Dominique Raynaud

650 pp. – This book is a continuation of the research on the representation of the eye initiated by Prof. Ludwig Choulant (University of Dresden) and Prof. Hugo Magnus (University of Breslau) at the end of the 19th and beginning of the 20th century. The aim of the book is to provide all those who need information on how the eye was conceived in a given historical context, with clear and concise iconographic and lexicographic data. The first section contains about 700 images of the eye (first handwritten, then printed) distributed among 450 authors. Each record reproduces the figures of the eye with their own specific anatomical terminology. The second section provides a cluster analysis of the eye figures: the result is a dendrogram, which accounts for the main types of representation of the eye found in the history of ocular anatomy. The work is complemented by a 40-page Index of Concepts containing all the anatomical terms found in the book.

Notwithstanding what the champions of post-truth may think, truth remains a key concept of scientific research. In this contribution, several theories of factual truth are evaluated with the help of a simple and straightforward tool, i.e., a logical table of contingency. Its application shows that most contemporary disconcerting theories of truth have critical flaws, and that, albeit imperfect, truth-as-correspondence is still the best theory. Further criticism of correspondence as adaequatio, compliance and isomorphism suggests that correspondence-as-mapping constitutes a more acceptable theory. This contribution provides a definition and examples in the empirical sciences.

In Résolution des quatre principaux problèmes d’architecture (1673) then in Cours d’architecture (1683), the architect–mathematician Nicolas-François Blondel addresses one of the most famous architectural problems of all times, that of the reduction in columns (entasis). The interest of the text lies in the variety of subjects that are linked to this issue. (1) The text is a response to the challenge launched by Curabelle in 1664 under the name Étrenne à tous les architectes; (2) Blondel mathematicizes the problem in the “style of the Ancients”; (3) The problem is reformulated and solved through the continuous drawing of the curve; (4) Blondel refutes the uniqueness of the curve by enumerating a variety of solutions (conchoid, spiral, parabola, ellipse, circle, hyperbola). This exuberance responds to an intention that does not coincide with the state of the art of mathematics at the end of the seventeenth century, nor with the taste for geometry of the Ancients, nor with any pedagogical project. This feature is explained by Blondel’s plan to found architecture on scientific bases. The reasons for his failure are analysed.

In this article, we publish the critical edition of Andalò di Negro’s De compositione astrolabii, with English translation and commentary. The mathematician and astronomer Andalò di Negro presumably redacted this treatise on the astrolabe in the 1330s, while residing at the court of King Robert of Naples. The present edition has three purposes: first, to make available a text missing from the previous compilations of works by Andalò di Negro; second, to revise a privately circulated edition of the text; and third, to help disseminating one of the rare Latin texts presenting the principles of the stereographic projection which underlie the construction of the astrolabe.

This article is a study of geometric constructions. We consider, as an illustration, the methods used for dividing the straight line into n equal parts (n-section). Architects and practicioners of classical Europe had at their disposal a broad range of geometric constructions: ancient ones were edited and translated, whereas new solutions were constantly published. The wide variety and reasons for selection of these geometric constructions are puzzling: the most widespread construction was not the simplest one. This article wonders why so many constructions were used to solve the same problem and why tedious methods were used. It is argued that the practical conditions and scale at which the problem was tackled could account for such diversity.

Unlike the physical sciences, sociology is frequently described as an interpretative non-experimental science. Comparative epistemology sheds new light on this claim. 1. Experimentation is not a constant character of the physical sciences; 2. Experimental hypothetical-deductive reasoning, including the test of predictions, is also practicable in sociology. The argument is developed by a detailed step-wise comparison of the prediction of light ray deviation within the Sun’s gravitational field made in 1919 (physics) and the prediction of 8% cosmopolitanism of Cambridge University between 1250 and 1350 (sociology). Extensive analysis of regent masters’ prosopographic notes yields the result of 9.5 percent cosmopolitanism, which is close to the theoretical prediction. Au contraire des sciences physiques, la sociologie est souvent décrite comme une science interprétative et non-expérimentale. L’épistémologie apporte un éclairage nouveau sur cette position : 1) L’expérimentation n’est pas un trait constant des sciences physiques ; 2) Le raisonnement expérimental est également applicable en sociologie. L’argument est développé en comparant en détail le test de la prédiction d’une déviation des rayons lumineux dans un champ de gravitation effectué en 1919 et le test de la prédiction d’un taux de cosmopolitisme de 8 % de l’université de Cambridge dans la période 1250-1350. Le dépouillement des notices prosopographiques des maîtres régents donne un résultat de 9,5 % proche de la prédiction théorique initiale.

