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November 2009
"Empathy provides X factor in GED tutoring program," by Sara Olkon. Chicago Tribune, 29 November 2009, page 8. Some people wear their passion on their sleeves, but Adrianna Collis wears it on her ears and her upper arm. She is a math tutor and the coordinator for the education and vocation program at a youth center in Chicago who has helped 200 people get their GEDs. She loves math so much that she has pi earrings and has the first few rows of Pascal's triangle tattooed on her left arm. Collis is not bothered by not fitting the stereotype of a math teacher: "It's kind of fun fooling the world." --- Mike Breen
"Invisibility Uncloaked," by Charles Petit. Science News, 21 November 2009, pages 18-23. Petit writes of scientists' efforts to make objects invisible. Most of the article is about physics, but there is some mathematics discussed, especially geometry and conformal mapping. (See also articles on invisibility summarized in a previous Math Digest as well as the Mathematical Moment on cloaking [pdf].) --- Mike Breen
Recent Math Masters Columns by Marty Ross and Burkard Polster:
"America’s Top College Professor," by Naomi Schaefer Riley. Wall Street Journal, 13 November 2009.
"Lincoln East top team at Math Day; LSW's Zhou top individual." Lincoln Journal Star, 12 November 2009.
"Q&A: The algorist," by Daniel Cressey. Nature, 12 November 2009, page 166. Jean-Pierre Hébert is interviewed about his artwork, which he creates using mathematical algorithms. Hébert is a former engineer who is now the resident artist at the Kavli Institute for Theoretical Physics. He prefers to work with physical objects, such as sand, rather than work only with computers. Are algorithms important in art? "Over the past century most artists were algorists, even if they did not know it. Mondrian has an algorithm; cubism was a set of algorithms. Algorithms are just a tool, as is a computer, a brush or a pencil. The personality of the artist takes over and should transpire through the work. Algorithms are not an end in themselves." --- Mike Breen
Recent articles on the state of mathematics education: The newspapers in Florida, Georgia and Oregon all report progress in their states regarding improving mathematics test scores and, importantly, generating interest of elementary through high school students. The Gainesville Times reports that "while using the state curriculum as a framework for math instruction, local schools are adding their own elements to support student achievement." This includes a successful program that puts students into three groups--remedial, standard and accelerated--to cater to the learning requirements and styles of those students. The article describes how a charter school, the Centennial Arts Academy, infuses math with the arts and how the Hall County schools are implementing Singapore Math, but notes budget cuts undermine teacher training. In Oregon, "math teachers have moved middle-schoolers far enough ahead in math that the typical eighth-grader now can do math at nearly the same level as many high school sophomores," and the article explains the reasons--new textbooks, workshop classes, and innovative methods. In Pasco County, Florida, the Bayonet Point Middle School has been charged with improving math proficiency. Among the new ideas launched--"something other than the well-worn drill and kill""--are peer tutors, smart boards and computerized projectors called Elmo to improve student interactivity, student math clubs, and math games. --- Annette Emerson
"Quantum Computers Could Tackle Enormous Linear Equations," by Laura Sanders. Science News, 7 November 2009, page 11. Researchers recently proposed a method much quicker than classical computers for solving very large linear equations: quantum computing, which operates using quantum forms such as the spins of nuclei and their properties. Very large linear equations are used to solve problems related to image processing, internet traffic control, and variety of other areas, and quantum computers offer a way to solve these equations in dramatically fewer steps and therefore less time. The advantage of quantum computers is their ability to store both 0 and 1 in a single bit of information, unlike classical computers in which a bit must be either 0 or 1, so an operation that would require many steps in a classical computer can be completed with just one in a quantum system. The idea of using quantum computing to solve linear equations is leading the researchers to seek out other new uses for quantum computing’s powerful abilities. --- Lisa DeKeukelaere
“Russia’s Conquering Zeros,” by Masha Gessen. The Wall Street Journal, 6 November 2009. In this article, writer Masha Gessen discusses the reasons that a Russian mathematician would solve the Poincaré Conjecture, one of the most difficult mathematical problems of our time. Several decades ago, mathematics was at odds with the Soviet regime: for example, Gessen observes that “math placed a premium on logic and consistency in a culture that thrived on rhetoric and fear; it required highly specialized knowledge to understand; and, worst of all, mathematics lay claim to singular and knowable truths—when the regime had staked its own legitimacy on its own singular truths.” However, mathematics had some factors in its favor, including its remarkable strength in Russia in the 1930s and, in 1941, the fact that it was needed to recalculate distances and speeds for the newly retrofitted civilian planes that would replace the recently destroyed Soviet air force. During the decades following World War II, Gessen notes, “the Soviets invested heavily in high-tech military research.” The number of people involved in this effort has been estimated to be as high as 12 million, a “couple million” of them employed at military-research institutes. By the 1970s, a mathematics establishment provided jobs, money, and other benefits—within a totalitarian system—to some of its privileged members. Mathematicians who were not welcome, including Jews and women, formed a mathematical counterculture, where, according to AMS publisher Sergei Gelfand, mathematicians did “math for math’s sake.” Their only reward was the respect of their peers. With the fall of the Soviet Union and the end of state investment in mathematics, mathematicians started coming to the United States. Here, Gessen writes, they would find a culture that “offers the kinds of opportunities for professional communication that a Soviet mathematician could hardly have dreamed of, but it doesn’t foster the sort of luxurious, timeless creative work that was typical of the Soviet counterculture.” --- Claudia Clark
