Hockney theory

In 2000 the contemporary artist David Hockney proposed that artists as early as 1430 secretly traced optical projected images for some passages in some of their works, and that this was a key source of the rise in realism in the ars nova or "new art" of that time. In the words of Hockney and his collaborator, thin-film physicist Charles Falco:

"Our thesis is that certain elements in certain paintings made as early as c1430 were produced as a result of the artist using either concave mirrors or refractive lenses to project the images of objects illuminated by sunlight onto his board/canvas. The artist then traced some portions of the projected images, made sufficient marks to capture only the optical perspective of other portions, and altered or completely ignored yet other portions where the projections did not suit his artistic vision. As a result, these paintings are composites containing elements that are "eyeballed" along with ones that are "optics-based." Further, starting at the same time, the unique look of the projected image began to exert a strong influence on the appearance of other works even where optical projections had not been directly used as an aid."

It is an intriguing and captivating theory, and before scholars had a chance to study the theory it was highly promoted in the public arena. Unfortunately, as stated, it isn't a scientific or testable theory because proponents give no unique and objective way to tell which "certain elements" in a painting would have been traced and which not. As such, proponents change and retreat from their claims as independent scholars prove these claims about "certain elements" incorrect—changes that are always ad hoc (a Renaissance painter would have traced this passage, but not that passage) so as to try to salvage their theory. This is the hallmark of a failed or even unfalsifiable theory: much as Wolfgang Pauli described one physics paper, "That's not right. That's not even wrong." Such backtracking and modification is clear in the documentary record, and has happened numerous times in the debate over the theory, for example van Eyck's Arnolfini portrait, Lotto's Husband and wife, and other works. Moreover, proponents give no method to even test the claim that projected images exerted an indirect influence on artists (given that there is no documentary evidence for this claim for the period in question, 1430–1550) and as such this claim falls outside the realm of scholarship. Regardless, the theory was intriguing and helped independent scholars of computer vision, image analysis and pattern recognition refine algorithms for the analysis of art.

Nevertheless, given that...

... after roughly nine years independent scholars have moved on to more productive areas of computer vision in the visual arts. The rejection of Hockney's tracing theory for the early Renaissance is thorough, complete, reasoned, evidence-driven, expert reviewed, broad, and international. Nevertheless, here, for those still interested, are some questions frequently asked during lectures on the tracing theory.

What exactly is the issue being debated?

In exploring the broad sweep of the development of western painting, the celebrated contemporary painter David Hockney pointed out that there was a change in art around 1420 that, he felt, indicated an "optical" understanding of the visual world. He feels his "strong" thesis is that artists and others saw the world differently after being exposed to optically projected images (projected by, for instance, concave mirrors), and this deeply influenced painting for centuries—artistic influence. That is, the projected optical image became an ideal, a target, to which some painters aspired. His "weaker" or secondary thesis is that artists actually used such optical projections during the creation of their works, specifically by projecting real inverted images onto a canvas or other support (oak panel, paper, ...) and tracing or painting over them—artistic praxis. In their own words:

"Our thesis is that certain elements in certain paintings made as early as c1430 were produced as a result of the artist using either concave mirrors or refractive lenses to project the images of objects illuminated by sunlight onto his board/canvas. The artist then traced some portions of the projected images, made sufficient marks to capture only the optical perspective of other portions, and altered or completely ignored yet other portions where the projections did not suit his artistic vision. As a result, these paintings are composites containing elements that are "eyeballed" along with ones that are "optics-based." Further, starting at the same time, the unique look of the projected image began to exert a strong influence on the appearance of other works even where optical projections had not been directly used as an aid."

The first thesis is most properly the domain of historians and art historians (and, of course, artists themselves). The debate in which technical optical and computer vision techniques can assist is this secondary claim of artistic praxis. It is where focal lengths, perspective analyses, aperture calculations, shape-from-shading algorithms, and more can shed light.

For the record, I do not see how one can definitively answer the claim about influence, particularly as we lack an documentary evidence that anyone had even seen an image projected by an optical device onto a screen by 1420. It is, nevertheless, valuable insight to be considered. It may be correct that artists saw projected images and these, in solving the thorny problem of how to render three-dimensional space on a two-dimensional support, helped us see in new, "optical" ways.

Notice, too, that the formulation above is not even scientific. How could scholars of today know which features "did not suit [an artist's] artistic vision"? Suppose modern scholar A (possibly an artist) believes that van Eyck's artistic vision would include tracing the full chandelier arms in the Arnolfini portrait while scholar B says van Eyck would have traced just the candleholders while scholar C says van Eyck would have traced just the decorative structures while scholar C says van Eyck would have traced nothing whatsoever? Which one is right?

In fact, just this methodological problem has plagued the Hockney/Falco theory from the start, and in numerous works. Early, Hockney says and demonstrates that van Eyck would have traced the full chandelier arms, specifically the portions most distant from the base arms. Then, when technical analysis shows that the full chandelier is not in proper perspective (and hence was not traced from a projection) the proponents retreat to say that actually, well, van Eyck's artistic vision would have led him to trace the arms, but not the decorative structures. Clearly, such retreating of claims under the guise of revisions of van Eyck's "artistic vision" are unscientific and vacuous. Unless and until Hockney and Falco can prove a priori what a particular "artist's vision" is, before the evidence is accumulated, then their "explanations" will be merely ad hoc, ex post facto attempts to avoid disconfirming evidence—that is, no explanation whatsoever. Again and again we find that Hockney and Falco reason "backward." For instance, after proofs that the Arnolfini chandelier is not in perspective (not even close) they try to salvage their theory by starting with their "conclusion" (that van Eyck traced a projection) and then arguing that the parts not in perspective (and hence surely not directly traced) must have been freehand. No justification other than that this is what is needed to salvage their theory.

Summary: My work, and other technical work, addresses only question of artistic praxis. It is conceivable that should the scholarly consensus reject this secondary thesis, the primary thesis will remain and gain adherents, leading to a revision of our understanding of the grand sweep of western art.

What has been the response of the scientific and technical and art communities to your evidence and counter-arguments to the Hockney theory?

The response of the scientific and technical communities to public presentations and scholarly papers questioning and rebutting Hockney's claims about artistic praxis have been warm and invariably supportive. The technical community recognizes the need to see evidence on both sides of the debate—pro and con—and while non-experts in optics and painting generally do not put forth all the relevant evidence or counter-arguments themselves, they can appreciate and evaluate it when they see it.