In the wake of Guido Hauck’s work on “subjective perspective,” Erwin Panofsky concluded that perspectives based on what he referred to as a “vanishing axis” could be interpreted as a form of curvilinear perspective. The present chapter aims to refute this conjecture by demonstrating that such constructions do not correspond either to the linear or the curvilinear perspective. They cannot be classed as linear perspectives because the distance between their two vanishing points is always greater than the maximum reconstruction error. Nor can they be considered curvilinear perspectives, in which the vanishing lines always converge in two well-defined vanishing points, because lines based on the mapping of projection circles on the picture plane do not end in points of concurrence. The refutation of the Hauck–Panofsky conjecture provides support for the interpretation set out in Chap. 8. Panofsky’s erroneous reading stems from his failure to recognize that if the vanishing lines taken from the same side of the axis are extended beyond this axis, they will converge on a defined vanishing point.

Thirty works painted between the end of the Duecento and the middle of the Quattrocento using two-point perspective are reconstructed here using the process of error analysis described in Appendix A. In terms of the classification of different systems of representation, these constructions do not correspond to any type of perspective recognized today. Notably, we show that they do not constitute either orthogonal projections or linear perspectives. Nor do they meet the criteria of the “bifocal perspective” that Parronchi believed could be identified in such representations. We then examine these works in relation to the principles of binocular vision laid out by Ibn al-Haytham and his Latin successors, and show that the reconstruction of their plans and elevations based on the perspective view produces coherent spaces that are in conformity with the architectural models of the period. In addition, a qualitative relationship linking the distance between the vanishing points and the position of the fixation point is brought to light.

During the classical period many theoreticians (Vignola, Danti, Bassi, Huret and Le Clerc) published detailed critiques rejecting the perspective system based on two vanishing points located on the same horizon. A study of their texts establishes unambiguously that the system, by then judged by the main theorists to be unorthodox, was closely linked to the principles of binocular vision. The very fact that these discussions were being carried on in the academies and in circles close to them, in France as well as in Italy, shows that the postulate of monocular vision, which was a prerequisite for linear perspective, met with considerable resistance from painters and architects during the classical period. The validity of drawing a perspective using just one eye was still being debated in 1679, two and a half centuries after Brunelleschi.

Andrés De Mesa Gisbert proposes that the perspectives in paintings from the Duecento and Trecento were drawn arithmetically, i.e. without resorting to vanishing points. The most convincing argument for this hypothesis is that the division of two parallel lines by straight lines intersecting each other at a vanishing point (the geometric method) is equivalent to the division of these parallel lines into proportional parts (the arithmetic method). If the arithmetic method was indeed used by medieval artists, then the vanishing points exhibited ex post should be purely fortuitous. There are sound objections to this assertion, however: the lack of simple multiples and submultiples of the measurement units, the absence of proportionality ratios, the lengths of the operating series, and the correspondence of the vanishing points to visible loci in the pictures. The application of optics and the geometric method is a more probative thesis, although it does not imply that painters were using concepts of linear perspective, which would have been an anachronism.

