The Metropolitan Museum of Art is current exhibiting a show titled “Picturing Math: Selections from the Department of Drawings and Prints”. The exhibit features work from the 15th to the 21st Century. It presents a cornucopia of beautiful work, and it was very difficult for me to choose just a few to discuss in this blog. Some of the most historically significant work was in the form of books that were opened to show prints.
This first image is a page from Durer’s “Treatise on Measurement” from 1525. This particular print Is “Construction of a Spiral Line”. Although the aesthetic significance of this work is undeniable, it is a technical diagram complete with measurements.
This next page is “Dodecahedron and Variants”, from “Perspectiva corporum regularium” (Perspective of Regular Bodies). This is a 1568 treatise by Jost Amman based on the work of Wenzel Jamnitzer. This work offers a progression of depictions of increasingly complex 3-D solids. Both of these books were created for the purpose of visualizing Mathematics as an expository tool, but because they are such gorgeous images they also highlight the beauty of the Mathematics.
This exhibition also include contemporary art. A great example is Mel Bochner’s 1991 lithographs in the series “Counting Alternatives: The Wittgenstein Illustrations”. This particular print is titled “Eight Branch”. Referencing Bochner’s drawings from the 1970’s, this 1991 portfolio relates to the philosopher Ludwig Wittgenstein and his ideas about certainty. The print features two different lines of counting series, both starting with 0 in the top left corner. One line of digits goes horizontally across to the top right corner with 23 and the other goes diagonally across the page to the lower right corner with 33. Both routes end in the bottom left corner with 54.
Unlike the historical texts Bochner’s work is not about presenting mathematical principles to educate. Instead, he is using mathematics to express ideas. This is truly an excellent exhibit it will be up through April and I suggest that if you are in NYC, go see for yourself.
James Siena artistic practice incorporates the use of rules to create art. I have written about his type writer work, as well as his sculptures, in earlier posts. Obviously I am a fan, and I was very excited to be able to see some of his recent drawings at the Pace Gallery on 24th st. This exhibition features work from three different series; “Manifolds,”, “Wanderers” , and “Nihilism”. All of the drawings are hand-drawn, geometric studies but the the series I feel that has the most Mathematical implications is “Manifolds”.“Manifold X” from 2015 addresses the artist’s interest in the field of Topology. Topology studies the properties of surfaces allowing them to change through the manipulations of bending growing and shrinking without being cut or broken or having attachments added. In “Manifold X” the orange, yellow and blue surfaces are homeomorphic, they each have nine holes within their shapes . The green surface is different because it ha sixteen holes. The four surface are woven together but each individual shape does not intersect itself. Siena has managed to take a fairly complex field in mathematics and develop a system of rules to create work that aesthetically beautiful and also expresses his affinity for the subject matter from which it is derived.Susan Happersett
Dan Walsh is known for his large-scale geometric work. I was introduced to his paintings at the 2014 Whitney Biennial. At his solo exhibition at the Paula Cooper gallery I was immediately drawn to his large scale square paintings. Not only do they feature geometry, they also present the theme of counting. In the painting “Fin” from 2016 the canvas is divided in to four horizontal rows of varying widths. Thickest on the top with 3 sections divided by black and white parenthesis and narrowest on the bottom divided into six segments.Since the width of each row is the same the progression 3, 4, 5, 6 segments presents a visual comparison of the fractions 1/3, 1/4, 1/5, 1/6.
“Debut” from 2016 the artist uses the same 3, 4, 5, 6 divisions in horizontal rows but this time groupings of thin lozenge shapes make up the pattern.There is a stack of 8 lozenges in the rows of three, 6 lozenges in the rows of four, 5 in the rows of five across, and 4 in the rows of six. Instead of having all of the shapes the same base color like in “Fin”, Walsh has created a scale with the more intense blues in the bottom row, grounding the picture space, almost like a landscape.
The painting “Circus”, also from 2106, presents a more architectural form. Working once again with rows of varying width this has seems to have more of a subject and background.The alternating black and white coloring of the vertical thin lozenge-like strips create a tower. The rows grow from 13 to 15 to 17 to 19. Each row gaining one strip on both the left and the right sides.
Dan Walsh’s painting style is both precise and systematic, but his choice of numerical subject matter that everyone can relate to creates a joyful imagery.
