Jan van Eyck, Portrait of Giovanni (?) Arnolfini and his wife

Jan van Eyck's Portrait of Giovanni (?) Arnolfini and his wife in the National Gallery London is one of the most important works of the early Renaissance: the first full-length double portrait in the west, one of the earliest works in oil, and more. It is one of the central works adduced by Hockney and Falco for their claim that early Renaissance masters traced optically projected images during the execution of their works.

The following technical image analysis is based on:

Warped image in convex mirror

The first technical claim from Hockney and Falco to be evaluated by independent scholars was: "van Eyck placed a convex mirror at the center of this [Arnolfini] masterpiece... the very mirror which, turned around, he may well have used to construct this image."

Stork estimated the focal length of a putative mirror (or lens) commensurate with the image evidence in the painting. He found it to be roughly 68 cm. Then he, building upon work by Antonio Criminisi, Sing-Bing Kang and Martin Kemp, estimated the radius of curvature of the mirror, R, and then computed the focal length of the convex mirror depicted in the painting, f = R/2. He found the focal length to be roughly 18 cm—much too short to have been used as Hockney and Falco claimed.

There are numerous other reasons we can be quite confident this claim by Hockney and Falco is wrong:

  1. The large Arnolfini mirror, even if perfectly shaped, would produce a blur spot too large for any of the fine details in the image, even of the coarse chandelier arms themselves.
  2. Regardless, such hand-blown mirrors are highly unlikely to be perfectly shaped anyway, and every inevitable deviation from perfect shape makes the blur spot larger (never smaller) and thus the projected image even blurrier, and even less useful for tracing.
  3. Curators of historical instruments and historians of optics inform us that such mirrors were made by from blown glass spheres, where mercury and other metals were swirled in the sphere to coat the inside and then a layer of black pitch poured in to seal the shiny material. (Then the final mirror section was cut from the sphere.) As such, the mirror couldn't have been turned around and used as a mirror anyway—the pitch could not reflect any light.

So it is clear that the depicted mirror could never have been used to project an image, as put forth by Hockney and Falco. But might another mirror have been used to project "this image" Hockney and Falco refer to? No. We can be fairly sure no mirror was used throughout the body of the painting.

  1. If any passage in the painting was traced, it should be in good perspective (just as a photograph is in good perspective). But there are numerous passages where the perspective is way way off.
  2. Infrared-reflectography shows that the Arnolfini portrait has a great deal of underdrawings or pentimenti throughout the painting. It would have been extraordinarily difficult for van Eyck to see and trace a second—or third or fourth—dim, inverted image on his support along with the image already committed to the support, much less trace over it.
  3. The room was not illuminated by direct sunlight and thus, as Hockney and Falco admit, van Eyck could not have produced a visible projected image—there simply was not enough light.

Chandelier

But what about the chandelier?

Hockney told 8 million viewers of CBS 60 minutes that the Arnolfini chandelier "...is in perfect perspective," as it would be had it been traced under optical projections. Then he goes on to demonstrate tracing an image of a chandelier, including the portions most distant from the base arms.

Later, Stork, and then Criminisi and Stork, using rigorous computer vision methods from Criminisi's ACM award-winning dissertation, proved Hockney wrong. The full chandelier isn't in perfect perspective—not even close. (Anyone with a ruler and a print of the painting can prove that for themselves.) Then Hockney and Falco wrote a paper saying that the decorative crockets were "hand soldered" onto the chandelier arms, and were haphazardly arrayed, and that this is why the perspective constructions did not conform to ideal theory.

A bit of intellectual history is in order here, so as to see how proponents try to salvage a flawed—indeed moribund—theory. (A good master's thesis in the sociology of science could be written on these developments and I urge some courageous and enterprising graduate student to do so.)

  1. In Hockney's book, Secret Knowledge, discusses the superb perspective of the chandelier and there is not the slightest of hints that part was in perspective, part not—part "eyeballed," part "optical."
  2. Then Hockney stated on CBS 60 minutes that the painted Arnolfini "...chandelier is in perfect perspective," as it would be had it been traced under an optical projection. He then goes on to demonstrate his optical projection method, even tracing the chandelier portions most distant from the base arms. Again, no hint—verbally or through demonstration—that one portion would be traced, another not traced.
  3. Later, Stork, and Criminisi and Stork proved Hockney was wrong. The chandelier differs wildly from being "in perfect perspective." Anyone with a ruler can prove that for himself by drawing lines linking corresponding structures on adjacent arms. These lines, extended, should meet at a single vanishing point but they absolutely simply do not—not even close.
  4. Faced with this evidence, Hockney and Falco in an SPIE publication then retreated and claimed that the decorative crockets were "soldered" onto the arms, and hence would be arranged haphazardly. In short, they still claimed that the entire chandelier was in perspective (and traced under projections), just that Arnolfini's metal chandelier was asymmetric, and irregular.
  5. Then Stork and Criminisi measured 15th-century chandeliers in situ (one small, others full sized), and did rigorous photogrammetry on photographs of appropriate chandeliers, prayer book holders and other dinanderie and found them far more symmetric than is consistent with the Hockney claim and the evidence in the Arnolfini portrait.
  6. Faced with this evidence, Hockney and Falco then retreated even further and claimed that the body of the arms were in good perspective, while the decorative parts done by hand. Clearly this is a profoundly different claim than they had been making to millions of people.
  7. Hockney and Falco flawed method: overlap whatever they want. Clearly, such ad hocism shows this a vacuous "theory." If evidence clearly contradicts the theory, then the proponents give the ad hoc "explanation" that oh, an artist would have traced this passage but not that passage, always magically to fit their pre-determined "conclusion." Suppose a talented professional realist artist says, "no, I think the Renaissance artist would have traced another passage, not that one." How can we tell which artist is right? Clearly you can't resort to fitting one set with optical parameters... a circular argument if there ever were one.
  8. Notice how hard to get the back arm, but not the exposed crockets or decorative structures.
  9. But why does getting the arms in reasonable perspective imply they were traced? Is using the world's most complicated optical system the only way to get an image in reasonable perspective? Of course not. Nicholas Williams, a talented realist painters, painted two chandeliers entirely by eye—no projections, rulers, or tools of any kind—and produced images in far better perspective than van Eyck (even just the arms) entirely without projections. So the fundamental motivation for Hockney's claim is without support.
  10. These facts force Hockney and Falco into the untenable position of claiming that some parts were "optical," others "eyeballed," with no principled or objective way to distinguish. Suppose two artists disagree on what portions would have been traced. Which one is right? For instance, suppose a highly accomplished realist painter disagrees with Hockney and says van Eyck would have traced the crockets. Or (far more likely) not traced an image at all. How can one distinguish between these two informal views. Certainly fitting Hockney's selection with an "optical" model is a circular of the clearest form, and hence no justification whatsoever. (The same flaw plagues the Hockney/Falco claims about Lotto's Husband and wife, where they arbitrarily decide ex post facto which image portions Lotto would have traced, and which not traced always, magically, to be consistent with their pre-determined "conclusion.") In statistics, we say Hockney and Falco are "fitting noise."