Pictured above is a plush paraboloid, z = x^2 + y^2. Click the link above if you want a math plushie of your very own! Reblog if this project interests you.
What if mathematical theories could be expressed using artworks instead of plus signs and pi symbols? Dorothea Rockburne has devoted four decades to the attempt, and the results are on view at the Parrish Art Museum in Southampton, N.Y., through Aug. 14. Take disjunction, the logical argument that if A is true and B is true, their combination must also be true. Math textbooks usually illustrate this idea with a pair of slightly overlapping circles. In the 1970s, Ms. Rockburne began exploring this idea by soaking long sheets of paper in crude oil, a substance that permeated the paper without breaking it down into pulp. Instead, both materials could co-exist. In one of her best-known works, 1971’s “Scalar,” she arranged a group of these oily, rust-colored sheets on a wall so that they slightly overlapped. Other series involved folding or layering linen or painted sheets into kaleidoscopes. In 1972, conceptual artist Mel Bochner praised her in an art magazine for doing “some of the most advanced thinking in art,” and museums like the Museum of Modern Art in New York and the Museum of Fine Arts in Houston have since collected her work. Earlier this week, Ms. Rockburne, age 78, sitting in her airy SoHo studio, said her artistic focus wasn’t always so cerebral. Growing up in Montreal, she drew nudes like every other academically trained student in the city’s School of Art and Design. When she arrived at North Carolina’s Black Mountain College in 1950, she said her classmates were mostly copying the messy abstractions of Willem de Kooning— except for a pair of “handsome” friends in her photography class, Robert Rauschenberg and Cy Twombly. Like them, she had wearied of Abstract Expressionism, and they encouraged her to toy with other styles. But as years passed and their work won fame, she found herself working as a New York waitress, a single mother who spent her evenings in an apartment with too little room left to paint. Then she remembered Max Dehn, a math professor at Black Mountain whom she had admired in part because he seemed to revel in the rigor of hard thinking. She started reading math texts like Henri Poincaré’s “Science and Method” and hit upon an epiphany: “I wanted to see the math I was reading about.” She eventually showed a few pieces to Mr. Rauschenberg, who put her work in a benefit group show at Leo Castelli’s gallery in 1966. Within a few years, her career began to take off. Some of the newest works in the Parrish show, “Dorothea Rockburne: In My Mind’s Eye,” depict blue and gold swirls, a nod to the theories that she’s been reading lately about what happens to star dust after neutron stars explode. “I never wanted to be a mathematician,” she said, “but I love the magic of it.”By KELLY CROW
Usually, when art and science, or science and religion, intersect, they are seen as being in opposition. Art is free-flowing where science is rigorous; religion is faith-based where science needs evidence. But sometimes, the three actually intersect in ways that, at least to my eye, actually heighten the beauty of all of them. One such example is medieval Muslim ornamentation.
Imagine you have a fixed set of tile shapes, but you can have as many of each as you want. Can you tile them in such a way that you fill an infinite plane, with no gaps? If you can, you’ve got yourself a tiling. If you can shift the pattern around in some way, say, one unit to the left, so that the end result is the same as you started with, you’ve got a periodic tiling. But if any shift at all in the pattern creates a unique pattern, the tiling is said to be non-periodic. And if you’ve got a set of tile shapes that can only form non-periodic tilings, no matter what pattern you make with them, the set of tiles is said to be aperiodic. Until the mid-20th century, mathematicians doubted that there could be aperiodic tilings. But in the 1970s, Roger Penrose discovered a set of very simple tiles that—if you apply a couple of restrictions to how they can be arranged (restrictions that can be made superfluous if you give the tiles some bumps)—are aperiodic, i.e., no matter how you arrange these tiles, and no matter how large a plane you tile, you will never find a periodic pattern. They’re called Penrose tiles.
This was new knowledge. No one knew about this until Western mathematics started exploring this in the mid-20th century. Or so we thought.
Because of Islam’s restrictions on religious iconography, such as depicting living beings, Islamic artists have found ways to make the most of abstract patterns and shapes. You see it in Arabic calligraphy, and you see it in the magnificent shapes on the walls of mosques and religious schools. In 2007, physicists Peter Lu and Paul Steinhardt discovered that the patterns on the walls of medieval Islamic buildings very closely resemble Penrose tilings. The crucial invention of girih tiles, basic shapes used to build more complex patterns, allowed Islamic architects to decorate their walls with non-periodic tilings. And in the Darb-e Imam shrine in Ishafan, Iran, built around 1450 (above), the tiles almost perfectly form a pattern that can be generalized as a Penrose tiling. If you deconstruct the pattern on the Darb-e Imam shrine into Penrose tiles, you’ll find that only 11 out of 3700 are mismatched, and the mismatch is so small that it’s “removable with a local rearrangement of a few tiles without affecting the rest of the pattern”. (more)
One Math Museum, Many Variables
For everyone who finds mathematics incomprehensible, boring, pointless, or all of the above, Glen Whitney wants to prove you wrong.
