arnolfini portrait perspective

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On the Mathematics of the Perspective of the Arnolfini Portrait and Similar Works of Jan van Eyck Author(s): John L. Ward Source: The Art Bulletin, Vol. 65, No. 4 (Dec., 1983), pp. 680-686 Published by: College Art Association Stable URL: http://www.jstor.org/stable/3050378 . Accessed: 25/01/2011 19:26 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at . http://www.jstor.org/action/showPublisher?publisherCode=caa. . Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. College Art Association is collaborating with JSTOR to digitize, preserve and extend access to The Art Bulletin. http://www.jstor.org

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Perspective in the Arnolfini Portrait

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Page 1: Arnolfini Portrait Perspective

On the Mathematics of the Perspective of the Arnolfini Portrait and Similar Works of Janvan EyckAuthor(s): John L. WardSource: The Art Bulletin, Vol. 65, No. 4 (Dec., 1983), pp. 680-686Published by: College Art AssociationStable URL: http://www.jstor.org/stable/3050378 .Accessed: 25/01/2011 19:26

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unlessyou have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and youmay use content in the JSTOR archive only for your personal, non-commercial use.

Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at .http://www.jstor.org/action/showPublisher?publisherCode=caa. .

Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

College Art Association is collaborating with JSTOR to digitize, preserve and extend access to The ArtBulletin.

http://www.jstor.org

Page 2: Arnolfini Portrait Perspective

680 THE ART BULLETIN DECEMBER 1983 VOLUME LXV NUMBER 4

savagery, and the "golden" style of Claude to depict the coming of civilization? In short, here, as in many other well-documented instances, Bingham seems to have tried to utilize the principles of

high art, as he had learned them from art manuals and other sources, to immortalize the development of the Western frontier.

Museum of Art, Carnegie Institute Pittsburgh, PA 15213

Discussion On the Mathematics of the Perspective of the Arnolfini Portrait and Similar Works of Jan van Eyck

John L. Ward

The arguments and evidence presented by David L. Carleton in his note, "A Mathematical Analysis of the Perspective of the

Arnolfini Portrait and Other Similar Interior Scenes by Jan van

Eyck," in the March, 1982, issue are inadequate to support any of what I take to be his major claims. These are as follows:

(1) Van Eyck's paintings, the Annunciation of the Ghent Altarpiece, the Dresden Triptych, the Ince Hall Madonna, the Rolin Madonna, the Arnolfini Portrait,1 the Madonna of Canon van der Paele, and the Lucca Madonna, employ a perspective with "two vanishing areas centered at the two foci of an

ellipse,"2 which is therefore referred to by Carleton as elliptical perspective.

(2) The Arnolfini Portrait has the basic optical effects of a con- vex mirror, which were derived from one such as that on the rear wall of the painting.3

(3) "Jan's convex mirror was also present at the time of the ex- ecution of his other interior scenes" and its use "led to his

development of a consistent application of a mathematical theory of perspective, best called elliptical perspective."4

To substantiate his first point, Carleton presents perspective drawings of the seven Van Eyck paintings discussed. Five of these drawings reverse the layout of the paintings without ex- planation or apparent purpose. On the basis of these drawings, Carleton concludes that each picture has a perspective with two central vanishing areas, that these are both lowered in each sub- sequent picture, until the last one, the Dresden Triptych, returns to an earlier, less monumental form, and that the two vanishing areas and their sequential lowering "lead to the conclusion that Jan probably did have a mathematical theory of perspective, and that he consistently applied and developed this theory.""

Carleton insists on the presence of only two vanishing areas for each of the pictures that he discusses instead of the three mentioned by G. Ten Doesschate or the four mentioned by Pan- ofsky for the Arnolfini Portrait.6 However, the imprecision of Carleton's drawings and the omission of certain orthogonals greatly exaggerate the consistency of the convergence into two vanishing areas. To be sure, the floor and ceiling converge in two precise vanishing areas in the Arnolfini Portrait and in more ap- proximate ones in the Van der Paele Madonna and the Dresden Triptych. But the Rolin Madonna has two vanishing areas for the floor alone, the upper one of which is slightly higher than the vanishing area for the orthogonals of the upper wall; the Ghent Altarpiece Annunciation has only one coherent vanishing area, that of the floor orthogonals,' and the Ince Hall and Lucca Madonnas are quite inconsistent in perspective.8

The Lucca Madonna is perhaps most instructive, since Carleton follows Panofsky in giving it a late date and one might expect it to be one of the clearest examples of a fully developed, mathematically consistent, "elliptical" perspective. My perspec- tive drawing of the Lucca Madonna (Fig. 1) shows that the floor does not converge accurately to a single area (if the receding lines of the rug were projected, the disparity would be much greater), in contrast to the floor of the Arnolfini Portrait and that of the earliest work analyzed, the Ghent Altarpiece Annunciation,

II have retained the familiar title of the painting for convenience, although Peter Schabacker's study of its iconography ("De matrimonio ad morganaticum contracto: Jan van Eyck's 'Arnolfini' Portrait Recon- sidered," Art Quarterly, xxxv, 1972, 375-98) reopens the question of the

subjects' identities. 2 David L. Carleton, "A Mathematical Analysis of the Perspective of the Arnolfini Portrait and Other Similar Interior Scenes by Jan van Eyck," Art Bulletin, LXIV, 1982, 119.

