David Stork's objections

No. There are several other problems I raised that do not reduce to the above three classes and Falco and Graves do not answer them, for instance Why the embarrassing lack of inverted brushstrokes (even in underpaintings) in Renaissance art? What about alternate explanations? Do they think the first is "unrelated" to the question of whether paintings were at least partially completed upside-down? These problems for the Hockney theory, and others not answered by Falco and Graves, as well as rebuttals to their points will be presented below.

First of all, nowhere do I invoke the phrase "artistic genius," as their quotation marks imply, or even that concept. On the contrary, I refer to "students" and state that there are thousands of paintings done "optically" -- hardly an appeal to "artistic genius." Under my title Drafting Talent (not "Genius"), I touted a single individual, a Texas police sketch artist... whom I suspect would be flattered indeed to be associated with the term "artistic genius" that Falco and Graves introduce into the discussion. Even for van Eyck I refer only to his "own patient talent" and summarize the whole discussion thus: "it seems plausible that van Eyck, Leonardo, Caravaggio and other Renaissance painters had the requisite talent." While Falco and Graves here and below may hope to portray my position as somehow relying upon "artistic genius," and thus somehow extraordinary or implausible, the simple fact is that I am not and never have. I don't need to.

Next, it is worth pointing out that neither Hockney nor Falco and Graves themselves had put forth the grid alternative to the optical explanation of the Albergati copy. Why not? Are they that unaware of the history of technology of the time? They ask "How else to account for the convergence except by way of some sort of optical projection?" as if the answer were self-evident. Do they hope their audiences will not bring up alternatives? How can they make claims -- including claims for "proofs"! -- without doing so?

Lorne Campbell, Research Curator at the National Gallery, London, author of Fifteenth-century Netherlandish art and van Eyck expert, claims that van Eyck did the copy by eyeballing (pers. com. 2002). A 1-mm resolution -- the thickness of a dime -- isn't particularly farfetched given that an artist can measure and scale distances (without a grid) and has his own source image in front of him, even if he's enlarging. Regardless, as I wrote, eyeballing is not my favored explanation, but neither can it be dismissed immediately, as Hockney and Falco do. Falco and Graves complain that the eyeballing explanation was not compared to the evidence, ignoring the fact that neither has the optical method.

The epidiascope is by not the simplest means to achieve this accuracy, and has never even been demonstrated in this regard. In the Renaissance it required an expensive and at best rare (but probably nonexistent) device along with strong lighting and complicated setup. A grid construction is simpler and, as I've demonstrated experimentally, gives more than enough accuracy.

Falco and Graves are in error here. Earlier I had considered an easel "explanation" but didn't even mention it because it could not account for the data. Because Falco and Graves cannot see this, it pays to show the contradictions inherent in their hypothesis. In short, they ignore my central point which was that, unfortunately for Hockney, Falco and Graves, there are TWO "lucky" bumps -- one horizontal and one vertical. Their new easel hypothesis may ensure that ONE bump is horizontal (and yield no image rotation), but their hypothesis precludes an orthogonal, vertical, bump (and no rotation) -- unless of course they ask us to accept that van Eyck's canvas levitated above an easel rail. (Incidentally, another ad hoc technique of moving the canvas forward and backward would change the magnification and hence cannot explain the vertical "bump.")

Furthermore, Falco and Graves conveniently speak about the rotation but mention neither the ratio of distances of the bumps, which is extremely unlikely in their ad hoc explanation, nor the existence of the lines at the right of the image. And of course their explanation relies at its heart upon complicated technology for which there is no persuasive evidence (see below) while mine relies on simple technology that was used at that period and indeed earlier.

Most importantly, they have stated nothing to cast doubt upon my grid construction and experiment, which remains the best explanation for the van Eyck images and is in every way superior to their optical theory.

This is quite surprising and welcome indeed -- Falco and Graves are sounding like me: claiming that an explanation is invalid because the required device wasn't yet invented. GREAT! They rest their argument on Kemp's book. Did they ever bother to try to look up in that book "epidiascope," or "mirror, concave projection" or anything that would support their projection hypothesis? There is nothing in Kemp's book or indeed any relevant book I've seen that gives support to their epidiascope hypothesis in particular or to mirror projection generally. How can they use Kemp's book to discredit pantographs, when in fact it discredits even more firmly their epidiascope hypothesis?
Of course, Falco and Graves cannot appeal to Kemp as an authority if they choose which parts of Kemp they accept and which they reject. To do so would be to undercut any appeal to Kemp's authority on the matter.

