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October 2012
Brie Finegold summarizes blogs on visualizing big numbers and on Martin Gardner: "The Best Graphics That Make You Realize You Don't Know How Big Anything Actually Is," by Rose Eveleth. Smithsonian.com blog: Smartnews, 22 October 2012 4:38 p.m. Piggybacking off Steven Strogatz's blog post on Visualizing Vastness, Rose Eveleth summarizes Strogatz's thoughts on why it is that we find it so difficult to comprehend large numbers such as those that measure distances between planets. She then goes on to list links to several descendants of the 1977 Powers of Ten short film that, as she writes, "melted the face off" anyone who watched it at the time. The film started with an aerial view of a couple picnicking in the park and zoomed out (and in) scaling by powers of ten in an effort to drive home the idea of exponential growth and decay. Even now, that video is instructive, but newer graphics such as one from XKCD, a beloved math and science-themed comic, have thrown their hats into the ring. Probably the most impressive are the two interactive sites Scale of Universe and Magnify the Universe. The latter has crystal-clear graphics that really suck in the participant. Both operate by the user dragging a slider all around to move both up and down through the powers of ten.
"Flexagon but not forgotten: Celebrating Martin Gardner's Birthday," by Evelyn Lamb. Scientific American Observations, 19 October 2012; Famed Scientific American columnist and puzzle-master Martin Gardner would have turned 98 on October 21. In tribute to his impact on the layperson's attitude towards mathematics, Vi Hart made a series of three wonderful videos about Hexaflexagons--pieces of paper folded and taped together to form a flat and malleable mobius strip that seems to reveal new "sides" at every turn. The blogger Lamb gives some of the highlights of the playful videos including links to more mathematics, and she also quotes the fast-talking Vi Hart describing Gardner as a "math-inspiration grandfather." Dana Taimina, who is well-known for crocheting extensive models of hyperbolic surfaces and creating fiber art inspired by low-dimensional topology also paid tribute to Gardner by posting a puzzle in the form of an online gallery of paintings that "all have something in common." The challenge is to find out what. She also describes how she was inspired as a young girl in Latvia by one of only two books of his that had been translated into her language. She went on to become a math teacher and lover of recreational mathematics, and to earn her doctorate. It seems that Gardner was in the math-inspiration genealogy of Taimina as well. --- Brie Finegold "A Mathematician Hacked Into Google Because He Thought It Was Part Of A Job Interview," by Geoffrey Ingersoll. Business Insider, 25 October 2012. When mathematician Zachary Harris received an email from Google he wasn't sure if it was real or a scam. The email's header information seemed legitimate but he noticed that "the cryptographic key meant to verify the email wasn't using encryption up to standards." Ror its own digital signatures, Google was using a 512-bit key rather than the standard and far more secure 1,024-bit key. In response to the email Harris then sent his own email to Google CEO Larry Page--assuming the identity of Google co-founder Sergey Brin. When Google caught on to the discovery the company upgraded its encryption. Harris told Wired, "I love factoring numbers. So I thought this was fun. I really wanted to solve their puzzle and prove I could do it." This story was picked up in other media and blogs, including "How a Google Headhunter's E-Mail Unraveled a Massive Net Security Hole," by Kim Zetter, Wired, 24 October 2012 and Google Says Google Apps Domains Were Protected From Massive Spoofing Vulnerability," by Elise Ackerman. Forbes, 29 October 2012. --- Annette Emerson "The maths that made Voyager possible," by Christopher Riley and Dallas Campbell. BBC Four, 22 October 2012. Voyager didn't write the song "Don't Stop Believin'" (that was Journey) or the song "Cold As Ice" (that was Foreigner). That's because Voyager isn't a rock band at all, but a pair of unmanned space probes that are rapidly approaching the edge of the solar system. But even if you never thought Voyager was a hit band from the 70s, this lovely article on the mathematics behind the Voyager program will edify and entertain you. For example, it reveals that Voyager's flight path is one of hundreds that were drawn up in 1962 (by hand) by NASA summer intern Michael Minovitch, and promptly ignored for three years. Minovitch, a UCLA graduate student in mathematics, had been stealing time from his qual prep to study the three-body problem on UCLA's IBM 7090, the fastest computer on Earth at the time. He discovered that an object flying close to a planet would experience acceleration due to that planet's gravitational force. Such acceleration could be used in a "gravity assist" or "slingshot maneuver" to accelerate a spacecraft away from the sun, propellant-free. Minovitch spent the summer of 1962 interning in the Jet Propulsion Laboratory, repeating his simulations with more accurate data. But then he ran out of funding, and the hand-drawn trajectories he used to sell his ideas were unable to distract the rest of JPL from the Apollo Project. It was the work of another summer intern, spacecraft engineer Gary Flandro, that lent the project that became Voyager some urgency. Flandro was also thinking about the three-body problem, but his practical perspective led him to chart the trajectories of the planets. Flandro realized that in the late 70s, just as Journey was pumping out their highest-grossing album, Escape, Jupiter, Saturn, Venus, and Neptune would all be on the same side of the solar system--an ideal configuration for a spacecraft to make its own escape, shooting past all four planets in only 12 years. Flandro's realization came not a moment too soon, considering the inertia of government bureaucracy, because the window opened up by the planets' can-can wouldn't reopen for another 176 years. The Voyager Project, consisting of two probes, combines Minovitch's idea of a planetary slingshot with Flandro's idea of a grand planetary tour. Launched in 1977, it's the result of long years of lobbying by Minovitch, Flandro, and influential space advisor Maxwell Hunter, and not a little planning. Voyager 2 ("the tourist") was launched first. It has completed its fly-by of the outer solar system, and is now approaching what's known as the termination shock--the ellipse where the solar wind first starts to slow from its speed of 1 billion miles an hour--about eight years after its younger sibling. Voyager 1 ("the slingshot") skipped the four planets, making a beeline for the edge of the solar system, and becoming the furthest man-made object from the earth. Voyager 1 is close to crossing the heliopause--the limit of the solar wind--and to becoming the first human artifact outside the heliosphere--the bubble of charged particles blown into interstellar space by the solar wind. The data from the two probes have yielded countless discoveries, such as the fact that the solar system is asymmetrical, and the presence of giant magnetic bubbles in the heliosphere. And to think that it all started with a couple of interns. I guess that's why they say... don't stop believin'. There's more to read on Wikipedia and NASA's homepage. --- Ben Polletta "Economics Nobel Honors Matchmaking Finesse," by Yudhijit Bhattacharjee. Science, 19 October 2012, page 314.
