Paula Cooper is currently presenting a wide range of the work of Sol Lewitt at all three of their Chelsea galleries, as well as at the book store 192 Books on Tenth avenue. Wall drawing and sculptures are included in this excellent homage to the artist, but I am going to focus on a photographic work from 2004: “A Sphere lit from the top, four sides, and all of their combinations”
This series of 28 photographs explores 2-D images of a 3-D sphere. It looks at how the figure changes in space based on how it is lit. A circle possesses infinite lines of reflective symmetry, diameters, and has an infinite order of rotational symmetry in 2-D space. Spheres take these symmetrical properties into 3 dimensions. Lewitt’s use of light from six vantage points reveals the myriad of visual possibilities in portraying what seems to be the purest and simplest of geometric solids. Although the subject of each photograph remains constant, all pictures have a different energy and personality.
I feel that photography is a fertile medium for mathematical art, especially serial work. It allows an artist to explore a geometric theme through different vantage points and permutations.
The subject matter, the title as well as the materials, immediately reminded me of Sol Lewitt’s 1974 installation “Incomplete Open Cubes”. But these paintings have an extra element of complexity. The 2-D paintings acquire their perception of depth without the use of shading. Instead foreshortening and lines are used to illustrate which elements of each cube is in the foreground or the background.
In this middle painting the center horizontal leg seems to be cutting across the front of the figure but it is attached to the vertical leg at the right of the image that seems to be in the background. So this is not really a cube. if all of the angles in the form are 90 degrees it is actually an impossible figure. What I found so interesting about this work is the way it appears to directly reference historically important work but up on closer inspection there is an unexpected twist that takes the work into a more complex geometry.
There are a number of Upper East Side galleries that display museum caliber exhibitions of historically significant art. The current show at the Dominique Lévy gallery “Drawing Then, Innovation and Influence in American drawings of the Sixties” is an excellent example. It features work by some of my favorite artists like Eva Hesse, Agnes Martin, and Cy Twombly. The list goes on and on, there is even a Sol Lewitt wall drawing.
There are two works on display that relate the most directly to Mathematics. Mel Bochner’s “3” from 1966, is an homage to a Sierpinski Triangle. An equilateral triangular grid formation has been strategically filled in with hand written number 3’s and words that begin with letters “Tri”. The positive and negative shapes created delineate the fractal construction of a Sierpinski Triangle.
The second drawing is Josef Albers’ “Reverse + Obverse” from 1962. This line drawing is a 2-D rendering of 3-D constructions.
Both the top and bottom pairs of the figures employ a 180 degree rotation, an order-2 rotational symmetry. This work is a geometric expression of a form turning through space.
This year is the 40th anniversary of the MOMA’s ground breaking 1976 exhibition, “Drawing Now”. The current show at Dominique Lévy gallery is true to this historical reference, focusing on work from the turbulent years from 1960-1969. There is a wide range of work on display from drawings with social commentary, to drawings exploring the aesthetics of minimalism and conceptual rule-based art.
Sol LeWitt’s ” Wall Drawing #370″ is currently on display in a long corridor on the first floor of the museum.
The directions for”Wall Drawing #370″ are: “Ten Geometric Figures (including right triangle cross X, diamond) with three-inch parallel bands of lines in two directions”. LeWitt wrote the conceptual plan for these drawings in 1968.
Each of the ten panels feature alternating black and white lines that run either vertically or horizontally. The shapes depicted, however, feature curves and non-right angles, and lines that cross do so in a perpendicular fashion.
Each shape also has some type of symmetry either reflective or rotational.
I have always been a huge fan of Sol Lewitt’s Wall Drawings. Besides the obvious geometric mathematical elements to the work LeWitts underlying conceptual process shares theoretical similarities with Mathematical Algorithms.
In 1967 Sol LeWitt published his “Paragraph’s on Conceptual Art” in Artforum magazine. Here is an excerpt:
“In Conceptual Art the idea or the concept is the most important aspect of the work….all planning and decisions are made beforehand and execution is a perfunctory affair. The idea is the machine that makes the art.”
As a comparison I want to look at what David Berlinski writes about algorithm in his book “The Advent of Algorithm”:
“As Algorithm is a finite procedure, written in a fixed symbolic vocabulary governed by precise instructions, moving in discreet steps,1,2,3…whose execution requires no insight, cleverness, intuition, intelligence, or perspicuity, and that sooner or later comes to an end.”
I feel there is definitely a relationship between Sol LeWitt’s description of Conceptual Art and the way that mathematical algorithms perform, I also see a connection in this early work of LeWitt and the birth of the computer age….. But I will leave that for another blog.
If you are going to be in NYC anytime in the next 14 months, go see the Wall Drawings at the Metropolitan. They are powerful and graceful and up until January 3, 2016!
Matteawan Gallery in Beacon, New York is currently exhibiting works on paper by Dominick Talvacchio, in a show named “The Eros of Mathematics”. Talvacchio has a background and education in mathematics. His work has been exhibited extensively throughout the United States and Europe. The visual dialog in his print and drawings express his interest in the inherent beauty of the order and structure found in mathematics.
In the print “Arcs Missing Arcs”, Talvacchio has created a 4 by 4 grid of touching circles with only sections of the circles visible. These arcs create a series of graceful and organic curves. The viewer senses the existence of the underlying grid pattern, but is allowed to enjoy the sensual aesthetics of the segmented curves.
The drawing “Kairovan Below” features two elements. First, an underlying, lightly-drawn tiling. Second, a selection of line segments from the tiling, drawn in a darker black. The tiling has a four-fold rotational symmetry. Within this symmetrical pattern there are five-point non-symmetrical stars. The juxtaposition of the overall symmetry of the tiling against the not-quite-symmetrical stars creates an interesting tension. By making some of the lines darker and more pronounced, Talvacchio allows a simplified but elegant pattern to emerge.
Artist talk and reception
On June 1st from 2-4 at Matteawan Gallery there will be an artist talk and closing reception for “The Eros of Mathematics”. I will be there to participate in the discussion about the relationships between mathematics and art. All are welcome.
Matteawan Gallery is located in Beacon. A small city north of New York City, situated on the Hudson River. It is the home of DIA Beacon, a museum dedicated to displaying long-term, large-scale gallery presentations of single artist displays, with emphasis on conceptual art and minimalist work. They have an excellent selection of Sol LeWitt’s wall drawings currently on view. I would suggest DIA Beacon as an excellent destination for a day trip for any math art enthusiast. While you are in town, check out the galleries on Main Street.