A related effect is that the lens produces a differentiation of focus throughout the depth of field, so that when objects in the middle ground are in sharp focus, objects in the foreground and background are blurred. Vermeer captured this effect most noticeably in The Little Street, where the façade of the building is painted in detail, while the foreground pavement and background houses are slightly out of focus. In The Lacemaker the white and red threads spilling out of the cushion-shaped box known as a naaikussen (sewing pillow) are so abbreviated as to look impressionistic; they are greatly unfocused relative to the forms in the middle of the composition. This effect is also seen in Girl with a Red Hat.
Another optical effect peculiar to the seventeenth-century camera obscura was the production of diffused circles of light forming around unfocused specular highlights, resembling those fuzzy spots of light in out-of-focus photographs called “disks of confusion.” In camera obscuras of the time, this optical effect was common because of the way instrument makers sought to minimize the spherical aberration. Taking Barbaro’s suggestion, they would place a diaphragm with a tiny hole at the center immediately behind the lens. This reduced the effect of spherical aberration by blocking out all the light except for that passing through the center of the lens. However, in order to succeed at that goal the hole had to be so small that it deprived the image of sufficient light, and would sometimes confuse the image with diffraction effects such as small halos of light.
Natural highlights are bright reflections often seen with the naked eye on wet or shiny surfaces, such as glass or polished metal, viewed in bright light. On the screen of a camera obscura, these natural highlights are often surrounded by hazy halos of light, which are not seen with the naked eye. In his later works Vermeer begins an effusive use of pointillés, globular touches of thick opaque paint, pure white or slightly yellowish, to indicate these halos or discs of confusion. He scatters these pointillés along the water’s edge in A View of Delft, accentuating the play of light on the different textures of water and wooden boats. In The Milkmaid the loaf of bread looks freshly baked in part because of the pointillés indicating light reflecting off its surfaces. In The Lacemaker thick impasted globules appear on the relatively unfocused foreground objects—the escaping threads and the tablecloth.
Yet, Vermeer did not literally transcribe disks of confusion he saw in the camera obscura. These occur only on shining surfaces in bright sunlight, but he felt free to apply these globules of paint to areas of deep shadow (in A View of Delft) and nonreflective, matte surfaces (bread in The Milkmaid, threads in The Lacemaker). His use of the specular highlights is not photographic, or even exactly naturalistic, but illusionistic: although matte surfaces would not really have those highlights, his use of them does, somehow, make the surface appear more real to us.
Vermeer looked at nature through the camera obscura to learn about light, shadow, tone, and color, but he did not slavishly imitate what he saw there. He seems to have taken to heart Leonardo’s dictum that “the painter who draws merely by practice and by eye, without any reason, is like a mirror which copies everything placed in front of it without knowing about them.” Sometimes his optical effects adhere strictly to physical laws of optics, and sometimes they ignore these laws. Vermeer altered the optics of the camera to suit his composition or the emotion he wished to convey.
Indeed, it sometimes looks as though Vermeer is playing up the optical effects of the camera obscura—as though he wanted his paintings to look as if painted with one, similar to the way Van Hoogstraten mimicked the camera obscura image in some of his works. For example, in both Girl with a Pearl Earring and Girl with a Red Hat, the lips show light reflections from moisture that are identical, and the out-of-focus way that Vermeer painted the yellow jacket in the first painting is comparable to the way he paints the lion finials of the chair in the second. As Jørgen Wadum, the former chief conservator of the Royal Cabinet of Paintings, Mauritshuis, asked, “Has this been done because the image was rendered via a camera obscura that would not focus well, or because the artist wanted us to believe that we were looking through such a device when viewing the girls?”
The camera obscura would have supplied new information to Vermeer, information about the way images are seen, and the way they can be manipulated. Just as we pick up an object and turn it around on all sides in order to learn more about it, we can manipulate the image in the camera obscura by moving it closer to and farther from the scene to be projected, by altering the lenses and the angle of the mirror, by focusing it on the foreground, or the background. By playing around with the camera obscura image, Vermeer would have gained new knowledge about how things appear to us in different conditions of light and space. As one artist has recently described it, “the painter [with] the camera becomes a researcher who, like Van Leeuwenhoek in his microscope, discovers new phenomena in the structures of the familiar environment.” That is how Vermeer used his camera obscura.
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Others have argued that Vermeer did imitate the camera obscura image—that he aimed the projection at his canvas and traced directly on it. In 1950, P. T. A. Swillens claimed that Vermeer traced some of his pictures from a camera obscura projection. Two decades later Daniel Fink proposed that Vermeer traced a camera obscura projection in twenty-seven of his paintings, nearly all his works after 1657. Most recently, Philip Steadman suggested that, because of the sudden appearance of perfect perspective composition and the other optical features in Vermeer’s pictures around this time, we can be fairly certain that Vermeer traced the images projected onto his canvases by a room-type camera obscura in no fewer than ten pictures. As Steadman’s analysis has been influential in discussions of Vermeer since it was published in 2001, it is worth taking a closer look at it.