3 Ibid., 123-24.

4 Ibid., 124.

5 Ibid., 121. 6 Ibid., 119. See Panofsky, Early Netherlandish Painting, Cambridge, Mass., 1953, I, 203, and G. Ten Doesschate, Perspective: Fundamentals, Controversials, History, Niewkoop, 1964, 139f.

7 Of course the orthogonals of the beams at the juncture of the side walls and ceiling in the two outer panels will cross somewhere. However, in sharp contrast to the consistency with which the floor orthogonals are plotted, the three orthogonals of each beam cross each other well before they meet any of the orthogonals from the opposite beam. A careful analysis clearly shows that the floor projection is constructed deliberately and carefully as a single system. G.J. Kern, whose fundamental studies

on Van Eyck's perspective are not cited by Carleton, observes that, with respect to the two central panels, "von fiinfzehn Linien sich nicht weniger als vierzehn genau in einem Punkte schneiden" ("Perspektive und Bildarchitektur bei Jan van Eyck," Repertorium fiir Kunst- wissenschaft, xxxv, 1912, 28. For a perspective drawing of the outer left panel, see fig. 19 in my article, "Hidden Symbolism in Jan van Eyck's Annunciations," Art Bulletin, LVII, 1975, 196-220). By contrast, no attempt whatever was made to join the orthogonals of the two beams in a single vanishing area. Carleton's perspective drawing, on the other hand, seems to imply that Van Eyck organized his space by plotting the convergence, on each side of the picture, of one of the many floor orthogonals with an orthogonal of one of the beams. Such a procedure not only disregards the strict accuracy of the floor convergence, but also implies that the artist would be more concerned over pictorial relationships not evident to a viewer than over those that would be dis- turbingly evident if the convergence of orthogonals was inaccurate. 8 The Ince Hall Madonna, presently owned by the National Gallery of Victoria, Melbourne, is now universally recognized by scholars as not by Van Eyck (see U. Hoff and M. Davies, The National Gallery of Victoria, Melbourne, Les primitifs flamands, I, Corpus de la peinture des anciens

Pays-Bas meridionaux au quinzieme sikcle, xII, Brussels, 1971, 29-50). Although I believe it to be a good copy after a lost Van Eyck, any conclu- sions with respect to the perspective must be cautiously made.

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DISCUSSION 681

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1 Lucca Madonna, perspective drawing

which do.9 Figure 1 also shows that the sides of the throne base meet at a point immediately next to the vanishing area of the

descending orthogonals of the cloth of honor,1o and that the

orthogonals along the walls are entirely independent of these areas of convergence. These deviations from a two-point central

perspective construction seriously weaken the claim that a mathematical system of perspective has been used, or any method based on two areas of convergence.

Generally speaking, in Van Eyck's pictures the more the ac-

curacy of the convergence of orthogonals can be visually estimated (because of length, uninterrupted visibility, number, proximity, and situation within the same plane), the more care Van Eyck takes to converge his orthogonals accurately. Hence the strict accuracy of the floors of the Arnolfini Portrait, the Ghent Altarpiece Annunciation, and the central section of the Rolin Madonna in contrast to the floors of the Ince Hall and Lucca Madonnas and the side sections of the Rolin Madonna's floor. Hence, too, the lesser accuracy, in the pictures analyzed by Carleton, of the orthogonals to the sides of the picture, which are

either non-existent or, as in the Arnolfini Portrait and the Lucca Madonna, shorter, fewer, more scattered, or otherwise less in need of treatment as a single system. On the other hand, where

orthogonals at the side of the picture are more numerous and longer, and they lie within an uninterrupted plane, as in the Annunciation in the National Gallery, Washington, or the very early Madonna in a Church in Berlin, they converge to a much more accurate vanishing area. These two works, deleted from Carleton's discussion "as being considerably different in their spatial objectives,"" only clarify, by means of the greater num- ber of side orthogonals, a tendency that is also evident in the pic- tures he does discuss, namely, for the orthogonals that belong to a side wall or vertical receding plane to cross the vertical axis passing through the vanishing area of the floor or ceiling orthogonals before they meet. Sometimes, as in Carleton's draw- ing of the Arnolfini Portrait,12 the selective diagramming of orthogonals will make ambiguous whether the side orthogonals meet in their own vanishing areas or can be divided between the floor and ceiling systems. But my drawing of the Lucca Madonna's perspective clearly shows that the side orthogonals do not belong to the same systems as do the floor or the cloth of honor.

