The transformer that provides electricity to the AMS building in Providence went down on Sunday, April 22. The restoration of our email, website, AMS Bookstore and other systems is almost complete. We are currently running on a generator but overnight a new transformer should be hooked up and (fingers crossed) we should be fine by 8:00 (EDT) Wednesday morning. This issue has affected selected phones, which should be repaired by the end of today. No email was lost, although the accumulated messages are only just now being delivered so you should expect some delay.
Thanks for your patience.
Summaries of Media Coverage of Math
Edited by Allyn Jackson, AMS
"Algorithm and blues:" review of Logicomix, by Apostolos Doxiadis and Christos H. Papadimitriou. Review by Jim Holt, New York Times, 27 September 2009.
"Well, this is unexpected--a comic book about the quest for logical certainty in mathematics." So begins this review of Logicomix, a comic book--or, as Holt notes, a graphic novel--based on the "crisis of foundations" that occurred in mathematics in the early 20th century. One of the central characters in the book is Bertrand Russell, who pinpointed a paradox that doomed efforts to put mathematics on an airtight logical foundation. As Holt notes, this paradox is captured in the question about the barber who shaves all men who do not shave themselves: Who shaves the barber? Many other stellar mathematical personalities appear in the book, along with the authors themselves; Doxiadis wrote a previous novel based on mathematical ideas, and Papadimitriou is a computer scientist at U.C. Berkeley. The book has fun taking liberties with the characters and the history, but does not tamper with the mathematics. As Holt writes, "for the most part the ideas are conveyed accurately, and with delightful simplicity." He also found the illustrations, by Alecos Papadatos and Annie Di Donnadecades, to be appealing.
--- Allyn Jackson
"Fold Everything," by Jennifer S. Holland. National Geographic Magazine, 15 September 2009.
Image courtesy of Robert J. Lang, www.langorigami.com
It is easy to see the beauty and enchantment of a piece of origami, whether you've actually gone through the process of folding a piece of paper to give it an attractive form or you've only seen the end result. What is surprising is that the strategies used to make intricate pieces are also extremely useful in math and science applications. Physicist Robert J. Lang, who quit his Silicon Valley job eight years ago dedicate himself to the art (and science) or origami, is on the forefront of innovation in origami, both aesthetically and technologically. He says that "it's now mathematically proven that you can fold pretty much anything," and that the insights gathered from solving these folding problems have actually proven useful in solving all sorts of other problems, from ancient mathematical ones to modern technological ones. He has applied his algorithm for paper insects to folding an airbag into a dashboard, and helped design a space telescope lens the size of a football field that collapses like an umbrella. He is not the first person to find an application for the ancient art, however. In 1995 Japanese engineers launched a foldable satellite so that it would fit into a rocket and open flat once in space. In fact, many researchers are working on all sorts of applications, like launching paper planes from space to inspire new spacecraft designs and creating origami stents to prop open arteries. According to Lang, "we haven't reached the limits of what origami can do. We can't even see those limits."
--- Adriana Salerno
"Google works on a different web," by Susan Milius. Science News, 26 September 2009, page 10.
Before there was a World Wide Web, there were food webs--directed graphs in which the nodes are species and edges signify that one species eats the other. Stefano Allesina, an ecologist at the University of Chicago, has adapted Google's PageRank algorithm to analyze which species are crucial to the survival of food webs. Analogous to how the importance of web pages depends on the importance of those pages that link to it, Allesina assigns importance to species based on the importance of species that eat them. He says that the algorithm does a better job of predicting food web collapse than previous methods. The research, "Googling Food Webs: Can an Eigenvector Measure Species' Importance for Coextinctions?", is in the September 3 issue of PLoS Computational Biology.
--- Mike Breen
"Erasing Dark Energy," by Veronique Greenwood. Seed, 24 September 2009.
Mathematicians Blake Temple (UC Davis) and Joel Smoller (University of Michigan) "have now found a way to explain the observation that led researchers to propose dark energy." While doing experiments with shockwaves, they found that "an expanding wave with its epicenter near the Earth could produce the dimming effects teams had observed." After consulting with astrophysicists and other mathematicians they concluded: "An accelerating wave of expansion following the Big Bang could push what later became matter out across the universe, spreading galaxies farther apart the more distant they got from the wave's center. If this did happen, it would account for the fact that supernovae were dim--they were in fact shoved away at the very beginning of the universe. But this would have been an isolated event, not a constant accelerating force. Their explanation of the 1998 observations does away with the need for dark energy." Some cosmologists dismiss the theory, others are open to it. NASA plans to send a telescope into space to gather more data about what dark energy might be, but that's not until 2016. See also: "Mathematicians' Alternate Model of the Universe Explains Away the Need For Dark Energy," by Jeremy Hsu, Popular Science, 25 September 2009.
