Overall summary

The following are lists summarizing some of the above analyses. Some of these points address relevant matters not discussed by Hockney and Falco. Thus when I list "murals and frescoes cannot be painted" by the projection method I do not claim that Hockney and Falco actually said that murals or frescoes could be painted by their method; I list these points merely to show the general limitations to the explanatory power of their theory.

General technical considerations

Using the mirror projection system proposed by Hockney and Falco...

• murals and frescoes cannot be painted because the images would be inverted (Botticelli, "Sistine Chapel," ...)
• ceilings cannot be painted (Michelangelo "Sistine Chapel," ...)
• moving objects cannot be painted (Leonardo "Rearing horse" in the Gabinetto Nazionale dei Disegni e Stampe, Florence, ...)
• self-portraits cannot be painted (Rembrandt "Self-portrait," ...)
• imaginary and non-existent objects cannot be painted (Tintoretto "St. George and the Dragon," ...)
• paintings done by artificial light require an implausibly large number of candles or oil lamps (van Honthort's "Supper party," ...)
• inverted brushstrokes should be plentiful, or at least present, but instead they are rare and possibly absent altogether (Rembrandt "David and Uriah," ...)
• capturing subtleties of color and shading is very awkward (Campin "A man," ...)
• painting large canvases requires an awkward shuffling of the arrangement in the studio (Caravaggio "Supper at Emmaus," ...)

Historical record

From the historical record of fifteenth-century Europe we see that...

• there is no evidence describing or depicting the long-focal length concave mirrors demanded by the Hockney/Falco theory, despite records for aids such as the pentograph and other optical elements that could not be used as described by the theory
• there is no evidence in fifteenth-century showing or describing the creation of long-focal length concave mirrors
• there are no records showing that any manufacturer made or distributed long-focal length concave mirrors required by the Hockney/Falco theory
• there are no reports about a purported mirror conspiracy
• there are no books or treatises on how to use the complicated concave mirror system, despite numerous books and treatises on alternate schemes, such as geometrical perspective and (later) pantographs

Specific art works discussed by Hockney and Falco

Below are summaries of reconsiderations of several specific works Hockney and Falco enlist in support of their theory.

• Lotto's "Husband and wife" As shown by Christopher Tyler, the Hockney/Falco explanation of "anomalies" in this "Rosetta stone" painting lead directly to conclusions (the pattern on the carpet) that are so implausible that we can reject the Hockney/Falco account for this painting directly.
• Holbein's "The Ambassadors" As shown by Christopher Tyler, the difficult globe contains errors that are unlikely to arise with the use of optical projections.
• van Eyck's "Portrait of Cardinal Niccolò Albergati" The faithful duplication of the silverpoint work can be achieved in several ways, possibly eyeballing, pantograph or (more likely) a grid construction, all consistent with the technology we know was used at some point in the Renaissance. Use of the grid method explains compellingly -- qualitatively and quantitavely -- numerous features of the images that the Hockney/Falco theory cannot, and relies on simple technology of the time, not complicated technology hypothesized for that time.
• van Eyck's "Portrait of Arnolfini and his wife" Mr. Hockney's specific proposal that the convex mirror depicted within this painting could be turned around and used as a concave mirror in the creation of this painting is untenable -- the focal lengths differ significantly. Moreover, the only visible brushstrokes go "downward," supporting the view that the painting was painted rightside up, not upside-down as might be done according to the Hockney/Falco method. The reflected image depicted in the famous convex mirror would show the concave mirror and dark tent setup, though no such setup can be seen.
• Robert Campin "A man" The remarkable "opticality" in this painting may be due more to subtleties in color and shading of surfaces than accurately drawn contours. The Hockney/Falco projection method does not aid -- and in most cases impedes -- artists in portraying such shading.

Modern "re-enactments"

The modern attempts to "re-enact" the Hockney/Falco methods for Renaissance painters...