I never planned to use this blog to discuss my political leanings but …
My sister Laura and I participated in the Woman’s March in Washington this past weekend. The size of the crowd was of a magnitude I have never experienced before. Anyone who has seen my work knows i have a predisposition for counting. Years ago, I developed a system of creating counted mark-making drawings. One project – from 1999 – titled “A Million Markings for the Millennium features 125 prints, each with a 40 by 20 square grid. Each grid square contains 10 markings. The number one million is thrown around freely in rhetoric and dialog, causing it to loose its gravitas. This work is my visual answer to the question “Just How many is a million?”
Standing on Indepence Avenue on Jan 21 I was overwhelmed by the sea of people all walking together. The societal effects of very large number was palatable. I had not planned on discussing these emotions in this forum but when the concept of counting becomes an issue with regards the Presidential inauguration crowd, I could not stop myself.
Artists, even Math artists, do not work in a bubble (although I have attempted to crawl under a rock for the last two months). Objective counting and measuring has become a source of political existential angst. There is really no such thing as “alternative accuracy”. Sometimes numbers speak louder than words.
I guess I will always be a Nasty Number Geek
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” 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” 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.
Anila Quayyum Agha’s installation titled “Intersections” is inspired by the intricate decorative elements she encountered in religious buildings as a child in Pakistan. The work consists of a laser cut steel cube lit from within. The lines of the lattice work on the cube are projected unto the painted walls, floor and ceiling of the gallery.
These symmetries get disrupted in the projection onto the gallery surfaces. Especially along the lines where the walls and floor meet. The geometry on the cube is precise but the shadows must bend to fit within the boundaries of the gallery.
Last week the Bridges organization held their annual conference in Jyväskylä, Finland. This international conference features lectures and workshops that highlight the connections between mathematics, music, art, architecture, education and culture. My favorite part of the five day event is the art exhibition. This year there was a wide range of styles, techniques and mediums on display. it is difficult to select only a few for this blog but I will try.
Sharol Nau repurposes unwanted hard cover books to create sculptures that contain parabolas. A parabola is a curve with reflective symmetry, in which each point on the curve is the same distance from a fixed focus point and a fixed line. The artist carefully measures and folds each page to the common focus point. The resulting portable sculpture preserves the exterior shape of the book but creates a new visual story for the interior.
Nithikul Nimkulrat hand-knots sculptures using paper string. Inspired by mathematical knot diagrams, the artist employs two colors of string to better indicate the positions of each stand within the knot structures.”Black & White Striped Knots”examines properties of knotted textiles.
Looking closely at the work, the circular patterns emerge. Overlapping circles cross to form four equal arcs. This creates a series of monotone circles with the arcs of adjacent circles forming a pattern with order-4 rotational symmetry. Nimkulrat’s intricate structure is a wonderful exploration of the mathematical possibilities in textile and fiber art.
I am always looking for exhibitions that reference the sociological implications of Mathematics in art. As I walked into this exhibition at the Guggenheim and read the introductory wall text I was immediately intrigued. Here is a portion of that text written by Sara Raza, (UBS MAP Curator, Middle East and North Africa):
But a Storm is blowing from Paradise: Contemporary Art of the Middle East and North Africa, which is presented on Tower Levels 4 and 5, focuses on geometry as a tool for the illumination of creative historical and philosophical inquiry. While rooted in the mathematical “thinking sciences” geometry is used here as a conduit for theories around logic and the origin of meaning.
The artists in this exhibition have referenced social issues through a geometric perspective.
This 2011 stainless steel and rubber installation by Nadia Kaabi-Linke titled “Flying Carpets” is based on the rectangular dimensions of carpets used by illegal street vendors to display and quickly carry away the wares they are selling to tourists in Venice Italy. Many of the vendors came from Africa and the Middle East and have traveled to Europe for a better, safer life. The title alludes to this exotic notion of travel on a Flying Carpet. Although the visual aesthetic is a complex geometric abstraction, it is merely the vehicle to express the plight of refugees.
Walking down Mulberry street I spotted this great sign in front of The Picture Room McNally Jackson Store.
The sign is the work of Benjamin Critton. It features a series of squares whose sides increase based on the Fibonacci Sequence. The first two squares are the same size. The third square has sides twice the side of the first. The fourth has sides three times as long as the first. This continues until the 7th square has sides 13 times longer than the first. They all are spiraled into a neat Fibonacci rectangle with sides in an 8:13 ratio.