The simple fact is that the pantograph was invented in 1603, long before the Dutch physicist Christian Huygens (1629-1695) invented the precursor to the epidiascope. The brilliant mathematician Leonard Euler was probably first to describe projector for opaque objects in 1750-51 nearly a quarter millennium after Falco and Graves claim it was used. Related technologies are the megascope of J.A.C. Charles (France) of the late 18th-century, the fantascope, which could also project slides; the episcope; Wunder Camera and Aphengescope, all long long after the time Falco and Graves claim such a system was in use. And if we want to talk about the availability of the components of these devices, the wood sticks of a pantograph were available to cave men tens of thousands of years before the sophisticated concave mirror required for an epidiascope, and the pantograph's parallelogram principle was known twenty-three centuries ago, long before ray tracing in concave mirrors had even been thought of. In short, the pantograph is far more plausible than the mirror projection method, and, as I pointed out, the grid construction is more plausible than either.

In arguing against the pantograph because it hadn't been invented, Falco and Graves are -- unwittingly -- arguing against their theory better than I ever could. Since the long-focal length concave mirror hadn't been invented -- surely not patented -- and there is no evidence that it was used for projections, all their explanations based on it succumb to the dismissal they serve to pantographs. Fortunately for me, I have an alternate explanation, which I clearly and explicitly prefer. Unfortunately for Hockney et al., they don't.

The explanation by grid construction is in every way superior to an explanation resorting to optics. The grid explanation relies on elementary technology known to be used at the time, which in modern re-enactments gives correspondence better than the originals, gives a natural explanation for the direction of BOTH bumps AND their relative distances, and gives a principled explanation for the vertical lines at the right. In contrast, the optics explanation relies on complicated and at best rare devices used in a way for which we have no corroborating textual or representational evidence whatsoever, requiring bright lighting, which has never been verified by re-enactments, can only explain BOTH bumps by appealing to levitation, has no principled explanation for the relative distances of the bumps, and has nothing to say about the vertical lines at the right.

It is no wonder the promoters are not eager to put forth alternatives to their optical theory. .

Lotto

I understand that Christopher Tyler will reply to this point in his After Thought.

As I stated in my piece, "I am aware of just three modern demonstrations" and describe them; of course I cannot comment upon experiments that have, to my knowledge, not been revealed to the public. We look forward to Mr. Hockney presenting his May 2001 results in sufficient detail and clarity in a scholarly forum so that others can judge them, including issues such as the consistency of viewpoints, direction of brushstrokes, color fidelity, and much more. Until Hockney reveals this evidence I'm afraid we'll have to withhold judgment on their claim that the results "were entirely consistent" with their theory. Regardless, knowledge of simple optics ensures us that if Hockney had refocused on Peter's right hand as he describes in his book, then he would have moved the both the lens and the canvas six feet, an awkward and unlikely step.

One throws up one's hands in exasperation! When I quote Mr. Hockney, the originator and driving force of the theory and the titular reason for the symposium, when he wrote that Caravaggio "...worked in dark rooms -- cellars -- very common in those days... He used artificial lighting" and his supporters respond instead "direct sunlight is the likely source of illumination" one doesn't know whether the proponents realize their blatant contradiction, or that they think we won't see it, or what. At the very least, Falco and Graves should take Mr. Hockney aside and tell him to stop misleading the popular press. To wit: one august periodical known for penetrating research and trenchant skeptical analysis, when interviewing and lavishing praise upon Mr. Hockney and his bold theory, states that Caravaggio "[w]orked in darkened cellars -- which you need for the lens to work. Strong artificial lighting (ditto)" [1].

Regardless of such contradictions on this central matter of illumination, their argument against the historical record of Caravaggio's estate which contained a convex mirror ("scudo a specchio" or shield mirror, almost surely the one depicted in "The conversion of the Magdalene" and completely useless for projections) and several candle holders, his working methods that included at least at some periods a dark cellar without sunlight, and so on -- reviewed over centuries by art historians -- seems to be that it is incompatible with their new theory. Caravaggio's biographer and rival G. P. Bellori wrote in 1672: "He never showed any of his figures in open daylight, but instead found a way to place them in the darkness of a closed room, placing a lamp high so that the light would fall straight down..." Joachim von Sandrart wrote in 1675: "He used dark vaults or other shadowed rooms with one small light (liecht) above, so that the light falling on the model made strong shadows in the darkness..." In 1617-21 Giulio Mancini wrote 'A characteristic of [Caravaggio's] school is lighting, from one source only, which beams down without reflections, as would occur in a very dark room with one window and the walls painted black, and thus with the light very strong and the shadows very deep, they give powerful relief to the painting, but in an unnatural way.' None of these support the Falco (revised) hypothesis that Caravaggio worked under bright direct sunlight.
Caravaggio lived in the Palazzo Madama, home of Francesco Maria Del Monte. Del Monte's brother, Guidobaldo, wrote Perspectivae, one of the most influential books on geometrical perspective in the Renaissance' working methods in the Renaissance. But this book says nothing about the mirror projection system which he would surely have learned around Caravaggio, had it been used. Why? The unjustified claim that Caravaggio used optics forces the proponents into the extremely awkward conclusion that he worked under bright sunlight.

