Brie Finegold summarizes blogs on Math Craft Monday and on math and art in Paris:
"Math Craft Monday: Community Submissions (plus How to Make a Sliceform Hyperbolic Paraboloid)," by Cory Poole. MathCraft, 28 November 2011.
Paper, scissors, card stock, and an X-Acto knife can provide hours of thought-provoking entertainment for readers of this blog founded by math and physics teacher Cory Poole. Mathematically inspired projects are submitted by the public on the "cork board" and discussed every Monday. This week one "community member" cut slits in card stock polygons that fit together like puzzle pieces to create polyhedra. Another member provided video directions for making a beautiful origami modular star designed by Meenakshi Mukerji. To keep with the holiday spirit, math foods have been a topic recently, including the Koch Snowflake pecan pie and fractal fondant designs for cupcake decoration.
Also each Friday an "inspirational" post features the work of a specific artist. A recent post featured the origami tessellations of Erik Gjerde whose page includes directions on how to fold his models. While the mathematics behind the math-inspired arts and crafts on this site are not often discussed in detail, the site provides not just a great resource, but a good place for people to showcase their original designs. Those seeking more math and art connections should check out the Bridges Conference, which will be in Baltimore in 2012. Also linked to by Math Craft is George Hart's Math Mondays blog, which is associated with the soon-to-open Museum of Mathematics in New York.
"Mathematics as the Raw Material for Art," by Kat Austen. New Scientist CultureLab, 14 November 2011.
Mathematics--A Beautiful Elsewhere is a new art exhibition presented by Fondation Cartier in Paris in conjunction with the Institut des Hautes Études Scientifiques, the European Space Agency and in partnership with UNESCO. While many of us have seen mathematically inspired art, this exhibit was a collaboration between world class artists and mathematicians. Sir Michael Atiyah, Alain Connes, and Misha Gromov were some of the mathematicians overseeing the accuracy of the exhibits which included film, sculpture, collage, and print media by artists such as David Lynch and Patti Smith.
The sculpture featured in the blog is Hiroshi Sugimoto's Surface of Revolution with Constant Negative Curvature which is also called a pseudosphere. This object is analogous to the sphere, which has constant positive curvature. While the idea of the surface being infinite is well-captured by blogger Austen, she seems a little confused when she talks about the sculpture's "rapidly decreasing curvature." According to the curator, the goal of the exhibit is to provide "an answer to the abstraction of mathematics." Even if the public does not come away with a completely accurate understanding, they may gain a sense of awe and some canonical and beautiful images associated with mathematics. See more coverage of the exhibit.
--- Brie Finegold
"How Algorithms Shape Our World, a TEDTalk by Kevin Slavin," Huffington Post, 30 November 2011.
Genes, memes--is your Roomba being run by the next replicator? In this TEDTalk--one of the Huffington Post's 18 best from 2011--game designer Kevin Slavin talks about how algorithms are becoming more than just tools for solving problems. As they proliferate in finance and in other online and customer service applications, they are in fact becoming forces of cultural and even geographical change. Slavin starts off his discussion of algorithms in finance. There, programs with nicknames like "The Knife" and "The Boston Shuffler", designed to hide sales of millions of shares of stock by breaking them up into many smaller sales, compete with programs designed to suss them out, and process transactions at microsecond timescales. Their activities constitute 70% of the trades made in the U.S. stock market. These algorithms, acting without human oversight, created the May 6, 2010 Flash Crash, in which the equity market dropped more than 600 points in 5 minutes, representing a disappearance of 9% of the market's volume. On amazon.com, algorithms acting without "adult supervision" priced an out-of-print genetics textbook at 1.7 million dollars--and then a few hours later bumped the price up to 23.7 million--even though "nobody was buying or selling anything". Slavin suggests the reach of such algorithms is extending: so-called pragmatic chaos recommendation algorithms used by Netflix determine 60% of the movies rented, and have been turned on their head to produce programs which are now used to vet movie scripts; elevators no longer have buttons, because algorithms determine their routes from one floor to another; and algorithms are even reshaping our physical landscape, as buildings and mountains are being hollowed to get computers closer to high-speed fiber optic cables, so trading programs can converse more rapidly. Even if he doesn't completely convince, Slavin discusses a number of interesting developments in culture and computer science. In a worthwhile online afterword, he muses about genetic algorithms, which take the intelligence out of design, and points the reader to a mesmerizing website that animates their slow and aimless magic.
