Brie Finegold summarizes blogs on Chaos theory and weather forecasting, and Recent difficulties with RSA.
"Forecast uncertain: Chaos theory, weather predication, and brain cancer," by Maggie Koerth-Baker. Boing-boing, 5 January 2012.
The mathematics used in weather forecasting may also help predict the spread of brain cancer (also called glioblastoma). Like the weather, a cancer's growth is chaotic in nature. A new algorithm for weather prediction is the Local Ensemble Transform Kalman Filter, which, as explained in the article, makes a forecast by synthesizing samplings from areas that are deemed the least predictable. This algorithm uses statistical techniques to analyze chaotic systems and is therefore relevant to the spread of cancer.
Mathematician Eric Kostelich is interviewed about how this method for forecasting next week's weather might extend to a method of forecasting the next six weeks of growth of a brain tumor. As part of a research team including cancer researchers, Kostelich published findings about cancer in December in the journal Biology Direct. Kostelich points out that just as small improvements in weather forecasting have saved many lives, even forecasting the direction or manner in which a tumor grows might greatly improve diagnosis and treatment. The fact that most brain cancers are inoperable was part of his teams' decision to focus on brain cancer as opposed to other cancers.
"The Recent Difficulties with RSA," by David Speyer. Secret Blogging Seminar, 16 February 2012.
RSA, an algorithm for public key cryptography has recently been found by several computer scientists to be susceptible to attack due to the over-use of certain large primes in creating keys. SSL (Secure Sockets Layer) certificates are used for website security, and are issued by only a small number of multi-national companies. Mathematician David Speyer writes "Key generators choose random pairs of primes from a set of size 10^{151}, multiply them, and hand out the products. With such a large range of primes to choose from, they should never need to reuse. But, apparently, they do. Some primes, it seems, are the Times Square of 300 digit primes. In a sampling of 4.7 million RSA keys from around the internet, one particular prime turned up 12720 times! The researchers estimate that as many as 2 in every 1000 RSA keys may be vulnerable in this way. Speyer then gives a short introduction to the mathematics that could be used to attack the encryption when too many keys are based off the same prime numbers. Comments include some ideas for solutions to the problem.
--- Brie Finegold
"Math equations could save drug-overdose patients," by Brian Maffly. ABC Action News, Salt Lake Tribune, 28 February 2012.
A mathematician-biologist at the University of Utah has built a math equation that could save the lives of hundreds of Americans who die each year of acetaminophen overdoses. Fred Adler's equation, which appears in the journal Hepatology, offers a way for doctors to quickly determine the timing and severity of the overdose based on biomarker values from a standard blood test. Such insight is particularly valuable in acetaminophen overdoses because patients are often comatose, making acquisition of critical information difficult, and early arrangement of a liver transplant, if needed, is crucial. Adler explains that "math helps you see the invisible," for cases such as drug overdoses in which doctors are unable to immediately, directly observe the liver damage caused. Adler's equation correctly predicted survivorship in 49 of 53 cases in a retrospective study, but more testing is needed to prove reliability before doctors can start applying the equation in the examining room.
--- Lisa DeKeukeleare
"Road Scholars Solve Pothole Problem." News, Science, 24 February 2012, page 897.
Keeping the streets of any city free of potholes is one of those impossible tasks. The city of Boston has a new weapon in its arsenal, smartphones armed with math algorithms to detect potholes. Massachusetts based InnoCentive organized a web-based challenge where anyone could submit a strategy to detect potholes and three different submissions received a $9000 prize. Undergraduates Nathan Marculis and SaraJane Parsons developed a method using wavelets and Kruskal clustering. A team headed by MIT grad Michael Nagle came up with a way of measuring the size of a pothole and distinguishing between potholes and railway crossings. A third winner Elizabeth Yip of Washington also received a prize. The three algorithms are now being merged into one mobile phone app that will be made available to the public.
--- Baldur Hedinsson
"Playing with infinity on Rikers Island," by David McConnell. Prospect, 22 February 2012.
In this personal perspective piece, the author discusses some of his experiences teaching mathematics to prison inmates and high school drop-outs. "I had strong anti-mathematical and sentimental leanings as a child," he wrote, but fell in love with mathematics when he was an adult and studied the subject "with great pleasure but little talent." He developed an affinity for the intuionism of L.E.J. Brouwer and writes, " I always liked the idea of building all of maths from the human experience of a moment of time." It was not easy trying to get his students to share in his aesthetic appreciation of mathematics, particularly the prison inmates. Both the inmates and the drop-outs cared more about job applications than about mathematics, but the latter group "were more curious and willing to peer across the glassy, abstract region of mathematics. That's what I wanted. With them I could be a tour guide and not simply teach a drab handful of methods."
