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.

The modern physiological optics introduces the notions related to the conditions of fusion of binocular images by the concept of correspondence, due to Christiaan Huygens, and by an experiment attributed to Christoph Scheiner. The conceptualization of this experiment dates, in fact, back to Ptolemy and Ibn al-Haytham. The present paper surveys Ibn al-Haytham's knowledge about the mechanisms of binocular vision. The article subsequently explains why Ibn al-Haytham, a mathematician, but here an experimenter, did not give the circular figure of the theoretical horopter, construction due to Gerhard Vieth and Johannes Müller. But, on the other hand, it is clear that Ibn al-Haytham's experimental study puts in place the notion of corresponding points, the cases of homonymous and cross diplopia, and even prepares the discovery of Panum area.