It's not odd at all that a painter would best paint what he sees, or arrange his studio to appear close to how he wants his final painting. Not odd at all, especially in the Renaissance. It is very odd indeed that a painter would try to make a painting look like it is night time when in fact the scene is illuminated by bright sunlight, or would work with very dim inverted images much of which are out of focus, or would use an extremely rare (and probably nonexistent) technology when he had done other methods, or had to constantly correct for color (see below) -- all as arising in the Hockney/Falco theory. Now THAT is passing odd! Hockney and Graves write: "There is no reason whatever to assume scenes were illuminated by the sources of artificial light depicted within those scenes" but in fact there is, and every representational artist I know (save possibly Mr. Hockney) would have chosen artificial illumination had they wanted to produce the painting de la Tour gives us. If de la Tour wanted to show light passing through the translucent fingers of the girl, to show the proper shadows of the man's left thumb and the wooden beam's left corner, to get the highlight on St. Joseph's forehead, he would use the candle. Even the slight irregularities, if any, can be explained by slight repositioning the models during the execution and does not require two exposures of sunlight. Arranging such "exposures" would be extremely awkward, where bright sunlight comes from the left for one figure, then must somehow come from the right for the other, all to make the light appear as if it emanated from a point at the candle! Mr. Hockney's suggestion that this painting was done by sunlight is extremely implausible.

I think it pays to pause for a moment, particularly for the artists reading these pieces who may be a bit bewildered by technical talk of focal lengths and so on, to rely on your eyes for a moment. I invite you to expand the de la Tour painting, study it carefully for several minutes, all the time saying to yourself "Hockney and Falco claim this painting was made with the models illuminated by bright sunlight" as described on page 128 of Secret Knowledge. For a few minutes, rely on your own visual intelligence and see if you agree.

[1] "Have you seen the new David Hockney?" by Andrew Marr, pp. 44-50, High Life (October, 2001) [British Airways inflight magazine]

I'm glad it is now clear to Falco and indeed everyone that my criticisms both at the symposium and on this website of the Arnolfini mirror have always been on its focal length and thus the size of the sphere from which it was cut (according to Mr. Hockney) -- not the areal size of the mirror face itself.

Hockney and Graves are quite correct that I was unaware of the Tomaso da Modena's two paintings. But I am especially grateful that they have managed to uncover these paintings because -- contrary to their claim -- the mirrors depicted in them do not reveal that they have the long focal lengths demanded by the Hockney/Falco theory, and the text does not support the use in the form required by the optical theory.

First, the issue of focal length. The focal length of the mirror in "The Blessed Pietro Isnardo of Vincenza" is difficult to determine, but upon very close inspection, a small highlight is visible. More relevant is a curved line at the right, presumably the reflection of the vertical edge of the shelf case. I estimate the diameter of the mirror face to be about 6 cm, and from the curved line and placement of the edge that its focal length is short -- roughly 4 cm. Admittedly, there are uncertainties, but there is no justification for claiming that the focal length is long (50 cm, say), such as needed for the Hockney/Falco theory. Likewise, the mirror in the conical holder in "St. Jerome" is hard to determine, but there's no evidence that it has a long focal length especially given the short focal length estimated for Pietro Isnardo's mirror. Further, the short-focal length mirror would give greater magnification in its reading mirror use; Pietro Isnardo wouldn't have even wanted a long-focal length mirror if he had one [2]. Falco and Graves are wrong to state that they have evidence that "appropriate concave mirrors existed at the time." The whole issue has always been long-focal length mirrors (I've conceded short focal length mirrors, as for burning for instance), and this new evidence fails here too.

Second, the question of evidence of imaging tasks. Falco and Graves are right that they have uncovered textual evidence of an imaging task. But it is important that readers understand some more optics. Up to now, we have nearly always spoken about the image in a concave mirror to be the image projected by that mirror, as in the Hockney/Falco theory. As mentioned many times, this projected image is inverted or upside-down. We must now note that this image is called "real" because light actually passes through the image -- after all, that's what illuminates the canvas. But a concave mirror can also produce a different sort of image -- a "virtual image" -- such as when you look at your nose in a makeup or shaving mirror. Here the image is instead erect or rightside up, and is on the other side of the mirror. This image is called "virtual" because no light actually passes through the position of the image; the light leaves the mirror as if it had come from the image. Such a virtual image cannot illuminate a canvas in the way the real inverted image can. (Incidentally, your image in a plane bathroom mirror is similarly virtual, and of course erect.) When I wrote that we have little or no persuasive evidence that concave mirrors were used for any imaging tasks, the context was for real images, as in the Hockney/Falco theory, not the virtual ones in the Tomaso da Modena paintings. Let me clarify my statement then to account for the context in which it was written: "We have little or no persuasive evidence that long-focal length concave mirrors were used for imaging any real inverted images as required by the Hockney/Falco theory."

