the arrow in the eye - university of...

The Psychology of Perspective and Renaissance Art

Michael Kubovy

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Edition 1.1, October 6, 2003c©Michael Kubovy

Contents

1 The Arrow in the Eye 1

2 The elements of perspective 17

3 Brunelleschi invents perspective 27

4 Brunelleschi’s peepshow 31

5 The robustness of perspective 41

6 Illusion, delusion, collusion, & paradox 49

7 Perceive the window to see the world 61

8 Marginal distortions 73

9 The Brunelleschi window abandoned 87

10 The psychology of egocenters 101

11 Perspective & the evolution of art 107

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iv CONTENTS

List of Figures

1.1 Mantegna, Archers Shooting at Saint Christopher . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Mantegna, Archers Shooting at Saint Christopher, detail . . . . . . . . . . . . . . . . . . . . . 31.3 Taddeo Gaddi, The Presentation of the Virgin . . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Piero della Francesca, Flagellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.5 Masaccio, Tribute Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.6 Piero della Francesca, Brera altar-piece . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.7 Domenico Veneziano, Martyrdom of Saint Lucy . . . . . . . . . . . . . . . . . . . . . . . . . . 71.8 Raphael, Dispute Concerning the Blessed Sacrament . . . . . . . . . . . . . . . . . . . . . . . 81.9 Domenico Veneziano, La Sacra Conversazione . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.10 Pietro Perugino, Virgin Appearing to Saint Bernard . . . . . . . . . . . . . . . . . . . . . . . 101.11 Copy after Mantegna, Archers Shooting at Saint Christopher . . . . . . . . . . . . . . . . . . 111.12 Mantegna, Saint Christopher’s Body Being Dragged Away after His Beheading . . . . . . . . 121.13 Alberti, Tempio Malatestiano . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.14 Alberti, Tempio Malatestiano, niche . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.15 Mantegna, detail of Figure 1.12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.16 Alberti, Self-portrait . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.1 Masaccio, Trinity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.2 Alberti’s window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.3 Camera obscura . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.4 Geometry of the camera obscura . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.5 Main features of central projection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.7 Jan van Eyck, Annunciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.8 Mantegna, Martyrdom of Saint James . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.6 The Flying Fish of Tyre (ca. 1170) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.9 Vanishing points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.10 Definition of the horizon line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.11 Plan and elevation of Masaccio’s Trinity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.12 Perspective representation of a pavement consisting of square tiles . . . . . . . . . . . . . . . 252.13 Leonardo da Vinci, Alberti’s construzione legittima . . . . . . . . . . . . . . . . . . . . . . . . 26

3.1 Depiction of Brunelleschi’s first experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.1 Wheatstone’s stereoscopic drawing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

v

vi LIST OF FIGURES

4.2 Fra Andrea Pozzo, St. Ignatius Being Received into Heaven . . . . . . . . . . . . . . . . . . . 334.3 Mantegna, ceiling fresco . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.4 Peruzzi’s Salla delle Prospettive seen from center of room . . . . . . . . . . . . . . . . . . . . 354.5 Peruzzi’s Salla delle Prospettive seen from center of projection . . . . . . . . . . . . . . . . . 364.6 Focus and depth of field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.7 Experimental apparatus for Smith and Smith’s experiment. . . . . . . . . . . . . . . . . . . . 39

5.1 La Gournerie’s inverse projection problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.2 Jan Vredeman de Vries, architectural perspective . . . . . . . . . . . . . . . . . . . . . . . . . 445.3 Stimuli in the Rosinski et al. (1980) experiments . . . . . . . . . . . . . . . . . . . . . . . . . 455.4 Displays in the Rosinski et al. (1980) experiments . . . . . . . . . . . . . . . . . . . . . . . . . 455.5 Data of Experiment 1 of Rosinski et al. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.6 Modified data of Experiment 1 of Rosinski et al. . . . . . . . . . . . . . . . . . . . . . . . . . 475.7 Data of Experiment 2 of Rosinski et al. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.8 Stimulus for Goldstein’s (1979) experiment: Rousseau, The Village of Becquigny (1857) . . . 485.9 Data from Goldstein’s (1979) experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

6.1 Stimulus for observing Emmert’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506.2 A classification of trompe l’œil pictures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526.3 Carlo Crivelli (attrib.), Two saints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536.4 Antonello da Messina, Salvatore Mundi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536.5 Jan van Eyck, Portrait of a Young Man . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536.6 Francisco de Zurbaran, Saint Francis in Meditation . . . . . . . . . . . . . . . . . . . . . . . . 546.7 Laurent Dabos, Peace Treaty between France and Spain . . . . . . . . . . . . . . . . . . . . . 546.8 Jacob de Wit, Food and Clothing of Orphans . . . . . . . . . . . . . . . . . . . . . . . . . . . 546.9 Cornelis Gijsbrechts, Easel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546.10 Jean-Baptiste Chardin, The White Tablecloth . . . . . . . . . . . . . . . . . . . . . . . . . . . 556.11 J. van der Vaart (attrib.), Painted Violin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556.12 Jacopo de’Barbari, Dead Partridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556.13 Edward Collier, Quod Libet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556.14 Samuel van Hoogstraten, Still Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566.15 Trompe l’œil (early nineteenth century) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566.16 Drawing used by Kennedy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566.17 The vase-face reversible figure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576.18 A Necker cube formed by phenomenal contours . . . . . . . . . . . . . . . . . . . . . . . . . . 586.19 The vertical-horizontal illusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.20 The double dilemma of picture perception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