I have little doubt that the theory's proponents have had supportive audiences as well. That's why the experiences with the NASA Goddard Space Flight Center Engineering Colloquium are especially revealing. Dr. Falco presented his case for the Hockney theory to this audience there and afterwards asked how many in the audience felt his evidence for the Hockney theory was "compelling." Only three raised their hands to say they didn't. Dr. Falco touts as evidence that the technical grounds for the Hockney theory are convincing.

Well, I had the good fortune to present my counter-arguments to the same NASA audience months later. After the question and answer period I asked the full audience how many agreed with several of Dr. Falco's claims, such as "You could convict OJ with this evidence" (quoted verbatim, in context). No one—not a single person—raised a hand for any of these claims. (A writer from Science News attended my lecture and reported this result in his article.) The case is virtually identical at a number of other venues, most recently Duke University. Likewise, I recently gave a lecture at the University of Illinois, Urbana-Champaign, unaware that Falco had spoken there the previous year. Unbeknownst to me, a professor who served as host to Falco sat in my audience. After my talk, this professor approached me on his own initiative to say he agreed with my conclusions, not Falco's.

Of course one can "accept" Hockney and Falco's evidence, and yet, in light of the massive counter-evidence and more plausible alternate explanations nevertheless reject the proponents' claims that artists as early as 1430 traced optically projected images. In fact, my experience is that upon hearing in full the counter-arguments from a wide range of independent scholars, every independent scholar rejects Hockney's and Falco's bold claims that they've"proven" early 15th-century artists traced projected images.

I sense that some of the initial support for Hockney's tracing theory arose from the falacy: It must be right because it would be so cool if it were.

Summary: From these lectures and numerous discussions I think it is fair to conclude that if a scientist hears only the arguments in favor of the Hockney theory, he or she is likely to find it persuasive. However, if that person hears the counter-arguments at the very least he or she is will not agree with theory proponents that the case for the projection theory has been "proven." More likely, the scientist will reject the theory altogether often because they learn of historical or other facts that they'd never even considered before. I am not aware of any independent expert in optics, image analysis and art who, upon hearing both sides of the debate, finds the Hockney case persuasive. (If such a person exists, I strongly urge him or her to make such a view public.)

What has been the response of the art history community to your evidence and counter arguments?

Christoph Lüthy wrote an article for the Frankfurter Allgemeine Zeitung which summarized the views of the four-day November 2003 Ghent workshop of historians of science and art (but not image analysts) Optics, Optical Instruments and Painting: The Hockney-Falco Thesis Revisited (which I did not attend), the most extensive scholarly inquiry into the theory: "With respect to the 15th century, the idea that the Flemish Realism could be derived from the use of mirrors was roundly rejected." (tr. Dr. Katrin Berkner) ["Was das fünfzehnte Jahrhundert betrifft, so wurde die Idee, daß der flämische 'Realismus' aus der Benutzung von Spiegeln abgeleitet werden könne, rundum verworfen."] In an abstract presented at the Optical Society of America, Lüthy wrote of the workshop, "Charles Falco's alleged mathematical proofs did not fully persuade participants. First, it was felt that it was viciously circular to invoke pictorial precision and aberrations likewise as evidence for the use of mirrors. Second, given the strong inaccuracy of patterns on oriental tapestry and of hand-made chandeliers, Falco's calculations based on perfectly symmetrical originals were found to be inconclusive." (Note especially that this rebuttal, and the lack of documentary evidence for the proceedure, apply with equal force to claims about lenses as well as mirrors.) This negative view of the Hockney thesis was confirmed by all of the several other participants I corresponded with. It also comports with the vast consensus of independent experts (not just in high-school optics, but art history, history of optics, specific painters, technical analyses of paintings, etc.) who reject the Hockney theory, as evidenced in the numerous negative reviews of Secret Knowledge in The New York Times Book Review, New York Review of Books, Burlington magazine, and many other venues.

Particularly important is the recent volume of Early Science and Medicine: Optics, instruments and painting, 1420-1720: Reflections on the Hockney-Falco thesis edited by Sven Dupré, Leiden the Netherlands, Brill Academic Publishers 2005, the first independent volume treating the Hockney-Falco thesis. Each paper by experts that studies Hockney's claims rejects them or finds there is insufficient evidence to accept them. Editor Sven Dupré summarizes thus: "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." Contributor Sara Schechner of Harvard words her rejection poetically: "Perhaps artists used mirrors as tools for self-portraits, as aids to perspective, as judges of the penultimate product, or a symbols, but their use of mirrors as projection equipment to achieve remarkable naturalism in their art is a chimerical as an argument for the existence of the unicorn based on the creature's clear reflection in the mirror held by the lady in the famous tapestry, La dame a la licorne: La Vue." A. Mark Smith writes with deference: "Furthermore, and more to my point, the fact that contemporary opticians were silent on image projection, and remained so until around the mid-sixteenth century, seems even more problematic for Hockney and Falco." Yvonne Yiu writes with force and clarity: "With regard to the Hockney-Falco thesis the silence of this considerable body of texts on the concave mirror projection method is deafening. Written by well-informed contemporaries who were keenly interested in the relationship between the mirror and painting and eager to impart any 'secret knowledge' to willing listeners, it seems inconceivable that they would not have described a method that according to Hockney and Falco revolutionised the art of their time." Sven Dupré writes "My argument was rather that Hockney has read the documentary evidence–one of Leonardo's drawings of a machine for making a concave mirrors–wrongly and out of context, and that if read correctly will actually turn Leonardo into an unlikely candidate for support of the Hockney-Falco thesis." Filippo Camerota writes "This [passage from Ludovico Cigoli] is one of the rare references to the camera obscura as an artist's aid to be found in Renaissance literature. However, the conclusions we can draw from this and other documentary evidence on the camera obscura and related optical devices are quite far from David Hockney and Charles Falco's assumptions." Christoph Lüthy writes "It will be argued that while for the fifteenth and sixteenth centuries, there is little evidence in favor of [Hockney's] strong thesis [that artists traced projected images], the case is different for the seventeenth century, for which the use of optical instruments by painters is a documented fact." These are relentless, clear, persuasive, well-documented, independent rebuttals of Hockney and Falco by sober, thoughtful scholars who (alas) will never get the media attention of a public figure such as Mr. Hockney.

Another important new, and excellent, book is Vincent Ilardi's Renaissance Vision from Spectacles to Telescopes—a thorough, detailed, investigation into optics of the time. Ilardi, who attended the Optical Society of America's symposium on the Hockney claims, was well aware of Hockney's theory and alert to find any evidence in his research that would support the theory. In fact, he finds no explicit corroborating evidence, in particular for Lorenzo Lotto: "On the other hand, the evidence on the use of concave mirrors to project clear images for pictorial compositions [by Lotto] seems to be scanty or missing altogether except for the paintings themselves, as Falco has contended," relying on—but not analyzing—Falco's claims that the paintings themselves "prove" that optics were used. Furthermore, Ilardi also rejects the Hockney/Falco contention that the lack of documentary evidence might be due to some "trade secrets," writing: "We can also assert with some confidence that [mirrors] were commonly found in their shops and that there was nothing secret or mysterious about their use given their frequent mention and availability."