Gibbs wrote: "Mirrors, despite their inconvenient habit of reversing the text..." and this is crucial. It proves that the concave mirror was being used much as a shaving or makeup mirror, and that the monk was seeing a virtual image behind the mirror (which reverses left-to-right), not the projected real inverted image of the Hockney/Falco theory (which does not). While Falco and Graves give a nb on the topic, there is no evidence the monks figured out the major task of how to project an image central to the optical theory, or that the quality of the mirror would have supported such a projection. After all, I surmise Mr. Hockney had spent many hours with shaving mirrors and only learned about their projection abilities from a PhD in physics in the 21st century when Hockney was into his 60s. Falco and Graves provide no evidence anyone in the Renaissance or before, including Pietro Isnardo, did.

The bigger question remains unanswered: WHY, after years of research by numerous historians of optics, technology and art, is it so hard to find such evidence that long-focal length concave mirrors existed, much less that they were used to project a real inverted image (or of course that such images were traced or painted over)? I'm happy to join the chorus refuting Mr. Hockney's claims about the Inquisition or trade secrets on this topic, but I'd like to know if Falco and Graves agree with him, or instead have another explanation. Although I urge Falco et al to comb the historical records, unfortunately for them the more anyone finds evidence such as they present above, the more the silence on appropriate mirrors and their projection use becomes deafening. This is because such new evidence makes more and more implausible at every turn that there was a conspiracy, that historians somehow overlooked the evidence, or that the Inquisition (Isnardo was a Dominican monk, after all) was suppressing such a conspiracy and leaving us no evidence in this regard. In my piece I listed several dozen optical instruments uncovered by historians of optics, and in light of these Hockney et al give us no reasonable explanation for the lack of corroboratory evidence of long-focal length concave mirrors and their use in projecting real inverted images.

Since they don't address it, I'll assume Falco and Graves agree with my refutation of Mr. Hockney's claim that the convex Arnolfini mirror could have been used in the making of the painting itself. The elementary fact is that it could not and I very much hope that Hockney and Falco will refrain from claiming otherwise in their public and other venues, such as this month's Smithsonian magazine which reads "Had Jan van Eyck turned over the convex mirror hanging on the wall in his Arnolfini Wedding, he would have held an optical tool suitable for creating the meticulous detail found there" [3].

The simple fact remains that STILL no one has shown corroboratory evidence that long-focal length concave mirrors existed in fifteenth-century Europe, or that anyone had ever seen the real, inverted image projected by such a mirror demanded by the Hockney/Falco theory. Mr. Hockney surely doesn't provide such evidence in the "Textual evidence" section Secret Knowledge and neither do Falco and Graves here. My summary from the conference paper website stands unaltered, and indeed strengthened because after further effort the proponents have yet to contradict it: "There seems to be no corroboratory depictions of any specific mirror from the fifteenth century that could have been used in the creation of the Arnolfini portrait, Lotto's 'Husband and wife,' or indeed any of the paintings for which Hockney and Falco and I computed an effective mirror focal length. In every case, particularly the mirror proposed by Mr. Hockney, the focal lengths are much too short."

[2] Seeing the Light: Optics in Nature, photography, color, vision and holography by David Falk, Dieter Brill and David Stork, Section 6.2D (2000, 14th printing)

[3] "Mirror Images," by Jennifer Lee Carrell, Smithsonian, pp. 76-82 (February, 2002).

Falco and Graves are mistaken on this point. Suppose you are looking at an image projected onto your white canvas for example the image of a red apple. What color paint should you apply to the canvas to make the painting appear correct to you under such circumstances? Artists especially: take a moment to think about it. Should you apply red paint? No. WHITE! You should paint the apple area, and indeed the whole canvas, white -- like a movie screen. That way the projected image appears to you in its proper colors.

Now suppose you're looking at the dark projection and you want to paint the apple area so that it will appear red under normal neutral illumination, that is, when the painting is hung on the patron's wall. What color should you paint it now? This is actually a very difficult problem and artists would have to work very hard to get it right [3]. The color your paint appears changes significantly under the colored light. If you put down red, it appears too saturated under the projection. The cognitive and perceptual force, so to speak, is for the artist to apply unsaturated colors, that is, more like white. But then the painting will appear washed out and unsaturated under neutral illumination on the patron's wall. It goes without saying that we have seen no corroboratory evidence from the historical record -- manuals, descriptions, guides for artists -- showing that anyone in the 15th-century had to confront this thorny problem. Didn't any artist get the colors wrong in this challenging task? All the 'optical' artists magically figured out this extremely complicated problem with no mistakes?

Then there are several relevant phenomena of which I suspect none of the proponents is aware -- one's I've studied for years. One of them is the Purkinje shift, in which colors appear to change in hue and relative brightness when they are dim, as in a projection in the Hockney/Falco theory. There's not a shred of evidence Hockney, Falco or Graves are aware of these problems -- again, a classic case of "they don't even know what they don't even know." As someone who has worked on color for a quarter century, starting with my thesis on color vision at MIT under Edwin Land, founder of the Polaroid Corporation and inventor of the Polaroid Land camera, I view Hockney/Falco/Graves understanding of the relevant science of color incredibly naive, at the very best.