Carleton's proposal goes beyond the claim that Van Eyck used two vanishing areas, which he regards as "Jan's heritage from the Boucicault Master."'3 In his view, Van Eyck's hitherto un- recognized innovation lies in the positioning of these vanishing areas "at the two foci of an ellipse.""4 What can that mean? Where is the ellipse of which he speaks? Perhaps Carleton's description of Van Eyck's perspective as elliptical is meant as a figure of speech to suggest that, just as an ellipse is a circle stretched by separating its center into two foci, so the spaces in Van Eyck's pictures are correspondingly stretched along an axis between the vanishing areas. For example, he argues that the in- terior of a cube drawn in "elliptical perspective" would be con- siderably narrower across its back surface than if drawn in one- point perspective. From this he concludes that "there would have been an overall approximate 43% increase in the area of the rear wall [of the Arnolfini Portrait] if Jan had used single vanishing point perspective."'5

In fact, however, nothing prohibits the redrawing of the pic- ture in one-point perspective while retaining the proportions of the back wall. I have done so in Figure 2. If this drawing is taken as an accurate representation of the room that Van Eyck meant to depict, his treatment of the perspective has the result of flaring the receding vertical planes outward and reducing the tilt of the floor and ceiling. This explanation of Van Eyck's perspective procedure has the advantage of assuming much less deviation from an accurate representation of the original space (if there was one) than does Carleton's.

Having shown to his satisfaction that Jan consistently used a mathematical perspective, Carleton next proposes to discover its sources. He begins with John White's observation of curvature in the Arnolfini Portrait floor.16 Although Carleton admits that

9 For a perspective drawing and analysis of the Arnolfini Portrait, see Kern (as in note 7), 29-30 and fig. 1, or Die Grundziige der linear-

perpektivischen Darstellung in der Kunst der Gebriider van Eyck und ihre Schule, Leipzig, 1904, pl. Iv. For the Ghent Altarpiece Annunciation, see note 7. 10 In the Van der Paele Madonna, there is also a separate area of con-

vergence for the orthogonals of the throne base, but it is lower than that of the floor.

11 I assume that these are the deleted works Carleton describes as "large- scale paintings with church interiors" (p. 119) simply because they are the only other paintings with church interiors by Van Eyck, except for

the porch-like space of the Maelbeke Triptych, completed after Van

Eyck's death. Given the dimensions of these pictures, however (36V2 x

143/8" and 12?4 x 521" respectively), I must assume that Carleton meant to refer to the churches' scale. 12 Carleton, fig. 8.

13 Ibid., 119. 14 Ibid.

15i Ibid., 120. 16 John White, The Birth and Rebirth of Pictorial Space, London, 1957, 234.

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682 THE ART BULLETIN DECEMBER 1983 VOLUME LXV NUMBER 4

there are no visible curved transverse or orthogonal cracks or any other visible evidence of spatial curvature, he argues that "assuming, a priori, that this curvature exists, we must account for its presence."'7 An attempt to explain the presence of cur- vature the very existence of which has not been demonstrated, and that is admittedly denied by the only visible transverse line on the floor, does not seem to be a promising undertaking. However, I will offer a suggestion below of why the picture in general may give an impression of curvature.

Carleton suggests that the artist's use of a convex mirror sup- plies the explanation for the intuited floor curvature. To demonstrate the effects of convex curvature on the layout of the floor, Carleton constructed a model on a 1:10 scale that he photographed from in front and again through a hole in the back wall (in the position of the mirror in Van Eyck's picture). The lat- ter photograph was taken of the scene reflected in a six-inch con- vex mirror placed at the front end. Carleton compares the two pictures and argues that the one taken in the mirror more closely resembles Van Eyck's painting. However, these conclusions are not justified by the evidence that he presents.

Carleton begins his analysis by arguing that the presence of curvature in the floor photographed in the convex mirror duplicates an optical effect of the Arnolfini Portrait. Yet the evidence that he points to - the curvature of the transversal in the center of the floor - is unlike the Arnolfini Portrait, where, as Carleton acknowledges,18 the transversal has no visible cur- vature. It should also be noted that Carleton's photograph of the convex mirror reflection introduces a curvature of all straight lines except orthogonals and that none of the lines that appear curved in the photograph are curved in the painting.

Carleton also cites as evidence of Jan's use of a convex mirror the fact that in the frontal photograph both upper corners of the background chair are visible, whereas in the mirrored photograph and in the Van Eyck painting "the upper right-hand corner of this chair disappears behind the head of Jeanne Cenami."19 However, the difference in overlap arises primarily from the use of a different projection point for the perspective (determined by the position of the camera in the frontal photograph and by its reflected, rather than actual, position in the photograph taken from the mirror). Specifically, the frontal photograph is taken with the camera placed just beneath the level of the crossbar of the window and to the right of the picture's center, while the reflected image has its projection point opposite the hole in the back wall. The distance of the projection point also seems significantly different, with the frontal photograph having been taken at a greater distance than the projection point of the reflected photograph.

