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)


February 2005

"Time Bandits," by Jim Holt. The New Yorker, 28 February 2005, pages 80-85.

The time bandits are Albert Einstein and Kurt Gödel. Holt gives background on the lives and research of each--especially on Einstein's relativity and Gödel's incompleteness theorems--and describes the pair's relationship while both were at the Institute for Advanced Study in Princeton, New Jersey. According to the article, neither Einstein nor Gödel was as comfortable with other colleagues as each was with the other. Part of their daily routine was walking together to and from work. After studying Einstein's relativity and discussing it with him, Gödel discovered a model of the universe in which the universe was rotating. In this universe, time travel was possible, which, given the paradoxes involved, led Gödel to conclude that time was impossible.

The author reports that although Gödel entered the University of Vienna in 1924 to study physics, "he was soon seduced by the beauties of mathematics, and especially by the notion that abstractions like numbers and circles had a perfect, timeless existence independent of the human mind." The article notes that Gödel's and Einstein's lives and concepts intersected, and both used mathematical formulas to support---and bend---theories of relativity, time and the universe. Holt concludes that "a certain futility marked the last years of both Gödel and Einstein. What may have been most futile, however, was their willed belief in the unreality of time."

--- Mike Breen and Annette Emerson

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"Too much information," by Mark Buchanan. New Scientist, 26 February 2005, pages 32-35.

A cellular automaton is a mathematical model in which complex patterns can evolve out of repeated application of very simple rules. The usual way to represent cellular automata is as a planar grid of black and white squares. It turns out that certain rules produce cellular automata that appear to be highly chaotic and unpredicatable. Now researchers have found a way to tame this unpredictability by taking a "coarse-grained" approach---for example, rather than looking at what happens to all of the squares in a planar grid, one looks at what happens to clusters of ten squares. This approach allows the researchers to perceive larger-scale patterns. In one application, researchers found that this approach provided a good way to model foreign exchange markets.

--- Allyn Jackson

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"A Complete Guide to the Laws of the Universe": Interview with Roger Penrose. NPR's "Talk of the Nation," 25 February 2005.

Roger Penrose

Sir Roger Penrose talks about his new book, The Road to Reality: A Complete Guide to the Laws of Nature, and states that he wants readers to see "the interrelation between mathematics and physics" and that "one drives the other, really." The entire interview can be heard on the NPR website.

--- Annette Emerson

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"Das Wunderkind der Mathematik," by George Szpiro. Neue Zürcher Zeitung, 23 February 2005.

This article is about the great matheamtician 19th century Carl Friedrich Gauss, on the occasion of the 150th anniversary of his death.

--- Allyn Jackson

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"So einfach ist es, einen Modetrend aufzuspüren," by George Szpiro. Neue Zürcher Zeitung, 20 February 2005.

This article discusses a search strategy developed by a pair of researchers at Harvard University, using graph theory, evolution theory, and economics.

--- Allyn Jackson

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"'Origins of Cyberspace' To Be Auctioned By Christie's," by W. David Gardner. InformationWeek, 17 February 2005;
"Relic of Computer History in New York Auction," by Claudia Parsons. Reuters, 18 February 2005.

These and other sources reported on the auction at Christie's in New York on February 23 of approximately 1,000 items---plans, books, sketches, and rare documents---related to computer history. Among the items to be acutioned were business plans for the first personal computers; the first English edition of a paper by Luigi Federico Manabrea, "Sketch of the Analytical Engine invented by Charles Babbage" published in 1843; a 1613 edition of a treatise by Lorenzo Pignoria which includes an illustration of a Roman table abacus; books on the history of mathematical calculation from the 17th century; papers concerning the origin of the Internet; items connected with ENIAC (the world's first working automatic electronic computer); and papers on Artifical Intelligence. Christie's has detailed information on "The Origins of Cyberspace: A Library on the History of Computing, Networking & Telecommunications".

--- Annette Emerson

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"Ramanujan's 'Lost Notebook' Astounds Americans," by Francis C. Assisi. INDOlink-NRI News, 18 February 2005.

The article notes a series of seminars from January 25 until March 22, 2005, at the University of Florida about Ramanujan's "Lost Notebook," which contains approximately 650 assertions without proofs. George Andrews of Pennsylvania State University is giving six lectures based on his 30 years of study on Ramanujan's output, number theory, and combinatorics. Andrews discovered the Lost Notebook at the Wren Library in Cambridge University and in the 1970s wrote several important papers of his research. Krishnaswami Alladi, chair of the mathematics department at the University of Florida and Editor-in-Chief of The Ramanujan Journal, says that the lectures will try to reveal "what did Ramanujan have up his sleeve?" The article summarizes the life and achievements of Ramanujan, quotes mathematician Richard Askey, and notes that analytic number theorist Bruce Berndt has devoted 31 years of study to Ramanujan's work---and directed over 20 students whose dissertations were inspired by Ramanujan's works.