Getting the color right is absolutely essential to the art of the Renaissance. While Falco and Graves may point to the fact that we don't really know the color of Mrs. Arnolfini's dress, we do know her skin color. Do they think she was purple? That Genevre de' Benci was really a black Ethiopian? That the peach in Chardin's painting is green and the cabbage in Cotán's still life blue? I displayed Campin's "A Man" favored by Mr. Hockney as my example because it is essential that his skin color appear correct, not because his red turban might have been instead ochre. Getting the color right is essential and despite Falco and Graves's unsupported assertion, getting this color correct is never aided by the projection method. In fact, if you paint under the projection, you'll get the colors wrong -- or at the very least, have to work extremely hard to get the colors right.

Perhaps color was just part of the Mr. Hockney's difficulties when he is reported to have said at the New York symposium: "I tried painting under an optical projection, but it was too hard. I gave up within ten minutes. I'm sure that if any Renaissance artists tried they would give up within ten minutes, too." (Christopher Tyler, James Elkins and Amy Ione, pers. comm., 2002).

And yes, it is human faces that most expose the problems in copier toners -- a slight error and faces look terrible. If you don't get the faces right in your color copier, no one will buy it; if you don't get the colors of the faces correct in your Renaissance portraits -- if you paint over the projected image using the Hockney/Falco method -- no one will commission you to do another portrait.

[3] Seeing the Light: Optics in nature, photography, color, vision and holography by David Falk, Dieter Brill and David Stork, Sections 9.6-9 (2000, 14th printing)

Again, it is Falco and Graves that are just a bit off the mark. In the context of previous discussions, or at least according to the relevant issue, by "producing an image (rather than burning)" I clearly meant producing a real inverted image such as that required by the Hockney/Falco theory. This new evidence fails to provide such evidence. Concerning this new evidence: the mirror is wrong, the image is wrong, the use is wrong.

Since I wrote at length about the absence of "upward" brushstrokes that would be produced according to the Hockney/Falco projection method, their silence on this matter can be taken to mean they have no answer to it.

I disagree profoundly with the assertion "optical evidence we have assembled demonstrates that some artists as early as c.1430 certainly did use lenses." At best, some might be consistent with the use, but in no case have they proven it, surely not with the Lotto nor the Albergati nor the Arnolfini portraits, which Christopher Tyler and I took to be their "best shots." I'll return to this in the summary.

I wrote a whole section on adoption of technology which Falco and Graves claimed was not relevant, but in fact it addressed and refuted the point they'd like to make here: "Also, neither Stork nor Tyler seems to realize that a lens would have been used by an artist as an aid when it helped them accomplish his or her goals, but would not have been used when it did not." It is by no means so simple.

Let me proceed by an example, literally at hand. Let us assume for the sake of argument that all computers support graphics and text processing, but that the Macintosh is better for graphics and the IBM PC is better for text. You produce colorful art newsletters, and thus must do both. It took you a few months to learn, but now you're a happy Mac user and do both graphics and, with occasional annoyances, text processing, producing your newsletter week after week. Now a salesman comes to your door and tells you that you could write your text better if you used a PC. The "search and replace" and spell checker functions are much better on a PC, he convinces you. All you have to do, he continues, is buy a PC and switch back and forth between computers, as needed. He doesn't say that you must buy an extremely rare and expensive PC on the black market, no one is advertising to let you know where to buy it, that it will take a while to learn how to use it, that there are no manuals, that your keyboard will be upside-down, that you must work under a dark tent, that your screen will be upside-down and nearly black, that you can't work except when the sun is shining, that the color of the text will come out wrong unless you make allowances at every keystroke and that if the police find you with the PC they'll put you in jail. "But some text functions would be better!" Would you buy a PC?

Now let's take Lotto. There's no question that Lotto and numerous Renaissance painters could paint optically without recourse to optical devices; the challenge image of "Angel of the Annunciation," Leonardo's "Last Supper," logic, and Falco and Graves's silence on such images shows that. Lotto could render convincing images of the face of the angel and of course much more. Now some late afternoon Lotto is painting two patrons in his studio -- a husband and his wife -- and has painted their faces, just as he had for the angel. Mr. Hockney, magically teleported to the early Renaissance, enters the studio and tells Lorenzo that he could capture the carpet pattern better if he uses a new "PC," or "projection contraption." All Lotto has to do is find this extremely rare and probably nonexistent wonderful contraption, learn how to use it without a manual, learn to deal with images upside-down that are very dark, set up a dark tent in his studio, wait until next morning when the sun is shining and hope the sky isn't overcast, struggle at each brush stroke to get the colors right, and make sure that the Catholic Church doesn't find out or they'll burn him at the stake. "But the carpet pattern would appear better!" Would Lotto use Mr. Hockney's "PC"?