Perspective, as a system of visual representation, draws its name from the medieval Latin term perspectiva which means ‘optics.’ We owe this linguistic connection to the fact that certain principles of perspective developed from theories of vision. Between the two sets of notions one can find relationships of both continuity and discontinuity. A study of textual parallels has established this continuity. However, there are clear distinctions between perspectiva and perspective. Apart from the close relationship between science and technique that characterized them both, medieval perspectiva was a tripartite science embracing optica, catoptrica and dioptrica, whereas perspective would focus exclusively on direct vision; perspectiva postulated the binocular vision whereas linear perspective would adopt the conditions of monocular vision. These were the two main bifurcations that led to the development of perspectiva artificialis.

The aim of this chapter is to deconstruct the notion that linear perspective formed a stable system of representation beginning in the Quattrocento. Doubts must be raised because the history of perspective is in fact quite conjectural due to the many lacunae scattered along its path; one crucial example is the exact nature of the contributions of Brunelleschi, Alberti, and Masaccio. A second obstacle is the fact that a multiplicity of approaches were in use from the end of the Duecento to the Cinquecento, when the academies formally introduced the teaching of perspective techniques. Between these two time points perspectivists explored numerous systems of perspective, introducing errors and variations that can be explained by the uneven distribution of knowledge regarding the laws of optics and geometry.

This chapter examines the question of errors in perspective from the viewpoint of the painter rather than the spectator, a distinction that significantly modifies the way in which the problem is approached. Perspective is therefore judged in terms of the methods used by the painter or architect who constructed it, that is to say, in terms of the goals that he set for himself and the means he had at his disposal to achieve them. We then explain the reasons why Renaissance painters accepted the three main types of error in perspective: “accidental errors” (type I), “ad hoc errors” (type II), and “systematic errors” (type III).

Est-il vrai que la science et la technologie forment un tout ? Qu’elles sont unies par des liens constants et nécessaires ? Est-il vrai que le raisonnement technologique prend toujours place dans un contexte industriel ? Que les bio- et nanotechnologies forment la part essentielle des technologies contemporaines ? Que l’application définit adéquatement la relation entre la science et la technologie ? Dans ce livre, Dominique Raynaud examine les limites de chacune de ces idées. Il dresse un panorama complet des problèmes que pose la technologie au moyen d’une étude détaillée des aspects cognitifs, ergologiques, professionnels et juridiques de la relation entre la science et la technologie et met à nu la fiction utilitariste de la prétendue « technoscience ». Tout aussi éloigné de l’apologie que de la critique radicale, ce livre défend une perspective empirique et analytique dans l’étude de la technologie.

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.

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.

This article aims at contributing to the methods of the sociology of science, from an empirical study of the determinations of the velocity of light between 1676 and 1983. Far from being constructed and deconstructed at pleasure, the values of c have undergone a tendentially unidirectional and irreversible process of revision. The competing methods remained in the running as long as they produced an uncertainty less than, or equal to, the best known value. The analysis of “entrances” and “exits” of the methods on the research front makes clear the nature of scientific competition, which is a form of “redistributive emulation” that owes nothing to political rivalry or economic competition. By achieving results that differ from constructivism on the themes of literary inscription, games of construction/deconstruction, negotiation, and persuasion, this article outlines a kind of internalist sociology of science, which aims at exploring all aspects that make science science.

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

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

This book provides the first critical edition of Ibn al-Haytham’s On the Shape of the Eclipse with English translation and commentary, which records the first scientific analysis of the camera obscura. On the Shape of the Eclipse includes pioneering research on the conditions of formation of the image, in a time deemed to be committed to aniconism. It also provides an early attempt to merge the two branches of Ancient optics—the theory of light and theory of vision. What perhaps most strongly characterizes this treatise is the close interaction of a geometric analysis of light and experimental reasoning. Ibn al-Haytham conducted his experiments in a systematic way by varying all that could be changed: the shape and size of the aperture, the focal length of the camera obscura, the distance and shape of the celestial bodies. This way, he achieved a thorough understanding. This work represents a decisive step in both the history of optics and the application of the experimental method that was just as efficient in medieval Islam as today.

