Abstract
In the wake of Panofsky’s work on perspective, John White and Bernard Carter identified the “axial construction” as the product of a system (denominated synthetic perspective) in which the measurements of an object on a projection circle are transferred to the picture plane by means of transfer lines. While this construction has been criticized for its complexity and therefore the limited possibility of its being put to use, it has never been studied in detail although it is regularly mentioned in discussions of perspective systems. We will show that none of the works of art examined here satisfies the mathematical property exhibited by synthetic perspective, namely, that three vanishing lines on the same side of the axis cannot be parallel nor can they meet in a point of concurrence. This refutation of the White–Carter conjecture should bring to a close the long succession of contradictory evaluations that have appeared over the course of the years; it also reinforces the explication presented in Chap. 8
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Notes
- 1.
Erwin Panofsky, “Die Perspektive als symbolische Form,” Vorträge der Bibliothek Warburg 4 (1924/5): 258–331, Perspective as Symbolic Form, pp. 31–45.
- 2.
Alan M.G. Little, “Scaenographia,” The Art Bulletin 18 (1936): 407–418; idem, “Perspective and scene painting,” The Art Bulletin 20 (1937): 487–495; Miriam S. Bunim, Space in Medieval Painting and the Forerunners of Perspective (New York, 1940); John White, Perspective in Ancient Drawing and Painting (London, 1956); idem, The Birth and Rebirth of Pictorial Space (London, 1967). See also Gezienus ten Doesschate, Perspective. Fundamentals, Controversials, History (Nieuwkoop, 1964), p. 85–99 and 105–118.
- 3.
Little, “Scaenographia” and “Perspective and scene painting,” op. cit.
- 4.
Miriam Bunim admits that, “In Giotto’s paintings, the vanishing-axis procedure for vertical planes in depth was not used according to the clearly defined systematic form of converging pairs of parallel receding lines,” Bunim, Space in Medieval Painting, p. 141. All the same, numerous cases in favor of the theory of the vanishing axis were then given apropos of Simone Martini, Barna da Siena, Bernardi Daddi and Italian painting in the Trecento generally; see pp. 148 and 154, 157, 166, 174, respectively.
- 5.
Bunim, Space in Medieval Painting, pp. 24–25.
- 6.
John White, Perspective in Ancient Drawing and Painting, London, 1956; idem, The Birth and Rebirth of Pictorial Space, London, Faber and Faber, 1967, French transl., Naissance et renaissance de l’espace pictural, Paris, Adam Biro, 1992.
- 7.
White, Naissance et renaissance de l’espace pictural, p. 213.
- 8.
André Flocon and André Barre, La Perspective curviligne, Paris, 1968. These principles were supposedly applied by Jean Fouquet in Entrée de l’Empereur Charles IV à Saint-Denis, ca. 1460. With regard to the theoretical foundations of this construction, we can only formulate conjectures.
- 9.
Bernard A.R. Carter presents the construction based on transfer lines in this light in the entry on “Perspective” in The Oxford Companion to Western Art, ed. H. Osborne, Oxford, 1987, pp. 840–861.
- 10.
The distinction between the conjectures of Hauck–Panofsky and White–Carter was made for the purposes of convenience. Panofsky recognized his debt to Hauck, who “suggested a procedure based on the projection of the object on a round cylinder with vertical generatrices emanating from a point on the axis, and the development of the image thus obtained on a picture plane,” Marisa Dalai Emiliani, “La question de la perspective,” introduction to Erwin Panofsky, La Perspective comme forme symbolique, Paris, 1975, p. 22. White and Carter did not link their construction hypothesis based on transfer lines to Hauck’s work on perspective. The difference between the two conjectured constructions was based on no more than a detail, John White following Panofsky’s lead regarding the signification of this alternative to linear perspective.
- 11.
