# Math Digest

## Summaries of Articles about Math in the Popular Press

Edited by Allyn Jackson, AMS
Contributors:
Mike Breen (AMS), Claudia Clark (freelance science writer), Lisa DeKeukelaere (Brown University), Annette Emerson (AMS)

### November 2005

"The Marvels of PostScript": Review of Mathematical Illustrations: A Manual of Geometry and PostScript by Bill Casselman. Reviewed by George K. Francis. American Scientist, November-December 2005, pages 568-570.

According to Francis, the subject of Casselman's book is "the geometry that best illustrates vector-graphing drawing methods" such as PostScript, a computer language widely used in computer graphics. Francis has some reservations about the book but recommends it "to all who are professionally or even casually interested in mathematical illustration."

--- Mike Breen

"Bettor Math," by Elwyn Berlekamp. American Scientist Online, November-December 2005.

In the November-December issue of American Scientist Online, Elwyn Berlekamp, a professor of mathematics at the University of California Berkeley, reviews the recently published book, Fortune's Formula, by William Poundstone. Berlekamp begins his review with a discussion of a paper published in 1956 by John Kelly. In this paper, entitled "A New Interpretation of the Information Rate," Kelly uses a racetrack betting scenario to present criteria for deciding how much to bet on each horse in a long sequence of races, assuming one knows, among other things, the probability each horse has of winning each race. Kelly applied the same formula to investing and proved that anyone who used his system (which became known as the Kelly criterion) would see their investments ultimately surpass that of someone using another strategy.

Berlekamp then provides an overview of the book, which includes biographical sketches of Kelly, Claude Shannon, Paul Samuelson, and Ed Thorp. On the one hand, Berlekamp finds the first part of the book a somewhat "gossipy approach to business history" as Poundstone "pursues a sequence of increasingly tenuous connections among moneymaking schemes." However, the latter half provides an overview of portions of the financial mathematics field, as well as an overview of "a now long-standing academic and philosophical debate about the relevance and appropriateness of the Kelly criterion."

--- Claudia Clark

"Plumbing the Depths of Rumor Research": Interview with Martin Bourgeois. All Things Considered, National Public Radio (NPR), 28 November 2005.

 University of Wyoming sociology professor Martin Bourgeois discusses current research being done on how rumors spread. A National Science Foundation grant is supporting work on the topic by him and other researchers at the University of Wyoming, the Rochester Institute of Technology, and the University of Southern Australia. Bourgeois says, "On one level, we'll use computer simulation, and you can use mathematical modeling to see how fast rumors would be likely to spread through a group depending on how easy it is for people to talk to each other in a group." The researchers also use a live group of individuals to spread rumors. These methods help determine the variables that make a rumor more or less likely to spread. --- Annette Emerson

"Is there anybody in there?," by Marcus Chown. New Scientist, 26 November 2005, pages 30-33.

Is there any way to search for extra-terrestrial intelligence, other than aiming receivers to the heavens and seeing what comes in? Stephen Wolfram, physicist and multimillionaire inventor of the computing software Mathematica, thinks there is. Rather than looking at the physical universe, he suggests, one should look at the "computational universe", which is the collection of all possible algorithms. Wolfram's book A New Kind of Science, which came out in ???, proposed that simple computational algorithms are what drives all phenomena we observe, be they physical, chemical, or biological. Following this logic, one concludes the entire universe of all algorithms contains recipes for creating everything---including extra-terrestrials. "[T]he ET in your PC won't be a flesh-and-blood alien, it will be a cyber version," Chown writes. "But that doesn't mean we couldn't communicate with it; we could still converse with a virual version of an alien civilization, and learn plenty from the conversation."

--- Allyn Jackson

"Montreal math whiz is scrabble champ," by Anne Sutherland. Montreal Gazette, CanWest, 21 November 2005;
"Montreal mathematician crowned world Scrabble champ," by CTV.ca News Staff. CTV.ca, 21 November 2005;
"Canadian wins world Scrabble title," by David Lazarus. The Canadian Jewish News, 15 December 2005.

 Mathematician Adam Logan recently won the World Scrabble Championship in London, England. He defeated 106 other players from 41 countries, and was awarded US$15,000. Logan, who graduated top of his class at Princeton University and received his Ph.D. in mathematics from Harvard University, currently works in the field of computational number theory at the Centre de Recherches Mathématiques at the Université de Montréal. He told reporter Sutherland that his background in math helped him to win the championship and that his one piece of advice to Scrabble players is to learn the two-letter words. He attributes his win to both luck and skill. Regarding the skill, Logan says "Somehow, Scrabble uses a lot of the same skills as mathematics. If you're in this case, then you use this method. And you have to, more or less, learn arbitrary information, like reading a dictionary. That's not unlike what you have to do in math." --- Annette Emerson Return to Top "Wellesley math whiz adds$2,000 scholarship," by Tenley Woodman. Boston Herald, 21 November 2005.

Kimberly Scott, a 16-year-old high school student from Wellesley, Massachusetts, wrote a paper on game theory that qualified her as a regional finalist in the prestigious Siemens Westinghouse Competition. She also won a US$2,000 scholarship plus US$2,000 for her school's math and science program. Scott wants to attend Caltech or MIT, but her long-term career plans are not set. "I'm not entirely sure about a career goal at this point," the article quotes Scott as saying. "I'm interested in math research and animal-rights activism."

--- Allyn Jackson

"Die Mathematik beginnt zu erzählen (Mathematics starts to narrate)", by George Szpiro. Neue Zürcher Zeitung, 20 November 2005.

This article reports on a meeting entitled "Mathematics and Narrative", which was held in the summer of 2005 and which brought together mathematicians and writers to explore connections between mathematics and literature, films, and plays.

--- Allyn Jackson

"Problems to Sharpen the Young," by Ivars Peterson. Science News Online, 19 November 2005.

 Alcuin of York (735-804). Peterson provides summaries of mathematical problems for young people in medieval times, including Gerbert of Aurillax (c. 950-1003), who went on to become Europe's leading mathematician (despite receiving virtually no formal instruction) and, in 997, Pope Sylvester II. According to Leigh Atkinson (in a paper in the November issue of College Mathematics Journal), among the few published mathematical works of the time was Propositiones ad acuendos juvenes (translated from the Latin as Problems to sharpen the young), commonly attributed to Alcuin of York (735-804). Peterson provides six examples of the problems, and concludes that the volume "provides fascinating glimpses of various aspects of life in medieval times and testifies to the enduring power of puzzles." Peterson also includes a nice list of references for further reading. --- Annette Emerson

"Spies, lies and butterflies," by Michael Brooks. New Scientist, 19 November 2005, pages 32-35.

This article discusses a new method to protect sensitive communications, by embedding them in a chaotic transmission signal. The sender of the message creates a chaotic signal that looks like noise, and then injects the message into it; the receiver must be able to recreate precisely the same chaotic signal, so that it can be removed and the message recovered. This synchronization is possible if the sender and receiver use the same method for producing the chaotic signal, such as identical lasers that are forced into a feedback loop. To a potential eavesdropper listening in on the communication, the transmission looks like noise. But there are limitations to this method. For one thing, the chaotic pattern created to enshroud the message is after all a pattern, and "patterns are a weak link in any cryptography system," the article notes. Nevertheless, this method could be useful in certain situations, such as a police sting operation, in which for a few hours the police need to hide their radio communications. Chaotic encryption would "make their communications look like noise: anyone trying to listen in with a scanner would be unaware of any messages traveling through the airwaves."

--- Allyn Jackson

"Moments of truth," by Alan Lightman. New Scientist, 19 November 2005, pages 36-41.

This article proposes a taxonomy of the process of scientific discovery. Lightman lists eight different ways that such discoveries come into being, such as an accidental observation, a timely clue, or an analogy. One of the ways listed is "The Mathematical Imperative". In this case, "a theoretical scientist, in exploring the mathematical world, is led to a discovery about the physical world." As an illustration, he offers Paul Dirac's 1928 discovery of the equation describing the electron. "The requirement that such an equation embrace both relativity and quantum mechanics in turn necessitated a particular mathematical structure," Lightman writes. "In following the narrow path of this mathematical landscape and its internal logical consistency, Dirac was directed to his discovery."

--- Allyn Jackson

"Tube Route." Random Samples, Science, 18 November 2005, page 1114.

 The title of this short article refers to the path of the recent Genesis space mission and its connection to quantum chemistry. The mission took advantage of what Martin Lo (Jet Propulsion Laboratory) called the Interplanetary Superhighway, an energy-efficient route in the solar system. Yet this path is similar to paths taken by certain electrons, a fact noticed by Charles Jaffe (West Virginia University). This similarity has led to collaboration between space engineers and quantum chemists. The Genesis trajectory, and the parallels between paths of celestial objects and paths studied in atomic physics, are discussed in the October 2005 issue of the Notices of the AMS in the article "Ground Control to Niels Bohr: Exploring Outer Space with Atomic Physics" by Mason A. Porter and Predrag Cvitanovic. (Image: Artist Concept of the Interplanetary Superhighway, courtesy of JPL, artist Cici Koenig.) --- Mike Breen

"Dimensions of superspreading, " by Alison P. Galvani and Robert M. May. Nature, 17 November 2005.

 Galvani and May summarize the findings of researchers on how infections such as SARS, measles, smallpox, monkeypox, and pneumonic plague spread across populatons ("Superspreading and the effect of individual variation on disease emergence," by J.O. Lloyd-Smith, S.J. Schreiber, P.E. Kopp and W.M. Getz, Nature, 17 November 2005, page 355). Prior studies considered individuals in populations to have an equal chance at transmitting disease, and "ignored stochastic fluctuations in transmission capability." Then scientists observed patterns involving disproportionate influence of "superspreaders." Based on the research paper by Lloyd-Smith et al, Galvani and May conclude that "analyses of contact-tracing data on the spread of infectious disease, combined with mathematical models, show that control measures require better knowledge of variability in individual infectiousness." --- Annette Emerson

"Math professor wins science award," by Olivia Winslow. Newsday, 17 November 2005;
"Nation's pride." Random Samples--People, Science, 2 December 2005, page 1423.

On November 14, 2005, Dennis P. Sullivan, a professor of mathematics at Stony Brook University, was named as one of eight recipients of the 2004 National Medal of Science. Sullivan was cited for "developing new fields of mathematics and for discovering ways to connect seemingly unrelated disciplines." The Medal was established to be given to individuals for "outstanding contributions to knowledge in the physical, biological, mathematical, or engineering sciences." Sullivan will receive his award from President Bush in a White House ceremony (date currently unknown).

--- Mike Breen

"Baseball prediction takes a geeky turn," by Dan Vergano. USA Today, 13 November 2005.

Rebecca Sparks and David Abrahamson, two mathematicians at Rhode Island College, modeled baseball writers' voting for the American League (AL) and National League (NL) Cy Young Awards (given to the best pitcher in each league). Their model predicted that the winners would be Bartolo Colón in the AL and Chris Carpenter in the NL. The number that the model gave to Colón was so low, however, that Sparks and Abrahamson overrode the model's prediction, which uses statistics more applicable to starting pitchers, and predicted that the AL winner would be Mariano Rivera, a reliever. When the baseball writers' votes were announced it turned out that the model's prediction was correct: Colón and Carpenter won the 2005 Cy Young Awards. Said Sparks, "We are a little mad at ourselves for not totally trusting the model." The article containing the model, "A Mathematical Model to Predict Award Winners," is available online and was published in the April issue of Math Horizons.

--- Mike Breen

"U.S. kids say math doesn't count much," by Jay Fitzgerald. BostonHerald.com, 12 November 2005.

A survey by Raytheon of 1000 students found that 84 percent of 11- to 13-year olds would rather do anything than their math homework (including taking out the garbage and cleaning their rooms). Raytheon has enlisted celebrities like Mia Hamm and Lisa Leslie in a program called Math Moves U to promote the benefits of studying math to middle school students and perhaps change attitudes towards math. Says Raytheon chief executive William H. Swanson, "As adults, we have a responsibility to make math more interesting. As business leaders, we need to be concerned about our future competitiveness in the global marketplace."

--- Mike Breen

"Math problems too big for our brains." Windsor Star (Canada), 8 November 2005.

"[M]ath problems have grown too big to fit inside our heads," states the opening paragraph of this story. "And that means mathematicians are finally losing the power to prove things with absolute certainty." The story reports on an article by mathematician E. Brian Davies, which appeared in the November 2005 issue of Notices. Davies' article, "Whither Mathematics?", discusses the limitations on mathematical knowledge. Although mathematical proofs remain as certain as ever, mathematicians are finding that, as larger and more complicated mathematical questions are posed, answering them definitively is becoming increasingly difficult. Many proofs are enormously long and complex, or require huge computer calculations that no one can entirely grasp. What mathematicians seek is not a "yes/no" answer, but understanding, and for large and highly complicated problems, such understanding may be beyond the capability of the human mind. The Windsor Star article quotes Davies as saying: "This idea that we can understand anything we believe is gradually disappearing over the horizon."

--- Allyn Jackson

"DaVinci Declassified." The Learning Channel, 6 November 2005.

Dan Brown's bestselling novel The DaVinci Code has inspired people around the world to read, to travel, and to carefully examine the details within the book's pages. Among these details is the importance of the golden ratio, a number that mysteriously appears in properties of nature and in the paintings described in the book. The ratio can be described as the relationship between successive elements of a Fibonacci sequence. Arthur Benjamin, Director of the Fibonacci Association, scrutinizes the validity of the novel's claims in "DaVinci Declassified." While successive Fibonacci numbers do, in fact, appear some in facets of nature, such as the number of spiral patterns on a pinecone, their importance has been exaggerated in their relationship to the human body. Experts interviewed on the show suggest that the presence of the golden ratio in DaVinci's paintings is a coincidental effect of his depiction of nature, not an intentional attempt to convey a message.

--- Lisa DeKeukelaere

"Pushing the Limit," by Erica Klarreich. Science News Online, 5 November 2005.

From cell phones to space missions, many current technologies depend upon the accurate transmission of data. In her recent article in Science News Online, Erica Klarreich discusses two specific advances in error-correcting codes made in the last decade that have brought the levels of accuracy very close to a limit first described by mathematician Claude Shannon in 1948.

Klarreich notes that Shannon showed that "at any given noise level, there is an upper limit on the ratio of the information to the redundancy required for accurate transmission." But until the mid-1990s, current codes were conveying information at about half of this rate. Enter two French engineers and their new "turbo codes," which "come within a hair's breadth of Shannon's limit." These codes involve the use of two decoders that start with different encoded versions of the same message, then compare their results and refine their solutions, repeating this process until the decoders agree on the message.

Klarreich then describes Low-density Parity-check codes (LDPC) codes, which require the use of a separate decoder for each bit of the message: they were first proposed almost 40 years earlier, but were "impractical at the time because [they] presented a computational problem far too complex for the computers of the day." Rediscovered and enhanced in the mid-1990s, these codes have sometimes "edged out" turbo codes, she notes.

Coding theorist Thomas Richardson summarizes the advances for Klarreich: "We're close enough to the Shannon limit that from now on, the improvements will only be incremental. This was probably the last big leap in coding."

--- Claudia Clark