Hans Memling, Flower Still-Life (c. 1490)
Given his motivations for the tracing theory as an explanation for the rise in realism, it is a bit unusual that Hockney would claim this Memling work in the Thyssen-Bornemisza Museum in Madrid was executed using optics. After all, the carpet pattern is extremely simple, especially for an artist of Memling’s stature and abilities and the painting surely lacks the “optical look” touted by Hockney. Why would an artist—any artist—employ a complicated optical system to draw such a simple pattern, one devoid of the subtleties and visual richness that motivated the projection theory?
Claim
Hockney’s claims for Flower Still-Life follow the arguments for Campin’s Mérode Altarpiece (cf., Section 8.3.5). That is, he believes Memling built a projector based on a concave mirror or converging lens, projected the image of the front of his table onto this canvas, and traced that image. Because such an optical system would have a limited depth-of-field (range of objects acceptably in focus), the artist might have had to then refocus his projector for the back half of the carpet. In doing so, he might have tipped and moved his mirror, thereby moving the horizon line and vanishing points. In support of this explanation, Hockney shows that the central vanishing point defined by the front half of the carpet are slightly higher than those defined by the back half. He shows no other vanishing points.
Rebuttal
Hockney failed to test the coherence of perspective in the front half of the carpet by drawing perspective lines at an angle to the direction of view, that is, construct additional vanishing points. Stork performed that additional perspective analysis and revealed that both the front half and the back half of the carpet are not in good perspective [37]. In fact, the angular deviations from perfect perspective within each half of the carpet are roughly twice those of the change in angle for lines from the front and the back halves defining the central vanishing points. In short, the evidence against the claim the carpet was in perspective is twice as salient as the evidence that is—at best—consistent with Hockney’s optical claim. As such, we must reject the optical projection claim.
Hans Holbein, The Ambassadors (1533)
Hockney uses Holbein’s The Ambassadors (1533) in the National Gallery London as a compelling example of the interest in optics, at least by the early sixteenth century.
Claim
Hockney and Falco point to two sources of visual evidence in support of their claim that Holbein traced an optical projection in this work. First, they point to perspective anomalies in the topics depicted on the lower shelf in the painting, anomalies Hockney claims show that each was traced under a different optical projection. Second, they point to the famous anamorphic skull in this painting and claim Holbein refocussed a projector to overcome its limited depth of field. They find that with careful selection of optical parameters, particularly refocusing positions, they can find a line on the skull’s jaw whose shape repeats [13].
Rebuttal
We can easily dismiss the optical explanation for the first source of visual evidence. Perspective anomalies of the sort found in the topics on the shelf appear very frequently throughout art of the time and before, including Medieval frescoes (which of course could not be executed using optics). In short, perspective anomalies of this sort prove nothing whatsoever about the possible use of optics.
However, the original anamorphic projection could have been readily realized by viewing a skull in a slanted mirror and reaching out to outline the features of the skull on the mirrors slanted surface. The outlines could then be traced onto transparent paper and transferred to the painting without any understanding of the geometry of the optical projection [62]. The other interesting feature of this painting is that, despite its central feature of a sidetable displaying numerous astronomical and geometrical instruments, not a single mirror, lens or optical device is depicted. This does not give much support to the idea that Holbein was enamoured with the use of optics for the depiction of difficult objects. Surely he would have shown at least a few of the lenses and curved mirrors that Hockney and Falco supposed to have been in such vogue among the artists of this time. Hockney also claims that the globes in this painting are “marvellously accurate in their foreshortening,” “perfect” and “precise,” providing further evidence for Holbein’s use of the optical projection method. Yet it is clear from inspection of longitude lines as they converge towards the handle that the longitude lines of the terrestrial globe are distorted, and the reconstruction of this geometry shows numerous inaccuracies consistent with brilliant painting “by eye” rather than accurate optical projection [65]. Thus the idea that Holbein was demonstrating a newfound infatuation with the use of optics with the anamorphic skull and other features of this painting becomes implausible on examination of the details of the painting.
Hans Holbein, Georg Gisze (1532)
Hockney mentions briefly and in passing Memling’s portrait of Georg Gisze [11] in the Gemaldegalerie, Staatliche Museen, Berlin. Given the context, however, it appears that he is claiming that Memling traced projections for this painting too.
Claim
Hockney points to a break in the perspective line in the carpet in the work, and suggests that such a break is consistent with Holbein refocusing a mirror projector, much as in the case of Memling’s Flower Still-Life (Section 8.3.8). Moreover, the coin box on the table is rendered in a different perspective than the front edge of the table, perhaps because it was executed under a projection from a different mirror position.
