## Math Digest |

- "Die Qual der Wahl mit dem Wahlcomputer,"
*Neue Zürcher Zeitung,*31 October 2004 - "Vodka + Movies = Pseudoscience,"
*The Chronicle of Higher Education*, 29 October 2004 - "How Strategists Design the Perfect Candidate,"
*Science*, 29 October 2004 - "What Makes an Equation Beautiful,"
*New York Times,*24 October 2004 - "Murphy at the Bat,"
*The New Yorker*, 20 October 2004 - "What do mathematicians do?,"
*The Chronicle of Higher Education*, 19 October 2004 - "Mad Math: Bending Time with
*Primer*Director,"*New York Times*, 19 October 2004 - "Manjul Bhargava: An Artist of Music and Math,"
*NPR's Morning Edition*, 18 October 2004 - "Science in the Fast Lane,"
*Nature*, 14 October 2004 - "Scientists win grant to study vibration,"
*Mercury News*, 11 October 2004 - "What is the Riemann Hypothesis and Why Should I Care?"
*IT Director,*6 October 2004 - "Rebuilding Rome,"
*New Scientist*, 2 October 2004 - "Oddballs: It's easier to pack spheres in some dimensions than in others,"
*Science News*, 2 October 2004 - "PopSci's Third Annual Brilliant 10,"
*Popular Science*, October 2004 - "Beautiful Minds, Beautiful Music,"
*Discover*, October 2004

**"Die Qual der Wahl mit dem Wahlcomputer," by George Szpiro. ***Neue Zürcher Zeitung,* 31 October 2004.

This article discusses how statistics can help detect the fraudulent use of election machines.

*--- Allyn Jackson*

** "Vodka + Movies = Pseudoscience," by Daniel Engber. ***The Chronicle of Higher Education*, 29 October 2004, page A6.

A purported formula for determining the scariest movie turned out to be a publicity stunt. A British television network, Sky Movies, recruited a former math major to watch 10 scary movies and quantify what makes them scary. Not much thought was put into the resulting formula which contained contradictory terms. The formula was reported by the BBC and *Chicago Sun-Times*, among others.

*--- Mike Breen*

** "How Strategists Design the Perfect Candidate," by Mark Buchanan. ***Science*, 29 October 2004, pages 799-800.

With the United States presidential election on the horizon, writer Mark Buchanan interviewed some political analysts about mathematical models they use to analyze how voters choose candidates. An often-used model depicts voters "as abstract points in a 'policy space'"; a politician can optimize his or her standing with a set of *x* voters by choosing a point equidistant from all *x*. (On the other hand, a politician may have a better chance of executing his or her preferred policies---if elected---by moving away from this central location.) A second model, presented by University of California, San Diego, physicist David Meyer, reflects voters inconsistent preferences, implying that a politician's best strategy is "roughly speaking, to be as inconsistent as the voters," according to Buchanan. Given that closer races resulting from candidates' use of the above models---and that unpopular third-party candidates can heavily influence an election---better voting systems were also discussed. These included eliminating the Electoral College in favor of popular voting, an option that seems unlikely to Eric Maskin of the Institute for Advanced Study in Princeton, New Jersey, since it would necessitate a constitutional amendment. What is clear is that there are no simple answers. As political scientist Larry Bartels of Princeton University says, "the surprising reality is that we still understand relatively little about how presidential campaigns affect the vote."

*--- Claudia Clark*

** "What Makes an Equation Beautiful," by Kenneth Chang. ***New York Times,* 24 October 2004, Week in Review, page 12.

In a column in *Physics World* magazine, philosopher and historian Robert P. Crease asked readers which equations they considered to be the greatest. He got 120 responses proposing 50 different equations. This article discusses Crease's experiment and also provides readers with a nice context to appreciate the power of mathematical equations. The top vote-getters were Maxwell's equations for electromagnetism and Euler's equation, *e ^{i π } + 1 = 0*. A list of 18 other winners is given in a sidebar. Most of the equations relate to physics, but the Pythagorean theorem and the Riemann zeta function made it onto the list.

