"Origami: A Blend of Sculptures and Mathematics," by Marina Koren. Collage of Arts and Sciences Blog, Smithsonian, 23 January 2013.
Complete with a short video of computational geometer and artist Eric Demaine, this post contains a link to Demaine's 2009 paper (coauthored by self-styled mathemusician Vi Hart) on the "hidden" creases that allow paper to "self-fold" after it has been folded along concentric squares or circles to create surfaces such as hyperbolic paraboloid. Some of these surfaces area currently being exhibited at the Smithsonian's Renwick Gallery.
The connection between mathematics and origami traces back to early 18th century Japan when a brain-teaser challenged the reader to create a particular shape by folding paper and making only one cut. Mathematical papers have been written about origami, but these concentric folds seem to have inspired papers recently in materials science and physics. Avid mathematically inclined folders can even check out a few computer programs meant for creating new origamis.
"Kenyon's squarespirals," by Danny Calegari. Geometry and the Imagination, 13 January 2013.
A fascinating look into how an artistic image can have roots in higher mathematics, this post relates tilings of a rectangle by squares to graph theory and Kirchoff's laws for current flowing through an electric circuit. A sentence of two later, homology and the Torus enter the picture, and the fact that the holonomy is a dilation and not a translation leads to an animation of squares whose simultaneous rotation creates an overall spiral. While the connections all seem pretty logical, the explanation of the animation seems to spiral outwards from elementary to advanced in a way that mimics the animation itself. Lastly, Calegari provides a .eps file for the reader that generates these square spirals.
--- Brie Finegold
"Making Math Pop," by Daniel N. Rockmore. The Chronicle of Higher Education, 18 January 2013, pages B10-11.
"As important as it is to instruct well, it is also important to inspire," says Daniel Rockmore in his review of Steven Strogatz's new book, The Joy of X. Perhaps even more than a clear understanding of subject matter, passionate investment in the larger project of science and mathematics is crucial for survival and success in research. Rockmore himself was inspired to take up mathematics by E.T. Bell's Men of Mathematics, a "spicy biographical tour" of modern mathematics and its creators. Aside from having an anachronistically gendered title, Bell's book is responsible for engendering feelings of inadequacy in countless mathematical professionals, with the fantastic exaggeration that Galois developed his eponymous theory in a single night. These days, there are no shortage of popular books about mathematics, but Rockmore wonders, "where are the Carl Sagans for the 21st century?" Who are the dashing heroes of modern science, and who is dramatizing their stories beyond recognition? For better or worse, it is not Steve Strogatz. If "Men of Mathematics" is golden-age Hollywood, The Joy of X, an outgrowth of Strogatz's 2010 New York Times column "The Elements of Math," seems to be reality television, or memoir, if we're going to mix media metaphors. In six chapters--Numbers, Relationships, Shapes, Change, Data, and Frontiers--Strogatz pursues concepts both simple and complex--from counting to calculus, the Riemann Hypothesis to the Pythagorean Theorem, group theory to geometry and topology. Weaving in his own daily life, his family, references to The Sopranos and avuncular puns and jokes, Strogatz ranges over mathematics pure and applied, in what seems a largely successful effort to make his subject relevant to a broad audience. In some cases--as with the Pythagorean Theorem and the area of a circle--this is accomplished by illuminating potentially confusing, commonly encountered mathematical concepts. In other passages--as in his discussion of "whispering galleries"--this is accomplished with pure gee-whiz factor. But where the book stands out, according to Rockmore, is in bringing across Strogatz's personality, and as a result, some insight into the mathematical life. "The reader is left with the feeling that this is a guy who is thinking about math all the time," writes Rockmore. "The mathematical outlook, odd as it may sometimes be, doesn't disappear after the office lights are turned off."
--- Ben Polletta
"What goes wrong when talks break down," by Rachel Ehrenberg. Science News, 12 January 2013, page 10.
Science has a news article on how a combination of social psychology and nonlinear mathematics can explain how negotiations often fail. University of Washington physicist Michael Gabbay developed a novel approach of simulating how groups make decisions. The approach captures the unpredictable nature of group decision and might be used to predict the behavior of governments, juries and corporate boards. Older methods for assessing how negotiations unfold assume a relatively predictable relationship between the group members' opinions and their sway over each other. "These methods can work well for small groups," says policy analyst Hilton Root of George Mason University in Arlington, Va. "But," he said, "there's a lot you can't do with them." Unlike previous research this new method helps reveal how forces may unexpectedly conspire to sabotage negotiations.
--- Baldur Hedinsson
"Mathematician stepping on thin ice," by Deborah Sullivan Brennan. U-T San Diego, 11 January 2013.
For most living mathematicians, fame and anonymity are nigh indistinguishable. Terry Tao may be the subject of gossip and blushing admiration among the 80,000 of us who work the U.S.'s second-best job, but I hardly think Professor Tao spends much time signing autographs. Things seem to be different for University of Utah mathematician Ken Golden, who gave one of two public talks at last month's Joint Mathematics Meetings (JMM). He is the subject of this profile in San Diego's former Union-Tribune, and did, in fact, manage a queue of autograph-seekers at the conference. Golden's claim to fame is a hands-on approach to climate science which has taken him to the Arctic eight times, and to Antarctica seven times--first as a senior in college, following the Drake Passage, a route Ernest Shackleton pioneered in a rescue boat after his ship was crushed by ice in 1914. "I have very vivid memories of crossing the Drake Passage,"Golden is quoted, "one of the stormiest seas in the world, and taking 50-degree rolls." (Sounds awful--if bread isn't hot, it isn't worth eating.) But Golden's closest call came on his second trip, when a fire destroyed his ship's engine, and he spent a nervous five days on the ice before a backup engine was cobbled together.