Personally, it has been especially gratifying to present my analyses to art historians and students in art history departments at major universities, elite international art institutes such as the Courtauld Institute in London, public lectures at major art museums such as the Metropolitan Museum of Art in New York, and one-on-one with curators. Most but not all art historians come with strong preconceptions against the Hockney theory, but are happy to see the kinds of optical evidence and counter-evidence. I have found that certain evidence (or lack thereof) finds receptive ears among art historians. Of course the lack of persuasive corroboratory documentary evidence over centuries for Hockney's theory means a great deal to them and few if any seem to subscribe to Hockney's statements about fears of the Inquisition or trade secrets. I've heard several "ahahs" when artists realize that tracing outlines (in the Hockney theory) does little or nothing to aid an artist in capturing subtleties in color and shading which they take as essential to the "optical" or realistic look of early Renaissance painting. I'm not so naive as to think that every art historian who has heard my rebuttals accepts them fully, but I am perceptive enough to say that if there are such people, they aren't making themselves heard. Even Hockney's long-time friend and contributor to Secret Knowledge, Professor Martin Kemp of Oxford University, states "My own view is that Campin and van Eyck [early 15th-century]...probably did not actually use [images] directly at any stage in the making of their pictures." In short, this author of The science of art is sceptical that the "optical look" arose in western art circa 1430 because some artists traced optically projected images.

I have met and corresponded with many leading curators and scholars on early Renaissance art, and have come across a somewhat perplexing stance. A few of these scholars say that the Hockney theory is manifestly wrong and will die of its own accord. "Why waste your time rebutting it?" they ask. I reply that at least at first I thought the theory was interesting and couldn't be dismissed immediately. I've also argued with them (generally unsuccessfully) that silence from the scholarly community will mean that the theory will live just in the popular press–always a very bad idea.

The independent follower of these debates should ask him or herself why acknowledged experts (Dr. Lorne Campbell, Curator at the National Gallery London and author of The fifteenth-century Netherlandish paintings, or Dr. Arthur K. Wheelock Jr., Curator at the National Gallery Washington and author of Perspective, Optics, and Delft Artists around 1650, or Dr. Keith Christiansen, Curator at the Metropolitan Museum, invitee to the Hockney Symposium and author of Orazio and Artemesia Gentileschi, or Dr. Samuel Edgerton, Professor of Art History at Williams College and author of The Heritage of Giotto's Geometry: Art and science on the eve of a scientific revolution and The Renaissance rediscovery of linear perspective, Antonio Criminisi perhaps England's leading expert in image analysis of art and author of Accurate visual metrology from single and multiple uncalibrated images, Sara Schechner, David Wheatstone curator at Harvard University, and many other scholars such as in the Early Science and Medicine volume) are not persuaded by the new revelation brought to light by Mr. Hockney. Is it because these scholars are obtuse or don't understand high-school optics? That their scholarly objectivity is somehow compromised by a desire to "preserve the honor" of painters such as Hans Memling?

I have found that the community of realist artists overwhelmingly rejects the Hockney claims. In fact, roughly 2400 people have signed a petition requesting CBS 60 minutes air a rebuttal piece. (This of course does not mean the signatories are correct—but it is an indication of their broad rejection of the Hockney-Falco claims.)

Summary: From these experiences I think it is fair to conclude that art historians who hear both sides of the arguments are unlikely to subscribe strongly to the Hockney theory, and are dubious of bold claims that the theory has been "proven."

Is there contemporary documentary evidence that artists in the early Renaissance painted using Hockney's projection technique? Or even saw images projected onto a screen such as a canvas by an optical device (mirror or lens)?

While there is documentary evidence that concave mirrors existed in early Renaissance Europe, and indeed earlier, we have no evidence in the 15th century, say, that anyone saw an image of a non-self-luminous object (e.g., not the sun) projected onto a screen by an optical device (concave mirror or converging lens), the first step in the Hockney projection procedure. (Early Chinese scholars explored complex and rather different "magic mirrors," but these were first brought to the west in the 19th century.)

It is important to understand the concept of "projection" by a concave mirror. If you look at the concave side of a shiny teaspoon, you'll see your image upside down. This real inverted image is indeed projected into the space between the spoon and your eye. The Hockney theory, though, demands a different form of projection: a projection onto a screen (such as canvas, paper or oak support), just as a movie projector projects an image of each frame from its film onto the white movie screen. Falco has presented quotations from The Romance of the Rose as evidence in support of the Hockney's theory but these and all other European texts of the time I'm aware of describe projections of the first type–not the second type needed for the Hockney theory.

It is much more difficult to see optical projections of the second type than the first as you can easily prove for yourself. If you look into the bowl of a shiny teaspoon you'll see a small (deformed) inverted real image of your face—a projection of the first type (no screen). But such a teaspoon cannot yield a visible image through projection of the second type, that is, onto a screen. Try it! There are three reasons for this inability:

  1. The first is that the image projected onto a screen is far too dim in this case. For the kinds of mirrors Hockney and Falco infer, the reduction in brightness can be nearly as much as a factor of 1000, the equivalent of looking through three stacked pairs of commercial sunglasses. Just imagine you're in Arnolfini's room (with its manifestly diffuse, non-direct illumination) wearing at minimum two stacked pairs of commercial sunglasses and trying to paint.
  2. The second reason is mirror quality. To produce a well-formed image through projections onto a screen, the concave mirror has to have a more precise shape. The bowl of a teaspoon does not have the required shape, and thus even though it can produce an image of the first kind, it cannot produce a well-formed one on a screen. In fact, even a well-formed spherical mirror of the dimension of the Arnolfini mirror Hockney and Falco repeated invoke yields a very blurry image, even when everything else has been set up correctly. Such a spherical mirror does not bring rays to a point, but instead what is known as a "blur spot." A large mirror should be the shape of a paraboloid (not a sphere). Sara Schechner, curator of historical scientific instruments at Harvard, has examined surviving optical devices from the 15th century and reports that they are not of sufficiently high quality to generate the fine details required by the Hockney theory.
  3. The third (admittedly weak) reason is that the arrangement of object, concave mirror and screen must be reasonably precise for the projections of the second kind. (Technically speaking, these distances must conform fairly well to the so-called mirror equation.) The requirements are far more lax in projections of the first kind. You can verify this for yourself with the image seen in the bowl of your teaspoon: Move the spoon toward and then away from you; you'll notice that within a wide range of positions, you'll be able to see the image. But even if you could create a projection of the second kind, you'd find the bowl has to be a fairly precise distance from the screen for the shape of the image to be visible, a tolerance of about the thickness of a dime coin. Admittedly, an optical technologist who knows to look for a projection of the second kind can fairly easily adjust distances to find the proper focus but we have no independent evidence any early Renaissance artists had even this basic knowledge. The greatest optical scientist before Newton, Alhacen (965?–1040?), in his 16 surviving books on optics and vision didn't even figure out how to create a projection of the second kind. Nor did the second-greatest optical scientist before Newton, Roger Bacon (1214–1294). Nor did Witelo (1230–1275). Are we really to believe that these scientists, who eagerly explored and wrote profusely about their optical discoveries, didn't figure out the key step in the projection technique but that a painter such as van Eyck (of whom we have no corroboratory evidence had knowledge of such optics) did?

