Technical and Historical Support for, and Objections to, Our Thesis

Note: to make the text easier to read, citations are in footnotes at the end of this section


We published our first paper in 2000, and David Hockney published his book in 2001. In addition to establishing the power of an artist’s practice-based visual skills for making discoveries in art history, the computer-based techniques we developed also established this approach as a powerful new tool for analyzing images in paintings. As a result, this has now developed into a field in its own right, as other scientists subsequently began developing computer techniques for analyzing aspects of these complex images (n.b. some of this computer-based work has been misguided—as has been known since shortly after the first computer was developed, when the input data and underlying assumptions are wrong, the output from even the most powerful computer is meaningless). As art professor Barbara Bolt writes, our work also is influencing research in art education: “Whilst he is probably unaware of his contribution to the developing field of creative arts research, Hockney’s [visual] investigation gives form to a particular and much maligned aspect of practice-led research.”[1] As mentioned elsewhere, in 2008 I gave the National Art Education Association’s ‘Ziegfeld Lecture’, awarded for my contributions to developing the Hockney-Falco Thesis, and for its implications for art education.

In this section I summarize the technical and historical arguments by others, pro and con, that have been published since 2000. Recent observations by the art historian Martin Kemp provide a useful context for evaluating the discussion that follows in this section: “The scholarly response has been almost predominantly directed towards the destruction of [Hockney’s] arguments about individual cases, often in the most blinkered manner. This has occurred even where, as in the case of Vermeer, the evidence about the use of optical devices is as about secure as it could be. … The professional reaction has, in short, been disappointing in its overall tone. The wider claims [Hockney] has been making have become lost in petty vitriol about details.”[2] Kemp continues to say that “The reactions seemed to have been conditioned by a series of factors. One is a sense of professional ‘amour propre’. What right—the unstated objection seems to run—has a “mere” artist, not a proper historian, to tell us the truth about histories that we have spent years researching? … Another objection is the old conviction that ‘great artists don’t cheat’.” Later in his article Kemp references a forthcoming publication of his own, saying that “As it happens, complex bodies of interlocking evidence about Caravaggio’s practice … are beginning to provide strong signs that he did indeed use optical devices.”[3]

Answers to Objections to Our Thesis

Starting with technical papers, David Stork et al. have claimed in a series of papers that there are alternatives (e.g. the use of a proportional divider to make enlargements) that explain the data as well as our optical hypothesis does. However, as I show elsewhere, without exception these papers are based on wrong assumptions, incorrect data, and/or selectively omitted data. As Lawrence Weschler recently wrote in ‘True to Life: Twenty-Five Years of Conversations with David Hockney’ (University of California Press, 2008) “And indeed, in the months and years that followed, from one academic conference ot the next (Ghent, Florence, etc.), Stork had been continuing to stalk Hockney and Falco with virtually Ahabian relish–marshalling mathematical arguments and counterexamples of his own, arguments Falco, for his part, just as quickly would parry and wrestle back to the ground.”

A March 9, 2006 article in Nature by Rex Dalton describes a disturbing situation involving systematically-erroneous data in a series of publications written over a period of several years by Stork, Chief Scientist of Ricoh Innovations, a small subsidiary of the office equipment company (Dalton also found problems with Stork’s CV that he didn’t have space to write about). Stork has used interest in our discoveries to generate publicity for his company by attacking our thesis in collaboration with a group devoted to the novelist/”philosopher” Ayn Rand who picketed the Metropolitan Museum in 2004 circulating a petition denouncing us, in seriously incorrect information he tried to post anonymously to Wikipedia, in his publications, in Letters to Editors, in multiple press releases, and in talks he has energetically solicited for himself based on his erroneous data. He has written letters to magazines saying that none of our publications have been peer reviewed, in spite of it being obvious that is false, and his claims on his web page that our Thesis has been “unanimously rejected” are totally disconnected from the reality of the situation. This behavior is simply not normal in academia and, taken together, it is quite disturbing. As Dalton explains in his Nature article, after Stanford became aware of the systematic problems with the data in Stork’s publications, in November 2005 they removed Stork’s web page from the Psychology Department’s server where for some reason he had managed to have it stored. Click here for a summary of the erroneous data in nine of his papers, and click here for details of the problems with the data in one of them. Also, at the invitation of one of the editors of IEEE MultiMedia, I wrote a manuscript pointing out some of his errors in three additional papers. However, even in the most egregious cases, editors of scientific journals have a “hands-off” policy of not withdrawing papers themselves. This leaves it entirely to readers to determine the veracity of Stork’s papers by examining them in the context of the systematic errors and his false claims I have detailed elsewhere. Unfortunately, although Stork (in a few cases with collaborators and Ricoh employees) is the only scientist who has purported to have data showing there are alternative explanations for our discoveries, his strenuous efforts to publicize his incorrect data and conclusions have done much to confuse the situation for non-scientists working in this area.