He believes that tens of thousands of visitors will flock to his Museum of Mathematics, to open in Manhattan next year, and leave invigorated about geometry, numbers and many more mathematical notions. “We want to expose the breadth and the beauty of mathematics,” said Mr. Whitney, a former math professor who parlayed his quantitative skills into a job at a Long Island hedge fund. He quit in late 2008 with connections to deep pockets and a quest to make math fun and cool. Two years ago, he and his team built a carnival-like traveling exhibit called the Math Midway, a proof-of-concept for the coming museum. It includes a tricycle with square wheels of different sizes that visitors can ride smoothly around a circular path ridged like a flower’s petals. An accompanying sign explains why: The undulating circular surface rises and falls exactly to offset the odd shape of the wheels, so that the tricycle’s axles — and the rider — remain at the same height as they move. Mr. Whitney hopes that colorful, interactive props will help his cause. “If we just pluck people in the street — ‘What adjectives would you use to describe math?’ — very few of them would say, ‘beautiful,’ ” Mr. Whitney said. His vision has enticed large contributions. The museum, which will be at 11 East 26th Street, has raised $22 million, including $2 million from Google and a lot from individual donors (yes, there’s some hedge fund money in there). It remains to be seen whether a math museum can succeed. There are currently zero math museums in the United States, and the one small one that did exist, on Long Island, closed in 2006. There are plenty of science museums that cover math topics, but Mr. Whitney’s museum, nicknamed MoMath, will be devoid of dinosaurs and planetarium shows and will instead focus on the abstract. “They’re a dedicated bunch of idealists,” Sylvain E. Cappell, a New York University mathematician on the museum advisory council, said of Mr. Whitney and his staff. Without a museum yet, Mr. Whitney periodically gives walking tours to point out the mathematical wonders that can be seen around Manhattan. At 42, he exudes a boyish, geeky enthusiasm as he talks about how the branches of ginkgo trees intersect at right angles more often than those of other trees, or points out that the bolts that open and close New York fire hydrants are pentagonal, rather than the usual six-sided variety. Three years ago, he was working with algorithms at Renaissance Technologies, a private investment firm that uses mathematical models to figure out where to put money. But after a decade there, he was looking for a new career path with a “more direct socially redeeming value,” he said. Then, he heard that the math museum on Long Island, Goudreau, had closed. He started thinking that there should be a math museum and that he should be the one to build it. “I really felt that I found my calling,” Mr. Whitney said. “I don’t mean to be grandiose, but it was something that felt like it really fit with my lifetime of experiences and abilities and likes and so on.” Under his vision, MoMath will be one small way to bolster mathematics education in the United States. For years, American students have performed in the middle range on international comparisons of math skills, and an oft-heard worry is that the United States might lose its technological prowess. While Mr. Whitney cites these dynamics as a reason for his quest, he is also a realist. Yes, the museum could serve as an intellectual catalyst and teaching resource, but it alone is not going to raise math scores. “I’m certainly not holding my breath for that,” he said. Rather, he said, the museum’s mission is to shape cultural attitudes and dispel the bad rap that most people give math. “It’s the only field you can go to a cocktail party and talk to people with pride about how lousy you are,” Mr. Whitney said. He hopes the museum can inspire at least a few to plunge into math more deeply. He imagines breaking down a piece of cutting-edge math research into pieces that enthusiastic visitors could help solve. “We want to be a place where that spark can ignite,” he said. For Mr. Whitney, the spark came after a broken collarbone. When he was 14, he attended a math camp at Ohio State University — he saw it as a chance to get away from home for the summer, he said, not to learn math, a tedious subject that he found easy. During a soccer game, he collided with someone bigger, leaving him injured. With nothing else to do, he looked over the problem sets he had been ignoring. The problems were different from the ones from school, spanning different branches of math and highlighting the connections among them. “I fell in love with mathematics that summer, and I’ve had a lifetime love affair with it ever since,” he said. After majoring in math at Harvard and earning a Ph.D. at the University of California, Los Angeles, he taught at the University of Michigan before joining Renaissance Technologies. He commutes to a modest office in Midtown scattered with math puzzles and sculptures, where he and a team of about 20 brainstorm about exhibits for the museum, which right now is 19,000 empty square feet. One idea is a large cube with square holes punched through each side, a structure known as a Menger sponge. When a visitor pulls the cube apart diagonally, the holes turn into six-sided stars. “It’s like a ‘gosh, that’s really cool’ kind of emotion people have,” said George Hart, the museum’s chief of content. “It’s a very nice example of how mathematics can give you these big surprises.” The opening is more than a year away, but Mr. Whitney is already dreaming bigger: a larger museum, a palpable cultural impact. “There are all sorts of myths about mathematics out there,” he said — math is hard, math is boring, math is for boys, math doesn’t matter in real life. “All these are cultural myths that we want to blow apart.”
Sketch for ‘Symmetry Break’, 2009
Steel chain and mixed media
17” x 20” x 8” (43 cm x 51 cm x 20 cm)
The spontaneous breaking of symmetry is a phenomenon that is ubiquitous in nature. In physics those situations are described by an energy landscape, called a potential that goes from having only one minimum (the lowest energy configuration to which the system is driven towards) to having more than one minimum. The appearance of a second minimum forces the system to ‘make a decision’ which minimum it will occupy. Seen from the outside, the system suddenly flips into a new state. In this sculptural sketch, I used pieces of chain that go from a physically possible hanging configuration to configurations that seem to violate the laws of physics more and more. The initial hanging curve gets penetrated from below with a narrower curve such that the chain successively develops two minima. This evolution suggests something miraculous, similar to the surprising and counter-intuitive phenomenon of symmetry breaking.
This is awesome!!