Steadman concentrated on ten pictures that look as though they were painted in the same room, sharing the same black and white marble tiles (though differing in the pattern of those tiles), and with the same or similar arrangement of casement windows to the viewer’s left. By assuming that the marble tiles are the same size in each case, and by assigning them a standard measure of 29.3 cm in length, Steadman claimed we could know the dimensions of the room. He next located the “theoretical perspective viewpoint”: that point within the room at which Vermeer would have had to put his eye to see the precise view in question. Everything that can be seen in each picture, Steadman proposed, is contained in a “visual pyramid,” whose apex is the viewpoint. If we extend the lines of the pyramid from the apex to meet the room’s back wall, we find that those lines define a rectangle on that wall. In six out of the ten cases, Steadman argued, this rectangle is almost the exact size of Vermeer’s painting. This “extraordinary geometrical coincidence” has only one reasonable explanation according to Steadman: “each painting is the same size as its projected image because Vermeer has traced it” from inside a booth-type camera obscura.
Steadman’s geometrical analysis was, in many ways, a virtuoso feat. And he has, importantly, drawn the attention of both a broad popular audience and art historians to the fact that Vermeer probably did use a camera obscura in some way. But Steadman was thrown off course by reading too much into the literal translation of the pictures. Pictures, especially of this period, are documents of history but are not to be read literally as exact transcriptions of life in the Dutch Republic. While Vermeer no doubt did paint his pictures in the same room—the attic studio at the home he shared with his mother-in-law—his pictures are not meant to be photographic replicas of that room.
For one thing, it is just about impossible that the attic room had black-and-white marble flooring.*5 Although many paintings of the day featured black and white marble floor tiles, they were not literal descriptions of the private homes depicted in the scenes. In the seventeenth century such expensive floors were present mainly in public buildings, where impressive public spaces were requisite. One of the few places such tiles actually existed in a domestic setting was in several rooms at the
palace of Rijswick, the Prince of Orange’s residence. Even in the homes of Delft’s wealthy merchants, marble floors were rare, and limited to the voorhuis, the vestibule, where guests would enter. The wealthiest Dutch families still preferred wooden floors in their living spaces—they are much more comfortable underfoot in damp and cold climates.
Like Turkish carpets and brass chandeliers, marble floors appear as decorative elements in the genre paintings of the day to connote the status and taste of prospective buyers, rather than the way these buyers actually lived. These pictures are less like photographs of actual spaces than like the imaginary tiled loggia through which Daniël Vosmaer represented Delft in his View of Delft through an Imaginary Loggia (1663). Indeed, there was a tradition in Delft painting of “imaginary architecture,” which combined realism and illusionism by depicting made-up spaces in an incredibly realistic way, with effects of light and shadow that made viewers feel they were transported there. Such paintings included Houckgeest’s Imaginary Catholic Church and Bartholomeus van Bassen’s Imaginary Palace for the Winter King (1639) and The Tomb of William the Silent in an Imaginary Church (1620). Even real spaces were depicted with imaginary elements, as in Johannes Coesermans’s Interior of the Nieuwe Kerk (1663) and in Louys Aernoutsz Elsevier’s Interior of the Oude Kerk, Delft, Seen through a Stone Doorway (1653). In these paintings the two Delft churches are depicted with black and white marble tiles, which neither of them had. Indeed, there is no evidence that church interiors ever contained black and white marble tiles, yet they often appear in the church interiors of the time, most likely for their perspective effect. These checkerboard floors even appear in scenes on the Delftware tiles of the day.
This tradition of imaginary tiled floors was continued in the interiors of De Hooch and Vermeer. The appearance of tiled floors in so many of the genre paintings and church interiors of the time is comparable to the imaginary element in the still-life paintings of the same period. Flower paintings, like those of Balthasar van der Ast, depicted flowers that did not bloom at the same time—and which, because of their costliness, would never have been cut, put in a vase, and allowed to wilt quickly. Rather, the flowers (especially the tulips) were kept in gardens designed for displaying prized specimens, much like the cabinets of curiosity of the amateur natural philosophers. These imaginary interiors, both of churches and of private homes, and the depiction of imaginary flower bouquets, all combined the realism and illusionism of seventeenth-century Dutch painting.
There would certainly be no marble flooring in the attic of a house, especially in a room used by no one but the penurious son-in-law of the home’s owner. So it makes no sense to “measure” Vermeer’s room from supposed tracings he made of the room’s checkerboard marble floor. Further, Steadman’s claim that there is only one reasonable explanation for the “extraordinary geometrical coincidence” of the six paintings (the fact that the rectangle formed by the extension of the visual pyramid is the size of the six pictures) is misleading. The six paintings Steadman points to are all just about the same size; five of them differing from each other only by a couple of centimeters in width or height. Another, even simpler explanation for this fact is that Vermeer was using standard-size canvases, and painted pictures of rooms that fit on those canvases.
