# Math Digest

## Summaries of Media Coverage of Math

Edited by Allyn Jackson, AMS
Contributors:
Mike Breen (AMS), Claudia Clark (freelance science writer), Lisa DeKeukelaere (2004 AMS Media Fellow), Annette Emerson (AMS), Brie Finegold (University of California, Santa Barbara), Adriana Salerno (University of Texas, Austin)

### July 2009

"Mathematical Biology Education: Beyond Calculus," by Raina Robreva and Reinhard Laubenbacher. Science, 31 July 2009, page 542.

Undergraduate and graduate-level course work in mathematical biology has tended to emphasize differential and difference equations as the key tools for modeling biological systems; the authors present several reasons, however, why more attention to algebraic methods would be beneficial. Algebraic methods, which use discrete variables, are less complex and easier for biology students to understand than continuous-variable differential equations. The authors demonstrate this using a specific example involving gene regulation in which a simple wire diagram of Boolean variables from an algebraic method reveals the same key points as a more complex differential equation. For mathematics students, greater use of biology-based examples could also help make algebra courses more interesting. According to the authors, the lack of emphasis on algebraic methods results in part from a lack of appropriate educational materials, which they are working to develop to address this problem.

--- Lisa DeKeukelaere

Articles about Rejecta Mathematica: "Huddled Maths," Economist, 29 July 2009.
"Turning Rejection Into Success?" Random Samples, Science, 31 July 2009, page 521.
"Hear the One About the Rejected Mathematician?" on Tweed (blog).
Chronicle of Higher Education
, 12 August 2009.

 With the symbol "not in" as its logo, Rejecta Mathematica is an online home for mathematical work which has been previously rejected by peer-reviewed journals, but which may still be interesting to the mathematical community. Reasons for rejection run the gamut and include: "negative" results, known results, or difficult to understand exposition. Even top scientists receive rejections for papers that are later published in highly respected journals. Having one of their own submissions rejected, the young editors of this newly minted journal contend that even flawed papers can be quite valuable. Seeing as the articles are available for free, declaring "Caveat emptor" ("buyer beware") under the journal title may be the founders way of taking a jab at the myriad of online journals that require payment to view their supposedly superior articles. But just because it is free does not mean any disgruntled mathematician can publish. Submissions are chosen based on content and an "open letter" giving the story of the authors attempts to publish and the reasons given for rejection. --- Brie Finegold

"Nancy Margried: Batik + Math = Innovation," by Matheos Viktor Messakh.The Jakarta Post, 27 July 2009.

 Margried has teamed up with mathematician Yun Hariyadi and architect Muhammad Lukman to create batik that is based on fractals. The article describes how the three people came together to form their company and the efforts they went through, first to create software to generate the batik, then to present their ideas at a conference in Milan in 2007. It was while preparing for the conference that they came up with their name, the Pixel People Project. Although their work is mostly with garments, they've also applied it to shoes and furniture. (Image: Pattern of kawung from Central Java, re-designed with fractals using JBatik software, courtesy of the Pixel People Project.) --- Mike Breen

"A Good Sign," Angela Saini, Science, 24 July 2009, page 391.

 Image courtesy of Tauba Auerbach and Byron Cook. The old adage "Necessity is the mother of invention" could be used to describe this story of a collaboration between a professor of computer science and an artist. In 2008, while working on the halting problem, professor and Microsoft senior researcher Byron Cook "made a breakthrough that could help to prove whether more real-life computer programs would come to an end or hang forever." However, his attempts to explain his work quickly and clearly to product developers and others were stymied by existing mathematical notation. At this point, he enlisted the help of artist and former sign writer Tauba Auerbach, whose work has "played with" language and technology. After an unsuccessful first draft, "Cook and Auerbach learned that new symbols should build on old ones, so they make intuitive sense at first glance." A glance at the nine final symbols shows just that: for example, one of the symbols consists of an equal sign within a capital "L", while four of the symbols consist of the familiar inequality signs, each within a capital "L." Cook noted, "I knew that Tauba had been successful after I used her final symbols in a lecture and people hardly noticed. Before I knew it, my students were using them, too." Cook hopes to have the symbols introduced into LaTeX, then “see what else needs simplification. We might invent some more.” --- Claudia Clark

"Scientific Observations." Science News, 18 July 2009, page 4.

Science News runs noteworty quotes in its "Science Notebook," near the front of each issue. This one is from Nobel Prize winner Dudley Herschbach, speaking at the International Science and Engineering Fair: "It turned out to be a great advantage to have overindulged in mathematics at an early age. [Arnold] Sommerfeld, a theoretical physicist, said math is like childhood diseases: the earlier you have them, the better."

--- Mike Breen

"Mathematician discovers 'potentially disastrous' soccer rule flaw," by Sarah Petrescu. National Post, 11 July 2009.

 Aaron Williams (University of Victoria, Canada) "has discovered what he says is a 'potentially disastrous' fault in international soccer rules for breaking three-way ties." Williams, who has a master's degree in mathematics and who is defending his Ph.D. in computer science this fall, posed the problem to an undergraduate logic class. "In a particular round-robin situation, three teams could argue they finished in the top two spots based on the rules as they're written." The problem arises when there are disagreements over the order in which tiebreaking criteria are applied. Depending on the scenario presented, the students, the Fédération Internationale de Football Association (FIFA), and the Canadian Soccer Association came up with different responses. Williams anticipates that this could cause problems when rulings are made at the 2010 World Cup tournament in South Africa, and urges FIFA to eliminate any ambiguities in the rules beforehand. Read Williams' explanation of the ambiguous logic of the 2010 FIFA World Cup tiebreaker rules. --- Annette Emerson

"Statistical Tests Suggestive of Fraud in Iran's Election," by Julie Rehmeyer. Science News, 10 July 2009.

 Dario Pignatelli / Reuters Iranian protestors may now have mathematical evidence to support their claims that fraud was behind Ahmadinejad’s victory in the June election. A University of Michigan at Ann Arbor statistician, Walter Mebane, posted an analysis of the data from the election in late June, which suggests that ballot boxes may have indeed been stuffed with extra votes for Ahmadinejad. The main tool of his analysis was Benford’s Law, which states that in many kinds of data, the first digit of the numbers will be 1 about 30% of the time, instead of the more intuitive expectation that it will be one time out of ten. In his analysis of other election data, Mebane discovered that vote counts tend to follow Benford’s Law in the second digit. When studying the poll data from Iran, Mebane found that the numbers didn’t conform to Benford’s Law well at all. One important find was that in towns where there were few invalid votes (a common mistake by ballot stuffers) the discrepancies were even larger. Mebane still cautions that the odd statistics may still have an innocent explanation, but that they are suspicious enough to warrant more scrutiny. --- Adriana Salerno

"Enigma codebreakers of Bletchley to be honoured," by Michael Evans. Times Online, 10 July 2009.
"It took me 60 years to tell my husband I was a wartime spy," by Elizabeth Mistry. Sunday Herald, 16 July 2009.
"How Poles cracked Nazi Enigma secret," by Laurence Peter. BBC News, 20 July 2009.

At long last, the surviving code-breakers from Bletchley Park--the U.K.'s main decryption site during World War II, in Buckinghamshire, England--will be honored. The individuals played a crucial role in cracking Germany's Enigma code and allowing the Allies to read Germany's military communications. Jean Valentine and Sheila Mackenzie are among the first civilians to receive the commemorative badge. During the war, Valentine also traveled to Sri Lanka (then called Ceylon), where "My new job was helping to break the Japanese meteorological cypher, which was very important to the Allies." (Sunday Herald) The same article reports: "Cryptographer and translator Sheila Mackenzie also kept her wartime work secret--she didn't speak of her code-breaking work with her mathematician husband, Oliver Lawn, until a few years ago, even though the pair met when they were both members of the Scottish Reels Club at Bletchley Park." The announcement that the code-breakers would be honored was also covered in the Guardian, Daily Mail, and other media in the U.K. Wikipedia has an overview of cryptanalysis.

Also this month, BBC News reports that Bletchley Park held its annual Polish Day, "a celebration of the Polish achievements that laid the foundations for British success in cracking German codes." Marian Rejewski, a Polish mathematician "had guessed correctly that the wiring connections between the [Enigma] machine's keyboard and encoding mechanism were simply in alphabetical order. Of course, there were numerous other problems to solve, but Rejewski had made a major breakthrough, by devising equations to match permutations in the machine's settings." Rejewski and two other Polish mathematicians, Henryk Zygalski and Jerzy Rozycki, were recruited to work at Bletchley Park. The BBC notes that the contributions of Polish cipher experts went unacknowledged for decades, but that the recent ceremonies at Bletchley have celebrated many whose discoveries are thought to have shortened World War II.

--- Annette Emerson

"Not luck of the draw, just some good math," by Dave Brooks. The Nashua Telegraph, 8 July 2009.
"Math teacher played the odds, won a million," by Dave Brooks. The Cabinet (Milford, NH), 9 July 2009.

If Milford (NH) High School math teacher John Kasparek is asked by his students where they can use the probability and statistics they learn in his class, he’ll have at least one answer for them. Last month, as David Brooks reports, Kasparek’s purchase of 50 New Hampshire “Millionaire’s Club” lottery tickets—costing $10 per ticket—led to his winning the million-dollar prize. But while Kasparek took a gamble on winning, his decision to purchase the tickets was carefully considered. When Kasparek recently learned that, of the 2.1 million tickets on sale for the last two years, 97 percent had been sold, and only one of the two winning tickets had been cashed in, he calculated the expected payout per ticket. It was positive. “I said what the heck. … You can run calculations all day long, but if you’re not willing to act on them, what’s the point of doing the calculations?” Kasparek will take the one-time$650,000 payout, getting about a half-million dollars after taxes.

--- Claudia Clark

"Marie Curie voted top female boffin," by Lester Haines, The Register, 2 July 2009.

It's been a year since L'Oreal put out the call for people to vote on their favorite woman scientist. The For Women in Science website posted profiles of over 40 women scientists throughout history, and readers were invited to vote for their favorite and nominate others. (The Daily Telegraph and New Scientist publicized the project.) Physicist Marie Curie rated number one. Down the list--garnering some votes--were mathematicians Hypatia of Alexandria, Ada, Countess of Lovelace, and Sophie Germain.

--- Annette Emerson

"Geek Chic: A Matter of Fractals," by Sandra Ballentine. The New York Times' The Moment Blog, 2 July 2009.

Jewelry designer Marc Newson has created a necklace inspired by fractals. The "Julia" necklace, introduced at a "couture-week" party in Paris, was "inspired by Newson's obsession with fractals--geometric shapes that can be subdivided into smaller versions of themselves, specifically the Julia Sets of fractals discovered by Gaston Julia in the early 1900s." The 2000-stone necklace took workers at the Boucheron company 1500 hours to make. The article quotes Newson: "Fractals are fascinating, complex and rich, and gemstones really lend themselves to exploiting their beauty." He also notes that due to the complexity of the piece, it is likely to be one of the most expensive pieces of jewelry the company has made.

--- Annette Emerson

"The Best Bits," by Brian Hayes. American Scientist, July-August 2009, pages 276-280.

Most photographs we see and songs we listen to are files that have been compressed. This article about compressive sensing (also called compressed or condensed sensing or sampling) first asks: Why collect all the data (with a camera or original audio recorder) if it's going to be discarded anyway? Hayes writes that compressive sensing works by finding a domain (e.g. frequency) where the signal is sparse and then recording the few significant components in that domain. He traces the history of compressive sensing, beginning with a 2006 paper (pdf) by Emmanuel Candès, Justin Romberg, and Terence Tao, and gives some of the mathematics behind capturing the signal and decompressing it. The motivation for compressive sensing was medical resonance imaging (MRI). By allowing data to be gathered faster than with a traditional MRI, patients won't have to remain immobile for so long.

--- Mike Breen

"Of Beauty, Sex and Power," by Andrew Gelman and David Weakliem. American Scientist, July-August 2009, pages 310-316.

Are certain attributes like beauty and power correlated with reproductive success? Scientific papers that address such hot topics are sure to attract media attention, and a 2007 paper claiming that beautiful people are 8% more likely to have daughters than sons did just that. The paper, written by evolutionary psychologist Satoshi Kanazawa, was published in a respected journal and its results were reported by The New York Times, Psychology Today, and Discover. But Andrew Gelman and David Weakliem (a statistician and sociologist, respectively) claim that such a paper should have sent up a red flag since existing literature pointed to an effect of no more that +/- 1 percent. The data Kanazawa displayed were correct: The percentage of people in his sample who were ranked 5 out of 5 for beauty and had daughters was 8% higher than that of the rest of the sample who had daughters. But he chose only one of several possible methods of analysis (comparing the top fifth to the rest as opposed to looking for a best fit line, for example). And he did not properly account for the small size (3,000 people) of his sample in judging the statistical significance of his results. Despite these flaws, Kanazawa co-authored a book entitled Why Beautiful People Have More Daughters, and he is a columnist for Psychology Today.

Gelman and Weakliem see the flaws in Kanazawa's paper as indicative of a wider problem. As more studies produce results that are "suggestive but not statistically significant," a challenge arises as to how to analyze these results constructively while preserving the credibility of statistical analysis in the public eye. The authors suggest that current methods such as Classical and Bayesian Inference are not sufficient for analyzing such small effects. They also point out that the structure of a study can sometimes lead to its becoming a "machine for producing exaggerated claims." While most people realize that large samples yield statistically significant results, they do not often realize that small samples yield results that must be considered in the context of the sampling distribution. In other words, one must determine the probability that the effect seen in a particular sample was a fluke by considering the theoretical distribution of all samples of the same size. Tools for considering this theoretical distribution exist but are sometimes overlooked, creating errors in magnitude (too small of a sample size) and sign (effect being judged as going in the wrong direction). In other words, it is possible (and also unproven) that beautiful people actually have more boys.

--- Brie Finegold