Here a word of explanation is necessary concerning the optical implications of a convex mirror in comparison with those of a flat mirror. A flat mirror creates a reflected space that is sym- metrical with real space, so that, if a photograph is taken in it, the representation will be equivalent to what would be visible at a point behind the mirror equal to the distance that the camera is placed in front of it. Without changing the mirror's position, dramatic changes in the overlapping of background objects can be created by small shifts in the camera's position. The curvature of a convex mirror means, on the other hand, that the view in a photograph taken in such a mirror will be equivalent to what would be visible from a point within the imaginary sphere

2 Arnolfini Portrait, tracing from a projected slide with orthogonals redrawn so as to converge in the Passion scene painted directly beneath the convex mirror

created by extending the curved mirror surface until it meets it- self. With a fairly small convex mirror, the surprising result is that wherever a viewer moves there is little change in the overlapping of forms by one another (except for the viewer's own reflected overlap). This is because the viewer's visual posi- tion is in effect confined to the space within the sphere. As the size of the sphere increases (or the curvature of the mirror lessens), changes in the position of the viewer or camera will produce greater changes in the perceived position of things. One of the consequences of compressing the space reflected in a con- vex mirror within a smaller compass than that within a flat mirror is that the viewer's spatial position (i.e., the projection point of a photograph taken from this position) is brought forward. Had the projection points of Carleton's two photographs been identical, the degree of overlapping would also have been identical. Or, rather, this would be true if the figures had been kept in the same place. Their altered positions, clearly evident from their relation to the orthogonals and transverse crack, also contribute to the difference in overlap.

The most confusing of Carleton's arguments for Van Eyck's use of a convex mirror arises from the extensive floor space in his

17 Carleton, 121. The only evidence of curvature in the flooring that I can discover is a barely perceptible leftward curve of the central orthogonal that extends from the dog to the shoes. However, this curve offers no support to Carleton's theory that the picture was painted from a convex

mirror since in convex mirrors orthogonals reflect as straight lines. This fact is demonstrated by Carleton's fig. 15. 18 Carleton, 121 19 Ibid., 123

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DISCUSSION 683

reflected photograph which, contrary to visible evidence, he takes to resemble the painting's foreground space. He writes:

Now the floor spaces of the painting and Figure 4 [I assume that Figure 15, the reflected photograph, is meant, since Figure 4 is a perspective analysis of the Ince Hall Madonna] are much

greater than the ceiling spaces. Hence, if a flat plane of glass were connected to the foremost edge of the rafters and to the foremost edge of the floors of both the painting and Figure 4 [sic], then the two figures would have to lean back on their heels to avoid being severed ... Thus a convex surface serves as the picture window through which we view the couple in the painting and in Figure 15, a surface not unlike that of the convex mirror on the wall of the painting.20 This reasoning is apparently based on the assumption that the

rafters meet the picture plane where they touch the top of the painting and that, since they cannot reach to the front of the space, the picture plane leans into the picture to meet them. But nothing requires that the rafters meet the picture plane at the top of the picture. If the picture frame were, for example, intended to suggest a doorway such as the one reflected in the convex mirror, then the beams would have to extend well above the top edge of the panel before they reached forward to the picture plane, since the top of the door seen in the mirror appears to be more than three feet below the ceiling. Multiple horizontal and vertical lines in the picture confirm that it is not a view through a curved mirror, much less one that is tipped. Early documents indicate that in its original state the painting was covered by shutters painted to imitate speckled marble.21 These shutters would have emphasized the flatness of the picture plane and the rectilinearity of the interior space.

After some further observations, Carleton concludes by noting that the Arnolfini Portrait "has the basic optical effects associated with the wide-angle lens ... There is the tendency of the figures to protrude from the picture space, the effect of tremendous depth in a narrow space, and the compacting of the background. Also, there is the presence of curvature and the radical divergence of both upper and lower orthogonals."22 The same effects, he asserts, are visible in convex mirrors, and Jan's use of one in the construction of the Arnolfini Portrait "led to his development of a consistent application of a mathematical theory of perspective, best called elliptical perspective."23 What connec- tion there is between Jan's presumed use of a mirror and his development of an elliptical perspective system is never ex- plained. Carleton's photograph in a convex mirror, of course, produces a perspective with a single vanishing point for the orthogonals. Even a mirror of elliptical curvature, which did not exist at the time, would produce a single vanishing point for orthogonals.

