November 2008
"Touring Turing": Review of An Annotated Turing, by Charles Petzold. Reviewed by Martin Davis. American Scientist, NovemberDecember 2008, page 520. Charles Petzold's book, An Annotated Turing: A Guided Tour through Alan Turing's Historic Paper on Computability and the Turing Machine, offers both avid and casual computer science readers access to Turing's most famous paper and his explanations of the theories behind the modern day computer. The paper is Turing's answer to David Hilbert's legendary Entscheidungsproblem, which asks if there exists an algorithm that can decide whether a mathematical statement is true or false. To solve this problem, Turing noted that his Turing machine (or universal computer) could perform any algorithm, and therefore if such an algorithm existed, his machine would be able to decide whether any mathematical statement is true or false by using that algorithm. By showing that his machine was unable to make such a decision, he showed that the algorithm in the Entscheidungsproblem must not exist. Turing's proof was the most persuasive among other attempts at a solution, but the key aspect of his paper was the description of the Turing machine, which John von Neumann later built upon to create basic computer architecture in the 1940s. In addition to explanations of Turing's paper, Petzold's book also provides background on Turing's fascinating life.  Lisa DeKeukelaere
"Your secret's not secret anymore": Review of The Numerati, by Stephen Baker. Reviewed by Tom Simonite. New Scientist, 29 November 2008, page 47. This book describes the activities of mathematicians and computer scientists whom the book's author has dubbed "the Numerati". These people "are tasked with processing the flood of electronic traces we leave behind, to reveal and ultimately influence the way we shop, vote or even fall in love," the review says. The book calls this process of extracting information about people from the data they generate "the mathematical modeling of humanity". The review notes that, as more and more information about people becomes available in vast databases, the Numerati will become ever more powerful. Although their methods have many flaws, the Numerati are "inexorably eroding our privacy" the review says. In the future, the Numerati might "come to dominate commerce, policing, healthcare and more", the review says. Despite these sinister possibilities, the book's author "seems unwilling to devote much space to how we might cope with this Orwellian future."  Allyn Jackson
"Move over Dawkins": Interview with Marcus du Sautoy. Interviewed by Paul Parsons. New Scientist, 29 November 2008, pages 4445. This interview with mathematician Marcus du Sautoy appeared shortly before he was to take over from Richard Dawkins as the Charles Simonyi Professor for the Public Understanding of Science at the University of Oxford. Unlike Dawkins, an avowed atheist who has clashed with many religious groups, du Sautoy said he will not be entering the religion versus science debate. "I think it's important for me to go in a new direction," he said. He intends to talk about science and mathematics and why they are exciting, entertaining, and important to society. One recent effort in this direction was du Sautoy's BBC series called The Story of Maths, which he told the interviewer "had fantastic viewing figures". Du Sautoy believes there is an untapped appetite for science and mathematics among the general public. He is also interested in the connections between science and art and says there is a "healthy breaking down of ... boundaries" between the two areas. Asked what he would like to see during his term as Simonyi Professor, du Sautoy said it would be a good sign if interviewers stop asking him questions like "So what's the point of science?" and start asking questions about science itself.  Allyn Jackson
"If You Liked This, You're Sure to Love That," by Clive Thompson. New York Times Magazine, 23 November 2008. If you have ever rented movies from Netflix, it's likely that some of your choices were influenced by the site's "recommendation engine," Cinematch. This software makes movie recommendations to customers based upon movies they have already seen and rated. In October 2006, Netflix chief executive, Reed Hastings, announced a US$1,000,000 prize for the first person or group to improve upon the software's predictions by 10 percent. In this article, writer Clive Thompson interviews some of the current top contenders. Many of these teams are using, at least in part, singular value decomposition to sort through the myriad aspects of different movies and then group together those that share similar qualities. Thompson also presents some of the challenges teams have faced: for instance, some people rate movies inconsistently or may change the way they rate movies over time. Many teams have found that, the closer they get to the goal, the more difficult it is to improve their predictions. At least one team blames this in part on hardtoclassify independent films like Napoleon Dynamite. "Some computer scientists think the Napoleon Dynamite problem exposes a serious weakness of computers," Thompson writes. "They cannot anticipate the eccentric ways that real people actually decide to take a chance on a movie." See the latest progress on the competition.  Claudia Clark
"The cosmic revolutionary": Interview with Neil Turok. Interviewed by Ivan Semeniuk. New Scientist, 22 November 2008, pages 4849. This article presents a profile of theoretical physicist and cosmologist Neil Turok, who was recently appointed executive director of the Perimeter Institute for Theoretical Physics in Waterloo, Ontario, Canada. The Perimeter Institute was established as an independent entity unaffiliated with any university and came into being with US$100 million from the founder of the Blackberry company, Mike Lazaridis. "Turok's mission is to bring promising young theoretical physicists from around the workd to Perimeter and offer them an environment in which to thrive," the article says. Turok expects many of them to come from lessaffluent countries, where young scientists must be extremely motivated in order to excel. Turok knows about such scientists, having founded the African Institute of Mathematical Sciences in his native South Africa. He is now working on an effort to raise US$30 million per year for the next five years, to establish 15 such institutes across Africa. "That's enough to graduate 750 students a year on an ongoing basis," he said. "I think that will change the face of development in Africa."  Allyn Jackson
Two views of Looking for the Order, courtesy of Dick Termes.
