Adapting the themes of this exhibition to the space at Greylock Arts has been a joy. My goal was to be minimally intrusive to the stunning integrity of the materials of the gallery space which are almost all original to when the building was made in the 1920’s. The ornamental high tin ceiling, period cabinetry, hardwood floor, original deep jamb windows, ornamental light fixtures, and clear uncluttered walls make artwork shine. In short, its magnificence is quite a bit more than a clean well-lighted space.
I’m also inclined to believe that the less you try to do the better. This “bias” has come from many encounters where trying to do “more” has always resulted in disaster. So there is also an inclination on my part to use less light, rather than more.
I hope I won’t put the reader off by using so many technical words, but they’re a vital part of what has been an important exploration for me, and the words have specific and clear meanings. The terminology is appropriate, because it is the language of geometry—and is more widely used than ever, so it ought to not be a threat—and it is the means that I’ve chosen to build the sculptures in ZERO SUM.
Most simply put, the objects—sculptures—are passive devices to help demonstrate certain conditions of seeing light and three-dimensional space such as drawing perceptual equivalency between light and matter. These geometric “solids” reflect and absorb light in specific, discrete ratios that minimize ambiguities that might arise from depicting anything.
ZERO SUM, the title of this exhibition, comes from the equation used to describe the tetrahedral (four-sided pyramids) that were used to build almost all of these sculptures. V-E+F-C=0=4-6+4-2=0, or The Euler Equation as it is called, states that the sum of the vertices, edges, faces and cells for a tetrahedron equals zero. The Euler Equation is used to describe all tiling patterns, and it applies in this case, to three-dimensional patterns too. It’s elegant and provocative equation because it explains how the pyramid exists in three-dimensions.
Also, to clarify an important point, in game theory the term Zero Sum means something entirely different, and doesn’t apply here.
There are three types of tetrahedra that I’ve used to build these sculptures. One is equilateral, all its faces and edges are the same size, another has a shallow apex so the base of each tetrahedron is a different size than the other three sides, and the third type has triangular faces where two of the edges are a different length than the third edge. A stellated (star-like) icosahedron is made from 20 equilateral tetrahedra.
The stellated dodecahedron variant is made from 60 isosceles tetrahedra. I build them so that one of the faces has a seam that bisects it. This limitation allows for only a few solutions, and those are the ones that I have to use. By origami or purely mathematical standards, it is neither an efficient nor perfectly rigorous technical solution. There are also many redundant edges, which is taboo in origami. The redundancy does tend to help make the pliable aluminum screen more rigid, so there is a structural advantage, if not a mathematically pure resolution to building the sculptures in this way.
Call it what you will, but for me there is great psychological satisfaction in seeing these straight linear elements result in the spherical forms of the icosahedron, dodecahedron, and fullerenes that are displayed in this exhibition. Time and time again, I’ve heard this same inexplicable response from other people I’ve met who have worked with these geometries.
In order that the sculptures generate a maximum array of moiré patterns, the strands of the aluminum screen or hardware cloth that these sculptures are made from must be parallel or roughly parallel to each other. The stereoptic, or three-dimensional property of being able to look at or through the sculptures, is probably the most gratifying aspect of their construction and it makes them intriguing to look at. These sculptures are about seeing, looking, and thinking in a very concrete way.
The following is a brief description of each of the three separate photographs and the video that will be included in this essay.
a. Newton Ring
This combination of light and sculpture is about distillation and paradox, showing this interaction in a clear and yet puzzling way. The vividly colored array that you see is called a Newton Ring. This effect is created when a highly focused diffracted white light passes through the air and hits the surfaces of the sculptures.
When this happens, the empty core of the sculptures becomes more obvious. The waves of light are then uniquely distributed in space over the surfaces of the sculptures. The rotating sculptures create moiré patterns which are a kind of periodic visual noise that is made from the parallel grids of the screen.
The large dodecahedral sculpture on the right is made from a roughly textured metal material called hardware cloth. The small fullerene on the left is made from aluminum screen, and as you can see, it is a more sympathetic medium for displaying the purity and vividly intense colored bands of spectral light.
This second grouping of sculptures displays variability. By simply altering the size, number, and surface characteristics that these objects are made from, we mentally compare and react to what those differences are.
In this instance, the sculptures and the shadows they cast have a kind of equivalency. This idea comes from camouflage theory. The shadow, or pseudomorph, as it is called, rivals the sculpture for our attention while providing an alternate view of the same geometry.
c. Large Stellated Dodecahedron
This very large stellated dodecahedral sculpture’s core is made up of twelve interlocking pentagons.
We are immediately riveted by the huge void at its core and the flickering moiré patterns created as we move around the sculpture. It demonstrates the concept of a “second cell” in the Euler equation, the space around and “inside of” the sculpture is the second cell. Objects are perceived in three dimensions, and the empty space at the core of the sculpture becomes as much a part of the object as any other part.
This large work, perhaps more than any of the sculptures, shows us that the “inside” and “outside” are actually one continuous surface. This perceptually paradoxical property is related to a branch of mathematics called topology.