--- Annette Emerson

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"The spice of life," by John Allen Paulos. The Guardian, 17 February 2005.

Paulos reiterates that the iPod Shuffle of your favorite tunes really is random and offers some whimsical ideas on other ways to test our skepticism of randomness (shuffle your favorite digital photos, television stations, route to work, etc.). He also touches on the mathematics involved (combinatorics, dynamical systems).

--- Annette Emerson

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"Math skills survive linguistic damage," by Philip Ball,. news@nature.com, 14 February 2005;
"Mathematics is a language on its own." The Economic Times Online, 17 February 2005.

Recent tests show that individuals who cannot decode written or verbal communication can still understand mathematical expressions and perform calculations---they can understand "mathematical grammar." The recent studies by Rosemary Varley (University of Sheffield, UK) published in Proceedings of the National Academy of Sciences counter the long-held view of cognition by Noam Chomsky (Massachusetts Institute of Technology), that "language processing is a fundamental skill that is used for related grammatical tasks in the brain, such as certain mathematical ones." Varley's tests indicate that individuals who could not determine subjects and objects in simple linguistic phrases could figure out analogous object-relation problems when posed in mathematical terms. They could not understand "three" but could interpret Arabic numbers like "3" correctly.

See also:
"Math Without Words." Random Samples, Science, 25 February 2005, page 1197.
"Math minus grammar," by Bruce Bower. Science News, 19 February 2005, pages 117-8.
"Math without Words," by Philip E. Ross. Scientific American, June 2005, pages 28-30.

--- Annette Emerson

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Obituary of Gerard Debreu. Times Online, 15 February 2005.

Debreu (1921-2004) was a French-born mathematician who "taught at Berkeley for three decades, pioneered what later became a widespread deployment of formal, and rigorous, mathematical analysis within economic theory. For his achievements, especially work regarding markets and the general equilibrium, he was awarded the Nobel Prize in 1983." The article notes that Debreu, with Kenneth Arrow, used mathematics to demonstrate the existence of market-clearing equilibrium prices, and reports that "in academic style Debreu was happier outlining his mathematical proofs and models than engaging in more policy-oriented debates."

--- Annette Emerson

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"Origami as the Shape of Things to Come," by Margaret Wertheim. Sciencce Times, New York Times, 15 February 2005, page D1.

This "Scientist at Work" article profiles Erik Demaine, a wunderkind mathematician who is the youngest person ever to be appointed as a professor at the Massachusetts Institute of Technology. The article discusses Demaine's work in the mathematical study of origami, which he hopes to apply to other disciplines such as architecture. Another topic of exploration for Demaine is that of linkages: A linkage is a set of line segments hinged together like a carpenter's rule. He and a co-author cracked a longstanding mathematical problem by proving that any linkage can be unfolded. This work may be applicable to the problem of protein folding. Demaine believes that the function and mechanism of proteing folding can be completely understood. "I am an optimist," he is quoted as saying. "I believe it can be done in my lifetime."

--- Allyn Jackson

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"You do sum-thing to me," by Corinne Abrams. The Sun Newspaper Online, 13 February 2005;
"Get your calculator, you've just pulled," by Chris Riches. Scotland on Sunday, 13 February 2005.

hearts

These and other newspapers published a formula developed by University of Edinburgh mathematician Al Phillips, psychologist David Lewis, and Cosmopolitan magazine's relationship expert Flic Everett, offered to reveal whether a blind date will lead to a successful relationship. The formula is quoted as:
Love = (((F + Ch + P) /2) + ((3 (C + I)) / 10)) / ((5 - SI) 2 + 2)
Both participants must assign high scores to the feelings and attributes. F is how much you fancy your love interest, I is how much you hit it off immediately, C is their confidence, SI is your self-image, Ch is their charisma. "The boffins say pheromones (P) should get an automatic rating of eight." Of course all acknowledged the formula is not foolproof, but it can be an ice-breaker, especially around Valentine's Day.

--- Annette Emerson

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"Life on the Scales," by Erica Klarreich. Science News, 12 February 2005.