--- Ben Polletta
"The Search For Analysts To Make Sense Of 'Big Data'," by Yuki Noguchi. National Public Radio, 30 November 2011.
In this digital age businesses are better able to capture vast amounts of data, but the challenge is to make sense of it in ways that can help predict patterns and behavior. This NPR segment is part two of a two-part series on data mining (the first was "Following Digital Breadcrumbs To 'Big Data' Gold," by Yuki Noguchi), and this part focuses on how companies are seeking mathematicians who have a "finesse with computers" and creativity. Noguchi says DJ Patil (Greylock Partners) likens data to clay: "shapeless until molded by a gifted mathematician. A good mathematician can write algorithms that can churn through billions or trillions of data points and show where patterns emerge." And companies are following and recruiting talented math students in a way sports coaches have sought athletes for decades. One company set up an office in Ann Arbor, Michigan, so it could recruit from the University of Michigan's math department. One student on another company's watch list is Dylan Field, a junior at Brown University, who is happy that his interest in mathematics and statistics is in demand. "You can understand something that is much bigger than yourself, and I think that is the most interesting property of creating a big data application." For now he is working at a big data startup called Flipboard, and after he graduates he plans to start up his own big data company.
--- Annette Emerson
"Setting the record straight about Jewish mathematicians in Nazi Germany," by Ofer Aderet. Haaretz.com, 25 November 2011.
Aderet writes about an exhibit "Transcending Tradition: Jewish Mathematicians in German-Speaking Academic Culture," which is appearing at different locations in Israel. Between 1914 and 1933 roughly one-third of the math professors in Germany were Jewish (whereas about 1% of the German population was Jewish), but when the Nazis came to power those professors either fled, were sent to concentration camps, or commmitted suicide. The exhibit, which is funded in part by Germany, was created to reveal what happened to these mathematicians and to show how non-Jewish mathematicians cooperated with the Nazis. Among the mathematicians mentioned in the article are Emmy Noether, Felix Hausdorff, and Georg Pick. Aderet begins the article writing about a violin once owned by Pick that was played at an opening of the exhibit, and closes with a suicide note that Hausdorff wrote in 1942:
By the time you receive these lines, we three [Hausdorff, his wife and his sister-in-law] will have solved the problem in another way ... in the way which you have continually attempted to dissuade us ... Forgive us, that we still cause you trouble beyond death; I am convinced that you will do what you are able to do (and which perhaps is not very much ). Forgive us also our desertion! We wish you and all our friends will experience better times. |
Six months later, the lawyer to whom Hausdorff sent the note was himself sent to a concentration camp.
--- Mike Breen
"Professors of the Year are Awarded for honing their teaching skills," by Brenda Medina. Chronicle of Higher Education, 25 November 2011, page A10.
Kathryn C. Wetzel, departmental chair at Amarillo College, is one of four professors to be chosen as 2011 Professors of the Year by the Carnegie Foundation for the Advancement of Teaching and the Council for Advancement and Support of Education. In this article, the four professors share how they've improved their teaching over the years. Wetzel says she became a better teacher by listening to students talk to one another: "I'd listen to one student explain something to another student, and a light would turn on,... I said: That is the key phrase I was looking for."
--- Mike Breen
"Herbert Hauptman (1917-2011)," by Carmelo Giacovazzo. Nature, 17 November 2011, page 300.
Nature pays tribute to mathematician Herbert Hauptman in its November issue. Hauptman pioneered the mathematical tools that allow scientists to decode the structure of molecules. By firing X-rays at a molecule and recording the patterns that are scattered by crystals inside the molecule Hauptman came up with a method that determines the structure of the molecule. For his discovery Hauptman shared the Nobel Chemistry Prize with his collaborator, chemist Jerome Karle. (Photograph: Herbert Hauptman by Gloria J Del Bel, Hauptman-Woodward Institute.)