--- Annette Emerson
"Mathematics expert: IRV not the answer," by Curtis Gilbert. Minnesota Public Radio, 23 September 2009.
The city of Minneapolis will use instant runoff voting in its 2009 municipal elections. Don Saari (University of California, Irvine), who has done a great deal of analysis of different voting systems, spoke to an audience at the Institute for Math and its Applications about instant runoff voting and its flaws. He is no fan of the most commonly used system, plurality voting in which the top vote-getter wins, but he said, "We haven't gotten rid of the cancer. The plurality vote determines who's going to go to the runoff. So, if we have a system that's distorted and gets us the wrong two people for the runoff, we're in trouble." The Minnesota Public Radio website has a nice video illustrating an example of an election using instant runoff voting.
--- Mike Breen
"'Genius' Mathematician Seeks New Problems," an interview with Lakshminarayanan Mahadevan. National Public Radio's All Things Considered, 22 September 2009.
L. Mahadevan, a mathematician at Harvard University, is among 24 innovators in art, science, writing who will each receive a MacArthur "genius grant" of US$500,000 over the next five years. Mahadevan "applies complex mathematical analyses to a variety of seemingly simple, but vexing, questions across the physical and biological sciences - how cloth folds when draped, how skin wrinkles, how flags flutter, how Venus' flytraps snap closed." In addition to the interview on his being awarded the MacArthur grant, hear his interview, "The Math of Folding Maps," (on NPR's All Things Considered, 15 March 2008).
--- Annette Emerson
"Go forth and multiply," by Penelope Debelle. Adelaide Now..., 17 September 2009.
Simon Pampena is Australia's stand-up math comedian. The newspaper covers his Super Mega Maths Battle for Planet Earth performance. "There are maths teachers and a smattering of older teens but it is mainly mums or dads with groups of children. The show is loosely based on the premise of an alien invasion from Planet Calculus and it hides maths inside a package of popular culture and audience participation. The songs include a feat of memory in which Pampena recites pi to the 50th decimal--he knows it to 100 places but could not cram it into a song." This "National Numeracy Ambassador" draws appreciative crowds around the country, which aims to improve its math literacy. "The problem is not just one of national standing and self-esteem. Maths is at the heart of inventions that make a nation great. As the national strategy points out, without maths there would be no cars, no planes, no mobile phone networks, and no computers. Our dependency on maths will only increase as we rely on future technologies." Another ambassador--by example--is Australian Terence Tao, who at the time of the article was visiting his Adelaide family during a national Clay-Mahler lecture tour. Tao was the first Australian--and youngest person ever--to win the prestigious Fields Medal. He started to learn arithmetic by the age of two from watching Sesame Street, and studied throughout his school years with a mentor who was a retired mathematician. Pampena's career path was "a combination of good teachers and Star Wars. It took him a while but Pampena finally understood that while the science in Star Wars was fiction, there was real science out there that was just as interesting." The article provides a nice profile of these two mathematicians, both of whom want to let young students know that math is present in some unexpected places, and is needed to pursue studies and careers in all the sciences.
--- Annette Emerson
"Super-30 Founder in Limca World Record Book." PatnaDaily.com, 16 September 2009.
Anand Kumar. Photograph courtesy of PatnaDaily.com
Mathematician Anand Kumar, who founded Super-30 Institute (the Ramanujan School of Mathematics) dedicated to training underprivileged boys and girls to take the prestigious India Institute of Technology (IIT) entrance exam, was inducted into the 2009 Limca Book of World Records for his pioneering work providing free coaching for students to pass the difficult IIT entrance test. Over the past seven years the Institute has coached 210 students, of which 182 have passed the exam. As a young student, Kumar himself was not able to attend Cambridge University due to his lack of money, but he since has become a highly-regarded mathematician who tutors and provides books, room and board for to 30 poor but bright students each year at the Super-30 Institute in Patna, India.
--- Annette Emerson
"OK Derren, now tell us how you REALLY did it: Experts pour scorn on illusionist's explanation," by Paul Revoir. Daily Mail, 12 September 2009.
Claiming to have used the "Wisdom of Crowds Theory" as explained by financial journalist James Surowieki in his 2004 book by the same title, Illusionist Derren Brown correctly predicted the result of a recent lottery in the UK. "The Wisdom of Crowds Theory" postulates that, in matters of estimation, the average of the responses across a large crowd is more likely to be accurate than an individual response. Brown supposedly applied this by simply averaging the responses given by 24 people who were asked to guess the winning numbers on "live" television. The problem: There is no evidence by which to make an educated guess or estimate as to what lottery numbers are the winning ones.
Several professors of philosophy and mathematics were quoted in the article and called Brown's pseudo-mathematical explanation "rubbish." The only rational conclusion is that the illusion was the result of tricky film editing. However, the illusionist's enthusiasm for math is appealing: "This was to lead me down a fascinating path into mathematics, superstition and a powerful, beautiful secret that can only be achieved when we all put our heads together," said Brown.