7.1 Donatello The Feast of Herod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627.2 Perspective drawing of a figure and determination of center of projection . . . . . . . . . . . . 637.3 How to project a transparency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657.4 Photograph of a photograph (Time, March 29, 1968) . . . . . . . . . . . . . . . . . . . . . . . 657.5 We can only compensate for one surface at a time: stimulus . . . . . . . . . . . . . . . . . . . 667.6 We can only compensate for one surface at a time: what you see . . . . . . . . . . . . . . . . 667.7 Plan of Ames distorted room . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 677.8 Distorted room as seen by subject . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

LIST OF FIGURES vii

7.9 Views of John Hancock Tower, Boston. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 687.10 Drawing of unfamiliar object that we perceive to have right angles . . . . . . . . . . . . . . . 687.11 Drawing of impossible object that we perceive to have right angles . . . . . . . . . . . . . . . 687.12 Drawing of cube indicating angles comprising fork juncture and arrow juncture . . . . . . . . 697.13 Drawing that does not look rectangular and does not obey Perkins’s laws . . . . . . . . . . . 697.14 Irregular shape seen as a mirror-symmetric — it obeys an extension of Perkins’s laws . . . . . 697.15 Figure that looks irregular because it does not obey extension of Perkins’s laws . . . . . . . . 697.17 Shepard and Smith stimulus specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 707.16 Objects used in the Shepard and Smith experiment . . . . . . . . . . . . . . . . . . . . . . . . 717.18 Results of the Shepard and Smith experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

8.1 Two central projections of a church & cloister . . . . . . . . . . . . . . . . . . . . . . . . . . . 748.2 Oblique cubes under normal perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 748.3 Oblique cubes under exaggerated perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . 748.4 Marginal distortions of cubes seen from above . . . . . . . . . . . . . . . . . . . . . . . . . . . 758.5 Four displays and response keys used by Sanders (1963) . . . . . . . . . . . . . . . . . . . . . 758.6 Median reaction time for Sanders (1963) experiment . . . . . . . . . . . . . . . . . . . . . . . 758.7 How Finke and Kurtzman (1981) measured the extent of the visual field . . . . . . . . . . . . 768.9 Raphael, The School of Athens (1510–1) Fresco. Stanza della Segnatura, Vatican, Rome. . . . 778.8 Marginal distortion in spheres and human bodies . . . . . . . . . . . . . . . . . . . . . . . . . 788.10 Detail of Figure 8.9 showing Ptolemy, Euclid, and others. . . . . . . . . . . . . . . . . . . . . 788.11 Marginal distortions in columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 798.12 Paolo Uccello, Sir John Hawkwood . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 818.13 Diagram illustrating argument about perspective made by Goodman . . . . . . . . . . . . . . 84

9.1 Edgerton’s depiction of Brunelleschi’s second experiment . . . . . . . . . . . . . . . . . . . . . 879.2 Droodle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 889.3 Kenneth Martin, Chance and Order Drawing . . . . . . . . . . . . . . . . . . . . . . . . . . . 899.5 Marcel Duchamp, Bottlerack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 909.4 Jean Tinguely, Homage to New York (remnant) . . . . . . . . . . . . . . . . . . . . . . . . . . 919.6 Advertisement for a 3-D (stereoscopic) film . . . . . . . . . . . . . . . . . . . . . . . . . . . . 939.7 Andrea Mantegna, Saint James Led to Execution . . . . . . . . . . . . . . . . . . . . . . . . . 949.8 Central projection in Mantegna’s Saint James Led to Execution . . . . . . . . . . . . . . . . . 949.9 Leonardo da Vinci, The Last Supper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 969.10 Perspective construction of Leonardo’s The Last Supper . . . . . . . . . . . . . . . . . . . . . 979.11 Plan and elevation of room represented in Leonardo’s The Last Supper . . . . . . . . . . . . . 989.12 Leonardo’s Last Supper seen from eye level . . . . . . . . . . . . . . . . . . . . . . . . . . . . 999.13 How the architecture of the refectory relates to Leonardo’s Last Supper . . . . . . . . . . . . 999.14 Leonardo’s Last Supper, cropped . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1009.15 Leonardo’s Last Supper, cropped, top only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

