"Half twist on a cliché," by Adriana Salerno. PhD + epsilon, 30 May 2011.
Having recently earned her PhD in 2008, Adriana Salerno gives us a look at the activities of a young faculty member at a liberal arts college (Bates College). With a few years of teaching and research under her belt, Dr. Salerno was invited this year to give a speech to graduating members of the scientific honors society Sigma Xi. Wanting to deliver a somewhat familiar message in a novel way, she chose to discuss connections between the sciences and humanities by introducing a mathematical concept. Rather than thinking of academic subjects as being linearly ordered, she asked members of the audience to place them along the moebius strip, linking back to one another even when they seem momentarily like they are on opposing sides.
Dr. Salerno's activities in everyday life follow the same "half-twist" philosophy as her speech as is evidenced in her other blog posts. Previous posts discuss matters such as how to interact (or avoid) students in social situations, how to network with other mathematicians, advice from others on how to write a blog, and how to give extra credit to point-preoccupied students.
"Monday Math: A Rant about Jargon," by Jason Rosenhouse. Evolutionblog, 23 May 2011.
Does mathematical language form a barrier that is nearly impenetrable to other scientists or even non-specialists with PhD's in mathematics? Jason Rosenhouse's Evolutionblog focuses sometimes solely on mathematics, sometimes solely on evolutionary biology, and often on their intersection. But in one of his more recent posts, Dr. Rosenhouse, a mathematician at James Madison University with experience reading papers outside of his field, expresses his opinion that mathematicians are overly fond of sacrificing clarity for brevity. Rosenhouse writes "In evolutionary biology I am definitely an amateur, but I find that I can often understand the introduction and discussion sections of a typical paper well enough to explain the gist to someone else. In math, it is usually impossible even to explain the problem to a non-mathematician."
A particular abstract from a recent issue of the Proceedings of the National Academy of Science (PNAS) is reproduced and discussed. Since PNAS is a publication read by a wide range of scientists, and since the article, entitled "Higher order dimension in low level topology," was featured on the cover of the issue, one might expect the abstract to be fairly approachable. Alas, it seems that this is not the case. To show he isn't the only one who feels that mathematicians should make more of an effort to communicate with those outside their specialties, Rosenhouse quotes mathematics educator Morris Kline and combinatorialist Gian-Carlo Rota. In the comments, there is also an illuminating quote from MIT professor Marvin Minsky. Some interesting points that are brought up in the 40 different comments as well as the article include the following. Perhaps, the jargon itself is not as much an impediment to understanding as it is intimidating. Perhaps the audience for the abstract should be more carefully considered. Or maybe, regardless of the context, there is simply no way to avoid terminology that only those in your specialty can understand. Whatever your opinion, this topic is certain to remain a source for vibrant discussion.
"How YouTube is popularising science," by James Grime. Notes & Theories Blog, Guardian, 17 May 2011.
New math videos on YouTube are making unlikely "stars" out of former hedge fund managers, math and science enthusiasts, and quirky professors. The classic math videos like Donald Duck in Mathemagic Land are easily found, but new math and science content is also being posted daily. For instance, James Grime, a British mathematician who works for the Millennium Mathematics Project, has created his own series of videos focused on mathematical games. In his blog article, Dr. Grimes encourages scientists to create their own content, and he points out the advantage of YouTube over television--your audience will find you. Those inclined towards art might seek out Vi Hart's doodles, while students looking for direct instruction might check out one of the thousands of videos made by Salman Khan and the Khan Academy.
Grimes also notes that even the Journal of Number Theory provides video abstracts of their papers, the most recent of which features Dr. Alain Connes discussing the paper entitled "Fun with $F_1$". Visualizations of topological and geometric transformations and ideas, including Dave Richeson's "Through one hole or two?"; James Tanton's "Curry's Paradox and the notion of area"; and "Moebius transformations revealed"; use the video medium to its fullest. Whether you are looking for videos to entertain and inform students or to feed your own mathematical interests, YouTube is a free resource that should not be overlooked.
--- Brie Finegold
"The Secret Sharer," by Jane Mayer. The New Yorker, 23 May 2011.
