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427663 1 En Bookbackmatter 215..297 Conclusion The intention of this book was to test the interdependence between medieval theories of optics and the practice of perspective. More particularly we chose to examine the question of physiological optics, because the proof of a connection between optics and perspective would be less probative if it took geometric optics as its starting point (for example, it is not possible to separate the respective influences of optics and geometry in the use of similar triangles, a method shared by the two sciences). In contrast, the theory of binocular vision is critically dependent on the particular way in which optics was addressed in the Middle Ages, combining as it did geometric and physical optics with anatomy and ocular physiology. It is within this framework that the differing interpretations of “axial perspective” and “two-point perspective” were examined here. As has been seen, these forms of representations do not correspond to any type of parallel projection that places the spectator at infinity, therefore excluding the possibility that they might constitute axonometric (isometric, dimetric, trimetric) or oblique (cavalier and military) pro- jections. One could go even further in the critical analysis of the two-point system of representation: 1. Two-point perspective is not a linear perspective, because the two vanishing points are separated by distances that are many times greater than the maximal metric error. 2. Two-point perspective bears no relationship to bifocal perspective (Parronchi’s hypothesis). 3. Two-point perspective cannot be considered a form of trifocal perspective, whose object verticals are always represented by parallel lines. 4. The two vanishing points are not the result of an absence of parallelism in the side walls nor of an alteration in the parallelism intended to highlight the subject of the scene. 5. Two-point perspectives do not fall into the category of curvilinear perspective, the object lines being represented by lines rather than by the arcs of a circle (Chap. 8). 6. Two-point perspectives do not represent the application of a modified curvi- linear perspective, since the development of projection circles prevents the © Springer International Publishing Switzerland 2016 215 D. Raynaud, Studies on Binocular Vision, Archimedes 47, DOI 10.1007/978-3-319-42721-8 216 Conclusion vanishing lines from concurring in a single point (the Hauck–Panofsky con- jecture, Chap. 9). 7. Two-point perspective cannot be categorized as a form of synthetic perspective, because the latter precludes the strict convergence of vanishing lines in one point (the White–Carter conjecture, Chap. 10). 8. Two-point perspectives are not based on the arithmetic method, because the distances measured in the compositions studied here are not the multiples or sub-multiples of any known units, nor can they be reduced to multiples of each other (the conjecture proposed by De Mesa Gisbert, Chap. 10). This critical review of the current interpretations of axial perspective supports the thesis that the principles of binocular vision were applied in the early stages of the development of artificial perspective. Two-point perspective was in general use during the period 1295–1450, and the exact same construction can be found much later, in the works of Passerotti, Caracci, Tibaldi, Le Brun and de Sève. In them we find two pencils of lines that cross the central axis before concurring in two van- ishing points, F and F′, on the horizon line. Three concluding questions remain to be examined: 1. Who were the actors responsible for introducing the theories of optics to the first practitioners of perspective? 2. To which disciplines does this cross between optics and perspective belong? 3. Why was the use of binocular perspective abandoned during the classical period? The Birth of the Optics–Perspective Nexus in the Late Duecento It is useful to begin by asking who introduced optics to the earliest practitioners of perspective, and notably including the artists commissioned to paint the fresco cycles for the Basilica of Assisi beginning in 1296. The theory of optics could have been transmitted in two ways: 1. A direct path through De aspectibus, the Latin translation of Ibn al-Haytham’s treatise on optics that began to circulate at the beginning of the Duecento. An Italian translation, De li aspecti, became available later in the Trecento.1 2. An indirect path, via the numerous Latin treatises and commentaries on Ibn al-Haytham’s optics produced during the course of the Middle Ages. The 1Enrico Narducci, “Nota intorno a una traduzione italiana fatta nel secolo decimoquarto del trattato d’ottica d’Alhazen,” Bollettino di bibliografia e di storia delle scienze matematiche e fisiche 4 (1871): 1–40; Graziella Federici Vescovini, “Contributo per la storia della fortuna di Alhazen in Italia. Il volgarizzamento del ms. vat. 4595 e il ‘Commentario Terzo’ del Ghiberti”, Rinascimento 5 (1965): 17–49; Eadem, “Alhazen vulgarisé:Le‘De li aspecti’ d’un manuscrit du