10.1 Definitions of two elementary camera movements: pan and tilt . . . . . . . . . . . . . . . . . 10210.2 The moving room of Lee and Aronson (1974) . . . . . . . . . . . . . . . . . . . . . . . . . . . 10410.3 Predictions for speed of “reading” letters traced on the head . . . . . . . . . . . . . . . . . . . 10510.4 The Parthenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10610.5 Horizontal curvature of Parthenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

viii LIST OF FIGURES

11.1 Paolo Uccello, Perspective Study of a Chalice . . . . . . . . . . . . . . . . . . . . . . . . . . . 11011.4 Kasimir Malevich, two Suprematist drawings . . . . . . . . . . . . . . . . . . . . . . . . . . . 11211.5 Piero della Francesca (?), Perspective of an Ideal City . . . . . . . . . . . . . . . . . . . . . . 11311.6 Gentile Bellini, Procession of the Relic of the True Cross . . . . . . . . . . . . . . . . . . . . . 11311.2 Sol LeWitt, untitled sculpture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11411.3 Leonardo da Vinci, A War Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

List of Tables

11.1 Gablik: cognitive development & megaperiods of art history . . . . . . . . . . . . . . . . . . . 111

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x LIST OF TABLES

List of Boxes

2.1 Drawback of the pinhole camera . . . . . . 192.2 The distance between the vanishing point

and a distance point equals the distance

between the center of projection and the

picture plane . . . . . . . . . . . . . . . 264.1 Photographing illusionistic walls . . . . . . 344.2 Viewing from the center of projection vs.

the removal of flatness information . . . . 377.1 How the visual system might infer the cen-

ter of projection . . . . . . . . . . . . . . 639.1 The aleatory process that generated Figure

9.3 . . . . . . . . . . . . . . . . . . . . 89

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xii LIST OF TABLES

Chapter 6

Illusion, delusion, collusion, andperceptual paradox

Optical illusion

The twinkling of an eye, and the boxes on thefloor

Hang from the ceiling. Really they are notboxes,

But only certain black lines on white paper,(The programme of an hour of magic and illu-

sion)And, but for the eye, not even black on white,But a vast molecular configuration,A tremor in the void, discord in silence.Boehme agrees with Jasper MaskelyneThat all is magic in the mind of man.

The boxes, then, depending on my mindHang in the air or stand on solid ground;Real or ideal, still spaces to explore:Eden itself was only a gestalt.

My house, my rooms, the landscape of my worldHang, like this honeycomb, upon a thought,And breeding-cells still hatch within my brainWinged impulses,(And still the bees will have it that the earth

has flowers)But the same dust is the garden and the desert.

Ambiguous nothingness seems all things and

places.

Kathleen Raine (Raine, 1956, p. 93)

The pictorial effects we have been discussing all fallinto the broad category of illusion. It is the purposeof this chapter to shed some light on the experienceone can have when confronted with objects that fallunder this rubric. The Oxford English Dictionarydefines “illusion” as follows:

Sensuous perception of an external ob-ject, involving a false belief or concep-tion: strictly distinguished from hallucina-tion, but in general use often made to in-clude it, and hence equals the apparent per-ception of an external object when no suchobject is present, or of attributes of an ob-ject which do not exist. (1971 compact ed.,s.v. “illusion”)

One of the best-known examples of such a percep-tion is called the moon illusion, the impression thatthe moon is larger when it is close to the horizonthan when it is close to the zenith. Lloyd Kaufmanand Irvin Rock confirmed in 1962 a theory that hasbeen attributed to Ptolemy,1 to wit, that the moonappears larger on the horizon than at the zenith be-cause the filled space between the observer and thehorizon makes the horizon seem further than thezenith2 (Kaufman and Rock, 1962; Rock and Kauf-

1Claudius Ptolemæus, a second-century astronomer and ge-ographer who lived in Alexandria, author of the Almagest.

2The Kaufman-Rock theory has recently been challengedby Baird (1982), Baird and Wagner (1982), and Hershenson

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50 CHAPTER 6. ILLUSION, DELUSION, COLLUSION, & PARADOX

man, 1962). There is an implicit inference here thatis based on the following law: All other things beingequal, the further away an object (of constant angularsubtense) seems to be, the larger it will appear to be.

An especially pure example of the operation of thislaw was discovered by Emmert, in 1881. It is also easyto demonstrate. Look at the black square in Figure6.1 for about a minute. When you look away, you willsee a dark spot in front of you; this dark spot movesas you move your eyes, because it is caused by theneurochemical process by which the photosensitivecells in your retina recover from the unusually pro-longed exposure that they sustained. Because thiseffect is impressed on the tissue of the retina itself,it must move with your eyes. At first blush, it mayseem surprising that such a purely internal activityfeels as if it were located outside vote; but that isa general rule in perceptual systems: If one stimu-lates sensory receptors in a nonstandard fashion, oneinvariably experiences an external object that wouldstimulate the sensory receptors in a similar fashion.