This article is about the upcoming trial of former National Security Agency (NSA) executive Thomas Drake, for being an enemy of the state, based on his handling of classified documents. Drake recounts that it was only after the 9/11 attacks that the agency surveillance systems had intercepted conversations in Afghanistan and Saudia Arabia that foretold the next day's attacks. In response, Drake, and a team led by crypto-mathematician Bill Binney, set out to pinpoint and solve the NSA's problem: data overload. An NSA intelligence analyst J. Kirk Wiebe describes Binney as "one of the best analysts in history." The program Binney had invented, called ThinThread, combines massive amounts and types of data about an individual (financial transactions, cell phone GPS tracking, phone and travel records, web searches, etc.), isolates the information useful to the agency, and provides a portrait. Such information would have been crucial before 9/11 if used as designed, but legal advisors were concerned about U.S. laws against the invasion of privacy. Binney, also interviewed in this article, claims that ThinThread could have detected the terrorist plot and protected the identity of Americans unrelated to the plot. Binney claims that after 9/11 a "new domestic-surveillance program employed components of ThinThread: a bastardized version, stripped of privacy controls" allowed for secret data-mining and surveillance ("domestic spying") on individuals in the U.S.--about which Drake and Binney had great objections. Binney resigned from the NSA October 31, 2001, convinced his ThinThread--a highly-sophisticated analytic, potentially-effective and legitimate tool--was replaced by "Trailblazer," a simpler (more expensive) and mis-used program that collected and retained warrantless data on U.S. citizens: "I couldn't be an accessory to subverting the Constitution." Drake informed a journalist at the Baltimore Sun about ThinThread, and the "expensive fiasco" of Trailblazer, and is about to stand trial for violating the Espionage Act.
There was wide media coverage of Mayer's article in May, and many mentions of crypto-mathematician Binney. Hear Jane Mayer interviewed on National Public Radio: "Thomas Drake Faces Espionage Charges," Talk of the Nation, 17 May 2011, and watch the segment "The Espionage Act: Why Tom Drake Was Indicted," on CBS 60 Minutes, 22 May 2011, in which Binney is referred to as a "legendary mathematician."
--- Annette Emerson
"Amazonian Children Understand 'Universal' Geometry Regardless of Schooling," by Elizabeth Lopatto. Bloomberg News, 23 May 2011.
"Amazonian children who never went to school understand the properties of points, lines and angles, proving the basic principles of geometry emerge regardless of education," begins this article, based on recent research ("Flexible intuitions of Euclidean geometry in an Amazonian indigene group," by Véronique Izard, Pierre Pica, Elizabeth S. Spelke, and Stanislas Dehaene. Proceedings of the National Academy of Sciences, 18 May 2011). U.S. adults and children, French children, and Mundurucu tribe children were asked questions about lines, planes, angles, triangles and spheres. They were given sketches of lines and asked questions such as "Can a line be drawn through two points?" and "Can two such lines be drawn?" The test results showed the same performance profile, suggesting that geometric-spatial intuition is innate across cultures, regardless of education. See also: "Geometric minds skip school," by Bruce Bower, Science News, 23 May 2011.
--- Annette Emerson
"A rectangle, some spheres and lots of triangles," by Burkard Polster and Marty Ross. The Age, 23 May 2011.
Math Masters columnists Polster and Ross examine the construction of Melbourne, Australia's striking new sports stadium, a "bubble dome consisting of pieces of what are approximately geodesic spheres," which is a network of small triangles. After providing some diagrams, the authors go on: "Architectural wizardry aside, your maths masters have recently discovered a beautiful new use for geodesic spheres. They can be used to create ideal, mathematically perfect cousins of messy rubber band balls." They conclude with a "Puzzle to ponder" about the image below: "How many corners, edges and sides do these geodesic spheres have?"
--- Annette Emerson
"Salman Khan: The Messiah of Math," by Bryan Urstadt. Bloomberg Businessweek, 19 May 2011.