Rebuttal
Recall again that the essence of the Hockney and Falco theory is that the perspective in paintings based on optical projection should be locally consistent yet globally disrupted. A telling feature of the tapestry carpet in this painting is that, transforming the perspective as if it were viewed directly from above reveals that many of the components of the rug and the objects upon it have distorted local perspective. None of the rosettes have consistent symmetry: one is strongly rhomboidal, one is rectangular rather than square, and one has inconsistent symmetry. This, of course, means that there were in fact no consistent cues by which the transformation could be rigorously performed, but it was done to the best compromise by eye. It should be clear that many of the features have inconsistent distortions, and that the circular bases of the glass and the sand shaker are particularly distorted (again in inconsistent directions). Note that Hockney’s entire analysis of the global inconsistency in this painting consists of just two white lines, the upper of which has no relation to any feature of the rug, and especially nothing that would align with the feature identified by the lower line. Thus the idea that it reveals a global inconsistency is not supportable [62]. We are arguing that all the features exhibit local inconsistency, and that the global organization is, in fact, largely consistent (as indicated by the straightness of the border lines in the rug). Thus the pattern of perspective disruptions is exactly the opposite from that expected on the Hockney and Falco hypothesis, and is completely consistent with what would be expected of an artist with an excellent eye (as Holbein undoubtedly was) attempting to approximate the design of a complex object viewed in extreme perspective without the use of any mechanical aids.
Another bizarre feature of the painting is that the table has the shape of a narrow triangle (after perspective correction), rather than having rectangular sides. The possibility of this construction being the actual shape of a real table is excluded by the fact that the topic at upper left would fall off the table if the far side did not have a corner.
In attributing the change in fabric depictions to optical projection, Hockney neglects 250 years of intensive development of the artistic culture, comparable to neglecting the difference between Joshua Reynolds and the artists of today. More tellingly, he neglects the classic work of Gentile da Fabriano’s The Adoration of the Magi (1423), which incorporates fabrics even more complex than those shown on pp. 37, 39 and 41 of Secret Knowledge. Fabriano’s fabrics are reproduced on p. 70 of the topic, where Hockney argues that they remain “essentially flat” and are judged as non-optical. Yet the complexity of their design is just the sort of thing that Hockney is offering as evidence for the use of optical projection. Moreover, close inspection of the cape of the kneeling Magi Melchior in this painting reveals that the texture is indeed strongly folded, though not as heavily shadowed as the van Eyck painting with which it is compared. The Fabriano work thus shows that artists before the supposed “transition” could paint complex fabric patterns without optics, and tends to support the idea of a gradual evolution of the painting style for fabrics from 1300 to 1600, as opposed to the concept of a sudden stylistic change attributable to optics in as early as 1420 [62].
Documentary Evidence
It has been noted by the projection theory proponents, and widely by experts in history of optics and art, that there is no documentary evidence that any artist saw an image of an illuminated object projected onto a screen and traced one during the execution of any of their works during the early Renaissance. A four-day symposium and accompanying proceedings devoted to examining Hockney’s theory, especially the matter of documentary evidence, unanimously rejected the tracing claim, in large part for this reason [7,40]. As workshop organizer Christof Luthy summarized, “With respect to the 15th century, the idea that the Flemish Realism could be derived from the use of mirrors was roundly rejected.” Likewise, “Taken together, the material, the visual and the textual evidence presented in these articles, makes the Hockney-Falco thesis extremely unlikely as far as its application for the period before the first textual reference to image projection around 1550 is concerned. The material evidence flatly contradicts the Hockney-Falco thesis, and while the textual evidence on its own cannot fully exclude the discovery of image projection, taken together with the material evidence of poor quality mirrors, the painterly use of image projection becomes extremely unlikely” [22].
The earliest scholar cited by Hockney and Falco in support of the tracing theory is the great Arab optical scientist, Ibn al-Haytham often Latinized to Alhacen [1,31]. A. I. Sabra, who has translated all of Ibn al-Haytham’s works, rejects any suggestion that this scientist created such projections:
Lefevre summarizes the evidence that artists traced projected images as early as claimed by Hockney and Falco:
But there’s a problem. There is, to date, not a single piece of direct evidence to support this [tracing] suggestion: there is not one example of a camera obscura or even a single part of one that dates from the 17th century, there are no written documents to confirm such devices were employed by artists of this time, no receipts for related materials or other unambiguous hints. [23, p. 5].