The earliest corroborating documentary evidence of a projection of an illuminated object onto a screen by an optical device (concave mirror or converging lens) is near the beginning of the second half of the 16th century, in the writings of Girolamo Cardano and the more widely known magician, playwright and optical experimenter Giambattista della Porta, both well-known to Renaissance scholars and historians of art and optics. (Projections of bright light sources such as the sun or candle flames may have occurred earlier, however.) Note that this evidence is separated from Jan van Eyck, Robert Campin and others claimed to have used the Hockney method by well ury, by over a thousand miles, and by language.As Samuel Y. Edgerton writes in his careful The mirror, the window and the telescope: How Renaissance linear perspective changed our vision of the universe, "In their controversial 2001 book Secret Knowledge, British artist David Hockney and University of Arizona physicist Charles Falco attempted to prove that Renaissance painters 'secretly cheated' by using parabolic mirrors to project images onto their picture surfaces that they then traced, rather than drawing them freehand. See Schechner for a convincing rebuttal of their claim. [there is] ...no documented evidence has been found to sustain the author's assertion that they employed or even understood how a parabolic mirror works as an image projector."

Summary: The simplest explanation for the lack of corroboratory evidence is, of course, that Renaissance artists, scientists, patrons, clergy, optical technologists did not create this corroboratory evidence because they did not use the Hockney projection method.

Were appropriate optical devices (long-focal-length concave mirrors) available in 1430?

It is well known that concave mirrors and converging lenses existed before 1420 (see Mark Pendergrast's non-technical book Mirror Mirror), but despite 21st-century demonstrations that one could have made reasonable-quality long-focal-length mirrors, the historical evidence does not seem to support claims that they were in fact made (let alone used as claimed). Sara Schechner, David P. Wheatstone Curator, Collection of Historical Scientific Instruments at Harvard University wrote CBS's 60 minutes to protest Hockney's bold claims: "There is a major flaw in Hockney's argument that I must call to your attention... Close inspection of surviving mirrors, lenses, and glass in museum collections show that these instruments were too crude to project a lifelike image... Surviving mirrors, whether flat or curved, and cultural references to them from the same period, strongly suggest that glass optical devices were far from offering the Renaissance painter a short-cut to a detailed and naturalistic image of his subject... Although Hockney stakes his claims on the use of glass mirrors and lenses, similar problems arise if one considers early metal mirrors. These too could not offer the user an undistorted view of the world... Our cheapest mirror today is at least 1000 times better than any mirror from 500 years ago... Historical arguments that do not take this into account are prone to error."

Summary: I am unaware of corroboratory evidence of actual surviving concave mirrors of sufficient quality and size to provide much benefit to artists of the early Renaissance under reasonable circumstances. Frankly, I wouldn't be particularly surprised or concerned if someone someday unearths such evidence as most of the rebuttals to Hockney's claims are not based on the existence or non-existence of high-quality devices themselves. Of course I urge historians to redouble their efforts in this regard.

What is the role of technical analysis given that the "artist's vision" is involved in creating paintings?

The following example illustrates well the methodological problems of the Hockney-Falco arguments. In his book, Hockney admires the van Eyck's Arnolfini chandelier image as "amazing for such a complicated foreshortened form." Note that he gives no hint that one part of the chandelier is in perspective and another part is not. Later, in December 2002 before 8 million viewers on CBS 60 minutes Hockney states "That chandelier is in perfect perspective," as it would be if it were traced from a projection. Then in demonstrating his theory he traces not just the image of the chandelier's arms, but also of the decorative structures most distant from the arms. This shows he believed van Eyck would have traced the whole arm and structures—that is, not trace one part and "eyeball" the rest. (Incidentally, on this show Falco told viewers that a jury of scientists would "convict OJ" with their evidence.)

Shortly after their show I (and then Criminisi and I) proved that the full chandelier is not "in perfect perspective." The decorative structures, such as Hockney had traced, are not even close to being in perspective.

To try to salvage their theory, then, Hockney and Falco retreated from their earlier claims, by publishing an article stating that the decorative structures were soldered onto the chandelier arm, and hence would be haphazardly arrayed on the arms and yield the (apparently) poor perspective that we find. They were explicit in stating they believed the full chandelier was in good perspective, just that the chandelier itself was asymmetric or poorly made.

Shortly after their laterpaper, Criminisi and I showed Hockney and Falco were wrong: In fact, experts in Renaissance metalwork point out that decorative structures are not soldered onto arms. Rather, these arms are highly symmetric because they are made from the same mold and there is no soldering. We verified this through computer analysis of several appropriate large chandeliers and prayer book holders surviving in museum collections, and by direct physical measurement (by tape measure) of their symmetry. Several conservators of such so-called dinanderie, including Richard Stone at the Metropolitan Museum of Art, confirmed Hockney and Falco are wrong.

To try to salvage their theory, then, Hockney and Falco retreated yet further from their earlier claims and started claiming in letters to the editor, in broad unsolicited emails, and correspondence with journal editors and so forth that the arms and candleholders were traced but the decorative structures not, i.e., that they were "eyeballed" and that rebutters were mis-understanding their theory. (Take a look at the Arnolfini chandelier and ask yourself if you—or anyone—could trace the back arms while getting the decorative structures so very wrong. An astoundingly implausible claim on several grounds.)

Clearly Hockney and Falco change their claims—an artist was or was not precise—under the guise of "artistic vision," whichever ex post facto and ad hoc alterations are to try to salvage their theory. Clearly, such an approach is methodologically vacuous.