Still, if Carleton's argument is unpersuasive, it may yet be useful to ask whether any of the properties of convex mirror reflections do in fact appear in the Arnolfini Portrait and, if so, why. Most evident is what Carleton calls "the tendency of the figures to protrude from the picture space." A possible cause of this effect not noted by him may be the tilting of the man's ver- tical axis to the left (depending on how his weight is distributed

on his legs, which is somewhat ambiguous), which produces a hint of perspectival convergence downward toward a second vanishing area (that is, one in a different direction). Since the bride's feet cannot be seen, her participation in this effect is even less clear. The effect of tipping forward is also suggested by the perspective of the pattens in the lower left corner, which appear to sit on a floor that tips drastically forward. The combination of the apparently tilted axis and tipped floor do indeed create a sense that the man's head is closer to the picture than his feet are. However, the tendency of the floor to tip and the figures to loom forward is not exclusively explainable by the use of a curved mirror or a wide-angle lens, which Carleton also compares with the Arnolfini Portrait in its optical effects.24 Comparable effects can be observed in the pictures of contemporary realist Philip Pearlstein, who remarked in a recent interview, "I seem to do a lot of what a wide-angle camera lens does. But that's simply because I work so close to the model."25

It is my belief that the magic of the Arnolfini Portrait space is not "done with mirrors," but instead can be accounted for on the basis of Jan's use of information derived from direct perception of the world. I will not attempt to consider the question of whether the scene ever existed in approximately the form in which it appears in Jan's painting or whether it is partially or completely contrived from his mind. In any case, his space, like that in his other paintings, is based on the scrupulous observa- tion of the surrounding world in the absence of a comprehensive theory of perception and with the use of a very close station point. In order to demonstrate the perspective effects of a close viewing distance, I constructed a model of the scene depicted in the Arnolfini Portrait that measures 11?" (height) by 13" (width) by 18" (depth). The depth does not represent the whole depth of the room; rather, the front edge of the model cuts

through the nearest window (the presence of which is visible in the mirror at the back of the painting). This was necessary to allow the camera to be placed in the proper position. It was necessary to make solid figures in order to measure the perspec- tive effect accurately. The model was photographed with a 35mm camera with a 24mm lens at a distance of 6" from the figures and with a vertical visual angle of 700, and agaifi with a 50mm lens at a distance of 19" from the figures and a vertical visual angle of

26V2?. Note, however, that the 24mm lens could have been used for both distances by enlarging the negative until the figures were the size of those in the other photograph and by cropping the picture to match the painting. The only observable difference that the 50mm lens produces is an increase in sharpness, because at an equal distance the 24mm lens takes in a much wider visual angle and consequently requires cropping and enlargement. To put the matter differently, Carleton is correct in stating that a series of optical effects that he observes in the Arnolfini Portrait is "associated with wide-angle lenses"26 - but this common association is based on the mixing together of some very dif- ferent things. One property - curvature - is in fact an optical property of curvilinear wide-angle lenses. Such lenses are designed to deform all straight lines systematically, except those passing through the picture center, in order to minimize the dis- tortion toward the edges of a wide-angle perspective image when

20 Ibid., 122.

21 See Martin Davies, The National Gallery, London, Les primitifs fla- mands, I, Corpus de la peinture des anciens Pays-Bas m&ridionaux au quinzieme sikcle, ui, Antwerp, 1954, 125-26. 22 Carleton, 123-24.

23 Ibid., 124.

24 Ibid., 123-24.

25 S.S. Shaman, "An Interview with Philip Pearlstein," Art in America, LXIX, September, 1981, 121.

26 Carleton, 123.

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684 THE ART BULLETIN DECEMBER 1983 VOLUME LXV NUMBER 4

3 View of reconstruction of Arnolfini Portrait with vertical visual angle of 700

it is viewed away from the (very close) projection point. The wide-angle lens I have used does not produce this curvature. The other optical effects associated with wide-angle lenses mentioned by Carleton are simply effects of natural wide-angle perspective after it has been translated into pictorial perspective. In other words, they are not a function of the lens but of the closeness of the station point or, more exactly, the wideness of the visual angle needed to take in the subject from a close station point and of the spatial deformation created by viewing a close-up picture from too great a distance. Since the effects of wide-angle photog- raphy (apart from curvature) are not a function of the lens but of the projection of a wide visual angle perspective onto a flat sur- face, a close-up photograph of my model of the Arnolfini Portrait should provide an effective means of testing whether spatial properties of the painting arise simply from the proximity of the artist to his subject or whether it is necessary to hypothesize the intervention of a curved mirror. At the same time, if it cannot be assumed that Van Eyck had formulated a comprehensive perspective theory, the absence of any tangible picture plane - such as a mirror - against which to check his empirical observations should lead us to anticipate deviations by the painter from a perfectly systematic perspective. The close-up