Saint Paul referred to the poor quality of Roman metal mirrors when he compared the flawed, dark view people have of this world to the clear knowledge of God that awaits them: “For now we see in a mirror dimly, but then face to face.” Sara Schechner, an historian of science specializing in early instruments, has further shown that other cultural and documentary evidence reinforces what we find in analyzing the extant mirrors of antiquity through the early Renaissance—that the images were crude and dim [28].
The earliest documentary evidence to support the possibility of tracing comes well over a century after Hockney and Falco claim the procedure revolutionized art, specifically in the 1558 writings of Giambattista della Porta—the well-funded and highly connected magician and optical experimenter in Italy.
It pays to take a moment to clarify a possibly misleading reference to mirrors and projections from before the time of van Eyck. Falco has pointed to a number of passages in Le Roman de la Rose which discuss concave mirrors and the images they form. However, every one of these passages describes an image projected into space between the mirror and the viewer, rather than the far more difficult procedure of projecting an image onto a screen such as a canvas. Le Roman de la Rose bears no description of such projection—the type needed by the projection theory.
Hockney and Falco speculate that this lack of evidence was because artists sought to preserve “trade secrets” but Pamela O. Long’s study shows, instead, that in the early Renaissance artisans and artists freely announced their discoveries in order to attract patrons and apprentices [21]. In the very rare cases of true secrets, such as those of the Venetian glass makers, knowledge about the existence of such secrets was well known. We have no credible documentary evidence about mirror projection “trade secrets.” In short, the proponents’ speculation for the lack of purported tracing procedure is not supported by expert scholarship.
Material Culture and Re-Enactments
Hockney and Falco assert that master painters of the early 15th century, such as Robert Campin and Jan van Eyck, used glass or metal mirrors to project images onto canvas where they could be easily traced to give lifelike detail. In particular, Hockney has pointed to the convex glass mirror in van Eyck’s Arnolfini portrait (1434) and asserted in the Art and Optics website, “If you were to reverse the silvering, and then turn it round, this would be all the optical equipment you would need for the meticulous and natural-looking detail in the picture.” Elsewhere Hockney claims that van Eyck also used a concave glass mirror to enlarge or reduce drawings and that later artists employed good quality, flat, glass mirrors to reverse images while retaining details. Falco, for his part, has made similar arguments for small concave metal mirrors. However, inspection of surviving mirrors and related objects shows that they were too crude to offer the early Renaissance painter an optical short-cut to a naturalistic image of his subject. Moreover, there was no mention of using mirrors to project an image in medieval optical works, and no material evidence survives that could have performed the task even if artisans or scholars had thought of doing this [28].
Bronze was the most common material for ancient mirrors which were cast into a slightly convex disk and polished by hand. The principal challenge was to prevent air holes and blisters, or the oxidization of impurities or threads of unmixed metal, which would cause pockmarks, cracks, or veins in the surface of the casting. Medieval mirrors of metal were also small, dark, and convex and their reflectivity was limited by the rough casting and being hand-polished. Moreover, such mirrors were extremely rare. Concave metal mirrors were seldom mentioned outside of the context of burning mirrors. Burning mirrors had very short focal lengths and were not figured or shaped accurately enough to project an image even at that range. Note that a deformed concave mirror yields a blurry, useless image—not a deformed sharp one [8].
Progress in the manufacture of glass mirrors was very slow and stymied by the difficulties in preparing the glass, making it transparent, shaping it, and foliating it. Glass made in Europe in the 14th and 15th centuries was tinted dark green or brown and filled with numerous air bubbles. The “broad” technique of forming glass panes produced a thick, almost opaque, uneven sheet of glass. The reflection off its surface was very distorted and mirrors made by backing it with lead were poor. The newer “crown” technique developed around 1330 produced thin disks of glass that had deep furrows and ridges, which could not be foliated with lead to make a mirror. The striations and bubbles in glass panes formed by either technique refracted light in a very irregular manner thus yielding poor images.
Crude spheres were much easier to form than plate glass. Consequently, glass mirrors that date from the 14th and 15th centuries were indeed convex like those seen in the Renaissance paintings that fascinate Hockney. The glass blower gathered molten glass on the end of his blowpipe and blew a bubble. While still on the blowpipe, small, thin spheres of glass were coated inside with molten lead, tin, antimony, or a mixture of these metals. When the metal and glass cooled, the sphere was cut into pieces to form convex mirrors. The reflected image from these convex mirrors was blurry since these were far from perfect spheres. Hockney’s assertion that the convex mirrors (like that depicted in the Arnolfini portrait) could be reversed in their frames in order to serve as concave mirrors is false. The metal-coated interior would not be smooth, polished, or shiny, nor could it stand up to polishing. No method existed to coat the outer surface of the sphere. In fact, no concave, converging glass mirrors are known from this period; there was no method to make them. Thus, Hockney’s claim that van Eyck and others used concave mirrors to project images onto canvas is moot.