Hendrick G. Beyen, Die pompejanische Wanddekoration vom zweiten bis zum vierten Stil, 2 vols., Den Haag, 1938; idem “Die antike Zentralperspecktive,” Jahrbuch des deutschen archäologischen Instituts 54 (1939): 47–72; Maurice Pirenne, “The scientific basis of Leonardo da Vinci’s theory of perspective,” British Journal for the Philosophy of Science 3 (1952): 165–185; Gezenius ten Doesschate, Perspective. Fundamentals, Controversials, History, Nieuwkoop, 1964; Luigi Vagnetti, “De naturali et artificiali perspectiva,” Studi e Documenti di Architettura 9/10 (1979): 3–520; James Elkins, The Poetics of Perspective, Ithaca, Cornell University Press, 1994; Gérard Simon, “Optique et perspective: Ptolémée, Alhazen, Alberti,” Revue d’Histoire des Sciences 54 (2001): 325–350.
- 12.
Andrés de Mesa Gisbert, “El ‘fantasma’ del punto de fuga en los estudios sobre la sistematización geométrica de la pintura del siglo XIV,” D’Art 15 (1989), p. 49.
- 13.
Antonella Ballardini, “Lo spazio pittorico medievale: Studi e prospettive di ricerca,” in Rocco Sinisgalli, ed., La Prospettiva. Fondamenti teorici ed esperienze figurative dall’Antichità al mondo moderno, Fiesole, 1998, p. 281. Like the views of Panofsky, those of White circulated widely; The Birth and Rebirth of Pictorial Space was reprinted three times (1967, 1970, 1972, 1987) and was translated into many languages.
- 14.
Panofsky, Perspective as Symbolic Form, p. 40.
- 15.
The results depend on the errors in the perspective drawing. In order to reach clear conclusions, we conducted a verification of possible errors following a procedure that is outlined in Appendix A.
- 16.
Kern, “Die Anfänge der zentralperspektivischen Konstruktion.”
- 17.
The principles of synthetic perspective were therefore unknown in the Middle Ages and it is highly unlikely that they were applied before the nineteenth century: Arthur Parsey, Perspective Rectified, London, 1836; William G. Herdman, A Treatise on the Curvilinear Perspective of Nature, London, 1853; Guido Hauck, Die subjektive Perspektive und die horizontalen Curvaturen des dorischen Styls, Stuttgart, 1879.
- 18.
“Ichnography (plan) demands the competent use of compass and rule; by these plans are laid out upon the sites provided. Orthography (elevation), however, is the vertical image of the front, and a figure slightly tinted to show the lines of the future work. Scenography (perspective) also is the shading of the front and the retreating sides, and the correspondence of all lines to the center of the circle [literally, the center of the compass]/Ichnographia est circini regulaeque modice continens usus, e qua capiuntur formarum in solis arearum descriptiones. Orthographia autem est erecta frontis imago modiceque picta rationibus operis futuri figura. Item scaenographia est frontis et laterum abscendentium adumbratio ad circinique centrum omnium linearum responsus,” De Architectura, I, II, ed. Granger, vol. 1, pp. 24–26.
- 19.
On this, Ian Verstegen, “A classification of perceptual corrections of perspective distortions in Renaissance painting,” Perception 39 (2010), p. 689.
- 20.
Hermann von Helmholtz, Optique physiologique, Paris, 1867; Yves Le Grand, Optique physiologique, 3 vols., Paris, 1948–1956.
- 21.
Luca Baggio, “Sperimentazioni prospettiche e ricerche scientifiche a Padova nel secondo Trecento,” Il Santo 34 (1994): 173–232; Francesca Cecchini, “Artisti, committenti e perspectiva in Italia alla fine del Duecento,” Rocco Sinisgalli, ed., La prospettiva. Fondamenti teorici ed esperienze figurative dall’Antichità al mondo moderno, Fiesole, 1998, pp. 56–74; Dominique Raynaud, L’Hypothèse d’Oxford, Paris, 1998.
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Raynaud, D. (2016). The White–Carter Conjecture on Synthetic Perspective. In: Studies on Binocular Vision. Archimedes, vol 47. Springer, Cham. https://doi.org/10.1007/978-3-319-42721-8_10
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