The same style of argument in Lotto's Husband and wife, where Hockney and Falco fit the image data to the astounding precision of three significant figures, showing they believe Lotto accurately—even "slavishly"—traced a projected image. But now that the severe problems with their explanation are clear, will they retreat from their explanation to tell us that Hockney's "artistic vision" has changed and that Lotto did not "slavishly" trace a projected image? One they previously claimed was traced to a precision of three significant figures?

Summary: Hockney and Falco retreat and alter their explanation as more and more disconfirming evidence arises. When careful analysis by a range of independent scientists and historians shows they're incorrect, they retreat and alter their claims until they rely on untestable "artistic vision." Clearly, this is no way to arrive at truth.

Are you trying to defend the "honor" of early Renaissance painters or otherwise motivated by preserving their status as "geniuses"?

I came to the Hockney proposal with an open mind, in fact, my first reaction was "this is pretty cool." It was only after finding persistent flaws and simpler alternative explanations for the phenomena put forth by proponents that I started to doubt—and then seriously doubt—the theory, at least in the breadth of its claims in the popular media. I, Christopher Tyler, Antonio Criminisi, Michael John Gorman, Thomas Ketelsen, Walter Liedtke, Sara Schechner, and many others have no particular "turf" or vested interest in preserving the "honor" of Renaissance painters, though I for one surely do view van Eyck, Campin, and many others as geniuses of great talent. Tyler and I were independently chosen to participate in the 2001 Art and Optics Symposium, not because we had some turf or stance, but because of our decades-long work in optics and painting.

By the way, I don't think that using optics is "cheating" in any ethical sense, a bugaboo that clouds the discussion. For instance, ever since I was a young child growing up in the suburbs of Philadelphia I have admired the work of Philadelphia-based master Thomas Eakins (1844–1916). The recent evidence brought forth by scholars that he painted over projections of a few of his black and white photographs is clear and convincing; I accept it fully for those specific paintings. This evidence, incidentally, is of a fundamentally different nature than that brought forth for Renaissance painters. And of course there's no question that relevant cameras, projectors, etc., were available to Eakins; in fact, Eakins was a talented photographer.

I should point out that I do not now claim—nor have I ever claimed—to have "disproven" the Hockney theory. To make such a claim would be extremely irresponsible. What I believe I and others have done is rebut the claims of proponents who have claimed many times to have "proven" the Hockney tracing theory. Because the burden of proof lies foresquare upon the revisionists, if one accepts my (and Christopher Tyler's and Thomas Ketelsen's and Walter Liedtke's and Antonio Crimnisi's and many others') rebuttals, then one must reject the Hockney theory, at least for the cases in question. Moreover, because the burden of proof lies with the revisionists, they must show that traditional (non-optical) methods are incompatible with the evidence, or far less likely than optical ones, given all the evidence such as documentary record. Note that it does not suffice for them to "fit" the optical and other evidence with an optical explanation; they must show that non-optical ones cannot.

If it somehow turned out that the best explanation for all the relevant phenomena in some early Renaissance paintings (the optical evidence, the corroboratory documentary evidence, the "re-enactments," etc.) demanded optical projections, I would accept it—tentatively, to be sure, as befits the scientific method. But the burden of proof lies squarely on the shoulders of the revisionists; in the absence of optical explanations that are more compelling than traditional ones, we surely must reject the theory.

Summary: My rejection–and, as far as I can see, the rejection by the vast majority of the many who reject the projection theory—is based on knowledge of contemporary praxis, the ease with which more plausible non-optical alternate explanations can be made, the implausibility of proponents' explanations for lack of documentary and corroboratory evidence, the misleading nature of their "demonstrations" made to an innocent public, and so on–not some reactionary protection of "turf" or obtuseness in understanding the proponents' arguments. Particularly irksome are their repeated claims in popular venues that the Hockney theory has been "proven."

Why does this matter?

In a great number of cases, we can best understand and appreciate an artwork if we understand how it was made. We can better understand Piero della Francesca's works if we understand the laws of perspective he was exploiting; we can better understand Jackson Pollock's later paintings if we understand how (and then why) he dripped house paint on canvases on the floor, and so on. Artistic tools, methods, and praxis influence the both the subjects an artists will choose to depict and style with which that artist depicts the subject. This is especially relevant in photography, where technical innovators such as Jean-Baptiste Frénet, Eadweard Muybridge and Doc Edgerton naturally gravitated to new subjects impossible to record by previous means. While art historians generally focus on the personal, psychological, aesthetic and social forces upon artists, the technical forces or opportunities deserve consideration too. For instance, the lowly paint tube had a profound effect upon the development of painting, particularly the ability to paint en plein aire. As Auguste Renoir noted, "Without paints in tubes there would have been no Cézanne, no Monet, no Sisley or Pissarro, nothing of what the journalists were later to call Impressionism."

Summary: My primary goal is to understand art more deeply, so we can see it with a more informed, perceptive eye and mind. Understanding how artists worked contributes to such an understanding. I believe Mr. Hockney would agree with this view.

You showed that the perspective lines in the Arnolfini chandelier do not conform to what we would expect had a "perfect" chandelier been imaged under optical projections. But if a "non-perfect" chandelier had been imaged by projections, couldn't that explain the results of your perspective analysis?

Of course! That's obvious, as I've written in my papers and demonstrate in my lectures. In fact you could always work backward and find an infinite number of distorted three-dimensional chandelier forms whose projection yields the image we find in the painting. In my talks and in several papers, I perform a sensitivity analysis of the Arnolfini image, in essence asking "how far would I have to move a point in the image to guarantee vanishing points line up properly," or more specifically "how sloppy would the chandelier craftsman have to be to yield the image we find?" Overall, the correspondence is fair, but a few points must be moved a fairly significant distance, for instance a trefoil moved by a whopping 10 centimeters in Arnolfini's room! Computer graphics expert James Schonberg and I have built a computer model and shown this more thoroughly. Scholars of 15th-century metalwork know that decorative structures (or crockets) were molded as part of metal arms in the time of van Eyck—not riveted or soldered onto arms. As such, there is very little inter-arm variation in such metalwork. Antonio Criminisi and I have confirmed this by photogrammetric analysis of photographs of such works in museum collections, and others have aided us through direct measurement of 15th-century decorative metalwork surviving in museum collections. Moreover, talented realist artists can achieve geometric accuracy surpassing van Eyck entirely "by eye," that is, without optical aids or geometric constructions of any kind. This last point alone would seem to demolish the Hockney and Falco claims for "proofs" that optics were used, at least for this painting.

Frankly, I suspect that the chandelier looks impressive and "in proper perspective" to the casual viewer because the contours are sharp and crisp (due to van Eyck's use of oil paint), not because the geometry of the chandelier reveals good geometrical perspective.