Obviously, when Falco and Graves write: "That is, both projected and eyeballed features are within a single painting" they haven't thought about points 4 and 5 on my technology section, perhaps because they feel they are "irrelevant." The simple fact is that switching back and forth "within a single painting" would be extremely difficult, costly, awkward and annoying, and would probably outweigh any putative benefit hypothesized for the projections.

I and many others would be very interested in seeing this. The statement "Although Stork has never been to Hockney's studio" seems to express dismay in this regard. If Mr. Graves and Mr. Hockney would open their studio to me, I'd be happy to come, and would bring a camera, light meter and measuring tape. Regardless, it is hard indeed to reconcile the above claim by Falco and Graves with Hockney's statement at the New York symposium: "I tried painting under an optical projection, but it was too hard. I gave up within ten minutes. I'm sure that if any Renaissance artist tried they would give up within ten minutes, too." (reported by Christopher Tyler, James Elkins and Amy Ione, pers. comm., 2002).

Again, it is impossible to argue against proponents of a theory who write that Caravaggio "...worked in dark rooms -- cellars -- very common in those days... He used artificial lighting" on the one hand and "direct sunlight is the likely source of illumination" on the other.

It does. And if Hockney, Falco or Graves had the slightest experience in this matter, they'd know it. As I wrote before, and in light of my discussion of Mr. Hockney's "PC," even if somebody someday finds some long-focal length concave mirrors from the Renaissance, it hardly means any artist would have one or would even want to use it. The proponents naively think that if a tool gave a "benefit" to artists then of course they would in fact use it, but this is often far from the truth.

Falco and Graves make a convenient misquoting of me. The actual text from my piece is "Because of the breadths of its claims, the theory then must be able to explain -- or at the very minimum, be consistent with -- other 'optical' paintings in the period." Contrary to their assertion here, I'm not saying that they have to deduce properties of the mirror used, just that they have to be consistent with the use of a mirror and inconsistent with other plausible explanations. It is clear now to all that these challenge paintings are not consistent with the use of a mirror. That was my only point, and they surely haven't refuted it.

The issue is not whether we can deduce properties (e.g., focal length) of a lens in a "platter" Lotto, but whether we can say that a lens was used at all. If there is no evidence, then we cannot claim it. Simple. And given the challenge images that prove that no lens was used, there's no reason to assume that a lens was used for the "platter" Lotto, especially when the evidence for mirror use is so contradictory or non-existent, as in "Husband and wife."

Falco and Graves make several errors in logic here. The first is their assertion "no question whatever that they were produced using lenses." But this is precisely the matter at hand in the case of Lotto; there is every reason to question that Lotto used a lens. Indeed there is no persuasive evidence that he did, and surely no disproof of the traditional explanation that he didn't use a lens.

Here's a parallel story. Suppose Mr. Falco analyzes a still from Steven Spielberg's film "Little Women" and finds there's enough information to properly deduce the focal length, aperture or other properties of the camera lens used. Now he turns to a still from a scene in a different film by Mr. Spielberg and finds there isn't enough evidence to deduce such properties of the lens. "Well, since there is no question Spielberg was using a lens," we imagine Falco stating, "the inability to deduce its properties doesn't disprove the use of a lens." Too bad for Mr. Falco, though. The later Spielberg film is "Jurassic Park," and the still came from a scene which was created entirely by computer -- no lenses (or even objects) whatsoever. Given we know for certain Spielberg, John Lasseter, and others can make films that contain images made without any recourse to standard cameras and lenses, as shown by "Toy Story II," and so on, the flaws in Mr. Falco's are clearly exposed. The whole discussion has been over whether Renaissance painters used optics, and Falco's flawed logic cannot salvage the inability to show optics was used in the hypothetical evidence-poor Lotto "platter" painting.

But it is even worse than that for the optical theory because Hockney, Falco and Graves have given us no evidence that a lens must have been used in any Renaissance painting, though they'd desperately like others to believe they have. By analogy, they haven't shown that Spielberg used lenses at all in "Little Women." The burden is entirely upon the theory's proponents to show that the traditional methods are insufficient to explain properties of any painting, and that the optical projection method must have been used. Despite being gven numerous opportunities, they have failed to do this in even a single case.

They state: "Within those paintings we have studied that show evidence of the use of lenses, every optical artifact we have identified is consistent with having resulted from the use of lenses to project portions of the images." Here's a counter-example: the local convergence of parallel lines in Lotto's "Husband and wife." Here's another: They claim that van Eyck used the convex mirror depicted in the Arnolfini portrait to paint the image itself, but this is impossible. Most importantly, every feature in every image Hockney and Falco put forth is consistent with non-optical explanations. Again, there are innumerable examples that are inconsistent with the optical hypothesis -- murals, ceilings, self-portraits, objects in motion, etc. Moreover the long-focal length concave mirrors implied by numerous paintings are unknown from that time.