"Global Perspectives," by Barbara Jasny. Science, 21 November 2008, page 1191. The small town of Spearfish, South Dakota, seems like an unlikely place for mathematical and artistic innovation, and yet one of its inhabitants, painter Dick Termes, has dedicated his life's work to both. The Termesphere Gallery is home to the Termespheres: paintings on rotating globes, which give the observer the illusion of being inside the sphere, rather than watching its surface. Termes says that these pictures provide a sixfold perspective. Much of his work is displayed in art and science museums, math departments, government buildings, and corporations. One of his creations even became a part of the 100th birthday celebration for M.C. Escher in 1998. Termes currently divides his time between creating more artwork and developing an outreach program targeted to middleschool students called "Up, Down, and All Around: Geometry in Your Visual World." Some of Termes' works are online.  Adriana Salerno
"Draft Class," by Paul Kix. ESPN The Magazine, 17 November 2008, page 28.
"No last hurrah": Review of The Last Theorem, by Arthur C. Clarke and Frederik Pohl. Reviewed by Michael Marshall. New Scientist, 15 November 2008, pages 5051. This review is one item in a special section on the theme "Is science fiction dying?" The answer seems to be no, judging from the number of new books reviewed here. The Last Theorem was cobbled together from a partial manuscript and notes that Arthur C. Clarke handed over to fellow science fiction writer Frederik Pohl, shortly before Clarke's death. The plot centers on a Sri Lankan mathematician who, dissatisfied with Andrew Wiles's proof of Fermat's Last Theorem, comes up with his own, simpler proof. But then the mathematician takes a back seat in the story as a group dedicated to stopping wars takes center stage and an alien armada threatens to attack Earth. "Disappointingly, the disparate plot threads never mesh," the review says. "The book only really works as a compendium of Clarke's best ideas."  Allyn Jackson
"Rappin' Math Teacher Gets Top Honor," by Ana Tintocalis. KPBS Radio: Local News (San Diego, CA), 13 November 2008. "The Rapping Mathematician"a.k.a. Alex Kajitani, a middle school math teacherwon California Teacher of the Year honors for his fresh lyrical approach to integers and decimals. Kajitani, a lifelong rap fan who grew disillusioned with the vulgar lyrics, came upon the idea when he noticed that his students had difficulty remembering new mathematical concepts but could memorize the words to a new rap song nearly overnight. His rap songs, such as "The Number Line Dance" and "The Itty Bitty Dot," not only provide students with catchy phrases to remember mathematical operations, but also pique their interest in the subject. While most of Kajitani's raps deal with specific mathematical concepts, he also tries to include some social messages to teach students how to be good people. The radio segment links to a previous interview on KPBS Radio's These Days program.  Lisa DeKeukelaere
"An Infinite Beautiful Mind," by Patrick Barry. Science News, 8 November 2008. Writer Patrick Barry begins this article with an informal definition of the Nash equilibrium, noting that Nash proved the existence of "at least one such equilibrium for games with a finite number of strategic choices. But not all imaginable games are so limited." Now, mathematician Jinlu Li at Shawnee State University in Portsmouth, Ohio, and his colleagues have proven that, under certain conditions, a game with infinite choices is guaranteed to have at least one Nash equilibrium. Those conditions require that "all possible scenarios for a game taken together are 'compact,'" writes Barry; in addition, "[Li's] work is also based on a simplified situation: A game with only two players in which, for one player to win, the other must lose." Li himself says, "This paper is still far away from completely solving this problem... Our dream is we want to find the necessary and sufficient condition, a characteristic of the game that will always guarantee that it has an equilibrium." The paper will be published in the February 2009 Nonlinear Analysis.  Claudia Clark
"Any Kid Can Learn Math," by Margaret Wente. Globe and Mail, 8 November 2008. This opinion piece advertises JUMP (Junior Undiscovered Math Prodigies), a math curriculum developed by John Mighton, a Canadian mathematician and playwright. While the article's author gives no examples of how concepts are taught using JUMP, she does lament that rote learning, which is portrayed as a large part of the curriculum, has fallen out of fashion. "Your regular math texts have too much reading," says one educator, who explains that Englishasasecondlanguage students are put at a disadvantage by traditional math texts but flourish with JUMP texts. Testimonials of test scores rising and students becoming more responsive dominate the article. One educator says, "We found that the regular textbook wasn't reaching all the kids," and the reader is led to believe that JUMP does reach all kids. Wente claims parents have been "beaten into submission" to accept the popular teaching methods of progressives, which include "discovery" and exclude didactic learning. JUMP may be an excellent curriculum, but Wente's article does little more than rehash the cynical perceptions that teachers and parents are powerless in the face of politics and that new teaching methods are fundamentally at odds with traditional ones. Both "traditional" teaching methods and "progressive" constructivist methods have roots that reach back centuries, intertwining along the way. And while the article focuses on textbooks, the need for inservice training for teachers, which JUMP offers but the article hardly mentions, may be the more pressing concern.  Brie Finegold

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