Art History Can Trade Insights With the Sciences explains a scientific discovery the art historians didn’t want to hear about:
The controversy over Hockney and Falco grew out of Hockney’s discovery of a sudden shift toward naturalism in the 1420s and ’30s in Flanders. Hockney claimed that the shift was too abrupt to have occurred without the use of optical aids that allowed artists to project images of the 3-D world onto a canvas and trace them. With the entry of Falco, evidence took the place of opinion. Falco pointed out that concave mirrors can serve as lenses that project images and that such mirrors were available as early as the 13th century. He went on to analyze anomalies in certain paintings that were consistent with the use of a lens and — most important — difficult to explain otherwise.Lorenzo Lotto’s painting called “Husband and Wife,” of 1523-24, depicts a carpet with a complex geometric design covering a table. The carpet recedes into space. Falco demonstrated that the lines on two of the borders of the design start off receding toward one vanishing point and then move slightly toward another vanishing point. It’s strange that there are two vanishing points. It’s even stranger that the vanishing points of both borders shift at approximately the same depth into the scene.
But Falco offered an intriguing (somewhat technical, very precise) explanation: Lotto’s use of a lens led to systematic and predictable errors. Falco calculated that Lotto must have placed his lens 150 cm. from the carpet he was painting and 84 cm. from the canvas onto which he was projecting the image of the carpet. He also calculated the focal length (54 cm.) and diameter (2.5 cm.) that Lotto’s lens had to be. Those calculations were all derived from one measurement: a comparison of the shoulder width of the woman in the painting with the average shoulder width of actual women today. The difference in size between the two widths showed how much the objects on canvas were reduced — in this case, by 56 percent.
When a lens is used to project an image, the less that image is reduced in size, the lower the depth of field that the lens can project. Because Lotto was projecting images reduced in size by only 56 percent, he had a problem — he could project only part of the image onto the canvas. Once that part was traced, he would have had to move the lens just a tiny bit to focus farther back. Hence a slightly different vanishing point and a slightly different magnification — both subtle errors. Falco calculated exactly how much the two vanishing points would diverge and the magnification would decrease, and his calculations agreed to within 1 percent with measurements he made from the painting. Falco tested his lens hypothesis against many paintings, and found other instances in which the errors were mathematically predicted by the use of a lens. His hypothesis did not rely only on such predictions; he also found that sometimes highly complex, three-dimensional, nongeometrical objects were rendered so precisely that use of a lens was highly probable. But the litmus test of the lens hypothesis was Falco’s ability to so precisely predict nonrandom errors.