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.
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.
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."
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.
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.
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.
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.
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.
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.