4 View of reconstruction of Arnolfini Portrait with a vertical visual angle of 26V2o

photograph (Fig. 3), in comparison to the middle-distance photograph (Fig. 4), does in fact reproduce most of the proper- ties singled out by Carleton as indicative of the use of a curved mirror, namely, the tendency of the figures to protrude from the space, the increased effect of depth, the position and angle of in- tersection of the picture top with the bed canopy, and the relation of the bride to the chair that she overlaps. The upper edge of the photograph does not cut off the top edge of the window, but this is because I constructed the window so that there would be a wall area above it as Van Eyck's mirrored window shows. The fact is, however, that there is an irreconcilable contradiction between the window as shown in Van Eyck's painting and in its painted reflection: it is not possible to construct it as it appears in the pic- ture and still include wall area above it as in the reflection. Carleton achieves his configuration without taking into account the information in the mirror. Had I done likewise, I would have obtained similar results, as can be seen by projecting the window in Figure 3 upward. Numerous discrepancies exist between the photograph of the model and the original painting, but most of them could be rectified, given enough time and patience, by ad- justing the size and placement of the objects and surfaces and the location of the camera.27

27 The back wall and the furnishings at the back of the room were originally designed with a slightly greater viewing distance in mind. Bringing the wall forward about 1v/2" would raise the top of the wall and the high-backed chair and lower and enlarge the low-backed seat, all of which would improve the accuracy of the correspondence to the paint- ing. My carpet is aligned with the orthogonals, but Van Eyck has shifted his to blunt the force of the convergence. It should also be remarked that even with the wall moved forward, there would be 31" between the head of the bed and the back of the wall in my model. Carleton apparently uses the length of the bed as a means of establishing the distance from the

wall to the bride; however, the result is that, even in his mirrored photograph, the space appears considerably more shallow than in the painting. Since Van Eyck undoubtedly meant the head of the bed to be understood as being next to the wall (as it appears in a very similar con- figuration in Petrus Christus's Virgin and Child in Kansas City [reproduced in Max J. Friedlinder, Early Netherlandish Painting, I, 1968, Leyden and Brussels, pl. 109]), it seems most likely that, if an actual chamber existed as Van Eyck's model, he moved the bed forward so that it would form a more effective spatial setting for the bride by defining a volume that seems to enhance her compact mass.

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DISCUSSION 685

The groom's apparent tilt in the painting was replicated by tilting the camera forward. The result is the creation of a second, downward vanishing point for all vertical lines and of a forward inclination to the space. Although this effect may be present in Van Eyck's bridegroom, it does not occur in the lines of his room (as it does in the photograph). Presumably, the tendency to represent vertical edges by vertical lines is so natural and per- vasive that, at least for geometric forms, any alternative rarely suggests itself.28

The photograph points out other discrepancies in Van Eyck's perspective: the dog is viewed from a distance corresponding to a position somewhere between the viewing point of my two photographs, as is the patten nearest to the man's foot. But the second patten is even more dramatically tipped than the corresponding one in my close-up photograph, and this also seems true of the groom's closest foot. Moreover, the chandelier is tipped in perspective even more strongly than mine is, even though the perspective of the ceiling beams is much less steep. These discrepancies support my belief that Van Eyck's perspec- tive in the Arnolfini Portrait is based on a collection of direct ob- servations that are extraordinary in their perceptiveness, but not subject to a uniform system or theory.

Since there are no curved lines in the Arnolfini Portrait and since the other resemblances between the painting and the reflec- tion of an equivalent scene in a convex mirror have been shown to be the result of the close perspective, Carleton offers no credi- ble evidence for his theory that a mirror was used. Still, the pop- ularity of the theory29 suggests that before dismissing it, we ask whether any supporting evidence not cited by Carleton might ex- ist. And, since Carleton acknowledged that "the interpretation of the floor as showing curvature will remain essentially intuitive,"" 30 we may ask whether any basis for this intuition, other than those already discounted, can be discovered. It is un-

deniable that Jan was fascinated by curved mirrors and reflec- tions; his paintings show that he carefully observed the general effects of curvature on the reflected forms, and the mirror retained for him the full force of medieval symbolism.'3 Further- more, in the Arnolfini Portrait the forward horizontal edges of the small stand by the window are slightly inclined toward the left and there appears to be a barely perceptible convergence of the masonry joints of the window frame toward the left, so that both surfaces appear slanted slightly out of the picture plane. Similar effects can be found in peripheral objects in other Van Eyck paintings.32 Such slantings away from the picture plane at the edges might conceivably be understood as vestigial traces of an effect noted in a convex mirror. However, when the rules re- quired to produce an accurate perspective picture are not known or are disregarded, the tendency to slant peripheral surfaces away from the picture plane will often result spontaneously from the transferral of the painter's direct observations to the picture surface. John White has studied this phenomenon in the four- teenth and fifteenth centuries33 (when, of course, finished paint- ings were rarely done directly from observation, but may nevertheless have resulted from the synthesis of a multitude of observations), and it may also be observed in pictures by nineteenth-century painters such as Van Gogh34 and C6zanne35 and in pictures by contemporary painters such as Rackstraw Downes36 and Bruno Civitico.37 Painter Robert Hansen has writ- ten an article proposing the availability of "subjective curvature" to direct perception.38 But whether or not an artist perceives straight lines to be curved, and despite the fact that in an ac- curately painted perspective picture with a central vanishing point no convergence of transversals or vertical lines is needed, the tendency for such peripheral convergence to occur spon- taneously in wide-angle paintings done from direct observation is very great.39