6-min. video showing some of the problems with the data in two of David Stork’s papers.

A question asked at Fermi National Accelerator Lab in 2006. This question illustrates the damage that incorrect papers such as Stork’s cause, showing how they can mislead scholars into believing wrong conclusions about an entire topic.

Stork’s collaborator, Christopher Tyler, published one paper by himself showing the entire octagonal pattern in Lorenzo Lotto’s carpet, taken as a whole, is not in “correct” optical perspective, from which he concluded a lens had not been used.[4] Unfortunately, Tyler based his conclusion on an elementary misunderstanding of optics. A simple calculation shows it would have been impossible for Lotto to make a single projection of the entire octagonal pattern of the carpet at the very large magnification of this painting (0.56×) with the necessary ~40 cm depth-of-field, unless his lens had been smaller than f/90 (i.e. less than 5 mm in diameter), in which case the image would have been far too dim even to be visible. A video shows how the shallow depth of field requires refocusing twice to produce the octagonal pattern, resulting in a composite that agrees to ±0.5% with the features we calculate. Tyler acknowledges Stork for help with his paper, indicating Stork too failed to understand this key optical principle (I explain elsewhere in this FAQ how the very optical features of the octagonal pattern that confused Tyler and Stork are what allowed us to calculate the focal length and diameter of the lens that Lotto used). To date, no papers have reported any errors in our calculations, and no technical papers other than the incorrect ones of Stork et al. have offered any alternatives to our optical hypothesis.

Turning to the historical, an issue of the journal Early Sciences and Medicine contains manuscripts by seven historians of art or science.[5] Six were selected by the editor from the 25 who presented papers at a 2003 workshop on the Hockney-Falco Thesis, and the other had not attended the workshop. For the pre-1550 period (i.e. prior to the earliest currently-known textural reference to projections), Sven Dupré writes in his Introduction that “The material evidence [provided by Sara Schechner] flatly contradicts the Hockney-Falco thesis, and while the textural evidence on its own cannot fully exclude the discovery of image projections, taken together with [Schechner’s] material evidence of poor quality mirrors, the painterly use of image projection [prior to 1550] becomes extremely unlikely.”[6] However, none of these historians addressed any of the scientific evidence we had published up to the time of the workshop, nor any of the visual evidence, limiting themselves to textural evidence alone.† The seemingly-odd failure of historians to consider any evidence other than textural is addressed elsewhere. Despite Dupré’s own overall summary, the manuscripts show that three of these historians actually were neutral on whether image projections were used prior to 1550, while the other four ranged from slightly negative to definitely negative. However, the historians were more sanguine about our claims for the post-1550 use of optics, with Dupré writing “Forcing historians of science to come to grips with the transformation that optics underwent in the sixteenth and seventeenth centuries… [is] research opened up by the Hockney-Falco thesis.”[6]

†note: although these historians certainly show images and diagrams in their manuscripts, they basically use those images as an alternate form of text, e.g. Christoph Lüthy shows a Dürer drawing of a perspective machine, which he treats as equivalent to a written document describing the existence of a perspective machine; he does not, as a simple example, extract information on perspective lines from any drawing or figure in his manuscript.