Salman Khan (far left) records and posts extremely popular videos on YouTube and on his academy's website to help people learn math. He started in 2004 when he agreed to help his niece with measurement conversions. Now he has more than 2000 videos on subjects ranging from addition to Green's Theorem. This article gives a history of Khan's efforts and describes some of the well-known people who are enthusiastic about his approach. Bill Gates is quoted: "What Sal Khan has done is amazing... I see Sal Khan as a pioneer in an overall movement to use technology to let more and more people learn things. ... It's the start of a revolution." The Gates Foundation has donated US$1.5 million to the Khan Academy and Google has given $2 million. Contrasting his approach with that of other companies who offer educational resources, Khan says, "What you have in most education software is that they're catering to the decision-maker who makes the budget allocations. ... They could care less about the end user experience. We're very bottom up. The for-profit guys, as soon as they incorporate, they start lobbying for grants and selling into school boards and become essentially dependent on navigating this huge bureaucracy, and they completely lose sight of the end user. It's the opposite of what we're doing." Erin Green, a principal at a school whose 5th graders use the videos, admires the work of the Khan Academy and plans to expand the use of its videos in the school's classrooms. "Many of the students are working at a level of mathematics that I have never seen in an elementary school before, maybe not even in a junior high school before. ... They're engaged and they're excited, and that's the most exciting part." (Photo: The Khan Academy team courtesy of the Khan Academy.)
--- Mike Breen
"Guest commentary: The mathematics of golf," by Mary Armstrong. Las Cruces Sun-News, 19 May 2011.
Armstrong begins her article by applying some math to putting, comparing the margin of error for a three-foot putt to that for a twenty-footer, and then asks a mathematician's advice on playing golf. She talks to Doug Arnold of the University of Minnesota, who is a former SIAM president and author of "The Science of a Drive" (Notices of the AMS, April 2010). Although he's not a golfer, Arnold says that the mathematics in golf could occupy an entire class (or course) and explains that a golf swing is "a double pendulum with fulcrums at the shoulders and the hands." A golfer can achieve a fast swing when the lower pendulum, the club, whips from the upper pendulum, the arms. In golf, this phenomenon is known as a delayed hit.
--- Mike Breen
"Latest Issue on the Ballot: How to Hold a Vote," by Carl Bialik. Wall Street Journal, 14 May 2011.
In this article, Wall Street Journal "Numbers Guy" Carl Bialik discusses a voting method called instant runoff, which has "sparked a feud among political scientists and statisticians." In such an election, voters can rank as many candidates as they choose. Then, "in the first round, all ballots are sorted by their first choice. If one candidate has more than 50% of the votes at that stage, she or he wins the election. But if no candidate secures a majority, the last-place candidate is eliminated, and ballots ranking that candidate first are reassigned to their second preference, if one is indicated. Again, any candidate with 50% of the votes wins." This continues until one candidate gets a majority of the votes. Some supporters of this system like the fact that "voters can rank a third-party candidate first without fearing their second choice will be derailed." Detractors point to some of the "quirky outcomes" that can occur under such a system: for example, "a candidate who would be preferred by most voters if pitted against just one of the other candidates can lose."
--- Claudia Clark
"Steven Orszag, Pioneer in Fluid Dynamics Study, Dies at 68," by Bruce Weber, New York Times, 7 May 2011.
On May 7th The New York Times paid remembrance to mathematician Steven Orszag (left), who passed away earlier in the month. Orzag advanced fluid dynamics, the complicated field of how liquids and gases behave in motion. Orszag's contributions touch people's daily lives in a number of ways, from better understanding the turbulent flow from a plane flying through the air, to explaining the flow pattern in a cup of coffee being stirred. (Photo: Michael Marsland/Yale University.)
--- Baldur Hedinsson
"Spiral symmetry is turning heads," by Devin Powell. Science News, 7 May 2011, page 9.
Science News reports on new symmetry that could lead to new insights in material sciences. A mathematical operation that transforms a clockwise helix into a counterclockwise led scientists at Penn State to discover this new spiral symmetry. This creates many new ways atoms can be arranged into crystals and can help explain why materials have certain properties.
(Image: Gopalan Lab, Ryan Haislmaier, Penn State University. A lattice composed of columns of squares that represent repeating molecular structures, one rotated clockwise (colored blue) and another counterclockwise (colored orange) with respect to each other. Such new symmetries also arise in helical structures such as DNA, proteins, and sugar crystals. These new symmetries lead to the prediction of new properties that relate to the rotations. Applications range from the discovery of materials that allow electrical control of magnetism to new insights into well-known crystals such as quartz.)
--- Baldur Hedinsson
"Cells can chart efficient course from A to Z," by Rachel Ehrenberg. Science News, 7 May 2011, page 14.