--- Allyn Jackson
"Finally, The Physics Of The Ponytail Explained," Scott Simon and Keith Devlin. Weekend Edition Saturday, National Public Radio, 18 February 2012.
NPR's "Math Guy" Keith Devlin chats with host Scott Simon about a recent research finding (by mathematical scientists in the U.K. and a scientist at Unilever) that the shape of a ponytail can be deduced from the properties of a single hair. There are "three factors of the individual hairs that are important. One is its elasticity, one is its density, and one is its curliness." Why is this important? Devlin points out that Unilever is a producer of hair care products (for which there is a $40 billion market worldwide), but also that just as a ponytail is made up of individual fibers, so are "fiber optic cables, which are of major importance now in communications transmission. The cables that hold up suspension bridges consist of many strands of steel that are bundled together. So we're talking about mathematics that holds up the Golden Gate Bridge, mathematics that tells us how fiber optic cables behave when they're twisted and bent through conduits. So this is actually much more than a question about hairstyle." --- Annette Emerson |
"How Companies Learn Your Secrets," by Charles Duhigg. New York Times Magazine, 16 February 2012.
"Seven equations that rule your world", by Ian Stewart. New Scientist, 13 February 2012.
"We are afloat on a hidden ocean of equations," writes Ian Stewart. This article discusses several equations that revolutionized scientific understanding and that today govern all kinds of phenomena with which we interact on a daily basis. Stewart, a noted mathematician and master expositor, has published several popular books, most recently In Pursuit of the Unknown: 17 Equations that Changed the World (Basic Books, March 2012). This article gives a flavor of what's in the book. Here he puts the spotlight on 7 equations: the wave equation, Maxwell's four equations, the Fourier transform, and Schrödinger's equation. He sets each equation in its historical context, showing the dramatic impact each had not only on innovations that have changed daily life, like cell phones and compact disks, but also on human understanding of the world. Writes Stewart: "A truly revolutionary equation can have a greater impact on human existence than all the kings and queens whose machinations fill our history books." See a related posting in the New Scientist TV blogs is Wall Street's sexiest model, he, "Animation reveals the world's hidden equations". --- Allyn Jackson |
"Big Ideas Monday: Maths," by Lynne Minion (Genevieve Jacobs). ABC-Canberra, 13 February 2012.
In this article, journalist Lynne Minion writes about an episode of the radio show Afternoons, which host Genevieve Jacobs devoted to the subject of math and why people either love it or hate it. Jacobs interviewed several math professors, a radio host (and self-professed math geek), and the 2010 Australian Sudoku champion, among others. Interviewees spoke about what drew them to math: radio host Adam Spencer described how math "simply made sense from an early age" while Australian National University professor Michael Barnsley spoke of how he "fell in love with fractal geometry." They also described the role that math teachers should play in their students' appreciation for the subject: for example, Professor of Mathematics Education Celia Hoyles stated that "I think most young children really start being intrigued by mathematical ideas. ... I think we have to work very hard so that we don't put them off and keep their interests engaged."
Hear the Jacob's interviews with Hoyles and Sudoku champion John Eales.
--- Claudia Clark
"At the Blackjack Ball, Card Counter Dr. Edward Thorp Is King," by R.M. Schneiderman. The Daily Beast and Newsweek, 13 February 2012.
If you love to play blackjack or are fascinated by stories of card counting, thank "card-counting mastermind" Dr. Edward Thorp. He "first got the idea that blackjack could be beaten in 1958 when he stumbled across an article about basic strategy, a blackjack theory developed in 1953 by four men in the Army." After reviewing the math behind the article, Thorp--a math PhD--used an IBM computer to create "the first-ever card-counting strategy." Schneiderman continued, "In 1961, he presented these findings to the American Mathematical Society." This led to an article in The Washington Post and attracted the attention of notorious bookie Emmanuel Kimmel, who gave Thorp $10,000 to try his strategy (for 90 percent of the cut). Thorp wrote about the success of his strategy in the 1962 book Beat the Dealer. Casinos responded to the resulting explosion in the game's popularity by changing the game's rules in their favor (for a short time in 1964), then changing the rules back but instituting new countermeasures that allowed the dealers to reshuffle more frequently. In the late 1960s, Thorp turned to Wall Street. Since then, card counters have developed a new way "to crack open the casino vaults: teamwork." --- Claudia Clark |
"The Age of Big Data," by Steve Lohr. New York Times, 12 February 2012.