Unfortunately, for the pre-1550 period, two of these historians relied on the information in Sara Schechner’s manuscript,[7] who failed to realize that no iron mirror could have survived for over 500 years without almost total degradation, i.e. all of them would have completely rusted away:


Nomarski Differential Interference Contrast (DIC) micrograph of the surface of an iron mirror approximately seven months (201 days) after I polished it. The small blue bars in the lower right corner of the image are 20 µm (787 µinch) apart, so this micrograph will be at a magnification of ~200× on a typical computer monitor. Although many scratches are quite apparent in the micrograph, this mirror produces a very nice image, showing that what scientists consider to be an “optical quality” surface is not required. Since I live in the Sonoran Desert, to somewhat simulate the humidity of Flanders, after polishing I placed this mirror on a window sill in a bathroom at home along with a digital hygrometer. The hygrometer showed the mirror was exposed to ~40% relative humidity for ~2 hours/day, and much less than that the rest of the time. The black-appearing blotches that cover approximately 16% of the surface are Fe2O3 (rust) patches. At this rate of formation, the entire surface would be covered by an opaque coating of rust in 3½ years. In Flanders, where the 24-hour, year-round humidity averages above 60%, the rate of rusting would be even faster.


Photograph of the same 2″-dia. (5.0 cm) iron mirror after 3½ years (3 yr., 6 mo., 9 days). As can be seen from this relatively low magnification micrograph (~2× on a typical monitor), roughly 80% of the surface is now covered by rust, consistent with the initial rate of formation determined from the micrograph at the left, taken seven months after polishing.

Although Schechner does not reference it in her paper, a detailed description for making large, bright, concave, ferrous, steel mirrors is in a manuscript known to date from no later than 1372 (i.e. a half-century before van Eyck). Although only minor periodic polishing would have been required at the time to maintain the imaging qualities of any of them, as the photographs of the iron mirror above shows, the subsequent 500+ years of oxidation means any such metal objects in museum collections today would be so degraded as likely to be unrecognizable as mirrors unless the museum staff had an understanding of the properties of materials. Metals other than iron that also might have been used for concave mirrors in the Renaissance (brass, bronze, silver, lead, tin, etc.) also deteriorate because of the growth of opaque oxides or sulfides.

Schechner claims images could not have been projected at the time of van Eyck because the metal was too poor to make mirrors of sufficient reflectivity: Medieval mirrors of metal were also small, dark, and convex.” … “The size of medieval mirrors was limited by the weight of the metal, and reflectivity was limited by the rough casting being hand-polished.” However, Dr. Schechner’s contentions are contradicted by countless artifacts. For example, it is obvious from the photograph below that metal was widely available of more than sufficient quality and quantity for making high reflectivity mirrors:

14th Century Battle Hammer

Fourteenth-century battle hammer in the Gravensteen Castle Museum in Ghent, Belgium, which is only a few hundred meters from the location of van Eyck’s fifteenth-century ‘Ghent Altarpiece’.

Since our results show the necessary concave mirrors had diameters of only ~1″ (2.5 cm), there is enough metal in the above hammer alone to make several such mirrors. As countless examples of armor on display in museums show, Dr. Schechner’s contention that hand-polished medieval metal would have had low reflectivity is simply wrong. Note that even though the above war hammer has been kept in a case in a museum, rust has formed on its surface since it was last polished. Whether they were rare at the time or not, a simple understanding of the properties of metals explains why metal mirrors would not have survived 500+ years in the climate of northern Europe without very serious degradation.

Historian Vincent Ilardi recently wrote in his book on spectacles and telescopes that “[Schechner’s] reservations cannot be entirely accepted in my view because comparing the clarity of metal mirrors 500 years old and ravaged by time with that of presumably new or fairly new mirrors used by Renaissance artists would not be an accurate comparison… It is more consonant with the above evidence, therefore, that the mirrors of the age were not perfect but were substantially adequate for artistic practice.”[8] Schechner’s historical knowledge is incorrect as well, as can be seen from her statement that “Medieval mirrors of metal were also small, dark, and convex… By the sixteenth century, the so-called ‘steel mirrors’ were non-ferrous and praised for their improved brightness.” Contradicting her understanding, there is a detailed description for making large, bright, concave, ferrous, steel mirrors in a manuscript about parabolic mirrors known to date from no later than 1372 (i.e. a half-century before van Eyck). The translation of this manuscript is in a 1980 monograph by a well-known historian of Medieval science at Princeton, who is not referenced by Schechner. Also, quite aside from mirrors, a simple pair of reading spectacles, such as those shown in van Eyck’s ‘van der Paele Altarpiece’, have the necessary focal length for projecting images of the size and quality to account for all of our data.

