The Museum of Modern Art in NYC underwent a big expansion and renovation project last year. The opening in the Fall the Museum introduced some exciting new exhibitions. “sur moderno journeys of abstraction” focuses on the work of participants in the post WWII avant-garde artists groups that were formed in South America. The work on display is all abstractions, many of which have geometric themes.
Willys de Castro’s 1962 oil on canvas on plywood wall sculpture, “Objeto ativo (cubo vermelho/branco)” (“active Object [Red/White Cube]”) explores the divisions within a cubic structure. The 3/4 of each of the 5 visible sides of the cube are painted red. A square measuring 1/4 of each side is painted white. This is done in such a way that it appears that there are white cubes embedded into the sculpture at two diagonal corners.
Eugenio Espinoza’s 1971 “untitled” half stretched canvas features a square grid pattern. By only stretching the top half of the painting the bottom of the canvas is slack. the grid has been altered as the sides of the canvas roll back.
Helio Oiticia’s 1958 gouache on board “Metasquema No.348” is an arrangement of bright blue non-overlapping rectangles. Positioned in a grid like pattern but skewed at various angles, the liner rectangles create a pattern that seems to have both kinetic and curvilinear properties.
It is the final two weeks of Adrian Piper’s MOMA retrospective titled “Adrian Piper A Synthesis Of Intuitions 1965-2016”. This exhibition features work from Piper’s diverse career. The first few rooms include excellent examples of early conceptual work with Mathematical themes.
“Nine -Part Floating Square” from 1967 features nine canvases positioned to for a 3X3 square each canvas is divided into 3X3 grid. A selection of grid squares on each canvas is painted with gesso to form a 6X6 square that stretches across all of the panels in an off center position.
“Infinitely Divisible Floor Construction” first constructed in 1968 consists of squares of particle board and lines of white tape.The first square is undivided, the next arrangement is four sections each divided into 4 squares (2X2 grid), the third arrangement is nine sections each divided into 16 squares (4X4 grid), the largest formation features sixteen boards each divided into 64 squares (8X8 grid). This work becomes an parade of squares with in squares that becomes more intense as it marches across the gallery floor, highlighting the geometric structure of the squares as well as referencing the more abstract concept of mathematical infinity.
Piper continued to use the tenets of conceptual art in her practice but the themes changed. Societal concerns, especially racial discrimination became the subject matter of much of the work. I realize the main emphasis of this blog is to discuss the Mathematical connections to Art, but I hope that anyone who is in NYC goes to MOMA to see this show not only for the Math Art but takes the time to experience the entire timely exhibition.
The MOMA in NYC is presenting an exhibition of work from their permanent collection, featuring abstract work produced by women between 1945-1968. Although abstraction was an important genre of art during this time period, the work created by women has been underappreciated. There is a wide range of art on display from gestural expressive paintings and drawings to the more geometric and calculated.
Běla Kolářová – “Five by four” – 1967
Běla Kolářová – “Five by four” – 1967 (detail)
For this assemblage “Five by Four”, Běla Kolářová used metal paper fasteners to count out the grid patterns that make up each of the 20 rectangles. These rectangles are then arranged in 4 columns, 5 rectangles high. The use of the paper fasteners (something found in any home or office) as a mark making vehicle adds extra personal element to the work.
Carmen Herrera – “Untitled” – 1952
This large scale canvas by Carmen Herrera features two isosceles triangles with their bases along the top of the painting. Using the tension of black and white vertical parallel stripes, Herrera has defined the shapes by swapping the colors at the sides of the triangles. This technique has created an visual energy along these lines that allows the triangles to pulsate. The geometry of this painting is so strong, you feel like you are being pushed back to view from a distance.
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.
Josef Albers -“Reverse+Obverse” – 1962 Picture courtesy of the gallery
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.
Currently on display Museum of Modern Art, “Scenes for a New Heritage” is a fresh reinstallation of the Museum’s collection of contemporary art. The first work you encounter as you enter the gallery is On Kawara’s “One Million Years (Past and Future)”. A limited edition Artist Book published in 1999 by Editions Micheline Szwajcer and Michele Didier, Brussels. Situated on a white pedestal in a clear vitrine the book features rows and columns of numerical years in sequence from 998,031 BC to 1.001,992 AD.
As you get close to the vitrine to study the book, a voice reads out the numbers of a year. There is a speaker in the front of the stand. If you stand close to the pedestal another year in consecutive order is read out. The voice on the recording alternates between male and female. The audio recording was produced by the David Zwirner Gallery NY in 2000. This installation at the MOMA is really two works of art, the visual component in the form of a book and a poetic component in the reading of the dates.