Figure 6.1: Stare at this square for about a minutein order to observe an afterimage. If you look ata distant wall after impressing afterimage on yourretina, image will appear to be larger than if youlook at a surface much closer to you.

Now this sort of effect on the retina could just aswell have been caused by a distant large square orby a close small one. Because an afterimage doesnot, so to speak, remember the distance of the page

(1982). It is too early to determine the extent to which this newresearch will force a revision of Kaufman and Rock’s theory.In any event, the purpose of the present discussion is to clarifythe notion of unconscious inference and to set the stage forthinking about the nature of illusion. My argument does nothinge on the survival of any particular theory.

on which the stimulating square was printed, the sizeand distance of the black square that one experienceswhen having an afterimage would remain indetermi-nate were it not that perceptual systems abhor in-determinacy. (Try to think of what a square of in-determinate size and distance would look like.) Toforestall such indeterminacy, the visual system usesthe best available information about the size and thedistance of the square: It assesses the distance of thesurface at which the observer is currently looking,and, using that information and information aboutthe size of the afterimage on the retina, it computesthe size of the square to be seen. So if — after youhave impressed an afterimage on the retina — youlook at a distant wall, the square will look large; andif you look at a sheet of paper that is close to you, thesquare will look small. We can now state Emmert’slaw: The apparent size of the object you see whenyou experience an afterimage is directly proportionalto the perceived distance of the surface at which youare looking.

The moon illusion and Emmert’s law are both ex-amples of an important way in which perceptual sys-tems are endowed with the ability to perform whatHelmholtz3 called unconscious inferences, an ideathat is central to what I wish to say about illusionand art in this chapter.4

Do we ever use the term “illusion” in the sensethat applies to the moon illusion when we apply it toart? I think not: I do not think there ever is “falsebelief or conception” when we look at a work of art.Arthur C. Danto’s discussion of illusion (in the senseof false belief or conception) shows clearly why weshould hold this view:

If illusion is to occur, the viewer cannot beconscious of any properties that really be-long to the medium, for to the degree thatwe perceive that it is a medium, illusion iseffectively aborted. So the medium must,as it were, be invisible, and this require-ment is perfectly symbolized by the plate of

3One of the great physicists and psychologists of the nine-teenth century.

4For a contemporary presentation of the theory of uncon-scious inference, see Rock (1977 and, especially 1983).

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glass which is presumed transparent, some-thing we cannot see but only see through(as consciousness is transparent in the sensethat we are not conscious of it but only ofits objects). . . So conceived, it is the aimof imitation to conceal from the viewer thefact that it is an imitation, which is con-spicuously at odds with Aristotle’s thoughtthat the knowledge of imitation accounts forour pleasure. But imitation evidently didnot entail illusion in Aristotle’s scheme. InPlato’s it evidently did, and it is this form ofthe theory I am working with now. Takenas a theory of art, what imitation theoryamounts to is a reduction of the artworkto its content, everything else being suppos-edly invisible — or if visible, then an excres-cence, to be overcome by further illusionistictechnology. (1981, p. 151)

I take it for granted that the reader agrees withDanto’s claim that the artwork should not be reducedto its content, or else that he or she will read his per-suasive argument in Chapter 7 of The Transfigurationof the Commonplace.

The only works of art that come close to exemplify-ing this sort illusion are the illusionistic architectureswe discussed in the preceding chapter and trompel’œil paintings. To better understand the role of illu-sion in art, let us examine this interesting aberrationart. I have classified the illusionistic paintings that gounder the name trompe l’œil (eye foolers) in Figure6.2. The pictures fall into two major groups accord-ing to what the artist has represented.

A trompe l’œil painting of the first kind looks likea painting; a delusory representation is superimposedon a painting that is taken by the viewer to be justthat — a painting. I group these paintings underthe rubric of extrinsic trompe l’œil. There are twosubgroups in this class. First, there are paintings inwhich an element foreign to the painting is paintedto look like a foreign element. For instance, CarloCrivelli’s Saints Catherine of Alexandria and MaryMagdalene (see Figure 6.3), shows a fly on the left-hand niche.5 We may say that such paintings are

5Two other examples of trompe l’œil flies: Portrait of

trompe l’œil of an adventitious element (e.g. thefly). The second sort of extrinsic trompe l’œil is aplay on the viewer’s expectations regarding the frameor framing elements.6 For example, Antonello daMessina, in his Salvatore Mundi (Figure 6.4), painteda cartellino (little card), a trompe l’œil representa-tion of parchment bearing an inscription. As Marie-Louise d’Otrange Mastai (1975) has pointed out, Ar-tonello’s use of the cartellino is in keeping with theearlier device used by portrait painters: Sometimesthey would paint an incised inscription on the para-pet or sill in the foreground that creates the impres-sion that the subject of the portrait is very close tothe picture plane. An example is Jan van Eyck’s Por-trait of a Young Man (Figure 6.5). Eventually, whenthe parapet was abandoned, whenever the cartellinowas retained, it became more thoroughly trompe l’œilby appearing to be pasted on the surface of the paint-ing itself. One such case is Francisco de Zurbaran’sSaint Francis(Figure 6.6). Another use of framingelements for the purposes of trompe l’œil is the rep-resentation of a broken glass in front of the painting.An example is a painting by Laurent Dabos (Figure6.7).