In a related story, the same six numbers came up in consecutive drawings of the Bulgarian lottery and 18 people picked the winning numbers the second time (no one chose the numbers the first time they came up). The coincidence led to an investigation in Bulgaria. The Wall Street Journal's Number Guy, Carl Bialik, writes about the coincidence.
--- Brie Finegold
“The Mysterious Equilibrium of Zombies…and Other Things Mathematicians See at the Movies,” by Samuel Arbesman, The Boston Globe, 6 September 2009.
While movies about mathematics or mathematicians are few and far between, many films incorporate mathematical ideas. In this article, Harvard Medical School postdoctoral fellow Samuel Arbesman discusses several films—Harry Potter and the Half-Blood Prince, The Dark Knight, Six Degrees of Separation, Reservoir Dogs, and zombie flicks—from a mathematician’s perspective.
For example, in the opening scene of the latest Harry Potter film, as London’s Millennium Bridge is being destroyed, the simultaneous buckling and lateral movement of the bridge would probably bother “those who think about math.” But math certainly was used to try to determine the cause of the real-life wobble experienced by the people who crossed the bridge after its initial opening in 2000. Or consider that latest Batman film, in which the Joker offers passengers on two ferries a choice that a mathematician would recognize as a form—albeit twisted—of the prisoner’s dilemma. Then there is the statement made by Stockard Channing’s character in Six Degrees of Separation about the number of people that separate every possible pair of people on the planet. Research by a few mathematicians has shown the number to be closer to an average of 6.6, at least in online networks. Go to last month’s Math Digests, for more on mathematical models applied to zombie epidemics. See you at the movies!
--- Claudia Clark
“Calls for pardon for code-breaker Turing,” by Susan Watts. BBC News, 4 September 2009.
“PM apology after Turing petition,” by Robert Hall. BBC News, 11 September 2009.
"PM sorry over code-breaker treatment," by Robert Hall. BBC News, 11 September 2009.
Alan Turing is most famous for his remarkable work in breaking the Enigma code during World War II (which is believed to have been crucial to the Allies’ victory). It is unfortunate that his success was overshadowed a few years later by his “gross indecency” trial (in other words, he was tried for being gay). He admitted to having a relationship with a man, and chose chemical castration over a prison sentence. Two years after he started “treatment” for his homosexuality, at 41 years of age, Turing committed suicide. The Number 10 website, led by computer scientist John Graham-Cumming, recently called for a posthumous government apology for the way this brilliant scientist was treated, and the government complied. Prime Minister Gordon Brown said in the Telegraph newspaper: “his treatment was of course utterly unfair and I am pleased to have the chance to say how deeply sorry I and we all are for what happened to him.” Perhaps the acknowledgment of the “appalling treatment” Turing received will give way to a more widespread recognition of one of the great minds behind the birth of computers and artificial intelligence.
--- Adriana Salerno
"5 College Majors On the Rise: Computational Science," and "How They Did It," by Karin Fischer and David Glenn. The Chronicle of Higher Education, 4 September 2009, pages A8 and A10.
The Chronicle identifies computational science—a field that involves modeling aspects of our world from weather to potato chips—as one of five undergraduate majors expected to grow in popularity. Like the other four selected, computational science is a blend of multiple disciplines, in this case mathematics and computer sciences, with other scientific fields. Bringing multiple departments together is key to a successful program, and state schools in Ohio have augmented their programs further by allowing cross-enrollment between universities. One of the oldest programs in the country, founded in 1998 at the State University of New York College at Brockport, successfully used its program to boost enrollment in hard science departments. Establishing a program can be difficult, taking for example the concerns of Oregon State professors about the importance of such work both for students and for their own academic careers, but the article discusses the positive prospects for computational scientists in the job market.
--- Lisa DeKeukelaere
The book, Mathematicians: An Outer View of the Inner World is the subject of a review in American Scientist and a multimedia presentation in Seed Magazine.
Hayes notes that the book's introduction is by Robert Clifford Gunning (who is also one of the subjects), and the afterword is by Brandon Fradd (who started the project). Hayes says the book of black & white photographs and autobiographical essays is simple and elegant, but wonders "from this outer view of mathematicians, can you really learn anything about their inner world?" especially if few of the subjects talk about "what it feels like to do mathematics at the highest level." He thinks this is a family album for the mathematical community, "but not quite the entire family" as it is "the world of mathematics as seen from Princeton, New Jersey. Fully half the subjects have some connection to Princeton University or to the neighboring Institute for Advanced Study."