Summary: There are many areas (notably arms at the left) where the perspective is not particularly good, or rather, where the inferred manufacturing error is much larger than can be expected. Talented realist artists can achieve perspective better than van Eyck (even on the "best" portions of the chandelier) entirely "by eye," that is, without optical aids. The image-based case that the Arnolfini chandelier was painted under optical projections is very weak indeed. Of course the historical case is even weaker.

What about the claim that van Eyck used optics to copy the silverpoint of Portrait of Niccolò Albergati?

Thomas Ketelsen, author of Künstlerviten, Inventare, Kataloge: Drei Studien zur Geschichte der kunsthistorischen Praxis (Artists' lives, inventories and catalogs: Three studies on the scholarship of art historical praxis) and curator at the Kupferstich Kabinett in Dresden (home of the silverpoint) along with his colleagues have discovered tiny pinprick holes along the contours of the silverpoint, very strong evidence indeed that van Eyck used mechanical copying/enlarging methods such as the Reductionszirkel, a simple copying/enlarging aid known from Roman times and found in Pompeii. Hockney's epidiascope, had it existed in van Eyck's time, would have been the most sophisticated optical system in the western world—their "Hubble Telescope." Of course, such pinprick holes play no role in the Hockney/Falco optical "epidiascope" theory.

Alas, the kind of slow, careful, peer-reviewed scholarship done by true scholars such as Dr. Ketelsen is unlikely to be featured on high-profile public presentations (such as 60 minutes) by charismatic proponents willing to make claims that the tracing claim is so strong you could convict OJ. Nevertheless, anyone interested in the truth behind the copying of the Albergati portrait can see that it is Dr. Ketelsen's research—not the popular proclamations by projection proponents—that deserve scholars' and the public's credence.

Moreover, there are a number of other reasons we should seriously doubt the optical explanation, as described in my Scientific American article. For instance, van Eyck would surely have seen the effects of his "bump" (mismatching image and committed tracing) and presumably corrected it had he followed the methods of Hockney's claim. Moreover, the relative offset "error" of the location of the ear is easily explained in the mechanical explanation, but awkward and implausible in the optical one: When van Eyck worked on the ear, he merely shifted the position of the ear, either deliberately or by "mistake." Falco has recently claimed that nine pinprick holes in five locations is not sufficient for the sub-millimeter fidelity found in van Eyck's work. I don't know how one can, even in principle, make such a statement—and surely there's no justification for such a statement without relevant evidence (Falco provides none). Nevertheless, Richard Taylor of the University of Oregon (a professor of physics) built a Reductionszirkel and used it to copy/enlarge the Albergati silverpoint, achieving a fidelity just a bit worse than in van Eyck's works. More to the point, Tim Stotz, an accomplished realist artist, copied the portrait "by eye" and achieved fidelity quite comparable to van Eyck's; in fact, Stotz's fidelity is a bit better than van Eyck's around Albergati's eye region.

Summary: Contrary to the extremely public (~8 million viewers), high-confidence ("you could convict OJ with this evidence") claims that the Albergati portrait was copied using optics, for many reasons it is abundantly more likely that van Eyck used a mechanical device such as a Reductionszirkel or reducing compass.

What about putative "re-enactments" or "demonstrations"?

The putative "re-enactments" or "demonstrations" of painting under optical projection—such as on Hockney's BBC documentary—are invariably flawed to the point of being of little use. Such "demonstrations" generally use high-quality modern optical devices (mirrors) larger and far superior to what was available in the 15th century (see above and the following paragraph). Demonstrations with small hand-made mirrors that produce acceptable images suffer from a different fundamental problem (see next paragraph). The illumination is from high-power modern theatrical stage lamps that are easily directed and controllable, but have no counterpart in the Renaissance; direct solar illumination required for the Hockney projector would not be available in Arnolfini's room, the scene in Campin's Mérode Altarpiece, and other paintings for the rendering of the room as has been claimed by Hockney, and so on.

But these putative "demonstrations" suffer more fundamentally from a historical error. Sara Schechner, David P. Wheatstone Curator, Collection of Historical Scientific Instruments at Harvard University, has written "Hockney and Falco's interpretation of the written historical record is invalid and erroneous. They do not understand what people knew and when and how. But even if they did understand, there is also a critical historical point that I must emphasize here. All re-enactments are misleading if there is no historical evidence (whether it be documentary or material) that back them up. Re-enactments with modern, store-bought mirrors and bright light certainly do not mimic past historical, material conditions. But even if one grinds one's own small mirror—like the small ones Falco now is using—this does not prove anything. The availability of materials at a given time does not mean that they were used in the same way that we moderns think of using them. To give an unrelated example: No one made an electrical battery producing current until Volta created his 'pile,' but surely there were coins or metal disks, paper, saltwater, and wires around since antiquity." To this I could add innumerable other examples, such as Isaac Newton's epochal prism experiment, which could have been done much much earlier; the materials for making a telescope existed more than a millennium before the telescope was invented; the fact that all the materials needed to create a helium-neon laser were available in the 19th century, though such a laser arose in the 1960s; and so on.

Summary: The putative "re-enactments" of 15th-century, such as in Hockney's BBC documentary, are invariably flawed, misleading and erroneous on technical grounds. As Dr. Schechner points out, too, they are invalid because they are based on a fundamental misunderstanding of what people knew and when and how, and in the ultimate quality of mirrors in the early Renaissance.

Can optical aberrations explain some of the visual evidence in paintings?

Optical designers are very familiar with the inherent limitations of even perfectly made simple lenses and mirrors to produce a "perfect" image; such deviations from the ideal are called "aberrations." The key aberrations for a simple elements such as a parabolic concave mirror are: spherical aberration, coma, astigmatism (not quite the same as the vision problem corrected by certain eyeglasses), curvature of field, and distortion (pincushion and barrel). Another aberration—chromatic aberration—plagues glass and plastic refractive elements such as lenses, but not mirrors, and is hence irrelevant to the Hockney/Falco claims about the 15th century. Designers use multiple lens elements to reduce and to "trade off" one aberration for another in any particular optical system; that's why the lens systems in your expensive cameras have many lens elements.

