Abstract
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).
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Notes
- 1.
Panofsky often engaged in this type of aesthetic evaluation: “The represented objects appear to stand, for the most part, more above than on the floor”; “It is also an inconsistent space, in that objects—for example, in our panel the table of the Last Supper—appear to stand in front of the ‘space box’ rather than in it”; “Space thus seems to extend forward across the picture plane; indeed, because of the short perpendicular distance it appears to include the beholder standing before the panel,” Erwin Panofsky, “Die Perspektive als symbolische Form” (1924/5), Perspective as Symbolic Form, pp. 55, 56, 60 (italics mine). Panofsky notes that the feeling of correctness is socially constructed, which suggests that one can only begin to evaluate a perspective by questioning the presuppositions that form the background to an axiological evaluation.
- 2.
Raymond Boudon, L’Art de se persuader, Paris, 1990, p. 7.
- 3.
The situation of a heuristic search for solutions in a context of limited information is reminiscent of the early attempts by individuals unfamiliar with mathematics to solve problems of probability; see Amos Tversky and Daniel Kahneman, “Availability: a heuristic for judging frequency and probability,” Cognitive Psychology 5 (1973): 207–232. We must not forget that most of the basic concepts of perspective, beginning with the “vanishing point,” were unknown in the Renaissance (for instance, Alberti speaks of a punctum centricus; the concept of punctum concursus still lay in the future). We owe the conceptualization of this notion to seventeenth-century mathematicians such as Guidobaldo del Monte, who was one of the first to study methods of projection; see Martin Kemp, “Geometrical perspective from Brunelleschi to Desargues,” Proceedings of the British Academy, 70 (1985): 89–132; Judith V. Field, “Alberti, the abacus and Piero della Francesca’s proof of perspective,” Renaissance Studies 11/2 (1997): 61–88.
- 4.
Here is a sample: “Objects of equal size unequally distant appear unequal and the one lying nearer to the eye always appears larger/Aequales magnitudines inaequaliter expositae inaequales apparent et maior semper ea quae propius oculum adjacet,” Euclid, Optica, sup. 5; “At distance, the same object makes a small angle in the eye which it would make great when it is close/Eadem res distans facit paruum angulum in oculo quae faceret magnum quando est propinqua,” Bacon, Perspectiva, II, III, 3; “Among equal and equidistant sizes at unequal distances from the eye, the closer will always appear greater, but they will not be seen in proportion to their distances/Aequalium et aequidistantium magnitudinum inaequaliter ab uisu distantium propinquior semper maior uidetur, non tamen proportionaliter suis distantiis uidetur,” Witelo, Optica, IV, 25; “Among objects of equal size, that which is most remote from the eye will look the smallest/Infralle cose dequal grandeza quella chessara piu distante dallochio si dimossterra di minore figura,” Da Vinci, MS. SKM II, fol. 63r.
- 5.
Panofsky, Perspective as Symbolic Form, French edition, pp. 229, 232.
- 6.
Alberti verified the correctness of the perspective construction by applying this property, but was unaware that the diagonals should converge at a distance point: “If the same line is extended in the depicted floor, it will form the diagonal of the joined squares. Indeed, among mathematicians, the diagonal of a square is a kind of straight line that is drawn from one corner to the opposite corner of the square, which divides it into two parts so that to make two triangles of it/Qui quidem quam recte descripti sint inditio erit, si una eademque recta continuata linea in picto pauimento coadiunctorum quadrangulorum diameter sit. Est quidem apud mathematicos diameter quadranguli recta quaedam linea ab angulo ad sibi oppositum angulum ducta, quae in duas partes quadrangulum diuidat ita ut ex quadrangulo duos triangulos fit,” De pictura, I, 20.
- 7.
Leon Battista Alberti, On Painting and On Sculpture, ed. C. Grayson, London, 1972; idem, De la peinture/De pictura (1435), ed. J.-L. Schefer, Paris, 1992.
- 8.
Panofsky, Perspective as Symbolic Form, p. 62.
- 9.
Other connections between abacus—a term that encompasses arithmetic and algebra—and perspective have been proposed in order to understand the construction methods of Piero della Francesca; Judith V. Field, “Alberti, the abacus …”.
- 10.
This construction point (P), which foreshadows the “distance point” of linear perspective as codified in the seventeenth century, does indeed seem to have been used by painters, since we can often find it in a conspicuous place in the architectural décor; for example, at the corner of a pilaster (Brunelleschi) or on the edge of a building (Ghiberti) or on the shoulder of a figure (Donatello).
- 11.
Alessandro Parronchi, “Le due tavole prospettiche del Brunelleschi,” Paragone 107 (1958), p. 16.
- 12.
Richard and Trude Krautheimer, Lorenzo Ghiberti, Princeton, 1956. p. 251.
- 13.
John White, The Birth and Rebirth of Pictorial Space, (London: Faber, 1967); trans. Catherine Fraise, Naissance et renaissance de l’espace pictural (Paris: Adam Biro, 2003) p. 172.
- 14.
Martin Kemp, The Science of Art. Optical Themes in Western Art from Brunelleschi to Seurat, New Haven, 1990, p. 25.
- 15.
White, Naissance et renaissance de l’espace pictural, p. 162.
- 16.
“Donato sculptore… fu grande imitatore degl’antichi, et di prospectiva intese assai,” as quoted by Pietro Roccasecca, “La finestra albertiana,” Nel segno di Masaccio, Florence, 2001, pp. 64–69.
- 17.
Alan P. Darr and Giorgio Bonsanti, Donatello e i suoi, Detroit, Firenze and Milano, 1986, p. 141.
- 18.
Kemp, The Science of Art, p. 39.
- 19.
Vittorio Sgarbi, Carpaccio, Bologna, 1979, p. 17.
- 20.
Marisa Dalai Emiliani, “La question de la perspective,” Perspective et histoire au Quattrocento, Paris, 1979, p. 17.
- 21.
Early on Panofsky recognized the problems raised by the use of this holistic notion. He wrote: “The term Kunstwollen usually refers artistic phenomena in their entirety, to the artworks of a whole era … whereas the term ‘artistic intention’ is more often used to characterize an individual work of art,” Panofsky, Perspective as Symbolic Form, French edition, p. 200.
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Raynaud, D. (2016). Understanding Errors in Perspective. In: Studies on Binocular Vision. Archimedes, vol 47. Springer, Cham. https://doi.org/10.1007/978-3-319-42721-8_3
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