Re-Enactments
There is also a problem with Hockney and Falco’s modern re-enactments of purported early Renaissance procedures. One practical mistake that Hockney made was to assume that a modern shaving mirror has optical characteristics similar to mirrors from the past. Our cheapest mirror today is far superior to any mirror from 500 years ago, even accounting for the well-understood effects of rusting, corrosion, and so on. We cannot expect modern qualities of reflectivity or image production from old apparatus. Historical arguments that do not take this into account are prone to error [28].
Falco sets out to make a “suitable concave mirror using only technology that would have been available in the 15th century, with the goal of producing a ‘mirror lens’ of the specifications we calculated from Lotto’s painting.” For this he uses modern aluminum and brass stock and five grades of grinding/polishing compound. He writes, “Historians tell us that artisans were grinding glass spectacles by the 14th century, so they certainly had abrasive compounds at that time.” While artisans did have abrasives, they were not as pure as modern ones. Moreover, they did not work in aluminum, and 15th century brass was a different alloy than modern brass. So, this purported re-enactment is not using materials comparable to historical ones.
Second, Falco uses a technique of grinding two pieces of metal together to generate a matched pair of concave and convex spherical surfaces. This is a well-known modern technique used by makers of telescope mirrors. However, this technique for grinding spherical surfaces was not introduced until the 17th century when astronomers required better telescope lenses (and later mirrors) than spectacle makers (and metal workers) were producing. Prior to that, lens makers ground their lenses in concave molds that were created by hammering copper into a rough, curved shape. They did not even use a template as a spherical control, much less a file to remove the hammer blows. As for metal mirrors, they were convex and made by casting. Two metal surfaces were not ground together in their creation. This means that lenses and mirrors were aspheric in Lotto’s day and not made by Falco’s method. In short, Falco’s reenactment is anachronistic.
There is, further, a significant logical problem underlying Falco’s “re-enactments.” Even if we grant that 15th century artisans had the “right” raw materials or tools at their disposal, there is no logical reason to conclude that they would have put these together in the same way and for the same purpose that later individuals have thought to put them together. To claim otherwise leads to silly conclusions—e.g., a claim that Aristotle could have discovered electrical current in the fourth century B.C. because he had coins of dissimilar metals, parchment, gold wire, and salt water; in short, all the ingredients of Volta’s electrical pile of 1800. The progression from “could have” to “did” is even more logically suspect.
Thus, Falco’s conclusion—“It is quite easy to fabricate concave mirrors of suitable focal length, diameter, and resolution for 15th century artists to have used to project images”—is fallaciously made [32].
Non-Optical Contexts
We mention that it may be no coincidence that the transition to the “optical look” Hockney identifies near 1430 is the same date as the emergence of the use of oil paints. Indeed, Jan van Eyck is sometimes called the “father of modern oil painting,” though oil paints were used in a few cases before him. Oil paints afford a wider range of lightness—whiter whites and blacker blacks—richer, more saturated colors, and a number of layering and glazing techniques, which reach the apotheosis in the works of Rembrandt, who would apply as many as 50 layers of oil paint in a given passage. Much of the “optical look” is due to shading, sfumato, chiaroscuro, unrelated to the accuracy of contours related to any putative tracing of projected images. Moreover, this is also the time in the well-documented rise in the use of spectacles [15], [62]. Spectacles would allow an artist, especially one over 35 or so, to see distant subjects and close painting.
We note in passing that sculpture changed dramatically during this period as well and became far more “realistic.” Consider, for instance, the evolution in style from the anonymous architectural statuary in Western (Royal) Portal of Chartres Cathedral (c. 1145) to Donatello’s David (c. 1440) to Michelangelo’s Pieta (1499). This remarkable rise in sculptural realism and expressiveness was, of course, unrelated to any development of technical tools analogous to those in the optical claim.
The “Value” in Tracing
Although the above discussion centered on the tracing claim, we must not forget the full extent of Hockney and Falco’s claim: that tracing itself helped lead to the heightened realism or “optical look” of the ars nova. Tracing surely aids in capturing contours, of course, but it does not help in capturing subtleties in color, shading, and tone. The sight of a full-color projected image might aid an artist, but the contours alone are much like a child’s color topic. It is extremely difficult to paint directly under projections (as Hockney himself admits), and it would impede rather than aid rendering of color.
