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In Brick (1983) a change has occurred that parallels Einstein's progress from the special theory of relativity in 1905 to the general theory in 1916: The global frame of reference has become local. The single rigid framework that spans all space has given way to a portable frame carried by each object. In the general theory of relativity, every massive object in the universe determines how space and time are configured in its own immediate vicinity. When all these different private frames of reference, which point in different directions, are connected together smoothly, the result is a web called curved space-time. Brick shows the gridlines around one object and invites speculation about how they would continue to the cosmos in the background, and then on to infinity.

The frame of reference, besides anchoring objects in place, plays an active role as part of the fabric of mathematics. The snaplines belong to the apparatus of projective geometry, and thus to the whole world of mathematics. They carry us off to realms of pure reason where human senses are irrelevant and infinity acquires meaning. Davis' objects help us visualize mathematical relationships. But which is fundamental, the abstract formalism, or its material representations? The rationalist position holds that mathematical truth exists independently of real examples. The empiricist counters that abstractions, like space and shape, must be derived from real phenomena. In terms of Davis' paintings, we ask: Which is primary, the objects or the lines? Are the objects merely flimsy bits of plywood or cloth stretched between gridlines like warning flags on guy wires or, on the contrary, are the lines actually defined by the edges of the objects? Which holds up which? We can assume either position, and even switch purposely from one to the other, thereby changing our reaction to a painting. Davis encourages this mental exercise by the balance he maintains between object and frame of reference.

And again, there is a parallel to Einstein's way of thinking about the world. In response to the charge, "Einstein's position .... contains features of rationalism and extreme empiricism...," Einstein replied, "This remark is entirely correct .... A wavering between these extremes appears to me unavoidable."

The difference between theoretical physics and mathematics lies in their tests for validity. Even as the physicist constructs his most elegant mathematical edifice, he keeps in mind the real world in all its messiness, confusion, elusiveness, and stubbornness. Into its tumultuous welter of phenomena he must eventually plunge his carefully wrought model to check whether it has any predictive value. If it doesn't, he must discard it. The mathematician is spared that ordeal. His criterion is spelled out by G. H. Hardy in A Mathematician's Apology: "The mathematician's pattern, like the painter's or the poet's, must be beautiful; the ideas, like the colors or the words, must fit together in a harmonious way; Beauty is the first test." On this authority, mathematicians might claim Ron Davis as a kindred spirit. But he paints like Albert Einstein thought, and Einstein, although his theories rank with the great monuments of mathematics, was a physicist. The wildness of nature was always in his mind, and it is always present in Davis's paintings, as in Frame Float (1975), in the form of the background behind the geometrical forms.

Objects, snaplines, and background constitute the three major elements of Davis' paintings, and we may see them as metaphors for the theoretical models, the mathematical apparatus, and the uncontrollable phenomena of the natural world that together comprise physics. Of the three, mathematics is the most artificial and controlled. Snaplines can be placed at will, and even the rules of perspective are largely arbitrary. Nature, on the other hand, goes her own way: we do not control her laws. The most natural element in Davis' paintings is the splashing of paint in the background and near the snaplines. The colors are selected with exacting care, but the droplets fall where they must. Their patterns are not like the patterns of mathematicians, but like those of the world of physics. Mathematical models, finally, mediate between the realms of mathematics and nature. The gravitational field, for example, is a mathematical construct just as surely as it is an observed fact. Much of the power of Davis' paintings derives from his ability to make this connection. His objects are rigid geometrical constructs, but they are also inextricable parts of the relaxed play of color around them.

Relative strengths of the three elements do vary from example to example, as they do in physics, but you can't look at a Davis painting without being aware of all three. By consciously varying the importance we attach to each of the elements, we can mentally manipulate the painting in an almost uncanny way. This game is reminiscent of Bernard Berenson's insistence on learning to associate tactile values with retinal impressions of paintings in order to gain "the illusion of being able to touch the figures" in Renaissance art, and thus to appreciate them. Only, in the case of Davis, the effort of the game is more cerebral than muscular.

The harmony between the objects and the background reflects the relationship between a mathematical model and the real phenomena. In Frame and Beam, the link between the objects and the great green splotch, which could be an exploding galaxy or a bursting amoeba, is provided by the gridlines. The lines themselves can be thought of as functions in an equation or, more empirically, as light rays. They are first established, defined, and manipulated in, structures we can control-the frame and beam themselves, regarded as mathematical equations or optical instruments. And then the lines are thrust forth and extrapolated to the almost inaccessible region where they impose order on a random natural event. In another example, the same hues that are separated on the model in Invert Span (1979) blend into each other in the surrounding background. And further, the surface of the object in Brick is treated in a manner that mimics the cosmic background, but doesn't copy it.

There is no fixed prescription for the relationship between object and surroundings, the way there are prescriptions for the construction of gridlines that date back to Renaissance perspective. The physicist recognizes this variability as an echo of the multitude of ways in which he tries to model nature. Some models are approximate, but universal; others precise, but of limited applicability. Some are mathematically rigorous, but unrealistic; others just the opposite. In theoretical physics, no less than in painting, there are many ways to come to terms with nature.

What remains constant, however, is the style. The great theoretical physicists have styles that are as personal and unique as those of the great painters. When Johann Bernoulli, a Swiss physicist of the eighteenth century, saw an anonymous solution to a difficult problem, he exclaimed: "Tanquam ex ungue leonem" (The lion is known by his clawprint! ). He had spotted the unmistakably imperial manner of Isaac Newton. Both Einstein's style, and Ron Davis', are marked by a peculiar blend of concreteness and abstraction, of empiricism and rationalism. Their affinity is rooted in the power of their visual imagination and the unfathomable common origins of artistic and scientific creativity. Both men are equipped with a kind of x-ray vision that allows them to see through the material objects before them to the underlying mathematical structure. And both are adept at expressing their deeply felt sense of awe at the beauty of the hidden order they discover there.


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