Seed Magazine features a slideshow of 14 photographs of mathematicians from the book. The mathematicians in this slideshow include both "celebrated icons" and others at the start of their careers. These include Margaret Dusa McDuff, Alain Connes, John Horton Conway, Adebisi Agboola, Sir Michael Francis Atiyah, Friedrich E. Hirzbruch, and Peter David Lax. Each photograph is accompanied by a short quote, assumedly from Cook's book, in which the subject shares one or two thoughts about mathematics, what mathematicians do, or their early interest in mathematics. For example, the quote accompanying the photograph of Marie-France Vigneras reads "As mathematicians, we play and dream but we don't cheat. You can't cheat in mathematics. Truth is so important. To solve a problem with a proof is exciting and rewarding because it is true forever."
In addition to the photographs and captions, a 3-minute audio recording provides some additional insights of 5 of the mathematicians pictured here. For example, David Mumford says "In my own experience, mathematics in general and pure mathematics in particular have always seemed like secret gardens, places where I could try to grow exotic and beautiful theories. You need a key to get in, a key that you earn by letting mathematical structures turn in your head, 'til they are as real as the room you are sitting in." To see the slideshow and hear the recording, go to Seed Magazine.
--- Annette Emerson and Claudia Clark
“Origin of Computing,” by Martin Campbell-Kelly. Scientific American, September 2009.
In this article, Martin Campbell-Kelly, author of the book Computer: A History of the Information Machine, describes some of the events that would eventually lead to the development of the modern computer.
During the French Revolution, the French ordinance survey office commissioned a new set of mathematical tables, known as the Tables du Cadastre, to aid in the republic’s effort to reassess property taxes. The work took 10 years to complete—the tables were computed by hand, of course—but the resulting manuscript was never published. After seeing the tables in 1819, a young Charles Babbage was inspired to replicate the project—with a machine that he would call the “Difference Engine.” Babbage completed a working model of his machine in 1832, but then abandoned it for a “grander vision”: the Analytic Engine. As Campbell-Kelly writes, “Whereas the Difference Engine had been limited to the single task of table making, the Analytic Engine would be capable of any mathematical calculation.” Babbage designed it to have a processor, memory, and the user input. However, his thousands of pages of notes would not be read by scholars until the 1970s!
Campbell-Kelly then discusses “the most important analog computing instrument” before World War II: the Differential Analyzer. The first digital computer would soon follow: the ENIAC, finished in 1945. But it would be the design of the EDVAC that would mark a shift from the computer as “a mathematical instrument to a universal information-processing machine.” Campbell finishes the article with an analysis of how computers have evolved since the EDVAC, and describes some of the “multiple possibilities for radical evolution” that exist today.
--- Claudia Clark
Joseph Marie Jacquard showing his loom to Lazare Carnot.
Among the "Origins" collection of articles on important scientific breakthroughs are some related to mathematics. "Buckyballs and Nanotubes," by Philip Yam (page 82), reports on the buckminsterfullerene, "a molecule comprised of carbon atoms that lie at each vertex of 12 pentagons and 20 hexagons arranged like the panels of a soccer ball, which forms naturally in many combustion processes involving carbon (even candle burning)" and may have future applications in technology. "Economic Thinking," by Davide Castelvecchi (page 82), touches on how humans make choices based on what they think is valuable and what they think is a rational decision. "Graphical Perspective," by George Musser (page 84), notes that "'realistic' imagery depends on relatively recent cultural assumptions and technical skills." For instance, 15th century Italian artist "Leon Battista Alberti worked out the math. Rigorous geometric constructions ensured that natural depth cues such as size, vertical position and tile patterns were mutually consistent for maximum verisimilitude." The question is whether viewing a perspective drawing requires "accepting and overlooking its limitations, such as a single viewpoint." Would aliens be able to decipher our drawings, and would we recognize alien artwork? "The Mechanical Loom," by Jonathon Keats (page 88), provides a good introduction to Jean-Charles Jacquard's use of perforated cards that were fed through a loom to make (program) patterns--an invention that inspired the player piano and the first computers.
--- Annette Emerson
"Applied Math," a collection of new applications of mathematics, by Katharine Gammon. Popular Science, September 2009.
Popular Science devotes a section to new ways math can be applied. "Red-eye Flight Relief" notes that researchers at University of Michigan and Harvard Medical school "wrote software that models complex internal timing systems like our circadian clock" that might one day help air travelers avoid jet lag and astronauts deal with different day-night cycles on the moon or on Mars. "The Sound of Sludge" reports that Alex Tolsoy (ATolstoy Scientific) used a mathematical tool called matched-field processing to analyze reflected sound and pinpoint [a clogged pipe] clog." The third piece, "Unscrambling Alphabet Soup," says Rajesh Rao (University of Washington) calculates the "conditional entropy--a measure of randomness" of Indus Valley pictograms and thinks the script is most likely a language and plans further analysis of the text's structure."
--- Annette Emerson
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