Clearly a glutton for punishment, Golden has returned again and again--spending two weeks last fall stranded on an iced-in vessel. These adventures are more than autograph-fodder. "It's one thing to sit in your office and prove theorems about a complicated system," says Golden. "It's another thing to go down there yourself. It informs my mathematics." During one Arctic storm, Golden noticed the ice around him turning to slush, and realized in a flash that it was reaching a percolation threshold that allowed sea water to flow through it. This epiphany led to his "rule of fives," which describes how ice's permeability depends on temperature, salinity, and saturation. Golden also studies the role of "melt pools" in determining the reflectivity of ice pack, and in speeding the melting of this ice. As Ian Eisenman of the Scripps Institute points out, "The topic of sea ice ... is of great interest today due to climate change." So not only is Golden a dashing adventurer; he's also do-gooder. No wonder he signs so many JMM programs.
Golden's talk was among several events to launch Mathematics of Planet Earth 2013. (Photo: Ken Golden giving the Porter Lecture, "Mathematics and the Melting Polar Ice Caps," at the Joint Mathematics Meetings in San Diego, CA. Photo by Sandy Huffaker.)
--- Ben Polletta
"The Always Playful Genius of Erik Demaine," by Daniel Engber. Popular Science, 8 January 2013, page 44.
Erik Demaine is an MIT computer scientist, artist, and mathematician well-known for his work in origami. This profile of Demaine focuses on his unusual working style--including his close collaboration with his father, Martin--and uses it as a jumping-off point for a discussion of creativity in science. An extraordinarily productive scientist, Demaine has published over 300 peer-reviewed papers at the tender young age of 31. His work might roughly be called applied combinatorics--Demaine himself refers to it as "recreational algorithms"--but it largely defies categorization, ranging broadly across mathematics, materials science, and the softer sciences and humanities. In his work on the box pleat--a basic origami pattern used to build up complex shapes--Demaine showed that the fold could be used to create arbitrary shapes, then collaborated to build a boat that tranforms into a plane. Other projects include conceptualizing a Star Trek-style replicator based on DNA and RNA, helping to decipher an Incan language, and studying the mathematics of glass-blowing. At the heart of Demaine's working life is his relationship with his father--who home-schooled him for four years on a cross-country trip, then followed him to college (at 12), to graduate school, and to MIT. The two live together, dress alike, and get all up in each other's projects daily. "We know each other so well that it makes for a really effective combination," Erik is quoted. "He's always trying to reinject some playfulness into my serious work. It lets us do things that neither of us could do." That playfulness is manifest in the games that crowd Demaine's office, and in the way he teaches his graduate course on "problems in geometric folding": a list of problems on the blackboard and a set of props on the desk, followed by problem-solving sessions that often lead to published papers. "I think this is a cool way of working, and more people should work this way," says Demaine--and the evidence seems to back him up.
Besides numerous examples from science history, the article quotes a pair of child psychologists. Kathy Hirsh-Pasek of Temple University tested the connection between play and creativity by asking children to play with a paper clip, aluminum foil, and a pipe cleaner. The children were either allowed to play freely, told to think about possible uses of the objects, or told to build specific tools with the items. After the play session, they were asked to use the materials to get a (presumably very small) bear across a river. The most creative solutions (presumably as judged by the tiny bear) came from the second group of children, who engaged in so-called "guided play". Hirsh-Pasek says the same idea applies to scientists, who are most productive when they are free to play around with a known set of problems. Alison Gopnik of U.C. Berkeley, whose work has illuminated how children run their own experiments to learn about the world, suggests that the link between science and play is even deeper. "It's not that children are little scientists," she says, "it's that scientists are big children. Scientists actually are the few people who as adults get to have this protected time when they can just explore, play, figure out what the world is like." Yet, as budget cuts and calls for accountability lead to the micromanagement of scientists and educators, this time for play and exploration--so necessary to creative problem-solving--is increasingly threatened. Perhaps we'd all do well to heed the example of Erik and Martin Demaine--whose current plans include imprisoning a pigeon in a cage of bread to watch it peck its way to freedom--by protecting the time and resources required to inject a little play into our work.
--- Ben Polletta
"Pleasanton student vying to win U.S. math prize," by Rebecca F. Johnson. Contra Costa Times, 3 January 2013.
National Who Wants to Be a Mathematician contestants Eugene Chen and Allan Garry were written about in their local media before and after this year's game. On the day of the game, Allan and the Joint Mathematics Meetings got front-page coverage in the San Diego Union-Tribune and he was interviewed by the San Diego CBS affiliate. In the article he talked about how as a toddler he taught himself to add and subtract "using a collection of toy boats" (easier to manipulate than say). Eugene, who was in the same semifinal as Allan, missed getting into the finals by one question. In the article before the game, Eugene said, "I have a lot of fun writing problems because it's a lot different from solving problems, which I normally do during contests." Eugene won $1000 and Anton's Calculus with Early Transcendentals. Allan won $500 and Mathematics Everywhere. In each case, the cash amount won by the contestant was matched by the AMS in a gift to the math department of the student's school. Photos by Sandy Huffaker. Left: Eugene, Allan, David Li, Shyam Narayanan, and Alexandr Wang; Right: Allan with classmates from Vista High School.
--- Mike Breen
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