Leonardo’s research on the eye and vision has given rise to contrasting assessments, ranging from the apology of his explanation of how the eye works as a camera obscura to the most critical attitude. The negative judgments derive some of their strength from the fact that the practice of anatomy and linear perspective are well documented in Leonardo. Thus one expects him to have had empirically based knowledge of the organs dissected, as well as comprehensive skills in optics. As we will see, none of these ideas is entirely right.

"Toute forme a été imaginée avant d'être construite". Cette formule classique, qui met en relief l'un des traits essentiels de la pratique architecturale, soulève plusieurs questions. D'où viennent les images-mères du projet? Sont-elles encore identifiables une fois construites? Existe-t-il des procédés réguliers dans l'imagination des formes architecturales? Cette enquête tente de résoudre ces problèmes par la reconnaissance de schèmes dynamiques de l'imagination. Si le processus de conception architecturale altère les images-mères au points que certains ont pu identifier une "non figurativité" de l'architecture, les schèmes dynamiques sont perceptibles de la première esquisse à l'édifice construit. La démonstration, au croisement de l'anthropologie des représentations et de l'architecturologie, adopte le principe d'une analyse comparée. Etayée par une sélection d'édifices couvrant toute l'extension historique et géographique, elle offre tout à la fois une lecture cohérente des premiers moments du projet architectural et une réflexion de portée générale sur l'imagination des formes.

In Scientific Controversies, Dominique Raynaud shows how organized debates in the sciences help us establish or verify our knowledge of the world. If debates focus on form, scientific controversies are akin to public debates that can be understood within the framework of theories of conflict. If they focus on content, then such controversies have to do with a specific activity and address the nature of science itself. Understanding the major focus of a scientific controversy is a first step toward understanding these debates and assessing their merits. Controversies of unique socio-historic context, disciplines, and characteristics are examined: Pasteur’s germ theory and Pouchet’s theory of spontaneous generation; vitalism advocated at Montpellier versus experimental medicine in Paris; the science of optics about the propagation of visual rays; the origins of relativism (the Duhem-Quine problem). Touching on the work of Boudon, Popper, and others, Raynaud puts forward an incrementalist theory about the advancement of science through scientific controversies. The debates Raynaud has selected share in common their pivotal importance to the history of the sciences. By understanding the role of controversy, we better understand the functioning of science and the stakes of the contemporary scientific debates.

Définir, à partir des traces graphiques d'un projet, les actions de conception et les motivations de l'architecte à les entreprendre, voilà l'objectif de l'enquête. Quel est le rôle de la représentation dans le développement de l'idée architecturale? Comment se transforme-t-elle tout au long du projet? En fonction de quoi l'architecte décide-t-il d'altérer ou de maintenir une représentation? Telles sont les questions que ces essais tentent de résoudre en s'appuyant sur les concepts de représentation, d'inférence, de modèle et d'échelle, et en portant une attention particulière au rôle que jouent les schèmes dans la conception architecturale. Les conclusions sont tirées d'études de cas qui portent sur des projets de l'Atelier Zô, Scarpa, Le Corbusier, Pei.

The perfect compass, used by al-Qūhī, al-Sijzī and his successors for the continuous drawing of conic sections, reappeared after a long eclipse in the works of Renaissance mathematicians like Francesco Barozzi in Venice. The resurgence of this instrument seems to have depended on its interest to solve new optico-perspective problems. Having reviewed the various instruments designed for the drawing of conic sections, the article is focused on the sole conic compass. Theoretical and empirical applications are detailed. Contrarily to the common thesis of an independant discovery, various elements suggest a direct descent between the birkār al-tāmm of the Arabic mathematical tradition and the Italian conic compass. Then we present the most probable transmission hypothesis involving: 1° Ibn Yūnus and his disciples of Mosul, 2° Sultan Malik al-Kāmil in Damas, 3° Master Theodore and Frederick II at the court of Sicily, 4° Andalò di Negro and Robert of Anjou in Naples, 5° Lorenzo della Volpaia, Vinci, Sangallo and Michelangelo in Florence, 6° Ausonio, Contarini, Thiene and Francesco Barozzi in Venice.