Contrary to the Falco and Graves assertion, it is the Hockney/Falco explanation that is ad hoc and inconsistent. For instance, Hockney tells us that Cardinal Albergati has small pupils because he's under bright illumination needed for the mirror method -- so then why don't Arnolfini, his wife, Campin's "Man," and innumerable others claimed to be made by the method also have small pupils? And why do some subjects in 'non-optical' paintings, such as Berhhard Strigel's 'Portrait of a man,' also have small pupils? We're told that the mirror projection method leads to "blur" in Lotto's "Husband and wife" -- so then why don't we see the same in Caravaggio's "Supper at Emmaus," Holbein's "The Ambassadors," and Arnolfini, also claimed to be made by the method? Each of these explanations is arbitrary and ad hoc. Finally, never I have employed some "opaque shroud of 'artistic genius'" -- I don't need to -- and Falco and Graves are attacking a strawman of their own making.

After Thought Summary

Hockney, Falco and Graves have yet to provide a single painting from the early Renaissance that requires the use of optical projections. Their favored Albergati portrait can easily be explained by non-optical methods, in fact much easier than with optics. The carpet in "Husband and wife" could not have been done with optics as they claim, as the local convergence lines are not consistent, though they would have to be in an optical projection. Moreover, the very slight blur (which curiously only occurs in this painting) can be explained by numerous non-optical ways. They have provided corroboratory evidence for neither the optical elements (long-focal length concave mirrors) employed by their theory, nor the projection method itself, even though there is every reason such evidence would otherwise be available, the Inquisition and conspiracy theories notwithstanding.

The optical theory is incoherent, arbitrary and ad hoc: Bright illumination leads a sitter (Albergati) to have small pupils -- except when it doesn't (all others). Blur in a painting (Lotto), "proves" a concave mirror was used -- but when there is no blur, well, a concave mirror was used there too (Caravaggio). There is an enormous number of Renaissance paintings that we know for certain were not created using optics (challenge images and related) and the burden is upon the proponents to disprove the traditional explanations (and account for ancillary supportive and contextual facts). The proponents give no persuasive explanation for the lack of inverted brushstrokes or why historians are so wrong (e.g., on Caravaggio's working methods). Contrary to the proponents' unsupported assertions, getting the color right is never aided by the projection method, and in other cases is impeded significantly, as explained above. This difficulty could explain part of Mr. Hockney's frustration with his technique, reported from the New York symposium: "I tried painting under an optical projection, but it was too hard. I gave up within ten minutes. I'm sure that if any Renaissance artist tried they would give up within ten minutes, too." If Renaissance painters didn't paint under projection, then there should be trace lines, revealed on at least some paintings of the time; the proponents have yet to provide them for any painters, let alone their favorites, such as van Eyck and Lotto. The proponents seem incapable or unwilling or both to give alternate explanations, and many objections; a look through Secret Knowledge, the OPN paper and elsewhere shows no identification and surely no resolution on many of these alternative explanations or problems, such as grids and color. The proponents espouse in print searing contradictions on central matters on their favorite examples (e.g., illumination in Caravaggio).

The breakthrough in these discussions -- and what should really let us all close the books and go home now -- is Falco and Graves's argument against pantographs for the Albergati portrait, that is, the commonsense statement that the simple device couldn't have been used since hadn't been invented yet. But neither had the far more complicated long-focal length concave mirror projection system, so mutatis mutandis, all their optical examples are similarly disposed of. Lucky for me, I have a preferred alternative explanation for the Albergati; unlucky for them, they have no alternate explanation for any of theirs.

Falco states at every opportunity that proof of their theory is a done deal, as if saying it enough times to himself, Mr. Hockney, and a supposedly uncritical audience will make it so: "Lorenzo Lotto used a lens to make this painting in 1556; of this there simply is no doubt" (SK), "It's science; I proved they used optics" (NY Symposium, twice), "some artists as early as c.1430 certainly did use lenses" (above), "This isn't a story... It's not your version versus my version. This is fact. This is science." (Smithsonian), and on and on. He must think Chris Tyler, I (PhD physics), and other skeptics are too thick to worry about... In fact he effectively says as much: "At this point there's enough evidence to convince any jury of physicists to convict Lorenzo Lotto of use of an unregistered camera obscura (a jury of art historians is another matter, of course)" (SK) and "Anyone arguing... that Memling didn't use a lens would be a person too thick to worry about" (SK, also quoted in NY Times review of SK). Finally my favorite, broadcast to over a million readers: "You could convict OJ with this evidence" (Smithsonian). .

Gentle reader: Flip back through the discussions and see if you don't think there should be at least a little doubt concerning the optical hypothesis. Consider a jury of twelve, made up of artists, art historians, optical scientists and general art lovers, say. Do you agree with Falco that all of them -- unanimously -- would vote to "convict OJ" in the optical case presented by Messrs Hockney, Falco and Graves?