Vatican (moitié du XIVe siècle) et le troisième ‘Commentaire sur l’optique’ de Lorenzo Ghiberti,” Arabic Sciences and Philosophy 8 (1998): 67–96. Conclusion 217 principal treatises—Roger Bacon’s Perspectiva,2 Witelo’s Perspectiva,3 and two works by John Pecham, Tractatus de perspectiva4 and Perspectiva com- munis5—dealt primarily with physiological optics. As we have shown in Chap. 6, all of these texts refer explicitly to the experiments carried out by Ibn al-Haytham using his binocular tablet and all differentiate between the cases of homonymous and crossed diplopia. One necessary condition for the transmission of this knowledge was that the texts had to be accessible to the earliest perspectivists. And in fact works on optics appear in the inventories of many libraries in Rome, Florence and Padua,6 intel- lectual centers where optics was studied and taught in the late Middle Ages, and where artists were beginning to use two-point perspective. The profusion of texts in circulation would certainly have multiplied the opportunities to derive a system of perspective from the laws of optics. This system—which appears unorthodox in the light of the modern conventions of linear perspective—becomes perfectly intelli- gible if examined in the context of the optical theories of Ibn al-Haytham and his Latin commentators. Access to authoritative texts is a necessary, but not sufficient condition for the transfer of knowledge. Key works might have been available to craftsmen but ignored for various reasons. In fact, one of the greatest obstacles to their trans- mission was the fact that these texts were—with the exception of De li aspecti— written in Latin, a language that was beyond the reach of artisans, who received their training in the atelier rather than at university. Various hypotheses regarding the actual processes of knowledge transfer have been advanced, ranging from personal contacts between savants and artists (for example, between Toscanelli and Brunelleschi), to the instruction lavishly dispensed in the scuole d’abaco by masters such as Grazia de’ Castellani in Florence. Alongside these hypotheses must be placed the rarely mentioned but central role of the art commission.7 Let us limit ourselves here to the earliest experiments in perspective—the frescoes in the Basilica of Assisi realized between the end of the Duecento and the 2The Opus maius of Roger Bacon, ed. J.H. Bridges, Frankfurt am Main, 1964, pp. 92–99, new edition: David C. Lindberg, Roger Bacon and the Origins of Perspectiva in the Middle Ages: A Critical Edition and English Translation of Bacon’s Perspectiva with Introduction and Notes, Oxford, 1996. 3Witelo, Opticae Thesaurus libri X, edited and published by Friedrich Risner, Basel, 1572; modern edition published by David Lindberg, New York, 1972, pp. 98–108. It should be recalled that many more copies of Bacon’s Perspectiva and Pecham’s Perspectiva were in circulation than Witelo’s Perspectiva. 4John Pecham, Tractatus de perspectiva, ed. D.C. Lindberg, New York, 1972, pp. 56–57. 5David C. Lindberg, John Pecham and the Science of Optics, Madison, 1970, pp. 116–118. 6David. C. Lindberg, A Catalogue of Medieval and Renaissance Optical Manuscripts, Toronto, 1975. 7Dominique Raynaud, L’Hypothèse d’Oxford: Essai sur les origins de la perspective, Paris, p. 319 and passim; this hypothesis was taken up in some detail by Jean-Philippe Genet, “Revisiter Assise: la lisibilité de l’image médiévale,” in Itinéraires du savoir de l’Italie à la Scandinavie (Xe–XVIe siècle). Études offertes àÉlisabeth Mornet, ed. Corinne Péneau, Paris, 2009, pp. 415–417. 218 Conclusion beginning of the Trecento in central Italy. During this period artists constructed perspectives based on a vanishing axis (The Approval of the Franciscan Rule or St. Francis Preaching before Honorius III) and worked out the correct reduction of receding intervals (for example, in Christ among the Doctors and The Recovery of the Wounded Man of Lerida).8 How can these significant advances, which took place during the course of a single decade from 1296 to 1305, be explained? We have shown elsewhere9 the direct contribution made by members of the Franciscan order to the spread of the science of optics. To mention just a few names, Bartholomew of England, Roger Bacon, and John Pecham, all of whom cited Alhacen’s De aspectibus in their works, were Friars Minor. Within the order many of them exercised the functions of Master Regent before becoming provincial ministers or Ministers-General. In their shift from academic to administrative duties, the friars were in no way required to repudiate the knowledge acquired during their formation as scholars. Furthermore, one of the responsibilities of the Ministers-General would have been to commission and supervise the work of architects and artists in building and embellishing their churches. Renato Bonelli10 has identified various inflections in the construction of the Upper Church of the Basilica of Assisi introduced by architects working under successive Ministers-General.
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