The second class of trompe l’œil paintings, if suc-cessful, are not read as paintings at all. I considerthem instances of intrinsic trompe l’œil. They fallinto three categories: (1) simulated texture or re-lief, (2) simulated objects or settings, and (3) displayboards.

To simulate a bas relief or a texture, one needs forthe most part to work in monochrome. When graystone is to be simulated, the technique is called gri-saille (the term comes from gris, the French for gray).If the material is not gray — such as bronze, terra-cotta, onyx, marble, or wood — a trompe l’œil paint-ing that simulates any of them is called camaıeu.7

Figure 6.8 shows an example of this technique.There are three sorts of trompe l’œil objects and

the Artist and His Wife by the Master of Frankfurt, andMadonna and Child by Adriaen Isenbrandt in the Akademieder bildended Kunste, Vienna (see Mastai, 1975, p. 87).

6On the cognitive psychology of explicit and implicit framesthat provide structure to our experience in society, see Goffman(1974).

7This French word once was synonymous with cameo, butits meaning became restricted in the early eighteenth century.


trompe l'oeil

extrinsic intrinsic

of an adventitious

element(e.g., a fly)

of a framing element

(e.g., cartellino)

grisaille and camaïeu

simulated objects and

settings

chantourné devant de cheminée

objects painted on

unlikely surfaces

display boards

vide poche letter rack poster boardbas relief simulated textures

Figure 6.2: A classification of trompe l’œil pictures

settings: (a) cutouts, (b) hearth screens, and (c) ob-jects painted on odd surfaces. Chantourne (literally,cutout), is a trompe l’œil representation designed tostand away from a wall. An example is Cornelis Gi-jsbrechts’s (Figure 6.9).8

The effectiveness of chantourne paintings relies onan impression of solidity derived from the shadowsthey cast on the walls behind them. Often, as inthe case of Easel the chantourne includes a paint-ing, usually a skillfully illusionistic one. The hearthscreen, devant de cheminee, a French invention, wasquite popular during the late seventeenth and theeighteenth centuries. This type of painting fools theeye because we do not expect a screen there, andwhatever is represented is mundane and does not vi-olate our expectations regarding what we might findin an unused hearth during the summer. The objectsare strongly illuminated in the foreground and quitedim in the background, where the niche of the hearthcasts a shadow. Even Jean-Baptiste Chardin paintedone (Figure 6.10). If the hearth screen is designedto disguise the existence of the surface on which itis painted, there is a similar trompe l’œil effect thatcan be obtained by painting on a surface that is anunlikely candidate to play such a role. An example

8See also Antonio Forbora, The Artist’s Easel (1686),Musee Calvert, Avignon.

is van der Vaart’s Painted Violin (Figure 6.11).We finally come to the best-known class of trompe

l’œil paintings — the several types of display boards.For example: Figure 6.12, the hunting trophy; Figure6.13, the quod libet (what you will), which eventu-ally evolves into the letter-rack; Figure 6.14, the videpoche (pocket emptier); and Figure 6.15, the posterboard.

Although it would take us too far afield to engagein an analysis of the significance and psychologicalbases of these trompe l’œil works, I do want to pointout the role of attention and expectation in creatingthe delusions to which these works can rise. JohnKennedy has taken the first step toward elucidatingthe role of attention in tromp l’œil phenomena. Heasked children to add a drawing of a figure in themidst of the children shown in Figure 6.16. Whenthey concentrated on the central region of the pic-ture, many of them absentmindedly tried to pick upthe pencil. This observation suggests that althoughthe standard claim about trompe l’œil — namely thatit requires the representation of an object of shallowdepth — is true enough, it fails to do justice to thepsychological complexity of the phenomenon. It isperhaps correct as a statement of a necessary condi-tion for the occurrence of the trompe l’œil effect, butit leaves the question of the effect’s sufficient condi-

53

(a) Saint Catherine ofAlexandria

(b) Mary Magdalene

Figure 6.3: Carlo Crivelli (attrib.), Two saints (1480–5). The National Gallery, London.

Figure 6.4: Antonello da Messina, Salvatore Mundi(1465). The National Gallery, London.

Figure 6.5: Jan van Eyck, Portrait of a Young Man(1432). The National Gallery, London.


Figure 6.6: Francisco de Zurbaran, Saint Francis inMeditation (1639). The National Gallery, London.

Figure 6.7: Laurent Dabos, Peace Treaty betweenFrance and Spain (after 1801). Musee Marmottan,Paris.

Figure 6.8: Jacob de Wit, Food and Clothing of Or-phans (1728).