"Somer Thompson's murder: A real-life 'Numb3rs' case?," by Ivy Bigbee. True Crime Examiner, 5 November 2009. Dr. Kim Rossmo, who earned his PhD in mathematics while he was a police officer in Canada, inspired the pilot episode of Numb3rs. Now at Texas State University, Dr. Rossmo combines his interests in mathematics and forensics by creating new algorithms which pinpoint the location of a serial criminal's homes or areas of activity. Dr. Rossmo has designed new means of geographic profiling, which are being used by law enforcement to narrow their searches for evidence. By taking into account that criminals are just as likely to behave according to patterns as the average Joe, the algorithms pinpoint zones where the perpetrator of a previous crime is most likely living or is most likely disposing of evidence. People do not commit crimes randomly, but have "comfort zones" as well as zones that are too close to home for pursuing their criminal activities. Little is said in the article about the algorithms themselves, what is new about them, or whether Dr. Rossmo is the first to use geographic profiling. As for Somer Thompson, Ms. Bigbee writes, "Should profilers suspect Somer's murder has similarities --'signatures' or modus operandi --to other area homicides, forensic data banks could be mined to produce a veritable map of the most likely suspects." Although there is no mention as to whether Dr. Rossmo's techniques are currently being used or not in Somer's case, these techniques have been extended to study the hunting patterns of sharks and the flight patterns of bees. Perhaps animals and humans have more in common than we care to think. --- Brie Finegold
"The Numbers Guy: Coincidental Obscenity Deemed Extremely Dubious," by Carl Bialik. The Wall Street Journal, 5 November 2009. How likely is it that you will accidentally spell out an obscenity with the first letters of each sentence in a short note? The chances are worse than one in 10 million. But in Governor Schwarzenegger's recent veto "the first letter of each of the seven lines spells out a profane rebuke that starts with 'F' and ends with 'you.'" Prof. Brendan McKay, a computer scientist at Australian National University in Canberra, warns "We shouldn't be too eager to claim a small 'probability' as a proof that something can't have happened accidentally." The Governor claims that this message was coincidental. Computational linguists, who study patterns in language by using probability and statistics, agree that "secret messages" may coincidentally show up in long written works like the Bible, but such messages are unlikely to show up in shorter documents. For instance, the letter "K" is rare as a first letter of a sentence, but is part of one of the Governor's frequent phrases. Whatever the origin of the message, it has sparked an interest in connections between math and linguistics. --- Brie Finegold
“Tomorrow’s Weather: Cloudy, with a chance of fractals,” by Robert Matthews. New Scientist, 4 November 2009.
“Alice Schafer, 94; math professor breached social barriers,” by Emma Stickgold. Boston Globe, 2 November 2009.
"The Brain," by Carl Zimmer. Discover Magazine, November 2009. Are our brains naturally wired for math? The answer seems to be yes, and that in fact our brains have been recognizing and understanding numbers for about 30 million years. Since the moment they are born, humans have an uncanny ability to understand numbers. But how does this innate sense develop as we grow older and learn new skills? Jessica Cantlon, a neuroscientist at the University of Rochester, and Elizabeth Brannon, of Duke University, investigated this question by designing an experiment that forced adults to rely on intuition alone. People would be shown two consecutive sets of dots on a computer screen, and then two sets side by side, and they scored points by selecting the set which represented the sum of the previous two. The scientists discovered that mathematical intuition consistently follows two rules. First, people scored better when the numbers were smaller, and second, they also scored better when the difference between the two numbers was large. These two rules have also been observed in babies and even monkeys, which suggests that our brains use the same mental algorithm throughout their lives, and have been for at least 30 million years. This begs the question: where in the brain is this happening? Neuroscientists have found that for both humans and monkeys the area that is most active while doing mathematical intuition problems is a strip of neurons near the top of the brain, surrounding a fold called the intraparietal sulcus. Andreas Niedler, from the University of Tubingen, developed experiments which show that monkeys can even learn written numbers, a skill children develop only around age 5. Monkeys seem to have a very solid foundation for numbers, so why are they not able to perform high-level mathematics? Nieder and Cantlon have both speculated that our ability to understand symbols enables us to transform our intuition into a precise understanding. Even though our ancestors probably started out thinking about numbers the way monkeys and babies do, once they linked their natural instincts with an ability to understand symbols, everything changed. --- Adriana Salerno
"Crash Test Anti-Dummy," by Bjorn Carey. Popular Science, November 2009.
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