--- Baldur Hedinsson
"So Crazy It Just Might Work," an interview with Paul Hoffman by Ira Glass. This American Life (Public Radio International), 11 November 2011.
Author Paul Hoffman and host Ira Glass lead into a segment on outside-the-box ideas by using the example of a mathematician who disproved a 250-year-old theory using simple arithmetic and hours of persistence. Hoffman describes mathematician Frank Nelson Cole's destruction of French monk Marin Mersenne's theory that 2^{67} - 1--a 21-digit number (147,573,952,589,676,412,927)--is prime, and therefore is divisible only by 1 and itself. Cole stunningly illustrated that he had found two other factors (193,707,721 and 761,838,257,287) for the number by performing silent, painstaking long multiplication before a room full of mathematicians at an AMS conference in 1903. The hour-long demonstration by Cole that the product of the two factors was the purported prime drew a round of applause and resulted from three years of Sundays spent meticulously checking number after number for divisibility into the proposed prime. Hoffman neatly sums up Cole's result as "what science is about--real people banging their heads against walls and years of false starts." Read more about Cole (who was secretary of the AMS from 1896 to 1920) on the MacTutor site and more about the Cole Prize.
--- Lisa DeKeukelaere
"When There Are Too Many Ants, Try Basketball," News of the Week, Science, 11 November 2011, page 744.
Ant colonies have too many individuals for us to comprehend all their interactions, so biologist Jennifer Fewell and mathematician Dieter Armbruster, both at Arizona State University, scaled down the problem--to basketball teams and players. This short article tells of how they are studying National Basketball Association team dynamics (who passed to whom and how often) and that they have found a successful strategy, distributed leadership, which is similar to a property of ant behavior. Arizona State has posted a news release about the research.
--- Mike Breen
"New Discoveries About Knots Boost Mathematicians' Case for Studying Them," by Paul Basken. The Chronicle of Higher Education, 10 November 2011.
This story was inspired by an article, "The Combinatorial Revolution in Knot Theory," by Sam Nelson, which appeared in the December 2011 issue of the Notices of the AMS. In the article, Nelson discusses how combinatorial codes can be used to represent knots and how the study of these codes gives rise to objects that are not knots but that behave like knots in some ways. The Chronicle story describes these "virtual knots" and presents the views of a few mathematicians---such as Nelson, Erica Flapan, and Colin Adams---about real-world applications of knot theory.
--- Allyn Jackson
"Only a Mathematician Could Love the World's Ugliest Music," by Andrew Liszewski. Gizmodo.com, 6 November 2011.
"The world's ugliest music" is not a description that most composers would want used to describe their work. However, one person--mathematician Scott Rickard--is proud to claim this distinction for his composition, The Perfect Ping. After all, Rickard reasons, repetition and pattern are key aspects of beautiful music, and his composition contains no repetition: the relationship between each pair of notes is distinct.
To construct the piece, Rickard generated an 88 x 88 Costas array, named after John Costas, a sonar engineer who wanted to design a pattern-free sonar ping for the U.S. Navy in the 1960s. At the time, Costas enlisted the assistance of discrete mathematician Solomon Golomb, who used prime number theory to solve the problem of how to generate pattern-free structures. Rickard's array is generated by repeatedly multiplying by the number 3 (3, 3 x 3 = 9, 3 x 9 = 27, etc.) and subtracting multiples of 89 once the product is greater than 88. Rickard then mapped this array to the 88 keys on the piano.
--- Claudia Clark
"Moneyball U," by Alan Schwarz. New York Times Education Life, 6 November 2011.