• use very bright illumination, such as the sun or high-powered electric stage lights with Fresnel lenses, which give bright collimated light that had no counterpart for the many Renaissance paintings created by artificial light
• use modern parabolic mirrors larger than the mirror Hockney and Falco claim was used in Lotto's "Husband and wife"
• are restricted to canvases much smaller than numerous "optical" paintings in the Renaissance
• employ tracing of boundaries rather than rendering of surfaces and color

Alternative: A traditional explanation for the increased realism or "opticality" in the Renaissance is the following. For myriad social and political reasons, artists turned increasingly toward painting commissioned portraits, where accurate rendering was of paramount importance. The new media of oil paint, the celebrated and widely disseminated discovery of the laws of perspective, and the general ethos of the budding Renaissance encouraged a greater fidelity to the seen world. The fact that thousands of painters have painted extremely realistic "optical" paintings without using optical aids shows that Renaissance painters could in principle as well. (Incidentally, there have been other "quantum leaps" in representational art that as far as we know were not due to advances in technology, such as the "Dying Gaul" on the Parthenon in c. 230-220 BCE.)

As far as I know, none of the claims in the traditional explanation contradicts any known facts.

As scholars, artists, and the interested public, our task is to choose between these two explanations of the creation of Renaissance paintings.

Acknowledgements

I'd like to thank Christopher Tyler (Smith-Kettlewell Eye Institute) for commenting on an earlier draft of this piece, for bringing to my attention Lotto's "Angel of the Annunciation," and permission to include his figure based on Lotto's "Husband and wife." I would also like to thank Molly Ann Faries (Department of Art History, Indiana U.) and Lorne Campbell (National Gallery, London) for correspondence about underdrawings in early Renaissance art, Gail Bardhan of The Rakow Library at The Corning Museum of Glass for information about blown glass spheres and Lois Gibson of the Houston Texas Police Department for permission to use her forensic sketch. Thanks too to the organizers and funders of the New York Symposium on Art and Optics.

Responsibility for the analyses and explanations presented here lies with me alone, except where otherwise explicitly stated.

References

*All above page references to Hockney refer to Secret Knowledge: Rediscovering the Lost Techniques of the Old Masters, by David Hockney (Thames & Hudson: New York , 2001); all page references to Hockney and Falco refer to "Optical Insights into Renaissance Art," by David Hockney and Charles M. Falco, Optics and Photonics News, 11(7) pp. 52-59 (2001). See also "Rosetta Stoned?" by Christopher Tyler for further discussion of the flaws in the Hockney/Falco explanation of properties of Lotto's "Husband and Wife," and see Bernhard Sharratt's "Darkroom of the Gods" (review of Secret Knowledge) New York Times Book Review pages 11 & 12, December 23, 2001 for a general discussion of the difficulties in the Hockney/Falco thesis, including an alternate explanation of the creation of van Eyck's portrait of Albergati that does not rely on optics. See Seeing the Light: Optics in Nature, Photography, Color, Vision and Holography by David Falk, Dieter Brill and David G. Stork (Wiley: New York, 14th printing, 2000) for general background on relevant optics, perspective, painting methods, artists' media, and visual phenomena. The image of Christoph Scheiner's pantograph methods appears in Devices of Wonder: From the world in a box to images on a screen by Barbara Maria Stafford and Frances Terpak (Getty Museum, 2001).

David G. Stork is Chief Scientist of Ricoh Innovations and Consulting Associate Professor of both Electrical Engineering and Computer Science at Stanford University, where he has taught "Light, Color and Visual Phenomena," "Pattern Classification," and other courses. He holds 15 patents and his five books include Seeing the Light: Optics in Nature, Photography, Color, Vision and Holography for non-scientific readers. He is working on a book about modern perspectives on the 14th-century philosophical principle of parsimony known as Occam's razor, i.e., "choose the simplest explanation." Questions and comments are welcomed.