Figure 6.9: Cornelis Gijsbrechts, Easel. 226 × 123cm. (ca. 1670). Statens Museum for Kunst, Copen-hagen.

55

Figure 6.10: Jean-Baptiste Chardin, The WhiteTablecloth (1737). Shows devant de cheminee. TheArt Institute of Chicago.

Figure 6.11: J. van der Vaart (attrib.), Painted Vi-olin (late seventeenth or early eighteenth century).Devonshire Collection, Chatsworth, England.

Figure 6.12: Jacopo de’Barbari, Dead Partridge(1504). Alte Pinakothek, Munich.

Figure 6.13: Edward Collier, Quod Libet (1701). Vic-toria and Albert Museum, London.

tions unasked.9

What is it about the delusion of trompe l’œil thatmakes such works interesting? After all, there isnothing fascinating in a trompe l’œil painting un-til the delusion has been dispelled; and once it hasbeen dispelled, the work is most often of no morethan minor aesthetic interest. We enjoy examiningan object endowed with the power to throw us into adelusory state of mind after it has divulged its secretto us; looking at it sends a shiver down our meta-

9See Liotard (1973, Chapter 1), cited in Gombrich (1969,p. 430). See also interesting discussions in Gombrich (1969,p. 430) and a major historical review in Mastai (1975), uponwhich the above discussion leans heavily. There are also brieferreviews in Dars (1979) and Leeman, Elfers, and Schuyt (1976).


Figure 6.14: Samuel van Hoogstraten, Still Life(1655). Gemaldegalerie der Akademie der bildendedKunste, Vienna.

Figure 6.15: Trompe l’œil (early nineteenth century).Nuremberg.

Figure 6.16: Drawing used by Kennedy

physical spines much in the way we shiver when wethink about an accident in which we were almost in-volved; we stare at it much as we might stare at thecarcass of a wild animal that almost got the betterof us. A trompe l’œil picture is an epistemologicalclose call, a reminder that Descartes’s evil being thatcontinuously fills us with error may be disguised as abenevolent painter. The point I wish to make there-fore is that what is interesting about a trompe l’œilpainting arises in our minds after the painting hasceased to trompe our yeux ; it is when we have ceasedto be the unwitting targets of a practical joke, andwe have decided to reflect upon the experience wehave just gone through, that the painting acquiresits meaning.

And then looking at a trompe l’œil painting afterthe delusion has been dispelled is fascinating becauseit shows us how utterly preposterous was Ruskin’sfamous idea of the “innocent eye.” One tries in vainto be deluded again, but one can’t; at best we areimpressed by an illusion, which we obtain by activelycooperating with the artifices devised by the artist.But there is always a sense of innocence lost, a ban-ishment from paradise, a fool’s paradise to be sure,but paradise nevertheless.

All illusionistic art other than trompe l’œil reliesfor its effect on a collusion between the artist and thespectator. Consider illusionistic paintings of architec-ture for a moment. None of these paintings places thespectator at the center of projection at the momentthe picture becomes visible. For instance, Pozzo’simaginary architecture in the Church of Sant’Ignaziolooks lopsided unless it is seen from the yellow mar-

57

ble disk in the center of the church’s nave: Therefore,only a visitor who would have asked to be led blind-folded to the prescribed vantage point would see thepainting correctly, as it were, at first sight; but tohave prepared one’s experience so carefully presup-poses prior knowledge of the spectacle one was aboutto behold and enjoy. Most viewers deeply enjoy theexperience despite having first seen it lopsided anddistorted. These viewers are in mental collusion withthe artist who designed and painted the illusionisticarchitecture because they know full well that theyare experiencing an illusion when they view the ceil-ing from the center of projection.

This concept of mental collusion is similar to Co-leridge’s “willing suspension of disbelief for the mo-ment, which constitutes poetic faith” (1907, Book II,Chapter 14, p. 6). The difference is one of degree:Willing suspension of disbelief refers to a cognitiveoperation, a voluntary adoption of a certain aestheticattitude; by mental collusion with the artist, I meanan operation much closer to the roots of perception,more on the order of a suggestion than a frame ofmind.

The concept of mental collusion appears in non-aesthetic perceptual contexts as well. For instance,certain illusions not occur spontaneously or involun-tarily; they occur only after the viewer is informedwhat he or she is expected to see. But once thatknowledge is imparted, there is little the viewer cando to escape its effect. As an example, consider theexperiment in which Girgus, Rock, and Egatz (1977)measured the time it took observers to experience afigure-ground reversal in Rubin’s (1915) vase-face fig-ure (see Figure 6.17), which was thought to sponta-neously reverse back and forth between the vase per-cept and the face percept. The observers were high-school students who had never seen the Rubin figurebefore. Every 5 seconds, the experimenter tappeda pencil to mark the moment at which the observerwas to report what he or she was seeing in the fig-ure. Every effort was made to communicate to theobservers that certain figures could be described inmore than one way, and that therefore their reportscould differ from signal to signal, but they were nottold that the Rubin figure was reversible and theywere not told what the alternative descriptions could

be. After having obtained the observers’ reports, theexperimenter interviewed them to ascertain whetherunreported reversals had occurred at every tap. Evenwith this scoring procedure, which was most likelyto overestimate the number of reversals seen spon-taneously, only So percent of the observers saw thefigure reverse within the first minute of viewing, afigure that went up to 6o percent within the first twominutes and to 65 percent within the first three min-utes. During the interview, observers were taught tosee both alternatives and to grasp the reversibility ofthe figure. Afterward, the observers were tested againand, as expected, all of them reported reversals.

