The Whitney Museum is currently presenting “Carmen Herrera: Lines of Sight”. This outstanding exhibition examines work from 1948-1978. Born in Cuba and educated in Havana, New York and Paris, Herrera developed a distinctive hard-edge geometric style. This is a large show and would require more than one blog post to discuss in fill. I have decided to limit this post to paintings Herrera created in NY after she returned from studying in Paris (1952-1965).
“Black and White”, 1962 Picture courtesy of the Whitney Museum
“Black and White” from 1962 is an excellent example from this time period. The shape of the actual canvas is an important element in the architecture of the work. By rotating the square there are no horizontal or vertical lines, this immediately disrupts the visual experience. Herrera limited her color pallet to two colors creating a dynamic tension of positive and negative space. In this work the thicker white strips are the same width as the thicker black strips but in the gallery there is an optical illusion where the white seems wider. The alternating of black and white parallel lines on the isosceles right triangles creates an order-2 rotational symmetry.
“Horizontal”, 1965 Picture courtesy of the Whitney Museum
“Horizontal” from 1965 also features two colors and a square. This painting again relies on the shape of the canvas to define its structure, but in this case a circular format. The thin horizontal wedges amplify the push and pull of the red and blue triangles and circle segments, formed by the edge of the canvas (arc) and the sides of the squares (chords).
“Lines of Sight” is a long overdue solo museum exhibition for Carmen Herrera It is a welcome opportunity to appreciate the artist’s exciting use of geometry.
This Spring the Metropolitan Museum of Art expanded its exhibition space into what used to be the Whitney Museum on Madison Avenue and is now called the “MET Breuer”. “Unfinished, Thoughts Left Visible” is one of the two of the inaugural shows. “Unfinished” features art which was never fully completed either by determination of the artist or by chance. On the forth floor of the museum there is a gallery with more abstract work that deals with the concept of infinity. The nature of the infinite creates a continuum in the work, thus alluding completion.
One of best visual interpretations that I have seen of Zeno’s Arrow Paradox is in the form animated video. “La Flecha de Zenon” by Jorge Macchi and David Oubina begins the way many movies begin, with a count down of numerals from ten to one, but, when you think some other action will start after one, the numbers are divided in two and expressed as a decimal. As the numbers get smaller and smaller the length of the decimal gets longer and longer until the digits get so small they seem to disappear. We are left to believe they go on forever and zero is unattainable.
Another artist in the exhibition that has a relationship with infinity is Roman Opalka. Beginning in 1965, he began a series of paintings on which he started to paint the numbers up to infinity. Each set of digits is hand painted in white on a grey background. The artist completed 233 canvases but of course never completed the project.
These examples highlight the way numbers can be used as a tool to express themes of time and infinity and their effects on the human condition.
Pictures courtesy of the Metropolitan Museum of Art.
Happy New Year!
I decided to start 2016 with a big show and the Frank Stella exhibition at the Whitney Museum definitely qualifies as a really big exhibition. When the elevator door opens into the first gallery,the viewer is met by two very different canvases: a large, geometric, consecutive squares painting, and a huge abstract that is exuberant to the point of being Baroque. The dichotomy of these two works highlights the the range of styles and themes explored throughout the galleries. On display are the all black paintings from the late 1950’s, as well as the colorful geometric square-and-shape canvases from the 1960’s. Also included are the wall sculptures from the 1980’s and the more recent work created using 3-D printing.
For the purposes of this entry I decided to concentrate on Stella’s paintings from the 1960’s. These works are clearly about geometry. Some of the artist’s sketches and schematic diagrams are on display as a group. I highly recommend taking a close look at these plans, they really highlight the mathematical processes involved in the paintings.
Stella – “Jasper’s Dilemma” – 1962
The two canvases of “Jasper’s Dilemma” each have the same spiral geometric structure, but the left canvas features a system of the color spectrum, while the right canvas is composed of shades of gray. Stella has built these spirals within the squares by creating two sets of isosceles triangles. The set with vertical bases are slightly larger than the triangles with the horizontal bases. This results in only one diagonal line on each canvas and the four triangles do not all meet at the same point.
Stella – “Empress of India” -1965 – Metallic powder in polymer emulsion on canvas
“Empress of India” is a monumental shaped canvas featuring a series of four V-shaped sections, each featuring a line of reflection symmetry and a 60 degree angle at the point of the “V”. There is also an interesting line of order-2 rotational symmetry running diagonally through the center section of the work.
Both “Jasper’s Dilemma” and “Empress of India” spotlight Frank Stella’s dedication to developing complex geometric structures in his work during the 1960’s.
Keep posted for many more observations on Mathematics and Art in 2016
On my recent visit to the Chelsea gallery district in Manhattan I noticed a number of exhibitions featuring art with Mathematical influences. At the Kim Foster Gallery there is a show of exquisite drawings by Paul Glabicki based on Einstein’s Theory of Relativity. These works have layers of scientific data, charts, and mathematical formulae. In drawing RELATIVITY #8 Glabicki has drawn a series of Pascal’s Triangles in the mix of images.
Glabicki- RELATIVITY #8
A Pascal’s Triangle is a triangular array made up of numbers. The number of terms in each row corresponds to the sequence number of the row. For example, the first row has one number (1) , the second row has two numbers (1,1), the third row has three (1,2,1). In Pascal’s Triangle, the first and last term of each row is 1. The middle terms are calculated by adding the two numbers directly above. Here is an example of a small Pascal’s Triangle.
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
In RELATIVITY #3 Glabicki has drawn Geometric studies of internally tangent circles. These circles share only one point and the smaller is inside the larger.
Glabicki – RELATIVITY #3
What I think is fascinating about these drawings is the way the mathematical and scientific elements are used as small pieces of the total work. They are transposed from abstract ideas into aesthetic elements of a much larger complex picture: the artist’s expression of the Theory of Relativity exploring the physics of time and space, through the arduous process of intense layering of images. Paul Glabicki is well known for his experimental animated films that use hand drawings.They have appeared at many film festivals and exhibits, including at the Whitney Biennial and the Venice Biennale.
Austin Thomas at the Hansel and Gretel Picture Garden
At the Hansel and Gretel Picture Garden there is a show of work by Austin Thomas. Exhibited are twelve drawings on paper, all of which have interesting proportions and geometric elements. The work that seems to really express mathematical principles is a sculpture the artist refers to as a “steel drawing”, made of two black and two white rectangular prisms. These are 3-D line drawings and by stacking them in this perpendicular fashion Thomas presents a nice study on squares and rectangles. Viewing the work from different angles and positions throughout the gallery offers many possible relationships between shapes, as well as the positive and negative spaces created by the open structures. Although it does not move, this is not a static sculpture. The prisms can be stacked in other ways offering Thomas a multitude of permutations to explore.