Ecologists Brian Enquist (University of Arizona, Tucson) and James Brown (University of New Mexico in Albuquerque), and physicist Geoffrey West (Los Alamos National Laboratory) have extended the scope and application of a long-held concept called the "quarter-power scaling law." Klarreich provides a concise background: "Scientists have long known that most biological rates appear to bear a simple mathematical relationship to an animal's size: They are proportional to the animal's mass rasied to a power that is a multiple of 1/4. These relationships are known as quarter-power scaling laws. For instance, an animal's metabolic rate appears to be proportional to mass to the 3/4 power, and its heart rate is proportional to mass to the - 1/4 power." Eight years ago this team of scientists published a model to explain quarter-power scaling laws in mammals and in 2001 extended the model to include plants, birds, and fish. In 2004 the team and colleagues published a paper in Ecology in which they propose that their equation "can shed light not just on individual animals' life processes but on every biological scale, from subcellular molecules to global ecosystems" (from the mutation rate in cellular DNA to Earth's carbon cycle). Klarreich goes on to explain the history of the concept of scaling, scaling up, scaling down, and the reactions (enthusiastic to skeptical) to the team's model.

--- Annette Emerson

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"Pomona's Prime Number," by Sara Lipka. The Chronicle of Higher Education, 11 February 2005, page A6.

Is there something significant about the number 47 at Pomona College? Some Pomona students think so, and the thinking goes back a long way. The 47 mania began in 1964 when a group of freshmen began to believe that 47 occurred at a "supernatural frequency" on campus. For example, to get to the college, you take Exit 47, and there are 47 pipes in the top row of an organ on campus. The mathematics department keeps scrapbooks of photographs and other documentation of 47-ness. Graduates of the college who got jobs on Star Trek and Alias did their best to insert 47 in the shows' episodes. Donald L. Bentley, professor emeritus of mathematics, who may have started the mania by using 47 in examples in class, says, "A lot of it is what is called biased sampling. We're looking for it, and so we see it. Nobody has ever done a valid experiment to confirm that 47 occurs more often than it should." After that statement Bentley added, "I shouldn't be saying those things about 47."

--- Mike Breen

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"Math luminary to show old masters' modern magic," Times of India, 9 February 2005.

In this brief article, The Times of India interviews mathematician Robert Langlands on the occasion of his giving a lecture on Descartes and Fermat at the Tata Institute of Fundamental Research in Mumbai, India. The writer notes the impact of Langlands' insights into the connection between representation theory of Lie groups and number theory, and speaks with Langlands about his contribution to the proof of Fermat's Last Theorem.

--- Claudia Clark

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"Doing the Numbers Carefully Adds Up to a Bit of Mystery," by Jack Anderson. New York Times, 7 February 2005.

Dancer Polly Motley's performance of the Fibonacci-inspired "Dancing the Numbers" was previewed by The New Yorker (in the Goings on About Town section, February 7 issue) and reviewed by the New York Times. The program consisted of a series of short dances that increased in time incrementally (as a Fibonacci sequence) and progressed along a spiral path. The performance took place as part of the City/Dans series of the Danspace Project at St. Mark's In-the-Bowery.

--- Annette Emerson

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"New findings super-size tsunami threat," by Tom Paulson. Seattle Post-Intelligencer, 7 February 2005.

Vasily Titov, a mathematician and computer modeler at the Pacific Marine Environmental Laboratory (operated by NOAA) in Seattle, is one of the researchers who have concluded that some of the waves in Indonesia in December 2004 reached 80 feet. The article provides a brief explanation and speculates whether the numerical models could inform researchers about potential tsunamis hitting the west coast of the U.S. The researchers' website has graphics and video clips of models showing the recent tsunamis.

--- Annette Emerson

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"Knot Divided in Snow," by Ivars Peterson. Science News Online, 5 February 2005.

Tired of pencil and paper? A team of American and German mathematicians recently turned to a 10x10x12 foot block of snow to express their mathematical musings. Peterson reports on the four men who spent four and a half days sculpting their masterpiece for the International Snow Sculpture Championships in Breckenridge, Colorado: a split Möbius band with three half-twists. Well known as interesting topological objects, Möbius bands can be easily constructed by twisting one end of a thin strip of paper, then joining the two ends. An odd number of half-twists will produce a band with only one edge and one side, and cutting such a band in half length-wise will produce one single band with a full twist. Performing this action is slightly easier with paper than ice, as discovered by the sculptors, who worked from three-dimensional scale models generated by designer Carlo H. Sequin. The team produced an elegant mathematical work of art, but the top prize went to a rendition another geometrically appealing object: a Nautilus shell.