*--- Allyn Jackson*

** "Murphy at the Bat," by Ben McGrath. ***The New Yorker*, 20 October 2004.

After the first two games of the American League Championship Series the magazine's Talk of the Town columnist speculates on whether Murphy's Law (basically stated as anything that can go wrong will) will apply to the Boston Red Sox in their playoff against the New York Yankees. The author cites a British study that concluded that the Murphy's Law corollary, "that bad things happen at the most inopportune times" is statistically significant. McGrath introduces a mathematical formula: "Let U, C, I, S and F be integers between 1 and 9, reflecting, respectively, comparative levels of Urgency, Complexity, Importance, Skill, and Frequency in a given set of circumstances. Let A, which stands for Aggravation, equal 7.0. (Don't ask.)... Let's give the Sox an 8 for Skill, and 9 for both Urgency and Importance. Complexity... a 5... Frequency ...9. So now we've got: [((9 + 5 + 9) x (10 - 8)) / 20] x 0.7 x 1 / (1 - sin (9 / 10)). The final Murphy's score, in other words, is 7.4." The author concludes, "No wonder Johnny Damon, the Red Sox' ordinarily dependable lead-off batter, lost his swing just as Curt Schilling, the team's most durable pitcher, went down with a bum ankle." Those who believed this mathematically-supported tongue-in-cheek then had to eat crow.

*--- Annette Emerson*

** "What do mathematicians do?," Magazines and Journals section of ***The Chronicle of Higher Education*, October 19, 2004.

The online edition of |

** "Mad Math: Bending Time with Primer Director," by Polly Shulman. **

*Primer* is a low-budget movie about two engineers who build a low-budget time machine and travel back in time. Shane Carruth, the director and co-star, was a math major in college whose favorite area was non-linear dynamics. The article makes some connection between non-linear dynamics and the film and includes this quote from Carruth: "I feel like math and writing are the same thing... You're putting together a lot of complex things to satisfy different requirements. It's got to be aesthetically pleasing; it's got to have subtext; it's got to convey information. In school, when I got into upper-level math, there would be times when I would wake up from a dream and have---not an answer, exactly, but a direction to pursue. My writing has always been like that. I wake up from dreams knowing which direction to go in. So I find it hard to believe that there's a part of your brain for math and a separate part for art."

*--- Mike Breen*

** "Manjul Bhargava: An Artist of Music and Math," by Richard Harris. **** NPR's Morning Edition, 18 October 2004. **

Manjul Bhargava is a 28-year old professor of mathematics at Princeton University. This report on Bhargava is part of a *Morning Edition* series on the intersection of art and science. Part of the intersection is Bhargava's mastery of the *tabla*, an Indian drum (the site has a link to Bhargava's playing). Another part is the art of doing mathematics. Bhargava compares doing mathematics to writing and painting. He also explains that "most of mathematics is not calculations; that's one of the misconceptions about mathematics. It's really more about what's behind those formulas, what explains those formulas, what's the theory behind those formulas." Much of this piece was recorded as Bhargava and Harris talked at the Institute for Advanced Study. Also included in the program are reactions from people at a talk by Bhargava in New York City.

*--- Mike Breen*

** "Science in the Fast Lane," by Karl Ziemelis and Charles Wenz. ***Nature*, 14 October 2004.

University-trained mathematician Christine Lear now works at the Switzerland-based Sauber-Petronas Formula 1 team, "with prime responsibility for developing key aerodynamics components on its Formula 1 car." The article notes that interdisciplinary teams---with many members from academia---design, test and refine the car designs; study wind tunnels, airflow, and materials; and enjoy plentiful resources and rapid results. The article reports that the National Science Foundation has awarded nearly US$1 million to a team of five mathematicians to investigate the question, "How does an object's shape influence the frequencies and geometry of its vibrations?" The answer may help to develop better MRIs and to study earthquakes, for instance. "Whether the 'body' you're studying is a human organ or planet---or even a minuscule computer chip at a manufacturing plant---the goal is the same." As Tataru explains to the journalist, "You send some waves into the body, they scatter, and you measure the output to understand what is happening inside." The three-year grant was awarded to Christopher Sogge and Steven Zelditch (Johns Hopkins Univesity), Hart Smith (University of Washington), and Daniel Tataru and Maciej Zworski ( University of California Berkeley). |

** "What is the Riemann Hypothesis and Why Should I Care?" by Robin Bloor. ***IT Director,* 6 October 2004.

This article talks about the Riemann Hypothesis and how its solution would provide new insights into the nature of the prime numbers. The author puts emphasis on the use of prime numbers in encryption schemes that are used to protect, for example, electronic banking transactions. If the Riemann Hypothesis is solved, the author argues, such encryption schemes could be at greater risk of being cracked. The occasion for the article is the claim by mathematician Louis de Branges that he has solved the Riemann Hypothesis. His work, available on his web site, has not yet been checked and verified by other experts in the field.