Not a sports fan myself, I was surprised to find the ranks of America's math departments swollen with sporting types. Perhaps I shouldn't have bee --lovers of numbers and odds are drawn to both fields. Given this, perhaps what's really surprising is that sports--seemingly beloved by all--is not more often used to bring outsiders into mathematics--which, unfortunately, has quite a different reputation. According to this New York Times article, which takes the recent movie Moneyball as an invitation to investigate the use of sports in statistics and probability classes, "numbers have earned a seat at the cool kids' table," so this may all be changing. Sports examples have long been used to bring an added level of interest to probability and statistics. As the article points out, not everyone is equally enthusiastic or knowledgeable about sports, but for many, sporting metaphors can be used to bring concreteness and excitement to otherwise dry and abstract concepts--and given the importance of statistical reasoning in modern life, teachers need every tool they can lay their hands on. Since the first course on sports statistics was taught by Gabriel Costa at Seton Hall University in 1988, courses specifically designed to bring the two subjects together have popped up at Stanford, Ohio State University, and West Point, and in 2003 Jim Albert of Ohio's Bowling Green State authored the textbook Teaching Statistics Using Baseball. The new Common Core mathematics standards, which include statistics, are bringing sports and statistics to the high-school level, says Christine Franklin of the University of Georgia, co-author of the new textbook Statistical Reasoning in Sports. According to Franklin, "Teachers are going to have to teach statistics, and many do not have the background. It motivates the teachers too." If these developments continue, we may witness the birth of a new field, says Costa: "There's sports law, sports medicine, why not sports mathematics?"
--- Ben Polletta
"It's more than just mathematics," by Harskikaa Udasi. The Hindu, 5 November 2011.
Roger Spottiswoode, famed director of action movies such as Tomorrow Never Dies and The 6th Day, starring none other than Arnold Schwarzenegger, is knee-deep in a film project about Indian mathematician Srinivasa Ramanujan. Ramanujan was born in British India, grew up poor and despite almost no formal mathematical training and a tragically short life, made incredible contributions to mathematical analysis, number theory and infinite series. Spottiswoode has been working on the story of the math genius for years. The script has been completed and filming is set to begin next year in England and Chennai.
--- Baldur Hedinsson
"This Professor Can 'Spit a 16' and Then Find Its Square Root," by Dan Berrett. The Chronicle of Higher Education, 4 November 2011, page A18.
If sports and statistics, after a moment's reflection, make reasonable bedfellows (cf my previous Digest), hip-hop and math are a stranger pair. While many hip-hop artists give lip service to the queen of the sciences--in his song "Mathematics", Mos Def proclaims "You wanna know how to rhyme, you better learn how to add"--and teachers have tried to bring rap to the classroom--LaMar Queen of Los Angeles Academy was prompted to rap by his students, who noted his resemblance to Kanye West. But experts in both disciplines are rare. Existence is proven, though--Peter Plourde (at left), a full-time lecturer in mathematics with Northeastern's Foundation Year program, has also been performing and recording as the M.C. Lyrical for twenty years. Foundation Year is designed to help Boston public school students--a majority of whom enter college, but who struggle to stay in school until graduation--to survive and thrive during their first year of college. The program emphasizes community by grouping its students together, and provides them with both academic and personal advising. This helps them develop the time management skills essential for all college students, as well as ways of coping with their "complicated lives outside class", as program director Molly Dugan puts it. Plourde, like the eight other dedicated Foundation Year instructors, was chosen for his mastery over his material, his ability to teach it in different ways, and his proficiency at connecting with students. His resume includes a bachelor's degree in business, a master's in mathematics from U. Mass. Lowell, and experience teaching courses in mathematics, statistics, entertainment, and event planning at a number of Boston-area colleges and high schools. Plourde's credentials as an M.C. are similarly impressive--he's opened for KRS-One and Rakim, rubbed elbows with hip-hop luminaries like Damon Dash and Sean Carter (Jay-Z), and the single "Focuz" off Lyrical's 2005 album reached the top ten on the national college hip-hop radio charts--but they had little to do with Dugan's decision to hire him, and were kept under wraps for his first year teaching for Foundation Year. After performing for his students during homecoming, Plourde has begun to bring his music career into the classroom, using it to provide inspiration, motivation, and real-life lessons: in a recent exercise, he asked students to calculate the vanishingly small profits rappers make off even platinum- or gold-selling records. Read more about Plourde and Lyrical. Image: Courtesy of Northeastern University.
--- Ben Polletta
"Jumping Rope by the Numbers," by John Bohannon. Science Now, 2 November 2011;
"Solved: The Aerodynamics of Super-Fast Jump Ropes," by Dave Mosher. Wired Science, 2 November 2011.