The traveling salesman problem asks for the shortest possible path passing through each city on a route exactly once. Elaborate algorithms and serious computing power are required to solve it when the number of cities hits double digits, and the best algorithm available--linear programming--works well only for routes of less than 1000 cities. The number of computations necessary to solve the problem grows exponentially with the number of cities, and it is unknown whether a complete solution will ever be found. (Image: Map of China, charting the closest route connecting 71,009 Chinese cities, courtesy of William Cook, Georgia Institute of Technology, Traveling Salesman Problem website.)
But it turns out that the traveling white blood cell problem--which asks for a pretty short route to each of a small number of infectious particles--can be solved knowing almost nothing at all. Put another way, mathematical biologist Andy Reynolds' new research asks how dumb you can be and still solve the traveling salesman problem. Simulating white blood cells tracking down and attacking invaders, he finds that these mindless unicellular organisms can find the optimal route to five targets using a strategy called chemotaxis. Basically, the cells follow their noses--they sample local concentrations of chemical signals, and move up the gradients. At ten targets, the white blood cell route is only 12 percent longer than the optimal route. In her article, Rachel Ehrenberg notes that when tackling biological problems, the emphasis is on efficiency, rather than optimality. As researchers seek to understand how living organisms obtain near-optimal results with limited information and cognitive resources, they're stumbling upon simple and flexible strategies that can be used to find all kinds of things.
--- Ben Polletta
"IBM celebrates tech behind first U.S. manned space flight," by Sharon Gaudin. ComputerWorld, 6 May 2011.
On the 50-year anniversary of the first U.S. manned space flight, IBM celebrates the mathematicians and engineers that made the launch possible. In order to send someone to outer space, NASA and IBM joined forces to work out the technical challenges. A team of mathematicians developed the math needed to calculate the spacecraft's trajectory and engineers created advanced software to communicate mission-critical information between the astronauts and NASA flight controllers during the space flight. (Photo, courtesy of NASA: NASA's Mercury-Redstone 3 blast-off, May 5, 1961, putting the first American in space, astronaut Alan Shepard.)
--- Baldur Hedinsson
"The Mathematician as an Explorer," by Sherman K. Stein. Scientific American, 4 May 2011.
In this reprint of an article that first appeared in the May 1961 issue of this magazine, University of California, Davis professor emeritus Sherman Stein writes about a problem with which he had recently tangled that illustrated the nature of mathematics. It began with a Sanskrit 10--syllable memory word—invented by Indian drummers more than 1,000 years ago--in which each syllable has either a short or a long beat. The beats are arranged in such a way that "as you pronounce the word you sweep out all possible triplets of short and long beats." By replacing each short or long syllable with a 0 or 1, respectively, Stein turned the memory word into 0111010001. Here he noticed "a lovely thing": because the first two digits and the last two digits are the same, the line of 10 digits could be seen as a "circle of eight"--which he described as "the snake swallowing its Tail". At this point, he asked himself, "Is there a "word" for listing quadruplets of 0's and 1's once and only once? For quintuplets? For groups of any size? And if so, does the snake always swallow its tail?" For the remainder of the article, he describes how he explored these questions, making connections to existing problems, and discovering the work of other mathematicians who had solved this and related problems in a variety of ways.
--- Claudia Clark
"Will maths kill the rhino?" by Burkard Polster and Marty Ross. The Age, 2 May 2011.
Two Australian mathematicians argue that a new, quantitative method for classifying animals' comparative danger of extinction is actually a step backward for the field. The new system, called the SAFE index, assigns each species a number based on it's the number of living animals compared to 5000, the "minimal viable population," on a logarithmic scale. SAFE has been touted as a leap forward from the previous index-of-choice, the International Union for the Conservation of Nature's Red List, which assigned mammals to one of three categories. The British mathematicians argue that SAFE's assignment of specific number values based solely on population size is misleading, however, because the values have less comparative meaning when population size is very small. Furthermore, they note that the odds of being able to rescue a species from the brink depends on more than population size alone. (Image: courtesy of Burkard Polster and Marty Ross.)
--- Lisa DeKeukelaere
"Bit Lit," by Brian Hayes. American Scientist, May-June 2011, pages 190-1904.