28 The most notable use by painters of non-vertical lines to depict ver- ticals occurred in Renaissance and post-Renaissance ceiling paintings, in which the position of the work created a dichotomy between a depicted vertical edge and the actual position of the line, which could no longer be vertical. Photography has created the other major group of pictures that does not always keep vertical lines vertical; this is because, among other things, in contrast to the spontaneity with which a painter tends to align his picture plane with a vertical axis (or to compensate for any discrepan- cies), a photographer must accomplish such an alignment with great deliberateness. 29 Other scholars who accept the idea that the Arnolfini Portrait derives from a convex mirror reflection are Decio Gioseffi, "Perspective," Encyclopedia of World Art, xi, 203, Elisabeth Dhanens, Hubert and Jan van Eyck, New York, n.d [1981], 204, and Jean Lejeune, "Jean and Marguerite Van Eyck et le roman des Arnolfini," Commission com- munale de l'histoire de l'ancien pays de Liege, Documents et memoires, fasc. xi, Liege, 1972; "A propos de Jean et Marguerite Van Eyck et du 'Roman des Arnolfini,'" Bulletin monumental, cxxxiv, 1976, 239-44. Le- jeune's theory is by all odds the most controversial: he believes that the men in the Arnolfini Portrait and in Van Eyck's Man in a Red Turban (National Gallery, London) are both self-portraits, and he accounts for the great discrepancy in their appearances by theorizing that Van Eyck painted himself in the double portrait with the aid of a convex mirror (but did not use it for the other parts of the picture) and subsequently ob- tained a flat mirror in which he painted himself as the Man in a Red Turban. Lejeune argues that this explains the more prominent nose and full mouth in the earlier work. To demonstrate his theory, he had a sculptor create a likeness of the later portrait which was photographed with a curvilinear wide-angle lens to approximate the appearance of the Arnolfini Portrait head. 30 Carleton, 121.

31 In addition to the mirror in the Arnolfini Portrait, there were a lost painting of bathing women, described by Bartolomeo Fazio as containing a mirror that showed the figures from behind, and a second lost painting of a single woman at her bath with a mirror, known from its inclusion in a "picture gallery" painting by Willem van Haecht. There are also reflect- ed images on the armor of Saint George in the Van der Paele Madonna, the Knights of Christ panel of the Ghent Altarpiece, and the Dresden Madonna's Saint Michael. Van Eyck also made four separate uses of a text, taken from the Book of Wisdom, in which Divine Wisdom (equated by him with the Virgin) is described as the "speculum sine macula Dei Majestatis." 32 This can be observed, for example, in the stand in the Ince Hall Madonna, in the chair of the Saint Jerome in Detroit, in the transverse axis of the basin in the Lucca Madonna, and, most dramatically, in the open chest of the early illumination, The Birth of Saint John the Baptist from the Turin-Milan Hours.

33 White (as in note 16). See also Panofsky's classic and controversial study, "Die Perspektive als 'symbolische Form,'" Vortrage der Bibliothek Warburg, 1924-25, Leipzig, 1927, 258-330.

34 See J.L. Ward, "A Reexamination of Van Gogh's Pictorial Space," Art Bulletin, LVIII, 1976, 593-604.

35 See Norman Turner, "Subjective Curvature in Late Cezanne," Art Bulletin, LXIII, 1981, 665-69. 36 See the painting reproduced in Newsweek, xcix, June 7, 1982, 66.

37 See the paintings reproduced in American Artist, XLVI, March, 1982, 43f.

38 R. Hansen, "Hyperbolic Linear Perspective," Journal of Aesthetics and Art Criticism, xxxII, 1973, 147-61.

39 Reasons for this are offered in Ward (as in note 34).

Page 8: Arnolfini Portrait Perspective

686 THE ART BULLETIN DECEMBER 1983 VOLUME LXV NUMBER 4

In summary, all available evidence points to the conclusion that Van Eyck did not paint the Arnolfini Portrait with the aid of a convex mirror,40 did not have a perspective theory, and did not

consistently converge his orthogonals in two vanishing areas

positioned at the foci of an ellipse. A careful analysis of the

perspective in all of his pictures indicates, first, that he

recognized early on that orthogonals in a single plane converge to a point; second, that he only bothered to construct this con-