Might the anomalies in paintings adduced as evidence for the projection theory be due to such aberrations? (The class of aberrations most relevant here are known as Seidel aberrations, after the 19th-century mathematician and optical expert Ludwig von Seidel. These describe alterations of the shape of a projected image, rather than merely the bluriness.) I have analyzed several key paintings and ruled out the role of aberrations. For instance, the Albergati portrait displays a distinct and discrete relative shifts—fully explainable by the use of a Reductionszirkel. Aberrations would instead give a gradual deviation as we move across the image. The chandelier in the Arnolfini double portrait possesses deviations in the crocket (and other structures) that are haphazard, and not explainable by any of the aberrations. Moreover, Hockney and Falco seem impressed that the more distant bobeches or candleholders are in reasonably good perspective. The relevant aberrations invariably lead to a greater deviation from ideal the further the image is from the central axis—the opposite of the case for the chandelier. Memling's Flower still-life has a deviation in the central vanishing point that might be consistent with barrel distortion, but the perspective tests within the front of the carpet argue against the use of projections of any kind.

Non-experts in optics often wonder whether an ill-formed (non-parabolic) concave mirror might produces the anomalies. However, a deformed mirror produces a blurry, useless image—not a sharp deformed one.

On the other hand a careful computer ray tracing study showed that when the necessary 116-cm-wide canvas is included into Lotto's purported projector, there are severe aberrations, contradicting the Hockney/Falco claims about depth of field.

Summary: Neither Hockney nor Falco make claims about aberrations as being the source of the "errors" in the paintings adduced as evidence for the projection theory, and thus it seems beside the point to refute a claim the proponents do not make. Nevertheless, a preliminary analysis of the possible role of aberrations in any of the key paintings shows that it is unlikely aberrations were the source of the anomalies. Of course, we would be interested if any scholar wishes to present a deeper analysis of the possible role of aberrations.

What difference does it make that artists can achieve realism–or even what Hockney calls "the optical look"–without the use of optical aids?

First, we must admit the obvious: that there are many artists from a wide range of periods–from the Renaissance onward (Jean-Auguste-Dominique Ingres, Gustave Courbet, Adoph William Bouguereau, Lawrence Alma-Tadema, Philip Pearlstein, and innumerable others) including contemporary realist artists—who can achieve highly realistic or natural images (i.e., possessing what Hockney calls "the optical look") entirely "by eye," that is, without the use of photographs, projections, or any other optical aids. A look through the Living Masters Gallery is a good place to start or any of a number of ateliers such as the Angel Art Academy in Florence. This fact has never been in doubt. But what is the relevance of this fact to our evaluation of Hockney's optical claims?

Recall that Hockney motivation for writing Secret Knowledge was his view that artists such as Ingres couldn't achieve such remarkable realism entirely by eye. In several venues he has also expressed skepticism artists of the early Renaissance could have done so either: Did they all just start drawing better in the early Renaissance? he asks, implying that he thinks not.

Falco has claimed the question of whether painters needed to use optics is logically distinct from the question of whether they in fact did use optics. (To illustrate this concept states that the question "Did Martha Stewart need to break the law?" is logically independent from the question "Did she in fact break the law?"). It is not so simple. The optical evidence (or the documentary evidence, or historical evidence, ...) taken alone is not sufficient to prove the case one way or the other, Falco's highly public claims notwithstanding. Our task as scholars and the interested public is to weight all the evidence, and in that case the question of whether early Renaissance artists could in fact paint "optically" entirely "by eye" is quite relevant.

It seems that it is only the fact that artists can paint realistically "by eye" that Hockney and Falco are eager to discount this fact. Imagine that it was clear that artists could NOT paint realistically by eye. In that case Hockney and Falco would be eager indeed to point out this fact in support of their theory. (And they'd be right.)

Or consider the case of murder so widely brought forth by Hockney and Falco themselves. The fact that OJ Simpson was in the neighborhood of Nicole Simpson and Ron Goldman at the time of their murder (and hence in that respect could have committed the murders) must be considered when judging OJ's guilt (and of course was). Had OJ been out of town, any defense lawyer would have pointed it out, thereby exonerating OJ.

Summary: In evaluating the plausibility of Hockney's theory, we must of course examine the full range of evidence–historical, optical, physical, and so on. Surely the fact that painters can paint realistically "by eye" not only undercuts Hockney's initial motivation, but more directly affects our judgement of the overall probability that they did so.

What disciplinary expertises are required to judge the Hockney claims?

Hockney's claims are first and foremost historical: they are claims about a specific place (e.g., Bruge, Florence), specific artist (e.g., van Eyck, Lotto) and most importantly a specific historical period (c. 1420–1550). Thus historical methods and evidence are central, for example contemporary texts in their original language, material culture, and so on. For example, someone might present optical evidence (e.g., image shifts in the Albergati portrait) and proffer an optical explanation. But it is the historian—an historian of optics or historian of art—whose expertise makes her suggest that perhaps a Reductionszirkel (known from that time) could be the explanation, and search for new physical evidence (pinprick holes). Scientists are generally unaware of such historical facts.

The most important scientific discpline required is computer vision, pattern recognition and image analysis. This field has developed a number of sophisticated algorithms for inferring illumination from images, rigorous and principled methods for inferring perspective transformations, metrics for quantifying differences in shapes, and so on. Many of these algorithms are only a few years old. (Few physicists have expertise in this enormous field of image analysis.) Another area is optics, but the optics required is simple indeed—little more than that presented in a good high-school science class (the lens equation, magnification equation, depth of field, f-number, ...).

Summary: A range of expertise is needed to make and evaluate claims about Hockney's thesis. Someone without firm educational foundation and professional experience in several of these areas is likely to be unreliable.