Figure 6.17: The vase-face reversible figure.

To better clarify the notion of mental collusion, letus look at the wonderful illusion invented by Bradley,Dumais, and Petry (1976; see Figure 6.18). The ini-tial impression one receives is of a white paper cutoutof a Necker cube superimposed on a sheet of whitepaper on which eight black disks have been drawnin order to enable you to see the figure’s critical fea-tures. Even though there are no lines joining thecorners, you see them, an unconscious inference re-garding the nature of the object that would createthis sort of configuration. You are not free to see ornot to see these phenomenal contours: If you see theNecker cube as I described it, you always see the con-tours. When you do, you also can see the cutout asa representation of a three-dimensional object, and,because the representation is ambiguous, you can seeit reverse, as does the Necker cube. Now the inter-esting twist to this illusion comes when one’s atten-tion is drawn to another way of interpreting the eightspots. Imagine a sheet of paper with eight holes init, and under it a sheet of black paper that can beseen through the holes. Now suppose we took the


white paper cutout of the Necker cube and slipped itbetween these two sheets so that the critical featureswere visible through the eight portholes in the topwhite sheet of paper. When you interpret the figurein this fashion, you can still “see” the Necker cube,and you can still experience reversals of its orienta-tion, but you do not see the phenomenal contours.The act of choosing to see the cutout of the cube be-hind a page with holes in it rather than in front ofthe page with spots on it is very much like a will-ing suspension of disbelief. But once one has made acommitment to that suspension of disbelief, the worldwe perceive is consistent with how we have chosen toperceive it. It is important to remember that we arenot in a position to reinterpret every facet of our per-ceptual experience and to see how the implicationsof our choice propagate through the remainder of ourexperience. But there are certain aspects of experi-ence that allow us to make such a choice, although,unfortunately, we do not understand what gives themthis power.10

We appreciate illusionistic art without being de-luded; we know that what we are seeing is mere ar-tifice; we experience illusion because we are in collu-sion with the artist. In contrast to illusionistic art,we appreciate trompe l’œil because we were initiallydeluded. Mental collusion has very little to do withour appreciation of these creations, which, if we ap-preciate them at all, are reminders of the fallibilityof knowledge acquired through the senses.

Having discussed the nature of delusion in trompel’œil and the nature of collusion in illusionism, we

10It is interesting to think of the complexity of representa-tion and to speculate on how many levels of representationcan be embedded in each other. The simplest case I know isthe drawing on a cereal box of a boy holding a cereal box,on which there is a drawing of a boy holding a cereal box, onwhich. . . This case is easy, because we need not keep track ofwhich representation is represented by which. All we have todo is invoke a perceptual “etc. experience,” well-described inGombrich (1969, pp. 219–21). In language, the limit is mem-ory: We are hard put to unravel the sentence, “The mousethat the cat that the fire burned ate.” Any more deeply em-bedded phrases would render the sentence incomprehensiblewithout resorting to syntactic analysis. In the case of Bradley,Dumais, and Perry’s illusion, we have two levels: a drawing ofa cutout and its background (one level of representation), andthe cutout representing a cube (an embedded representation).

Figure 6.18: A Necker cube formed by phenomenalcontours as a perceptual analog of willing suspensionof disbelief

turn now to a third anomalous state of mind we some-times experience when viewing a painting, namely,perceptual paradox. In the preceding chapter, wediscussed the sorts of deformations we perceive inpaintings despite the fact that in general perspec-tive is robust. Although it seems paradoxical that,at one and the same time as one passes in front of apainting, the scene appears to turn and to remain thesame, it is possible because not all aspects of our per-ception are processed by the same mechanisms; thereis a division of labor that usually works so well thatit is not noticed. The well-trained bureaucracy of themind can deal with practically all the contingenciesthat occur in our environment. But when psychol-ogists contrive devices that stimulate us in unusualways, ways that are unlikely to arise in our environ-ment, perception can be made to reveal the divisionof labor without which it could not function. Therules by which the bureaucracy has been accustomedto work may now lead to incompatible decisions.