There is much evidence that canvas sizes in the Northern Netherlands were starting to become standardized at this time, as they were in Britain, Italy, and France. Some support for this is that pictures in a particular genre tended to be painted on canvases with the same ratio. Sea paintings were generally painted on narrow canvases with a height-to-width ratio of about 1:1.60. Landscapes often had a ratio of 1:1.40 and portraits a width-to-height ratio of 1:1.20. Many of Vermeer’s paintings have a ratio of 1:1.14, which suggests that he bought portrait-size canvases and cut them down slightly. Of course, it could also be that Vermeer simply chose canvas sizes he liked to work with, or that his clients preferred to purchase, and then fit his scenes onto them. In either case, it stands to reason that Vermeer would compose his pictures to depict a room that could fit into the canvas he was using—that he would choose to paint marble tiles and chairs and windows and ceiling beams that were the right proportions to make the room look like a real three-dimensional space, even if the pictures were not photographic replicas of the room and its contents.
Vermeer did not trace his paintings wholesale from the camera obscura image. But one need not conjecture that Vermeer traced a camera obscura image in order to see a role for it in his toolkit. He used the camera obscura much as the natural philosophers used it: to experiment with light, to investigate and discover its optical properties. His object would have been to learn how to create the “semblance of reality”—how to attain that sense of houding, that make-believe space that feels real. Since the ideal of a painting in the seventeenth century was an image that makes things that do not exist appear to exist, thereby deceiving the viewer in a pleasurable way, Vermeer needed to learn how things appear to exist—how things are seen by us. His success is confirmed by how strongly we feel that we have stumbled upon a private moment, that we are spying upon a woman alone in her thoughts, reading or writing a letter, pouring milk from a pitcher, or measuring silver with a balance.
While using the camera obscura, we may imagine, Vermeer would have felt as though he had entered Kepler’s eye itself and was seeing the image “painted” on the retina. He was not merely reproducing nature but evoking the way nature manifested itself to human vision. He was experimentally exploring the concept of sight. Like Leeuwenhoek, and following Leonardo da Vinci’s dictum, Vermeer needed to “learn how to see.” In the seventeenth century, Dutch painters—Vermeer foremost among them—began to use optical instruments to help them learn how to see—and how to translate sight, itself a picture, into the language of paint on canvas.
*1 Huygens was not the only one who viewed Torrentius with suspicion—the painter was later condemned by the Dutch Reformed Church for his libertine ways. He was tortured on the painbench (the “rack”), condemned to life imprisonment, and his paintings were burned. After serving two years Torrentius was released at the urging of King Charles I of England, who wanted Torrentius as his royal painter. Today, only one of his paintings is extant, the stunning Emblematic Still Life with Flagon, Glass, Jug and Bridle (1614), which hangs in the Rijksmuseum in Amsterdam.
*2 In 1639 Jeremiah Horrocks used a telescopic camera obscura to observe the transit of Venus across the sun. My son and I used a similar device to observe the Venus transit in 2011.
*3 Unlike these other writers, I believe that Leeuwenhoek may have been using a form of camera obscura himself, as I discuss in part 11.
*4 While looking through a modern box-type camera obscura pointed out the window from an apartment on a high floor, I have seen dark shadows on buildings outside that I had not noticed with my naked eyes.
*5 Steadman believes that Vermeer’s studio was on the ground floor, but its location on the top floor of the house is clearly stated in the probate inventory taken after Vermeer’s death; and, of course, the light would have been better on the top floor, so it makes sense that Vermeer would have made his studio there.
PART 6
Mathematical Artists
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IN 1669 VERMEER painted a picture known today as The Geographer, but that depicts a surveyor at work, with the tools of his trade: a pair of dividers, used by surveyors to make measurements, a terrestrial globe, and two maps (one unrolled on the table, one hung on the wall behind him). Vermeer’s surveyor is a solidly built man in his late thirties, his hair in fashionably cascading dark ringlets. His left hand firmly grasps the table over which he leans, while his right hand holds the dividers. Light streams into the room from a leaded glass window to the left of the man, illuminating his face and the map on the table.*1
Vermeer’s surveyor is dressed in scholarly robes, blue with red trim, and his hair is pulled behind his ears, testifying to the seriousness of his studies. He
shows an energy and active nature absent from Vermeer’s quieter, more contemplative pictures of women from this period. Even the brisk furrows of the blue robe give us a sense of the surveyor’s intensity. Yet he shares an attitude with Vermeer’s women: he is shown absorbed in his own doings, not posing for the viewer. We have come upon him unawares, and are now eavesdropping on him as he works.
Later, when the picture was sold at auction, it was described as depicting a “mathematical artist.” Why did Vermeer abandon his studies of women in domestic settings to depict a male natural philosopher actively pursuing his studies? And who was this mathematical artist? Could the model be, as some writers have casually speculated, Vermeer’s neighbor Antoni Leeuwenhoek?
Eye of the Beholder: Johannes Vermeer, Antoni van Leeuwenhoek, and the Reinvention of Seeing Page 18