3/17/14
Robleh Wais
This is an excellent film by the famous skeptical duo of Penn and Teller. It offers a new perspective on how the seventeenth-century Dutch painter Johannes Vermeer may have created his dazzlingly realistic oil paintings. Teller directed the film, while Penn Jillette serves as host and narrator. What interests me most about the film is the range of metaphysical questions it raises. Penn, in his familiar role as skeptic, does not directly pursue these questions as I will, but they are suggested throughout the film.
Before turning to the metaphysics, let us review the film, its subject, Tim Jenison, and some elements of its cinematic structure. Jenison describes himself as an inventor, and he has had a brilliant career in video-graphics design, especially in computer graphics for television and film. He has spent several decades creating what we would now call special effects. The opening section of Tim’s Vermeer sketches his achievements and early life, succinctly narrated by Penn. From the beginning, then, the film presents itself as a blend of documentary and narrative exposition.
Because the film centers on Jenison’s attempt to replicate Vermeer’s The Music Lesson (TML), much of it focuses on how he carried out the project. At times, the film seems to promote Jenison a little too enthusiastically, but that is forgivable. Tim appears capable of constructing nearly anything required to achieve his purpose. One montage shows him rebuilding the original setting of TML while employing four or five different crafts, despite claiming little prior knowledge of them. The sequence is somewhat overdone. One begins to wonder whether Tim is being presented as a kind of technological Superman. Still, this is only a minor distraction.
What is genuinely eye-opening is Jenison’s discovery. He concluded that Vermeer may have used a device called a camera obscura (CO)—Latin for dark room—together with a small mirror that reflected the projected image onto the area being painted. A brief explanation is necessary.
A camera obscura is a box or room with a small opening containing a convex lens. Light passes through the lens and projects an image of the outside scene onto an interior surface. The image appears inverted because the light rays cross as they pass through the aperture. The lens preserves the spatial relationships of the original scene while allowing the image to be focused with varying degrees of sharpness. In this respect, the device resembles the basic optical principle used in telescopes and cameras.
A lens can sharpen or blur an image depending on its focal length and its distance from the object and projection surface. Jenison supplemented the projected image with a small mirror positioned above the painting surface. The mirror allowed him to compare the optical image directly with the paint beneath it. By shifting his attention between the reflection and the painted area, he could match color, tone, texture, and detail with extraordinary precision. Once the apparatus was properly aligned, the projected image could also serve as a guide for producing an accurate drawing of the original scene.
The process is a little like painting by numbers—remember those kits from the 1960s?—but it is considerably more demanding. The optical apparatus does not apply the paint. It merely presents the painter with a precise visual standard. Jenison still has to mix the colors, place each stroke, and repeatedly compare his work with the reflected image. Every variation in hue, texture, light, and shadow must be observed and reproduced by hand.
The film repeatedly emphasizes that Jenison is not a trained painter. He is following what he sees in the mirror down to the smallest detail. In that sense, he is painting by a visual code rather than by conventional artistic intuition. If there were ever a film that deserved a three-dimensional presentation, this is one. I wanted to see more clearly how a man looking into a mirror could reproduce on a surface exactly what he perceived there. We watch him create, from a photograph of his father-in-law, a painted likeness of almost photographic accuracy. The effect of this first experiment is spellbinding.
We can now turn to the metaphysics. Is Tim Jenison a painter? The objection likely to be raised by art critics and aficionados is already apparent. An artist creates new images from the mind; an artist does not merely copy or mechanically reproduce what is seen through a sophisticated optical method. Art, one might say, requires an afflatus—a creative spirit. Could software not do what Jenison did?
I disagree with that objection. Tim Jenison possessed intentionality. He wanted to create a replica of one of Vermeer’s most acclaimed works. Yes, he used an intricate method, but at every stage he was consciously striving to complete the work. A piece of software might perform some of the same operations with human assistance, but would it understand what it was doing? Would it recognize an error as an error, rather than merely register a deviation from a predefined condition?
Jenison was therefore not engaged in painting mechanically. He was creating a painting by reconstructing what he believed to be Vermeer’s method. In this sense, Jenison, despite his own denial, is a painter and an artist. Stated differently, what Jenison did is operationally indistinguishable from what Vermeer may have done. If the same intentional process and the same kind of skilled correction are involved, then both men qualify as artists. This is a more profound claim than it may first appear. To be an artist—or, in this case, a painter—one must possess the intention to create a work of art.
One might still argue that a sufficiently sophisticated computer could be an artist. I do not think that follows. A computer produces output according to a predefined architecture and set of operations without possessing an independent intention to create. The same objection applies to images generated by LLMs, or large language models. The system may generate the image, but the purpose that gives the activity direction originates with the human agent.
The next major metaphysical question is this: If Jenison meticulously recreates TML through an optical method, has he in effect photographed it? Penn raises this issue in the film. There is truth in the suggestion. If the resulting painting reproduces what a camera would capture through digital patterning, then it is, in a meaningful sense, a photograph made with paint—a photographic painting, to coin a phrase.
To illustrate the point, consider a simple example from analytic geometry. Let P be a circle consisting of all points d located at a fixed distance r from a center O. Now translate the circle by a vector L. The translated circle P′ consists of points d′ obtained by adding L to the original points, while its radius remains unchanged.
P′ = {d′ : d′ = d + L and dist(d′, O′) = r}
Is the translated circle P′ identical to circle P, differing only in location by the vector L? In shape, size, and internal structure, it is indistinguishable from the original. This resembles what Jenison accomplished with his copy of TML. The more difficult question is whether the two works are therefore the same thing. I will not pursue that issue fully here, but it invokes the philosophical principle known as the Identity of Indiscernibles: if two things cannot be distinguished by any property, then they are the same thing.
There is an even more robust mathematical interpretation of Jenison’s procedure. His method may be viewed as an iterative approximation process. Let Pn denote the state of the painting after the nth correction, and let T denote the optical comparison-and-correction operation. The successive approximations are then given by
Each application of T compares the current state of the painting with the optical image and reduces the remaining error. More formally, if the space of possible painting states is equipped with a distance function and there is a constant c, with 0 ≤ c < 1, such that
then T is a contraction mapping. Under the conditions of the Banach Fixed Point Theorem, repeated application of T converges to a unique fixed point P*, satisfying
The fixed point represents the completed painting, where no further correction is necessary because the painted image and the optical projection coincide to the required degree of accuracy. The theorem explains why an iterative correction procedure can converge. It does not explain why the procedure was undertaken in the first place. That requires intentionality, which remains a property of the conscious artist rather than of the mathematical process itself.
It was mesmerizing to watch Jenison create the work over a period of approximately six months. He consulted prominent British artists and pursued the project with a grueling regularity that made me want to try the method myself. A film that I expected to find boring instead inspired me. Take the time to see it.