On Kawara is very famous for his paintings of single dates on canvas. I feel this installation reflects a deeper connection to Mathematics. The emphasis on the listing of numbers makes the viewer think about how we mark time using digits and order. The act of counting to this huge number of one million creates an extremely emotionally charged audio experience. The number are just as poignant as any other words in expressing the vastness and continuity of time.
The current exhibition at the Luring Augustine Gallery in Chelsea, “Empty House Casa Vazia”, features sculpture that is associated with the Neoconcretism movement in Brazil from 1959 until 1961. Neoconcretism was a reaction against the rationalism of Concretism. Although Neoconcretism continued the use geometry to create abstractions, they were not interested in pure form. Instead, they introduced a human element.
Lygia Clark was an important member of the Neoconcrete movement. She added a participatory element to her sculptures. The viewer was encouraged to manipulate her hinged metal sculptures. I have written an earlier blog post about the MOMA exhibition of Clark’s work, but I was not permitted to take any photos, so I was thrilled the gallery is allowing me to share a photo now.
“Bicho” consists of a series of sheet steel isosceles right triangles (isosceles triangles whose vertex angle is 90 degrees). They are hinged together to form a complete loop that can be arranged in many different positions.
Lygia Pape’s series of wooden wall sculptures titled “Livro da noite e dia” features a series of 6 1/4″ squares. Each square has at least one geometric shape removed from the edge or corner. Then those shapes, triangles, squares, trapezoid….are shifted and layered onto another part of the square resulting in interesting symmetries.
“Estrela”, a copper sculpture by Amilcar de Castro, is made up of three rectangles. Each rectangle has been bisected diagonally and folded and joined together to make a sculpture with all sorts of triangular possibilities.
These practitioners of Neoconcretism employed mathematics in their work, particularly Geometry. But their art was about something even deeper, it was about how humans interact with the geometry. This is achieved in a different way by each of the artists: In the case of Lygia Clark through tactile manipulation, Lygia Pace’s intriguing puzzle-like squares encourage the viewer to ponder the missing pieces, and De Castro’s sculpture invites the viewer to walk around the work, because it changes dramatically depending on the location and angle from which it is viewed. In some ways these sculptures reveal more about our relationship with Mathematics than many other artistic movements.
The Museum of of Modern Art is currently hosting an exhibition of the work of 17 diverse artists entitled “The Forever Now, Contemporary Painting in an Atemporal World”. The work is all made in the 21st Century, and the general theme of the show is that this work does not have defining elements that would indicate when the work was produced. The term “atemporal” refers to timelessness, as well as the way the art incorporates ideas from the past. The internet offers contemporary artists access to massive amounts of images and texts about previous generations of artists and their work. This knowledge is then incorporated into this new 21st century art.
Dianna Molzan has two works in the show that relate to the traditional rectangular dimensions of a stretched canvas paintings. The first, “Untitled 2010”, features a set of wooden stretcher bars with canvas attached on the two vertical sides. the painted canvas has been slashed with a series of horizontal cuts that creates ribbons of canvas that drape down in curve.
The second painting, “Untitled 2011”, is also based on a rectangle, but instead of having all four sides made out of wood, the left side of the frame and the bottom edge have been replaced with a stuffed and painted canvas tube. This has created a slack curved line.
Both of these works address the idea of the rectangular perimeter of traditional easel paintings. Molzan has distorted the geometry of the shape by either slashing the canvas or replacing the stretcher bar with a fabric sculptural element.
The Museum of Modern Art in NYC is currently hosting a huge retrospective of the work of Lygia Clark (1920-1988). Clark was a member of the Brazilian Constructivist movement. The walls of the first few rooms of the exhibition display the artist’s geometric abstract paintings. On platforms in the center of the gallery, an assortment of her hinged metal sculptures are on display. It is these sculptures I would like to discuss. There are a number of excellent reviews of the show online – the Brooklyn Rail is an example – but I would like to focus on the sculptures. Clark created these sculptures so that viewers could manipulate the shapes, creating different
forms, becoming part of the artistic process. At the MOMA show work tables are set up throughout the galleries with reproductions of the sculptures available for the public to participate. Photography is forbidden in these galleries so I decided to reproduce one of Clarks’s more simplistic forms using paperboard and tape and taking photos of my model.
Here is the construction process, in case you want to make one. You will need seven congruent isosceles right triangles.
Lay out four triangle to form a square and make three hinges leaving two triangles attached on only one side.
Take a fifth triangle and attache it to one those single attachment triangles so it is on top of the other triangle with one attachment .
Add the sixth triangle to the fifth so they form a parallelogram.
Turn the structure over and attach the seventh triangle to the fourth triangle from the original square so you have like a trapezoid. Now you can stand up the structure in many positions.