---Lisa DeKeukelaere

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"Murder by numbers": Review of The Oxford Murders, by Guillermo Martinez. Reviewed by Marcus du Sautoy. The Guardian, 5 February 2005.

du Sautoy, a professor of mathematics at Oxford University, appreciates that mathematics plays a key role in this murder mystery by Martinez, who has a Ph.D. in mathematics. Mathematical symbols are left behind with the murdered bodies as cryptic clues, and the investigator---the reader---is invited to solve the crimes with the help of those clues. du Sautoy thinks that this is the first book in this genre to successfully combine mathematics and murder mystery elements and recommends this whodunit.

--- Annette Emerson

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"Cyberdad": Review of Dark Hero of the Information Age: In Search of Norbert Wiener, by Flo Conway and Jim Siegelman. Reviewed by Simon Singh. New Scientist, 5 February 2005, page 52.

This book tells the life story of Norbert Wiener, the brilliant mathematician and pioneer of the field of cybernetics. Singh says that while the book's explanations of Wiener's work "lacked clarity", he nevertheless found the book to be a successful recounting of the life of this outstanding scientist. "[It] rightly emphasizes his attemtps to warn the public and politicians of the social implications of technology," Singh writes.

--- Allyn Jackson

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"Math from the Ground Up." NetWatch, Science, 4 February 2005, page 651.

This website is a virtual textbook that offers a "comprehensive take" on the foundations of mathematics. The site was put together by Alexander Sakharov, a computer scientist, and has contributions from several other authors.

--- Mike Breen

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"Freudian quips: Mathematicians' jokes betray a deep-seated anxiety about the size of their proofs," by Philip Ball. Nature, published online 4 February 2005.

In this charming piece, Philip Ball muses on the deeper meaning of mathematical humor, drawing on examples of jokes presented in the article "Foolproof: A Sampling of Mathematical Folk Humor," by Paul Renteln and Alan Dundes, which appeared in the January 2005 issue of Notices of the AMS. The typical caricature of a mathematician as inhabiting a place far removed from the "real world" and having no sense for practical matters is found in abundance in these jokes. While the Dundes-Renteln article is "fascinating", Ball writes, "[i]t is also a little alarming. To judge from this selection, mathematicians embrace and even revel in their own caricature." The jokes are very different from what usually makes audiences laugh in stand-up comedy routines. "None of the jokes are about the usual things that people find important, such as money, sex and power," Ball quotes Renteln as saying. Rather, they center on themes like the uselessness and abstraction of pure mathematics, and the disquieting intersection between the ideal of a self-contained mathematical proof and the human impulse to appeal to authority.

--- Allyn Jackson

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"Deconstructing Eiffel," by Jean Thilmany. Mechanical Engineering, February 2005.

This brief story recounts an effort by a mechanical engineer, Patrick Weidman of the University of Colorado, and a mathematician, Iosif Pinelis of Michigan Technological University, to uncover the mystery of how Gustave Eiffel designed his famous tower in Paris. One theory that had been proposed suggested that Eiffel had used the weight of the tower to counterbalance wind loads. After examining all possible solutions to the equation underlying this theory, Pinelis concluded that this theory did not account for the tower's shape. Weidman consulted letters written by Eiffel and found plans to use tension among the construction elements as a counterbalance to wind loads. Pinelis, Weidman, and colleagues then used this information to produce a new equation, the solution to which fits perfectly the tower's shape. Pinelis and Weidman reported on their work in the article "Model Equations for the Eiffel Tower Profile: Historical Perspective and New Results," which appeared in the journal Comptes Rendus Mecanique (2004, Volume 332, No. 7, pp. 571-584).

--- Allyn Jackson

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"The Eye of the Beholder": Review of Symmetry and the Beautiful Universe, by Leon M. Lederman and Christopher T. Hill. Reviewed by Laurence Marschall. Discover, February 2005.

Noether

The premise of the book under review is: "No matter how complex the universe appears, there are underlying mathematical principles that describe the material structure of everything, from movie stars to neutron stars. And these laws are based on symmetry." Lederman and Hill explore the work of Emmy Noether, who "proved that this simple symmetry alone implied that energy could neither be created or destroyed" and, further, "proved that every natural symmetry implied a conservation law." The reviewer recommends the book as the authors "show the surprising and powerful implications of Noether's theorem."

--- Annette Emerson

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