Finally, I have one simple request to Hockney, Falco and Graves: Please stop calling a concave mirror a "lens" (or even "mirror-lens"), as in the book, OPN paper and elsewhere. It is not a 'lens,' and this abuse of standard terminology only confuses things, particularly when the matter of left-right reversals, chromatic aberration, flare, etc., arise. As the Encyclopaedia Britannica Volume 15 (1964) states on page 591: 'Calling an astronomical [concave] mirror a lens is also a common error.'. Likewise, I have no idea whether you call a convex mirror a "lens" or "mirror lens" as well.


Remarks

Earlier, both Christopher Tyler and I outlined numerous errors and severe problems in the Hockney/Falco theory -- the glaring omission of any corroboratory evidence that long-focal length mirrors existed in the fifteenth century, or that they were used to project real inverted images, or that anyone traced them, and on and on. I made very specific quantitative and scholarly rebuttals to their claims on their primary evidence -- I showed that the convex mirror in the Arnolfini portrait could not have been used in the painting's creation as often claimed by Hockney and Falco. Tyler showed that the Hockney/Falco explanation of Lotto's "Husband and wife" led to implausible patterns on the carpet. I exposed searing contradictions in the writings of the theory's proponents (Caravaggio used artificial lighting; no he worked by bright sunlight). I did specific re-enactment/experiments, such as the grid construction of the Albergati portrait, showing alternate explanations were not merely possible, but in fact more probable and explained all the data much better.

While Tyler and I become more and more convinced of the profound technical difficulties with the Hockney/Falco theory with every analysis, correspondence with acknowledged scholars, careful reading of the historical record and of the writings of Hockney and Falco themselves, I think even the most ardent independent supporters of Mr. Hockney would have to admit that there is at least some doubt about the theory. At minimum, the fact that the first two scientists to analyze the theory, independently chosen to attend the NY symposium, both reject it for complementary sets of technical reasons should give anyone pause.

Nevertheless, Falco makes the following claims in highly visible public venues that proof of the theory is a done deal:

By comparison, to see if I am so out of line as Falco claims consider the two most recent published documents to cross my desk in this matter, both reviews of Secret Knowledge. In the New York Review of Books, Ingrid D. Rowland conveys the point I was trying to make in the passage Mr. Falco found so objectionable and, one must admit, in a personal and unflattering way:

"In the debate engendered by Secret Knowledge, David Hockney spoke of his own deafness, and it is hard to resist taking this condition metaphorically; it brings on inner visions at the price of stopping convesation. He and Charles Falco have become true believers in a world that is to a great extent of their own making."

The second appears in Blake Gopnik's review in the Washington Post:

"...Hockney has at last set out his idea in detail in this lavish coffee-table book, and it's left me staggered: It's hard to imagine how you could fit more errors of fact, technical ignorance, philosophical incoherence and logical inconsistency between two covers. To come to grips with all of Hockney's missteps would take many more words than he has used to set them out." and "The book is a mess, in fact and in thinking." and "[Hockney's] whole argument really derives from buying into his own hype." and "Our culture doles out attention, even authority, based on celebrity, rather than on evidence of talent, brains or knowledge."

Gentle reader: please re-read my After Thought in its immediate context and those of other writers on the topic, and the list of quotations from Falco, and judge for yourself whether it is Falco or I who has "chosen to leave the arena of serious scholarly debate" in the phrase given by Falco.

Christopher Tyler and I are submitting articles to scholarly forums, and have just begun giving public presentations refuting the claims of Hockney and Falco; we will continue to do so. Of course we are at a tremendous disadvantage -- caught off guard, late to the gate, and without the media draw guaranteed by Mr. Hockney. For instance, the same day (March 1) I gave a roundtable presentation to roughly 20 scholars in the Stanford University Art History Department (including a Caravaggio expert), Mr. Hockney gave a big public lecture in New York to hundreds, no doubt with extensive popular media coverage.

I am very glad indeed that Falco will begin to present evidence to scholarly forums, rather than unrefereed or public media that has bouyed interest in the theory up to now -- such as Optics and Photonics News, Smithsonian magazine, High Life magazine, the BBC film which contained no alternate views or countervening evidence... I am confident that with the careful and appropriately skeptical analysis by those with expertise in optics and art (and perception) the correct negative verdict will be rendered, just as to my knowledge not a single scholarly review of Secret Knowledge has been positive.

Unfortunately, even when -- as I predict -- the theory will not survive such scrutiny, it will be too late. The public will have lost interest, hundreds of thousands of copies of Secret Knowledge will have been sold, millions will have seen the BBC documentary, and Hockney's profoundly flawed theory will have seeped into the cultural fabric.

Incidentally, I submitted a letter to Smithsonian magazine pointing out what I felt were gross errors in their February article and interview with Hockney and Falco -- an article most noteworthy in that its author apparently spoke with not a single person with an alternative view! The resulting letter, as printed in the April issue, was edited severely and changed to introduce errors, all without my being given an opportunity to see the revisions. (For instance, they inserted the error that Caravaggio worked in a "cave," whereas I had written "dark cellar," as Mr. Hockney and scholars attest.) For the record, the original letter I submitted is below: