# Math Digest

## Summaries of Articles about Math in the Popular Press

Edited by Allyn Jackson, AMS
Contributors:
Mike Breen (AMS), Claudia Clark (Northeastern University), Annette Emerson (AMS)

### August 2004

"Election Prediction," by John Allen Paulos. ABC News.com, 29 August 2004

Paulos uses the occasion of the upcoming November 2004 U.S. presidential election to present and analyze Ray C. Fair's Predicting Presidential Elections and Other Things, a 1978 paper that described presidential elections going back to 1916. Paulos describes Fair's model (predicting the presidential popular vote as going to the incumbent party) as dependent on six factors: which candidate is the incumbent, which party is in power, "party fatigue," the per capita growth rate for the GDP (higher is better for the incumbent), the number of quarters during the preceding 3 3/4 years in which the growth rate exceeded 3.2% (higher is better), and the inflation rate (lower is better). However, Paulos points out that the model hasn't always proved correct, and Fair himself notes caveats and weaknesses. Paulos, as he has done in many past columns, points out that "after-the-fact torturing of data to reveal accidental relationships and meaningless correlations" (retroactively fitting predictions) is not hard to do and can lead to comfortable (or uncomfortable) and false conclusions.

--- Annette Emerson,

"A Better Distorted View," by Ivars Peterson. Science News Online, 28 August 2004.

Cartograms are maps where the sizes of different regions are proportional to the sizes of some variable like population density. These types of maps allow the user to get information quickly and easily, but they are time-consuming, and difficult, to construct. Now, in the May 18, 2004 issue of Proceedings of the National Academy of Sciences, physicists Mark Newman and Michael Gastner of the University of Michigan in Ann Arbor report the use of a new technique that has significantly decreased the time necessary to generate cartograms. By applying the principle of diffusion---the way gas disperses in a space until the density of the gas is the same throughout---Newman and Gastner created cartograms using U.S. population data. The article includes a striking image of a cartogram of lung cancer rates among men in New York State, as well as one of the United States showing the number of wire-service news stories reported by state between 1994 and 1998.

Future directions for Newman and Gastner will include developing software that can deal with a curved surface, allowing the generation of larger, including global, cartograms. Other researchers, such as Daniel Dorling of the University of Sheffield in England, applaud this recent development, but note that additional research is needed to attain "perfect" cartograms, which will look like normal maps at a very local level. Dorling believes that "the solution has probably already been found in another area": it's a matter of applying it to this field.

--- Claudia Clark

"You Can Get There From Here." NetWatch, Science, 27 August 2004, page 1219.

This short article points readers to a website rich with resources about the traveling salesman problem, which amounts to finding the shortest route that visits a collection of cities. The site gives the history of the problem and several examples.

--- Mike Breen

"The First Eureka Moment." NetWatch, Science, 27 August 2004, page 1219.

NetWatch describes a website with information about Archimedes, one of the greatest mathematicians ever. There are pictures, quick facts, details about some of his inventions (including animations), and problems that Archimedes worked on.

--- Mike Breen

"Mathematics: Building a gold medal team," by Mark H. Thiemens, San Diego Tribune, 27 August 2004

On the eve of the closing ceremonies of the 2004 Summer Olympics, Thiemens takes the opportunity to praise the young U.S. students who competed in the recent International Math Olympiad, and bemoan the fact that these talented young mathematicians aren't given the attention and respect that the current U.S. athletes received during the Summer Games in Athens. Although he concedes that math competitions may not be as exciting to follow as the Summer Games, he explains that the ability of U.S. youth to compete in the international arena of math--not to mention to be "functionally literate" in math---is far more important to the future of the U.S. and its citizens. "The reason is that mathematics is the language of science. And without math and science, our progress in science and technology--the economic engine of our nation and state--would be seriously compromised." He hopes that the U.S. can better train its students and re-develop and nurture a sense of pride in a new generation of mathematicians, scientists and engineers.

--- Annette Emerson

Articles on floating paraboloids:
"Floating Bodies," by Ivars Peterson. Science News, 21 August 2004;
"Whatever Floats Your Paraboloid," Constance Holden, editor, Science"Random Samples" column, 20 August 2004

Both articles cite and summarize a recent article in the summer issue of Mathematical Intelligencer in which current research builds on Archimedes' On Floating Bodies, a treatise that provided mathematical analysis of how a paraboloid floats. Archimedes determined that a paraboloid's shape and its density determines the way it floats. Peterson reports that mathematician Chris Rorres (University of Pennsylvania) has computed "all possible floating positions (both stable and unstable) of a paraboloid for all possible shapes and densities" and has illustrated and animated his results. The "Random Samples" column reports that Rorres' use of "a 35-year old branch of mathematics called catastrophe theory" may help the naval community predict the tumbling behavior of melting icebergs.

--- Annette Emerson

"Life Without Numbers in the Amazon," by Constance Holden. Science, 20 August 2004, page 1093.

Does language reflect our ideas, or does it shape our thinking? The results of a study published in the 20 August 2004 issue of Science imply the latter. The study's author, Peter Gordon of Columbia University, tested the mathematical thinking of the Pirahã, a hunter-gatherer tribe who live in the Amazon. In their language, words for numbers other than one and two do not exist.

By giving a series of tests to the adult males, Gordon found that the Pirahã had difficulty recognizing the concept of numbers greater than three. For example, when asked to distinguish between boxes that had different numbers of fish pictured on their lids, these people did very poorly---"no better than chance, " according to Gordon. Linguist Daniel Everett, who also worked with the Pirahã,has a different view. Because the Pirahã children readily learned the Portuguese words for numbers that he taught them, while the adults claimed their "heads were too hard" to learn, he believes that a "cultural constraint against quantification" is responsible for the lack of mathematical words and ideas.

--- Claudia Clark

"Fonda, Garbo, Headline Stamps." CBSNEWS.com, 14 August 2004.

The 2005 U.S. stamp program has announced the subjects of the 2005 stamp releases. Among them will be a series of American scientists. "Failor, executive director of Stamp Services for the U.S. Postal Service, said there will also be stamps for non-celebrities, such as the four stamps for geneticist Barbara McClintock, thermodynamicist Josiah Willard Gibbs, mathematician John van [sic] Neumann, and physicist Richard Feynman." Failor is quoted as saying, "These 4 American scientists that we picked out are people that have had a tremendous impact on our history and on our culture over the years."

--- Annette Emerson

"Tribeca Calls for Tech Scripts." Backstage, 13 August 2004.

The news section of this media outlet reports that the Tribeca Film Institute is interested in "scripts that have a scientific or technological theme and story line or have a leading character who is a scientist, engineer, or mathematician." The Alfred P. Sloan Foundation is funding the program, which will provide financial support and input from an advisory panel on script revisions for production. Individuals are urged to visit www.tribecafilminstitute.org for more information and guidelines for submission. Proposals are due before October 22, 2004.

--- Annette Emerson

"Expectations are rising: Algebra's for everyone now," by Greg Toppo. USA Today, 12 August 2004.

The number of students taking high school algebra is on the increase, this article reports. Twenty-one states have even made passing algebra a requirement for graduation. In years past, algebra was a course taken only by those bound for college. A chart accompanying the article shows that 35.6 percent of high school students in 1982 took Algebra II, compared to 64.3 percent in 2000. "Thirty years ago, we taught algebra to a select group," one veteran teacher, Linda Antinone, is quoted as saying. Now teachers are expected to reach a much broader group. These changes have been accompanied by calls to "reinvent" algebra, as the article puts it, to make it more practical and more connected to real-world problems. This has in turn produced backlash reactions that the teaching of algebra is being "dumbed down." The article also notes a positive correlation between success in high school algebra and college graduation.

--- Allyn Jackson

"Playing dirty": Review of the play Calculus by Carl Djerassi. Reviewed by Philip Ball. Nature, 12 August 2004.

Djerassi's new play, "Calculus," is about the dispute between Isaac Newton and Gottfried Wilhelm Leibniz over the mathematical technique each scientist claimed to have developed first, independently. Ball briefly describes the chronology of Newton's work on differential calculations (which he called 'fluxions') and subsequent publications, Leibniz's own published version of calculus, the ensuing arguments, and Newton's influence on the Royal Society (of which he was president at the time). Ball notes that the play doesn't attempt to settle the dispute but rather "centers on the deliberations of a Royal Society committee appointed in 1712 to pronounce on the priority issue." Ball acknowledges that Newton's actions were "deplorable," and of the play he notes that overall it is about "scientific reputation." He seems to agree with the playwright that it is positive that "we no longer seem compelled to sanitize the history and sociology of science." The play was performed at the New End Theatre in London until 28 August.

--- Annette Emerson

"Quantizing the classical cat," by Ian Stewart, Nature, 12 August 2004.

Stewart's "news and views" piece is summarized this way: "a mathematical analysis of a pendulum system reveals the relevance to quantum systems of the classical concept of 'monodromy'---why a falling cat always lands the right way up." Stewart explains the recent work of R.H. Cushman et al (Phys. Rev. Lett. 93, 024302; 2004) who use a modern technique of analysis known as reduction. "The central topic of the paper is this: how does monodromy show up when the system is quantized? The answer, obtained in the specific context of the carbon dioxide molecule, is both elegant and remarkable," which leads Stewart to speculate that "maybe we will soon be able to see how Schrödinger's cat turns itself upside down."

--- Annette Emerson

"Japanese deploy solar sails," by Mark Peplow. news@nature.com, 10 August 2004.

The Japanese Aerospace Exploration Agency has reported a successful experiment in which solar sails---spacecraft without engines---unfurled and floated in space. Peplow sums it up this way: "'origami' technique boosts pioneering propulsion technology." "As the Sun's light beats down on the sheet's surface, each photon transfers a small amount of momentum to the sail, accelerating it away from the Sun. The energy involved is tiny, but over considerable time it can boost the sail to tremendous speeds because there is no friction in deep space to slow the craft down." This experiment---similar to one the Russians launched in 1993---"tested improved ways of folding a sail, which are crucial for efficiently packing the structure into a small rocket and then deploying it in space." Although the origami technique is far from being applied to space exploration in the near future, the successful test is encouraging to scientists in Europe, the U.S., and Russia who have similar goals.

--- Annette Emerson

"Your Last, Best Chance to Improve Your Erdős Number," by Richard Monastersky. The Chronicle of Higher Education, 6 August 2004, page A16.

This article appeared n the "Hot Type" column in The Chronicle and tells of the second eBay auction of an Erdős number (the first was in April and is written about in this item from the June Math Digest). Paul R. Pudaite, with an Erdős number of 1, auctioned off the rights to collaborate on a paper about the World Poker Tour. The opportunity for collaboration sold for US\$127.50, which Pudaite plans to donate to his softball team.

--- Mike Breen

"Shaping up at Olympia," by Stafano Grillo. Nature, 5 August 2004.

The pediment of the Temple of Zeus at Olympia (erected around 450 B.C.) is now in the recently-renovated Archaeological Musuem at Olympia. The author describes in detail the subject and composition of this early Classical period sculpture and likens the work to paintings by Renaissance painter and mathematician Piero della Francesca. "In both artistic styles, geometry plays an important role." Grillo (physicist at the University of Perpignan and PROMES/CNRS, France) goes on to explain why: the symmetry, the angles of the rotation of the horses' heads, and other angles and pleasing lines. "Of course, geometry by itself does not make good art---but...in the Olympia pediment, geometry contributes to the harmony and serenity of the composition..."

--- Annette Emerson