Schechner is not the only historian whose knowledge of the relevant history of optics is incorrect. On the National Gallery of Art’s web page entitled ‘The Art of Science’, art historians write that “It was only in the 16th century, when concave lenses were introduced, that spectacles allowed short-sighted people to see objects in the distance.” This date is incorrect by at least a half-century. In the monograph cited in the previous paragraph,[8] historian Vincent Ilardi describes spectacles for short-cited people that are documented in a 1462 letter to have been available at least as of that date. Although Ilardi’s book was published in 2007, the article that contains the translation of the 1462 letter, and describes its significance for the availability of concave lenses, was published in 1975, so the information about concave lenses on the National Gallery of Art’s web site has been known, at least by some historians, for over 30 years to be incorrect.

Support for our Thesis

In addition to Vincent Ilardi, other scholars who have published work partially or entirely supportive of our findings for the use of optics starting c1430 include the science historian Michel Jansen, who uses the Hockney-Falco thesis as supporting evidence for his own thesis on the scientific method,[9] science historian Mark Pendergast who writes that “Hockney has convincingly demonstrated that this method works… [and] Hockney’s arguments, bolstered by evidence found in the paintings by optical scientist Charles Falco, are fascinating,”[10] semiotician Eduardo Neiva, who writes that “David Hockney and Charles M. Falco dissected with precision the workings of paintings that deceived so many experts in visual composition for so long,”[11] and engineer John M. Henshaw, who writes that “Reading Hockney’s book, I was convinced that he is onto something. His qualitative descriptions, juxtaposed with reproductions of the paintings, are compelling.”[12] In another work on mathematical perspective, Neiva writes that our “analyses have suggested that mirrors and lenses could have been used to produce the impression of perspective,…”[13] As already mentioned in the second paragraph of this section, in a forthcoming publication art historian Martin Kemp (with Clovis Whitfield) concludes that Caravaggio used optical devices.[3] In addition to the paper co-authored with Kemp, Whitfield recently produced a 10-minute video recreating how he believes Caravaggio used concave mirrors for projecting images. Physicist Robert Greenler (former President of the Optical Society of America) also produced a 70-minute video, ‘Early Optics and the Painters’ Art’, showing our discoveries in an even broader historical and scientific context.[14]. In her master’s thesis in art education, Aimee Allen analyzed the ways in which Hockney and I collaborated in the context of our respective backgrounds in imaging, and used her findings to propose a new “…interdisciplinary approach for K-12 instruction and research in art education; specifically, the instruction of imaging as an ‘arts-based practice’ for comprehensive study of visual art, and its synergistic relationship with the history of science.”[15] Citing “the quality of your research,” her thesis was selected by the Arts Based Educational Research Group of the American Educational Research Association for their Outstanding Thesis Award, presented at the 2008 AERA annual conference in New York. Also in 2008, I presented ‘The Ziegfeld Lecture’ at the annual meeting of the National Art Education Association, awarded for my role in developing the Hockney-Falco thesis, and for its significance for art education, the Optical Society of America placed my biography on their website of Optics Celebs, designed to interest youth in careers in optics, and the Society of Photo-optical Instrumentation Engineers (SPIE) elected me as Fellow, citing in part my work demonstrating the use of optics by artists. The SPIE also gave me an ‘Education and Outreach Grant’ in 2008 to design this web site to use our discoveries in art history to interest students in the science of optics. In 2009 Susan Grundy received her Ph.D. for a dissertation extending our thesis to Italian artists.[16]

Art education professor Graeme Sullivan writes “That art historians did not notice what Hockney did may be because they did not know what to look for, as practical-theoretical knowledge is not normally part of a connoisseur’s toolkit.”[17] He makes the same point again in another publication where he writes that “…practice-based understanding is not normally part of a curatorial skill set.”[18] After acknowledging there has been “considerable criticism” of our thesis, art professor Barbara Bolt argues that “According to [Martin Heidegger’s] perspective, we come to know the world theoretically only after we have come to understand it through handling,” basing her paper on our discoveries that were initiated by David Hockney’s skill set as a practicing artist, stating “Thus Hockney did not set out to find the new, but the new arrived to confront him.”[1] Significantly, the conclusion of art historians Martin Kemp and Clovis Whitfield that Caravaggio used optical devices was informed by actual optical experiments they conducted themselves (in collaboration with Gilbert McKerragher, Glen Thornley, Thereza Wells, and Sarah Weale).[2] I address the difference between what historians and practice-based disciplines consider evidence elsewhere but, because of this difference, for many historians this is an evolving story, since new textural evidence continues to be located. On what recent discoveries have revealed, historian Vincent Ilardi wrote in 2007 that “This monograph is based on a great number of new archival documents discovered only in the last half dozen years. … In 1549 [Lorenzo Lotto] paid the enormous sum of 22 Venetian lira for a ‘big crystal mirror’ ordered from Venice to replace a broken one while he was working in Acona. … In sum, these few entries in Lotto’s account book and the evidence presented above demonstrate that mirrors were used by most or many artists to project images and/or control the accuracy of their visual observations.”[8]

Summary of Pros and Cons

To summarize, to date the only technical papers addressing our thesis, all by David Stork et al., have been based on false assumptions and flawed data. To the extent the above conclusions of a small number of historians can be viewed as representative of the entire discipline, roughly half are neutral to positive on the full chronological range of the thesis, and half are negative. However, historians rely almost exclusively on textural, not scientific nor visual, evidence, so most are likely to remain no more than neutral unless contemporary written accounts are located of projected images being used by artists. Given this background, this website largely answers questions about the scientific and visual evidence for our thesis that certain features in certain paintings (e.g. the geometry of the chandelier in van Eyck’s ‘Arnolfini Marriage’) produced as early as 1425 are based on optical projections.

Letters in the Popular Press

To end this section, following are comments of mine in the popular press, all written in response to a large number of letters and press releases issued by David Stork exploiting interest in Hockney’s name to draw attention to his own incorrect papers.

Letters to Editors:

AdvancedImaging.pdf  Letter in the July/August 2003 issue of the trade magazine Advanced Imaging in response to incorrect claims a computer scientist named David Stork made in an article that ran in their June issue.

OPNLetter.pdf Letter in the June 2004 issue of Optics & Photonics News that points out numerous errors in fact and logic in a publication by David Stork purporting to refute some of our evidence.

Chronicle.pdf Three letters in the August 13, 2004 issue of The Chronicle of Higher Education’ In the first letter I write that interdisciplinary research is especially prone to objections based on flawed logic. The flawed logic in the second letter by David Stork illustrates precisely this point, the errors in which are addressed by Ellen Winner in the third letter.

SundayHerald.pdf Letter in the August 29, 2004 issue of a Scottish newspaper that addresses a misunderstanding of the optical thesis in a story based on a press release by David Stork purporting to refute some of our evidence.

Independent.pdf Letter in the January 25, 2005 issue of an English newspaper addressing errors in fact in a story based on a press release by David Stork purporting to refute some of our evidence.

Harpers.pdf Letter in the August 2005 issue of Harper’s Magazine commenting on the indirect and direct uses of optics, and mentioning an organization affiliated with acolytes of the novelist/”philosopher” Ayn Rand so perturbed by our discoveries that they picketed the Metropolitan Museum in New York in 2004 with a petition denouncing us for having “defamed” the Old Masters, and insisting that David Stork be given coverage on national TV to present his data. For his part, David Stork had a link to this organization at the top of his web page until Fall 2005 under the heading “Sign the Petition!”