Author Brian Hayes explores some of the fascinating questions that a database of words recently released by a team from Harvard and Google has the power to answer. The Harvard-Google database, which is publicly available, is comprised of strings of one to five words that have appeared at least 40 times within the more than 5 million books that Google has scanned and used software to "read" into digital text. As Hayes explains, searches on the database can offer insight how the popularity of words has changed over decades, which words were censored or suppressed during certain eras, and even how the duration of celebrity fame has declined?insights the database creators have called "culturomics." Hayes also takes a look at numbers in the database, comparing the frequency of the first digits of those numbers to Benford's law, which describes the distribution for the first digits of numbers in everyday life. Hayes notes that although the data still needs some cleaning up and the accuracy of the digital "reading" could be improved, the database is a powerful tool for studying our language and culture.
--- Lisa DeKeukelaere
"Why Bayes Rules," by Sharon Bertsch McGrayne. Scientific American, May 2011, page 28.
Bayes rules in Google's fleet of driverless cars. According to Sebastian Thrun, the director of Google's driverless car project, the cars use Bayes' Theorem to process the large amount of data they collect and update probability estimates based on the gathered facts. McGrayne write that the small fleet of cars "have driven themselves for thousands of miles on the streets of northern California without once striking a pedestrian, running a stoplight or having to ask directions." She also mentions other modern uses of Bayes' Theorem in this short article, such as fighting spam. McGrayne is the author of The Theory That Would Not Die, How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines & Emerged Triumphant from Two Centuries of Controversy. (Photo of Bayes' Theorem in blue neon at the offices of Autonomy in Cambridge, UK from Wikipedia.)
--- Mike Breen
"The Strangest Numbers in String Theory," by John C. Baez and John Huerta. Scientific American, May 2011, pages 60-65.
String theory, if it ever wakes up from its coma, may end up breathing new life into the octonions. So explain mathematical physicists John C. Baez and John Huerta in their informative romp through the history of real division algebras, supersymmetry, and string theory. A real division algebra is an algebra over the real numbers which supports division, and there are only four of them--the reals, the complex numbers, the quaternions, and the octonions--appearing in one, two, four, and eight dimensions, respectively. One nice thing about real division algebras is that multiplication has a geometric significance--it corresponds to a combination of dilation and rotation. When Gerolamo Cardano started using the square root of -1 to solve polynomials, he didn't realize the geometric significance of multiplying complex numbers. Sir William Rowan Hamilton was well aware of it, however, during the years that he attempted to replicate the algebraic structure of complex multiplication in three dimensions. While walking along the Royal Canal in Dublin, he realized that he could achieve this structure in four dimensions, with three square roots of -1. (Each imaginary coordinate corresponds to a distinct direction of rotation in three-space; a real coordinate supplies the dilation.) In his excitement, Hamilton carved the fundamental equations of his quaternions into Brougham bridge. His friend John Graves wondered whether it was possible "to create imaginaries arbitrarily." Graves found his answer in the non-associative octonions, but his creation failed to elicit any bridge-carving from Hamilton. Hamilton put off introducing the octonions to the Irish Royal Society for two years, and in that time Arthur Cayley rediscovered the octionions and beat Graves to publication. Neither Graves nor Cayley, however, discovered fruitful applications for their eight-dimensional numbers.
This is where supersymmetry enters the picture. It postulates a fundamental symmetry between matter and the forces of nature. Every matter particle should have a supersymmetric twin which carries a force, and vice-versa. Furthermore, the laws of physics should treat matter and force particles interchangeably. Unfortunately, three-dimensional quantum mechanics--the current working model--treats matter particles as spinors and force particles as vectors. These are two very different objects, and mediating interactions between them requires making up for their differences with a clunky imitation of multiplication. If only we lived in two, four, or eight space dimensions! In a division algebra, spinors and vectors coincide. Then again, maybe we do. String theory--which is a theory in n space dimensions, plus one string dimension and one time dimension--happens to work only in ten dimensions. And M-theory, a variant of string theory which adds three dimensions to space, works only in eleven dimensions. Whether or not the octonions have these very deep applications in their future, they are fun to read about.
--- Ben Polletta
"Quasirandom ramblings," by Brian Hayes. American Scientist, May-June 2011, pages 282-287.
Brian Hayes writes about random numbers in the May-June issue of American Scientist. Brian explains how computers are used to generate numbers that come close to being random called pseudorandom and quasirandom numbers. Both preserve important characteristics of random numbers and are of use in solving complex real-world problems. Currently there is a renewed interest in applying these methods in both computer graphics and the financial sector.
--- Baldur Hedinsson
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