For instance, take the waterfall illusion: On ascreen, we display an unbroken series of horizontalblack stripes moving downward. After a viewer staresat this stylized waterfall for a while, the motion isstopped, and he or she is asked to report what the dis-play looks like. The display looks paradoxical: Thestripes appear to be moving upward, but at the sametime each stripe does not seem to be changing its po-sition relative to the frame of the screen. This sortof perceptual decomposition has led to the hypoth-esis, now well-supported by experimental evidence,

59

that motion and location in space are processed bydifferent mechanisms (Attneave, 1974). No less in-teresting, though, is the following implication of thephenomenon: The visual system makes no attemptto reconcile these contradictory pieces of informationabout the world; we experience these unreconciledcontradictories, this perceptual paradox, as illusion.

Figure 6.19: The vertical-horizontal illusion

It is important to keep in mind the distinctionbetween illusion as perceptual error, which we havecalled delusion, and illusion as an awareness of per-ceptual error, which we have called collusion. As wehave seen in our discussion of the vase-face illusion,most illusions do not provide us with the experienceof illusion unless we are given an opportunity for col-lusion, an understanding of what we are to expect toexperience. Take, for instance, the vertical horizon-tal illusion (Figure 6.19). The vertical looks longerthan the horizontal: That is a perceptual error. Butit is only when you are put in a position to experi-ence a perceptual dilemma — such as being told torotate the drawing slowly, and becoming aware of thechanges in the relative lengths of the two lines duringthe rotation, while realizing that the drawing itself isinvariant that you may experience an illusion: Thisis a metaperceptual experience: It is an awareness ofperceptions; the visual system does not try to recon-cile the two experiences, and that non-reconciliationgives rise to the experience of illusion.

The impression of following in a painting is one ofthose rare instances where an object spontaneouslygives rise to the experience of an illusion. My ex-planation of this phenomenon is schematically sum-marized in Figure 6.20. The experience of the pic-ture turning stems from two perceptions: On theone hand, even though we are walking around the

picture, we perceive the spatial layout of the rep-resented scene as if it remains unchanged. This iswhat we have called in Chapter 5 the robustness ofperspective (which we will discuss at length later).On the other hand, even though the spatial layout ofthe scene remains unchanged, we perceive our ownmotion in space as we walk past the picture. Theexperience of rotation of the painting is one way toresolve this dilemma: To perceive the scene as be-ing invariant while we are walking past it, we mustperceive the picture to be rotating.

as I walkpast thepicture,

my vantagepoint is

changing

because of therobustness

of perspective,

the sceneisn't

changing

the pictureis rotating

to follow me

the pictureis rotating

to follow me

but, fromother evidence

therefore,

I experienceperceptualparadox

I call it anillusion

DILEMMA 1

DILEMMA 2

Figure 6.20: The double dilemma of picture percep-tion that leads to the experience that the turning ofthe picture, as we walk past it, is illusory

As Gombrich has pointed out,11 this resolution ofthe dilemma is reinforced in paintings that containobjects with a pronounced aspect such as a foreshort-ened gun barrel, a pointing finger, a human eye, or aroad receding into the distance from the center fore-ground to the horizon (such as the Rousseau paintingdiscussed toward the end of the preceding chapter).These are objects that are represented in an orienta-tion that is visually unstable: If you are looking downthe barrel of a gun, you need to take only a very small

11See Gombrich’s essay, “Perception and the Visual Dead-lock,” in Gombrich (1963); also see Gombrich (1973).


step sideways in order not to be looking down thebarrel of the gun. We say here that objects are rep-resented in a visually unstable orientation by analogywith objects that are in a physically unstable equilib-rium, such as a pyramid that has been balanced onits tip: You need to apply only a minuscule changeto the forces exerted upon the pyramid to cause it tofall.12 It is quite natural, therefore, that we performthe unconscious inference: The object is shown in avisually unstable orientation; I am moving enoughto destabilize the view; the view is not destabilized;therefore, the object must be turning to follow me.

But that solution to the dilemma is, so tospeak, shortsighted, because it gives rise to anotherdilemma: If the picture is turning, how is it that itlooks so well attached to the wall? Why does its re-lation to the room not change? The experience ofillusion stems from the visual system’s inability toresolve this dilemma within a dilemma.

Although we have shown that some distortions dotake place in the perception of paintings that areviewed by moving observers, it is the robustness ofperspective that emerges most clearly from our anal-ysis. As we will see presently, it is this robustnessthat is probably the most important justification fornot using Brunelleschi peepholes to view perspectivepaintings.

12This formulation is inspired by Shepard (1981, pp. 307–9),who refers to Rene Thom’s (1975) catastrophe theory. A sim-ilar notion can be found in the work of Huffman (1971), whocalls accidentals what we have called “visually unstable orien-tations.” See also Draper (1980). Anstis, Mayhew, and Morley(1969) have shown that the position of the iris and pupil withrespect to the eye socket and the eyelids is sufficient to de-termine the perceived direction of a gaze. If the iris and thepupil are centered, we feel that the person is looking directlyat us. Hence, if we move and the gaze remains directed at us,we perceive the gaze to be following us.

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