NatureCorrespondence.pdf Letter in the January 26, 2006 issue of Nature explaining a fundamental misunderstanding about the use of optics in “the Hockney-Falco thesis” that was published by several historians in the proceedings of a conference. My letter was in response to a review of the conference proceedings by David Stork, in which he propagated a fundamental misunderstanding of the optical thesis by the historians; a misunderstanding that Stork helped create with the erroneous data and incorrect conclusions of his papers.

VisionSystemsDesign.pdf Letter in the December 2007 issue of the trade magazine Vision Systems Design, commenting on an article David Stork wrote in their October issue. Stork cited his own (incorrect) papers on van Eyck and de la Tour as examples of “a new era in the evolution of the study of fine art,” without ever mentioning that his papers are simply derivatives of Hockney’s and my own prior publications. Stork wrote a subsequent letter to the magazine justifying his article, stating that none of our publications have been peer reviewed, that it is the “unanimous consensus” of scholars that we are wrong, and in any case his article was limited to discussing contributors to a one-day conference that he organized. All of these claims are so obviously false that it is bizarre he would even make them. Also, his letter cites “several scholars” who have published technical papers disagreeing with us, failing to mention that all of these papers were co-authored by Stork.

Books and Manuscripts Cited in this Section

  1. Bolt, Barbara. A Non Standard Deviation: Handability, Praxical Knowledge and Practice Led Research, in ‘Speculation and Innovation: Applying Practice Led Research in the Creative Industries’ (Queensland University, 2006).
  2. Kemp, Martin. Imitation, Optics and Photography: Some Gross Hypotheses, in ‘Inside the Camera Obscura – Optics and Art under the Spell of the Projected Image’, Wolfgang Lefèvre, ed. (Max-Planck-Institut für Wissenschaftsgeschichte, 2007).
  3. Kemp, Martin and Clovis Whitfield (to be published, 2008).
  4. Tyler, Christopher. Rosetta Stone? Hockney, Falco and the Sources of “Opticality” in Lorenzo Lotto’s Husband and Wife. Leonardo, vol. 37, p. 397 (2004).
  5. Dupré, Sven, editor. Early Sciences and Medicine, vol. 102, (2005).
  6. Dupré, Sven. Introduction. Early Sciences and Medicine, vol. 102, p. 125 (2005).
  7. Schechner, Sarah. Between Knowing and Doing: Mirrors and Their Imperfections in the Renaissance. Early Sciences and Medicine, vol. 102, p. 137 (2005).
  8. Ilardi, Vincent. Renaissance Vision, From Spectacles to Telescopes (American Philosophical Society, 2007).
  9. Jansen, Michel. COI Stories: Explanation and Evidence in the History of Science. Perspectives on Science, vol. 10, p. 457 (2002).
  10. Pendergast, Mark. Mirror, Mirror: A History of the Human Love Affair with Reflection (Basic Books, 2003).
  11. Neiva, Eduardo. Eyes, Mirror, Light: History’s Other Lenses. Semiotica, vol. 155, p. 281 (2005).
  12. Henshaw, John M. Does Measurement Measure Up? How Numbers Reveal and Conceal the Truth (Johns Hopkins Press, 2006).
  13. Neiva, Eduardo. Perspective, Pictorial. in, International Encyclopedia of Communication (Blackwell, 2008).
  14. Greenler, Robert. Early Optics and the Painters’ Art. 70-minute DVD (Blue Sky Associates, 2002).
  15. Allen, Aimee. The Hockney-Falco Thesis: An Arts-Based Case Study of Interdisciplinary Inquiry. M.A. Thesis (University Microfilms, 2007).
  16. Grundy, Susan. The Projected Image and the Introduction of Individuality in Italian Painting around 1270. Ph.D. Dissertation (University of South Africa, 2009)
  17. Sullivan, Graeme. Art Practice as Research: Inquiry in the Visual Arts (Sage Publications, 2005).
  18. Sullivan, Graeme. Painting as Research: Create and Critique, in Handbook of the Arts in Qualitative Research, J. Gary Knowles and Ardra L. Cole, eds. (Sage Publications, in press).

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