vergence carefully when its accuracy was visually significant, and, third, that his approach to perspective varied with the ex-

pressive requirements of a given picture and of a given area of a

picture. Thus, the high position of the vanishing area of the floor

orthogonals in the Ghent Altarpiece Annunciation and the Rolin Madonna - Van Eyck's only interiors with exterior views - results from the need to lead the viewer into the outside space. By contrast, in the Arnolfini Portrait and the Van der Paele and Lucca Madonnas, the desire to achieve a sense of monumentality and stability while retaining the effect of a closeup perspective leads him to lower the vanishing area for the floor well below the

vanishing areas for the orthogonals of the receding top and side

planes. This has the effect of reducing the effect of the floor tip- ping forward, a characteristic of wide-angle pictures when they are viewed from a position further back than the (very close) projection point, 41 while preserving the intimacy of the close-up. view.

I would like to conclude my discussion of Carleton's study by remarking on its valuable aspects. The idea of constructing a model to test his theory concerning Van Eyck's methods of space construction is an original contribution and inspired me to try my hand at it. Especially valuable is the comparison that his model permits between the reflection in the mirror on the back wall and that in Van Eyck's mirror, since it makes visible the deviations in the painted reflection from the relationships that would have been reflected in an actual mirror in Van Eyck's room.

University of Florida Gainesville, FL 32611

40 Even the representation of the reflection in the depicted mirror seems not to have been done directly from a mirror, in view of the numerous

points at which it fails to correspond to the scene it mirrors. The most notable discrepancy in the depicted optics is the forward edge of the stand at the left, which remains resolutely horizontal, whereas the

corresponding edge in Carleton's mirror (fig. 18) follows the curve of the mirror.

41 See M. H. Pirenne, Optics, Painting, and Photography, London, 1970, and J. L. Ward, "The Perception of Pictorial Space in Perspective Pic- tures," Leonardo, ix, 1976, 279-88.

Reply

David L. Carleton

My hypothesis on "elliptical" perspective in Jan van Eyck's room-size interior scenes has been questioned by Ward in three primary aspects. Ward basically says: (1) Jan did not consistently use two vanishing areas in the construction of these works; (2) the optics of the Arnolfini Portrait show little if any relationship to the optics of a convex mirror; and (3) the convex mirror did not lead Jan to a consistent use of any type of perspective of these interior scenes.

Regarding the first aspect, Ward observes correctly that the

Arnolfini Portrait, the Van der Paele Madonna and the Dresden

Triptych have separate vanishing areas for their upper and lower

structures.1 The four works questioned by Ward are the Annunciation in the Ghent Altarpiece, the Rolin Madonna, the Ince Hall Madonna and the Lucca Madonna. He provides a perspective drawing only of the Lucca Madonna, which he says has a random scattering of vanishing points, especially in the area of the floor.2 I will show that Ward's conclusions regarding this work and the first aspect in general are the product of a form of circular reasoning, wherein he derives a random pattern of vanishing points using a random pairing of orthogonals.

In order to analyze the perspective of Jan's interior scenes

meticulously, agreement first must be reached as to which

orthogonals are of primary value and which orthogonals are of secondary value. Ward agrees with this premise, saying that cer- tain orthogonals are: "... shorter, fewer, more scattered, or otherwise less in need of treatment of a single system." I classify Jan's secondary orthogonals as those which were probably not used in the actual structuring of his rooms, which was probably the first thing he did in the construction of these interior scenes. Most of these secondary orthogonals are either short in length and/or placed to the sides of the rooms. Jan generally drew these

orthogonals without using vanishing points. It then follows that a primary orthogonal is one that plays a dominant role in deter- mining the structure of the parallelepiped that defines the space of the room. Examples are corner edges, floor lines, roof lines, and certain window edges. Jan generally uses these orthogonals in

symmetrically matching pairs. The Lucca Madonna will suffice to demonstrate both those

orthogonals which have primary importance and those which have secondary importance. I have prepared a perspective draw-

ing of the Lucca Madonna by using digital entry of Ward's draw-

ing into a computer which projected the orthogonals in sym- metric pairs for their vanishing points (Fig. 1). For the upper portion of the painting, I consider the outer edges of the canopy to be of primary importance. These converge in the vicinity of the knee of the infant. Ward's perspective drawing indicates this. His drawing also indicates that the inner orthogonals of this canopy converge in the same vicinity. Ward has shown this by matching these orthogonals in symmetric pairs, a procedure that he does not use in the lower portion of the painting. These four orthogonals largely define the upper space of the room. The only

1 reversed several perspective drawings during the editing process of

my note. However, this does not have any effect on the hypothesis of

elliptical perspective. 2Ward says that I agree with Panofsky on the date of the Lucca Madonna. I did not in fact take a position on its date but instead pointed out the various ramifications of the different dates in contention for the work.