If you haven't been living under a rock for the past ten years, you know that the amount of data available to science, business, and government is exploding--and that the attention and innovation devoted to making sense of it are following suit. Thankfully, this article goes beyond the hype to explore why and how data is growing, and give a glimpse of where big data might take us. The amount of data available grows by 50 percent each year. Much of it is generated on the internet-user comments, images, videos, facebook "likes" and the, er, like. And data that was once archived in an analog fashion is now making its way onto the web. But more and more data is being generated by sensors embedded in the technology all around us--in automobiles, shipping crates, and industrial equipment, not to mention cellphones--capable of measuring temperature, humidity, location, vibration, and even chemical concentration. These sensor networks are giving rise to a new Internet of Things. Analysis of nontraditional data types--known by the umbrella term "unstructured data"--is possible thanks to new techniques that depend largely on advances in artificial intelligence. The result is software capable of sorting through massive amounts of data, making quick decisions about its significance, and even learning from its mistakes. As the amount of data and user feedback available to network-based machine-learning programs--like the iPhone's Siri--increases, these programs get better at doing their jobs. An evocative metaphor for the changes taking place is provided by Professor Erik Brynjolfsson of M.I.T.'s Sloan School of Management, who suggests that the effect of "Big Data" on science and society will be akin to the effect of the microscope. Just as the microscope allowed the observation of biological and chemical processes at previously undreamed-of spatial resolutions, Big Data allows us to measure social, behavioral, and even emotional processes on previously undreamed-of timescales. In other words, Twitter and Facebok represent, not the death knell of deep and nuanced public discourse, but a powerful new research tool--already yielding useful results, like the fact that Google searches for terms like "flu symptoms" precede flu-related visits to emergency rooms by a couple of weeks, and that the volume of housing-related Google searches predicts the housing market better than real estate economists do. The academy, business, and government are all putting this new tool to use, and there are plenty of new initiatives in the offing--such as the U.N. initiative Global Pulse, which will attempt to forecast disease outbreaks and regional economic downturns using "sentiment analysis" of text messages and social network data. Of course, not all these initiatives will pay off, and the possibility for incompetent, thoughtless, or pernicious uses of Big Data will only grow. One way to safeguard against such errors is to train a data-adept workforce, and the article quotes a McKinsey Global Institute report calling for about 200,000 more workers with "deep analytical expertise". Those of us with quantitative training seem particularly well-positioned, from the perspectives of both economics and, for perhaps the first time, popular culture. As data analysis becomes less and less about crunching only numbers, says Columbia University political scientist Andrew Gelman, "there is this idea that numbers and statistics are interesting and fun. It's cool now." --- Ben Polletta |
"Self as Symbol," by Tom Siegfried. Science News, vol. 181 no. 3, 11 February 2012, pages 28-30.
Scientists including the famous DNA-discoverer Francis Crick toiled for years to understand human consciousness, but the parallels between consciousness and the fundamental axioms of mathematics reveal that the problem might not be solvable. Austrian logician Kurt Gödel demonstrated that mathematical systems such as arithmetic must be based on at least one axiom that cannot be proved true within the system, and therefore there is no set of self-consistent axioms for deducing all of mathematics. Similarly, as Douglas Hofstadter explains in his book "I Am a Strange Loop," consciousness--like a set of mathematical principals--is a feedback loop that references symbols it has generated itself. Just as Gödel's work enriched the field of mathematics, thinking of consciousness as a "strange loop" may lead to a better understanding of how the biological and chemical processes within the brain work together to make us who we are.
--- Lisa DeKeukelaere
"Born in the USSR," by Kaustuv Basu. Inside Higher Ed, 9 February 2012.