*--- Allyn Jackson*

** "Rebuilding Rome," by Erica Klarreich. ***New Scientist*, 2 October 2004, pages 37-40.

The Severan Marble Plan, created in the second 2nd century AD, was a huge map of ancient Rome carved onto marble slabs. When fragments were discovered in the 16th century, many were fitted together to reconstruct the map. But the fragments that remained were like a puzzle without a picture to follow: How to fit them together? "By the late 1990s, placing a single piece was viewed as a major breakthrough," Klarreich writes. A Stanford team has now brought the power of computing and algorithms to bear on this problem. The team made high resolution scans "of every nook and cranny" of the fragments and created a digital file describing each one. A Stanford computer science graduate student, David Koller, created algorithms that test various ways of fitting the pieces together. As a result of these efforts, 12 new pieces have been placed. Koller is working on new versions of the algorithms that will let scholars experiment with different ways of fitting the pieces together. The image shows Severan Marble Plan fragment number 010g (marble, 3 feet long, 150 pounds). The image is courtesy of Marc Levoy, Digital Forma Urbis Romae Project. |

** "Oddballs: It's easier to pack spheres in some dimensions than in others," by Erica Klarreich. ***Science News*, 2 October 2004.

Consider the following two questions: What's the maximum number of spheres that can be packed into n-dimensional space? How many spheres can touch or "kiss" another sphere in n-dimensional space? In this article, Erica Klarreich describes the work done since the early 1970s to answer both of these questions: the sphere-packing problem and the kissing number query. She begins by recalling Johannes Kepler's early 17th century conjecture, that in three dimensions the maximum number of spheres that can touch another sphere is 12---as well as Thomas Hale's newsworthy announcement in 1998 that he had proven it.

What about higher dimensions? Philippe Delsarte's work in coding theory in the early 1920s led to kissing-number and sphere-packing proofs in other dimensions. In the late 1970s Andrew Odlyzko and Neil Sloane---and, independently, Vladimir Levenstein---announced proofs that the kissing numbers for 8- and 24-dimensional space were 240 and 196,569 respectively. Nearly 20 years later, Oleg Musin surprised the mathematical world with the announcement that he had proven that 24 is the kissing number in four dimensions, using a modification of Delsarte's work.

Also applying the work of Delsarte, Henry Cohn and Noam Elkies announced in 2003 their finding of upper limits on the sphere packing arrangements in 8 and 24 dimensions. Klarreich then notes that Elkies and graduate student Abhinav Kumar have since used computer analysis to show, "just shy of [proving]," that these optimal sphere packings are two special lattices: the E8 lattice and the Leech lattice. These packings are also very tight, not allowing the "wiggle room" found in any packing of 12 spheres around a 13th in our more familiar three dimensions. As Cohn notes, "It seems that dimensions 8 and 24 are much better behaved than dimension 3."

*--- Claudia Clark*

**"PopSci's Third Annual Brilliant 10," by various authors, Popular Science, October 2004.**

First on the list of this year's new generation of brilliant scientific innovators is mathematician Maria Chudnovsky of Princeton University. Her area of research is graph theory, and author Ir Minkel summarizes how "in 2002 Chudnovsky helped prove the perfect-graph conjecture, which states that only two kinds of flaws can make a graph imperfect." Chudnovsky is described as a mathematician who greatly enjoys abstract mathematics. She is quoted as saying, "It's like solving a crossword puzzle all day long." Others profiled are in various fields and use mathematics in their work: James Walker's "complex equations describe the havoc wreaked by catastrophic collisions;" Robin Canup "spends her days tweaking computer code" and "has begun developing new models to simulate the formation of other planet-moon systems;" and Henrik Jensen has devised "complex computer algorithms" to develop sophisticated computer graphics used in movies. Adam Voiland's sidebar "Brilliant 10 Update: What's New With Past Winners?" reports that UC Berkeley computer scientist David Wagner's critique of an Internet-based voting system for U.S. citizens abroad led to the program's cancellation, and that M.I.T. mathematician Erik Demaine won the MacArthur Foundation "genius" fellowship.

*--- Annette Emerson*

**"Beautiful Minds, Beautiful Music," by Josie Glausiusz. Discover, October 2004**

Glausiusz notes that several recent winners of the Siemens Westinghouse high school math and science competition are also accomplished musicians (62% of the finalists played musical instruments). The competition's organizers invited four of the medal winners to perform at Carnegie Hall on June 17, 2004. One of the recitalists had won a medal for "the design of a fractal-based computer program depicting an animated, Earth-like, three-dimensional globe." Harpist Heather Wood studies math and music at St. Olaf College, and pianist Elliott Prechter is an engineering student at MIT. The author notes that perhaps some day brain imaging will help answer whether or not there is a connection between musical and mathematical processing.

*--- Annette Emerson*

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