[Editor's note: Read more about matchings in two AMS Feature Columns, "School Choice" and "Mathematical Marriages."] --- Ben Polletta "Penn State offensive lineman's life is proof that higher mathematics and college football can mix," by Mark Dent. Pittsburgh Post-Gazette, 17 October 2012.
The sports section of the Pittsburgh Post-Gazette has a portrait of John Urschel, who is a Penn State offensive lineman and a rising star in the mathematics department. Not only is Urschel a starting guard on the Penn State offensive line, he is also on course to graduate with a 4.0 grade average in mathematics and is working on research projects generally reserved for students with much more experience. Urschel has been working on a research paper on celestial mechanics with Professor Vadim Kaloshin, who now teaches at the University of Maryland. Together they have discovered the possibility of asteroids in the belt around Jupiter crashing into Mars. Urschel is also working with Xiaozhe Hu, a postdoc, on a research paper about parallel computing. After Penn State, Urschel plans on playing professionally if he can make the NFL after which he wants to get his doctorate preferably at Stanford, MIT or Princeton. --- Baldur Hedinsson "Mathematics and What It Means to Be Human, Part 1," by Michele Osherow and Manil Suri. The Chronicle of Higher Education, 12 October 2012, pages A33-34.
This is the first of a three-part article. Part 2 and Part 3 are also posted online. Photo: José Villarrubia (Parts 2 and 3?) --- Baldur Hedinsson
"A mathematician and computer scientist with area ties wins a MacArthur fellowship," by Tom Avril. The Philadelphia Inquirer, 3 October 2012;
Two mathematicians, Daniel Spielman and Maria Chudnovsky (pictured above), were among the 23 recipients of the 2012 MacArthur Fellowships. The prizes, which the MacArthur Foundation awards annually based on anonymous nominations of individuals who excel in medicine, science, and the arts, include $500,000 over five years for each honoree. Spielman, a Philadelphia native and professor of computer science and mathematics at Yale University, was honored for his work on methods for solving linear equations with large numbers of variables, which could be applied to helping computers learn to recognize speech and images. Chudnovsky, who was born in the Soviet Union, raised in Israel, and works as an assistant professor at Columbia University, received a fellowship based on her work in graph theory, in particular her solution to a 40-year-old theory on graph classification. For more information, check out the profiles for Spielman and Chudnovsky on the MacArthur Foundation website. Evelyn Lamb, 2012 AMS-AAAS Media Fellow who now writes for Scientific American, also wrote about the two winners in "Perfect Graphs and Perfect Harmony: Meet 2 of the 2012 MacArthur 'Genius' Fellows." --- Lisa DeKeukeleare "Mandelbrot: Art, math, science, and works in progress," by John Timmer. Ars Technica, 1 October 2012.
The oldest works include sketches by Edward Lorenz of three-dimensional representations of chaotic attractors, as well as some drawings and "a simple visualization, done with an analog computer" by Otto Rössler. The majority of the work displayed here is Mandelbrot's, including large numbers of hand-drawn sketches and computer print-outs, as well as photographs, objects, and films. This exhibit, curated by Visiting Assistant Professor Nina Samuel, runs through January 27, 2013. Image: Quarternion, 1983. Computer-generated prints on photographic paper. Benoît Mandelbrot and Alan Norton, programmer. Collection Aliette Mandelbrot. Courtesy of the Bard Graduate Center (along with much help from John Timmer). --- Claudia Clark
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This year's Nobel Prize for Economics rewards two scientists who've used game theory to better understand pairwise matching - and to improve how residency programs match with residents, how high schools match with their students, and even how kidney donors match with their recipients. The winners of the prize are Lloyd Shapley, who along with late mathematician and economist David Gale developed the so-called Gale-Shapley algorithm of pairwise matching (the Nobel is not awarded posthumously), and Alvin Roth, who showed that the National Residency Matching Program was unwittingly applying the algorithm, and then went on to improve the NRMP by wittingly using it. Shapley and Gale's algorithm was originally formulated at UCLA, in the case of 10 men and 10 women trying to pair off as married couples. In this scenario, each man proposes to his first choice, and each woman rejects all but her top choice out of her suitors, whose proposal she holds without accepting or rejecting. Then, each man without a proposal in play proposes to his second choice, the women hold onto their new favorite proposal, and a new crop of untethered bachelors proposes to their third choice. Eventually, the matchings stabilize (you might like to get a few friends and a justice of the peace together and try it for yourself), although Shapley and Gale showed that the matchings are more favorable to the proposers than the proposes. Roth, who calls himself a "market designer" and is currently making his way from Harvard to Stanford, used the Gale-Shapley algorithm to make the NRMP more friendly to dual-doctor couples, and to improve New York City's specialized high school admissions system, reducing the number of students who end up at schools they haven't ranked by 90%. Now if only he could do something about matching high school students with pleasant high school social experiences. (Photo: Lloyd S. Shapley, courtesy of UCLA.)