Jumping rope seems pretty simple, kids all over the world do it. However it is not until now that scientists have properly described how the swinging rope bends in the wind. Applied mathematician Jeffrey Aristoff and mechanical engineer Howard Stone, both of Princeton University, were at the gym waiting for a pickup game of basketball when the idea of studying jump rope struck them. With the help of a high-speed stroboscopic camera they figured out how the rope bends and using nonlinear differential equations they made a mathematical model that describes the phenomenon. Image courtesy Jeffrey Aristoff, Numerica Corp.
--- Baldur Hedinsson
"Test scores show modest gains in mathematics," by Sally Holland. CNN, 1 November 2011.
Results from the 2011 National Assessment of Educational Progress were released in November. Math scores for fourth and eighth graders were the highest ever, but did not represent a significant gain over results from the most recent report in 2009. Secretary of Education Arne Duncan said that scores, which were one point higher (on a 500-point scale) than in 2009, continued "a path of modest progress," but "achievement is not accelerating fast enough for our nation's children to compete in the knowledge economy of the 21st Century."
--- Mike Breen
"An Adventure in the Nth Dimension," by Brian Hayes. American Scientist, November-December 2011, pages 442-446.
As a first-year graduate student, I distinctly remember being impressed by the nifty derivation of the unit n-ball's volume in Folland's Real Analysis. But I never took the time to explore the actual volumes attached to that formula. Perhaps that's what makes me a mathematician, and not a computer scientist. In his American Scientist column Computing Science, Brian Hayes take a long, deep look into the abyss that swallows up the unit ball in higher dimensions. The volume of the unit n-ball not only grows more slowly than the volume of the smallest n-cube containing it--becoming vanishingly small relative to the cube for large n--but in fact stops growing at all at dimension 5. As n increases to infinity, the unit n-ball vanishes in absolute terms, as its volume decreases to zero. Hayes' several attempts to explain (and also to understand) these bizarre facts yield nice insights. He points out that we might expect the unit n-ball to grow more slowly than the n-cube containing it, since what the cube has over the ball are its corners, of which there are 2^n. And while the ball fits tightly inside the box--"we are not talking about a pea rattling around loose inside a refrigerator carton", he says--touching each of its faces, the number of those faces is only 2n. Most enlighteningly, Hayes points out that every diameter of the ball has length 2, while only the 2n shortest diameters of the cube are this long. The 2^{n-1} longest diameters of the cube - the ones passing through opposite corners - are much longer, at length 2\sqrt{n}. Hayes is a self-identified layman, but he manages to cover a lot of ground in this column, discussing fractional dimension and fractals, the gamma function, and the relative growths of exponential and factorial functions. He even gives a nice explanation, involving onions, of the integral for the volume of the n-ball that was so impressive to both Hayes and I, if for different reasons.
--- Ben Polletta
"This Man Could Rule the World," by Gregory Mone. Popular Science, November 2011, pages 62-66.
In this profile, Mone describes the groundbreaking work of complex network scientist Albert-László Barabási, distinguished professor and director of the Center for Complex Network Research at Northeastern University in Boston, Massachusetts. Mone begins in the late 1990s with Barabási's work mapping different large and complex systems. In each case, his discovery that "highly-linked nodes were the defining characteristics" of the network--"not just an anomaly but an organizing principle"--led to an update of the Erdős-Rényi model, which previously "held that complex networks were random, and if they grew large enough each node would have roughly the same number of links as any other node over time." In 2006, Barabási was able to turn his attention to predicting the behavior of complex systems when he was given access to the anonymized records of more than 6 million mobile-phone subscribers. Upon analyzing the data, Barabási and colleague Choaming Song "found that they could predict a person's location, within a square mile, with up to 93 percent accuracy."
Most recently, Barabási has been studying the control of complex systems. "Like prediction," writes Mone, "control required evaluating an object as a system with nodes of varying importance." For instance, a car is made up of several thousand components, but the driver can control the entire system using essentially three nodes: the steering wheel, brake pedal, and gas pedal. Barabási wanted to know if he could find these control nodes in any network. After testing 37 different networks, he and his team "found that denser, more interconnected networks tended to have fewer control nodes per capita." Image: Arc map showing worldwide Internet traffic, by Stephen G. Eick, courtesy of Albert-László Barabási.
--- Claudia Clark
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