Math and economics are familiar bedfellows, but it's a rare study that examines the economics of mathematics. George J. Borjas of the Kennedy School of Government and Kirk B. Doran of Notre Dame have used a "natural experiment"--the migration of physicists and mathematicians to the U.S. immediately prior to and during the collapse of the Soviet Union--to explore how the presence of highly-skilled workers affects the productivity of their colleagues and competitors. In contrast to the experimental sciences, which suffered from a lack of resources and lagging technology, the theoretical sciences thrived in the U.S.S.R. Mathematics and theoretical physics served as a refuge from Party politics - and stifling repression - for many bright minds. Mathematical development in the U.S.S.R. diverged widely from that in the U.S., due to different historical conditions and a dearth of communication between the two countries. While mathematicians in the U.S.S.R. took a liking to differential equations ordinary and partial, mathematicians in the U.S. focused on statistics and operations research. (The fields exhibiting the biggest differences in the two countries were integral equations--half again more developed in the Soviet Union than in the U.S.--and statistics--which saw about 17 times more publications in the U.S. than the U.S.S.R. Readers may not be surprised to discover that other fields of Soviet specialty were probability and stochastic processes - thanks to Kolmogorov and his school--and analysis on manifolds--thanks to Kolmogorov's student Arnold, and his students in turn. In the absence of Milnor and Bott, the topology of manifolds never saw the light of the Soviet day, and American computers allowed American mathematicians to make greater strides in computer science and numerical analysis than their Soviet counterparts.) All this changed when the Soviet Union began to fall apart. According to Borjas and Doran, 336 Soviet mathematicians migrated to the U.S. as a result. Examining a database containing every mathematical publication in the last 70 years, the two found that the eastern emigres had a significant negative impact on western mathematicians working in "Soviet-style math". While new ideas and theorems enriched their fields, these mathematicians had a harder time publishing "home-run" papers than their colleagues in the lee of the Soviet tide. Many were pushed into lower-tier academic positions, or out of academia altogether. And although the students of Soviet emigres have been more productive than their native-advised counterparts, these productivity gains are more than made up for by the losses in productivity suffered by students in Soviet-dominated areas with non-emigre advisors. This lost generation of U.S.-born mathematicians must be balanced against the new ideas and new directions the Soviet mathematicians brought with them, and the refuge they found here.
Be sure to check out the link to the very entertaining and interesting 1990 New York Times article, starring Persi Diaconis and representation theorist Victor Kac, which Times science writer Gina Kolatta penned while the migration was in full throttle.
--- Ben Polletta
"An Israeli professor's 'Eureqa' moment," by Asaf Shtull-Trauring. Haaretz.com, 3 February 2012.
A computer program by Israeli Professor Hod Lipson recently garnered attention for its ability to generate formulas accurately describing natural phenomena, and indirectly highlights questions about the future role of computers in science. His program, named Eureqa, is based on the concept of "evolution" algorithms and works off of large data sets from observations of systems such as swinging pendulums. Eureqa randomly generates a set of equations, then makes random modifications to the equations in a series of "generations" while continually filtering out the equations that best fit the data and discarding the rest. Lipson has touted Eureqa as a tool for identifying the laws of nature, and he cites several examples such as wing-flapping motion and tire/road interaction for which Eureqa has generated formulas similar to those previously developed through years of scientific work. Several other scientists note, however, that one must understand the underlying concepts of a system in order for Eureqa's output to be meaningful. This argument central to a larger conversation within the scientific community about what using computers to solve proofs unverifiable for humans means for the future of research and progress. See the Distilling Free-Form Natural Laws from Experimental Data on the Cornell Creative Machines Lab website. (Photo: Professor Hod Lipson with research student Michael Schmidt. Lindsay France, Photographer, University Photography, Cornell University.) --- Lisa DeKeukelaere |
"Beauty, Truth, Math, Art," by Sarah Reynolds. Studio360 and National Public Radio, 3 February 2012.
WNYC's arts and culture radio program, Studio 360, aired a segment about an art exhibition at the Joint Mathematics Meeting in Boston. The meeting is the largest annual gathering of its kind, attended by thousands of math enthusiasts to hear about exciting mathematical advances. The conference is also a major social event in the math community and includes workshops, banquets, sessions for students, a game show and much more. Dr. Robert Fathauer organized this year's exhibit, which had over 120 works by some 80 artists. A video that accompanies the radio segment and can be found online truly captures the beauty of the math inspired art displayed at the exhibition. Among those interviewed are Fathauer, who says "Art and math might seem different on the surface, but there certainly are similarities, both are about beauty and truth." Dr. Gabriele Meyer (Mathematics Department, University of Wisconsin) who makes crocheted hyperbolic shapes, says "In math if you want to prove something really beautiful, you have to understand the structure. And the structure means you understand the beauty of an object and with that knowledge you often times can make a very important and deep proof. That's why beauty matters tremendously in mathematics." The segment also features Eddie Beck (undergraduate at University of Georgia), Jesse Louis-Rosenberg (Generative Desginer and Co-Founder of Nervous System, which generates objects using a 3D printer), and a mathematics student at the exhibit who says of the mathematical art exhibit, "I really love math. I'm trying to explain it's really cool, really dynamic, really like this engaging topic.... but you don't need a bunch of 4000-level classes to see why this is cool. This is innately beautiful in and of itself." --- Baldur Hedinsson |
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