What errors would you like to clear up?
  1. In my posting for the Art and Optics Symposium, when addressing the question of whether Jan van Eyck used an epidiascope for copying Portrait of Niccolò Albergati, I posited three methods that I felt were more plausible than Hockney claim of use of an epidiascope: eyeballing, grids, and pantograph (mechanical device). I stated that Leonardo used a pantograph but this is an error. While Leonardo used all manner of complicated mechanical systems (levers, pulleys, "machine guns," helicopters, and so on), there is no evidence he used a pantograph. The earliest documented use is attributed to Christof Scheiner—later, around 1603. As soon as I learned of my error I contacted the symposium web master, who alas informed me that it was too late to correct the postings. (We must never forget that that Hockney and Falco's epidiascope hypothesis has no persuasive contemporary documentary support either, including in the works of Leonardo.) My error is small, I feel. It in no way undermines my point on that website that both eyeballing and grid construction are more plausible than the complicated epidiascope theory. And there are several other physical drawing aids that existed in the early Renaissance that perform the same scaling function, for instance the Reductionszirkel, as described in "Did Jan van Eyck build the first 'photocopier' in 1432?" available above. In short, while the particular pantograph did not exist, other devices that performed the same task did. Moreover, van Eyck's use of such a device explains the distinctive tiny pinprick holes in the Albergati silverpoint, but Hockney and Falco's optical epidiascope hypothesis does not.
  2. Marguerite Rigoglioso's article on my work in Stanford magazine states "There are no historical records before 1598, notes Stork, of any concave mirror being used to project an image except through burning." I don't know how that error crept in, but I do not believe I made that statement (and I was not given a chance to review the article). To the best knowledge of historians of optics and art, the earliest documentary record of an image projected onto a screen (as is required by the Hockney theory) is around 1550, and clearly from Giambattista della Porta in 1558, nearly 120 years after Hockney and Falco claim it was done. While della Porta suggests artists might trace such images, we have no corroborating records they did before the 17th century.
  3. In "Hockney pet theory challenged" the reporter Senay Boztas wrote "Stork, said the computer techniques clearly disprove Hockney's theories that the old masters apparently 'cheated.' 'We showed that Williams's chandeliers are in better perspective than van Eyck's. Williams's achievement came from his doing what we know for sure artists of the early Renaissance did: practice careful drawing from life for years and decades. Williams's paintings are one piece in the emerging scholarly consensus that rejects Hockney's deeply flawed theory.'" The quotes of my statements are accurate but not her statement that our results "clearly disprove." I've never said we've "disproved" Hockney's theory—just cast great doubt upon his claims, surely enough to refute his and Falco's claims they've "proven artists as early as 1420 certainly did use optics—of this there simply is no doubt."
  4. The French translation and re-edited version of my Scientific American article for Pour la Science contains an error. It correctly states the fact that the Arnolfini mirror, turned around and used as a spherical concave, could not yield a sharp image because the light would be spread out into a miniumum blur spot (also called the circle of confusion). However, the article incorrectly states that this blurriness is due to the wave nature of light (technically, is an Airy disc, due to diffraction of light). In fact, the bluriness is due to the fact that the mirror is a section of a sphere, rather than a paraboloid. The Scientific American article has the correct explanation; the Pour la Science article (which I was not permitted to see before publication) does not. This error does not affect the argument rejecting the Hockney and Falco conjecture that the convex mirror depicted within the painting could have been turned around and used as a projection mirror for creating the painting.
  5. In the poster at the Optical Society of America discussing the Albergati portrait and in my Scientific American article I stated that the fidelity of the copy made (by a professor of physics on his first try) using a Reductionszirkel was comparable to that in the van Eyck works. While there are portions for which the fidelity is this good, there are others where it is not, so it is not correct to state that overall the fidelity matches that in the van Eyck works. However, the copy made by eye by a professional artist is far better and closely rivals that of van Eyck. In fact the fidelity is a bit better than van Eyck's in some areas, such as the eyes. This artist used purely mechanical methods and achieved excellent fidelity. Moreover, it is quite likely that van Eyck—often considered the greatest draftsman of the 15th century—achieved the fidelity of a modern realist artist, particularly as he was copying a drawing by his own hand. As such, I hold to my conclusion that a talented artist can achieve the fidelity found in the van Eyck works using mechanical methods and without the need for optical projections. And of course, the pinprick holes discovered by Ketelsen and his team play no role in the optical projection theory but are precisely what results from the use of mechanical devices used at that time.
  6. In my first cast shadow analyses of Georges de la Tour's Christ in the carpenter's studio, the shadow line for the rear of the beam was not tipped enough, by a few degrees. (I think Charles Falco for pointing out this.) In subsequent publications, such as here and here, I corrected that line and the rebuttal to Hockney's claim remains unchanged. In fact, the rebuttal is strengthened since Kimo Johnson and I extended our analyses to include occluding-contour algorithm, which yields an independent confirmation that the light source is very close to the location of the depicted candle, not as Hockney claims "in place of the other figure." Moreover, I and Yasuo Furuichi built a computer graphics model that yielded yet a third independent analysis method that confirms the rejection of Hockney's claim for this painting, and shows that the shadow of Christ's left shin is far more consistent with the light in place of the candle than "in place of the other figure" (St. Joseph). I also analyzed the pattern of light on the floor depicted in the painting and it too shows the light was in place of the candle.

Scholars who have published scholarly publications rejecting all or part of the Hockney theory:

  1. Dr. Shotaro Akaho, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan
  2. Dr. Antonio Criminisi, Research Scientist, Microsoft Research, Cambridge England
  3. Dr. Marco Duarte, Department of Applied Mathematics, Princeton University
  4. Dr. Jun Fujiki, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan
  5. Mr. Yasuo Furuichi, Kanagawa Japan
  6. Dr. Hideo Hino, Waseda University, Tokyo, Japan
  7. Dr. M. Kimo Johnson, Department of Brain and Cognitive Science, Massachusetts Institute of Technology
  8. Mr. David Kale, Department of Computer Science, Stanford University
  9. Mr. Ashutosh Kulkarni, Department of Computer Science, Stanford University
  10. Dr. Silke Merchel, Research Physicist, Bundesanstalt für Materialforschung und ­prufung, Berlin Germany
  11. Dr. Noboru Murata, Waseda University, Tokyo, Japan
  12. Dr. Ina Reiche, Research Physicist, Centre de Recherche et Restauration des Musées de France, Paris France
  13. Dr. M. Dirk Robinson, Research Scientist, California Research Center, Ricoh Innovations, Menlo Park CA
  14. Dr. David G. Stork, Chief Scientist, California Research Center, Ricoh Innovations, Menlo Park CA
  15. Dr. Christopher W. Tyler, Associate Director, Smith-Kettlewell Eye Research Institute, San Francisco CA
  16. Ms. Yumi Usami, Waseda University, Tokyo, Japan
  1. Dr. Filippo Camerota, Istituto e Museo di Storia della Scienza, Florence Italy
  2. Dr. Sven Dupré, Ghent University, Ghent Belgium
  3. Dr. Samuel Y. Edgerton, Williams College, Williamstown MA
  4. Dr. Michael John Gorman, Arkimedia, Dublin
  5. Dr. Christoph Lüthy, Radboud University Nijmegen, Nijmegen Netherlands
  6. Dr. Antoni Malet, Universitat Pompeu Fabra, Barcelona Spain
  7. Mr. Olaf Simon, Kupferstich Kabinett, Dresden Germany
  8. Dr. A. Mark Smith, University of Missouri, Columbia Missouri
  9. Dr. Yvonne Yiu, Universität Basel, Basel Switzerland
  1. Dr. Thomas Ketelsen, Kupferstich Kabinett, Dresden Germany
  2. Dr. Alexander J. Kossolapov, Hermitage Museum, St. Petersburg, Russia
  3. Dr. Sara J. Schechner, Harvard University, Cambridge Massachusetts
  1. Jacob Collins, New York City
  2. Nicholas Williams, UK

 

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