With this large lens made to modern standards, the scene has a depth of field of only an inch or so of sharp focus. All the rest of the objects are heavily blurred. Hockney argues explicitly that it is precisely the characteristics of the projection of the optical image, including out-of-focus regions, that should have appeared in paintings at the time that optical projection first came into play.
In contrast, the large-scale van Eyck paintings that supposedly represent the style inspired by the “optical look” are almost preternaturally sharp throughout the scene. This property of ubiquitous clarity had, in fact, been characteristic of paintings since Greek and Roman times. It was nothing new. Conversely, as one can see from the projected image of still life [11, p. 104], the true “optical look” is extremely fuzzy, and would have been more likely to have inspired French Impressionism than the Renaissance precision. In fact, there have been compelling suggestions that the looseness of the late paintings of Impressionists such as Claude Monet was due to the reduced optical quality of their own eyes over time [61]. Thus, the look of the paintings is essentially the opposite of what would be predicted from Hockney’s “optical look” hypothesis [62].
Scholarly Consensus
As far as we know from published scholarly works (rather than websites, blogs, letters to the editor, YouTube videos, and so on), the independent scholarly consensus—indeed unanimous consensus—is to reject the Hockney direct tracing claim. Nearly a dozen scientists or technologists, eight historians of optics and art, and two curators have published scholarly works rejecting the theory, at least for the works in question. Participants in the four-day workshop devoted to testing the tracing theory unanimously, and in no uncertain terms, rejected its claims [40].
Consider, too, the more informal literature of topic reviews.
My own view is that Campin and van Eyck may well have been inspired by optically generated images—the camera obscura was well known to mediaeval natural philosophers— but probably did not actually use them directly at any stage in the making of their pictures.
In short, Kemp too is skeptical about the central and explicit claim of the Hockney theory: that the “optical look” arose in Western art circa 1430 because some artists traced optically projected images.
Conclusions
We have examined the claim that some European artists secretly traced optically projected images during the execution of passages in some of their works as early as circa 1430 and that such a procedure was key to the rise of a newfound realistic, photographic, or “optical” look in the ars nova or new art of that time. We find that the theory itself, as stated, relies on subjective and ultimately untestable premises about which portions of an image an artist would or would not have traced. The theory’s proponents have exploited this lack of a theoretical foundation to alter and retreat from claims in an ex post facto and ad hoc way. Further, the theory’s proponents rarely explore in adequate depth alternative non-optical explanations for the visual evidence in paintings. We analyze the visual evidence in key paintings adduced in support of the tracing theory and find, without exception, that alternative, non-optical explanations are as plausible—and indeed generally far more plausible—than the optical explanations, especially in light of independent physical evidence and constraints. We also review briefly the documentary record for the period in question (c. 1420-1550) and find no persuasive evidence to support the direct artistic use of such projections. We examine, and ultimately reject, the speculation that this lack of documentary evidence was due to artists protecting “trade secrets” or fearing the Inquisition.
It is clear that the overwhelming—and to our knowledge unanimous—conclusion of independent scholars writing on this subject is to reject the Hockney direct tracing theory, at least for the period in question (1430-1550). Moreover it has not been demonstrated that tracing was needed for this rise, or in fact helped it at all. Of course, every scholar should be, and to our knowledge indeed is, open to new evidence that may arise, and no rebutter is so irresponsible as to have claimed to have “disproven” the tracing claim. Instead, we—and rebutters more generally—claim merely to have rebutted every aspect of Hockney and Falco’s frequent claims to have “proven” their direct tracing claim, at least in the early Renaissance.
Despite this broad scholarly rejection of the direct tracing claim, we reiterate that we do not take a stand—for or against—Hockney’s alternative claim of artistic influence, i.e., that some artists saw and were indirectly influenced by projected images. None of the technical analysis, such as referenced in Section 8.3, shed much light on the influence claim, though the lack of supporting contemporary documentary evidence in the early Renaissance and the issues of burden of proof for a revisionist theory argue against the indirect influence claim.
Although computer vision, pattern recognition, and image analysis long predate Hockney’s speculations, his theory has motivated the development of a number of algorithms in particular, and the general acceptance of computer methods in the study of art. We feel that this, then, may be Hockney’s most important legacy in this general domain. A number of scholars have moved past the tracing claims to address a wider range of questions in the history of art, research that is leading to new techniques and shedding new light on art and art praxis [41,42,44-48,50,52].
