Brie Finegold summarizes blogs on cosmology and a mathematics potpourri
"Critical Opalescence: You Can't Just Go 1,2,3,..." by George Musser. Scientific American Blog Network, 6 August 2012.
The nature of infinity is fascinating, and even more so when it might be connected to cosmology. While mathematicians will take issue with some of Musser's statements like "There's no unambiguous way to count items in an infinite set," the fact that he talks about p-adic numbers and fractals in his blog entry is pretty remarkable. Musser complains about mathematicians' tendency to "bury the beauty of math," but then quickly adds that he appreciated the "sheer awesomeness" of the p-adics after listening to a talk by physicist Leonard Susskind. He goes on to give a description of the p-adics including a nice picture of an infinite binary tree. After discussing how distances are calculated, Musser writes "This distance rule messes with your mind. Two parallel universes that look nearby can be far apart because they lie on different branches of the tree." One can't help but think that Musser gets carried away when he starts mentioning words like "Non-Archimedean." Musser closes by discussing the ways in which p-adics capture the granular nature of distance in real life. His entry is the math-iest popular piece out there-- unless of course there is a parallel universe inhabited only by mathematicians.
"Visualizations, Inspirations, and the Super Ultimate Graphing Challenge," by Paul Salomon. Math Munch: A Weekly Digest of the Mathematical Internet, 27 August 2012.
Written by three math teachers from Brooklyn's Saint Ann's School, Math Munch highlights mathematical websites or projects that would attract everyone from novice to expert. This "issue" focuses on three websites, all of which have wonderful graphics. Want to look at an interactive model of an Apollonian Gasket? Well, Welsh mathematician Jason Davies has created one and included the definition as well. Were you busy in trigonometry class playing with your graphing calculator in the polar coordinates mode? You might like Davies' table of Rhodonea Curves. Wondering what M.C. Escher's ideal office space might look like? Explore the mathematical objects in that imaginary office by watching animator Cristóbal Vila's short movie Inspirations. Freeze the video at any point, and you will find an image worth contemplating. Vila's earlier work, Nature by Numbers, was mentioned in the September 2011 issue of Math Digest. Lastly, have you always wished for an educational math game as addictive as Angry Birds? Well, yearn no more because physics teacher Michael Blackman has designed a game (don't let the name "Super Ultimate Graphing Challenge" deter you) that models simple first- and second-order differential equations. You can play it right now.
--- Brie Finegold
"What's in a Name?" News, Science, 24 August 2012, page 897.
Earlier this year the National Science Foundation (NSF) floated the idea of changing the name of its Division of Mathematical Sciences to the Division of Mathematical and Statistical Sciences. Feedback was invited from the research community. The feeback from mathematicians was not favorable. In August, NSF officials announced that the agency would not change the name. An external committee has been appointed to "review the role of statistics in science and how NSF should fund statistical research." Also, the NSF will now include the word statistics along with "mathematics" in budget requests and solicitations for research proposals.
--- Mike Breen
"Nothing nerdy about math’s role in society," by Mark Thiemens. San Diego Union-Tribune, 23 August 2012.
Thiemens, dean of UCSD's Division of Physical Sciences, is glad of recent media coverage of mathematics, but deplores the use of "nerds" and "geeks" as descriptors that often accompany stories about mathematicians, and counters the widespread thought that "the work of mathematicians has remained fundamentally unchanged since the days of the ancient Greeks and has little to do with solving contemporary problems in society." He gives examples of how mathematics plays a key role in science and technology research and careers:
At UC San Diego and at other major research universities around the world, mathematicians are developing sophisticated tools to make critical advances in fields as disparate as biology, economics, finance and climate-change research. Laboratory automation and the revolution in information technology have allowed scientists to generate and store more data than they can ever analyze in their lifetimes. So mathematicians are being called upon with increasing frequency to develop mathematical models to find ways to make sense of all of that data.
He gives examples of mathematics related to the discovery of the Higgs subatomic particle, modeling climate change, economic and military strategies, predicting the complex behavior of living organisms, and even regulating traffic lights to make commuting easier. He says our future depends on recognizing the role of mathematics in contemporary society and the importance of a mathematics education. When students ask him how to best prepare for a career as a scientist he advises, "Take as many mathematics classes as you can." [Note: Order a printed copy of the 18 x 22" poster pictured above by emailing paoffice at ams dot.org using the subject line "Powered by Math poster - MD"]
--- Annette Emerson
"William P. Thurston, Theoretical Mathematician, Dies at 65," by Leslie Kaufman. The New York Times, 22 August 2012;
"The Mathematical Legacy of William Thurston (1946-2012)," by Evelyn Lamb. Scientific American blog, 23 August 2012;
"Remembering Bill Thurston, Mathematician Who Helped Us Understand the Shape of the Universe," by Edward Tenner. The Atlantic, 23 August 2012.
The death of William P. Thurston on August 22, 2012, reverberated around the globe and led to many affectionate postings on blogs frequented by mathematicians, as well as the three mainstream-media obituaries cited above. Thurston's extraordinary ability to visualize mathematical objects allowed him to understand those objects in great depth. His contributions revolutionized topology and geometry in the 20th century. One of his most important achievements was the so-called Thurston Geometrization Conjecture, which provided an entirely new view on the nature of three-dimensional manifolds. As Lamb explains it in her obituary, "The geometrization conjecture states that three-manifolds that are closed and bounded can be decomposed into pieces, each of which has one of eight well-understood geometric structures. The Poincaré conjecture, posed in 1904, was considered one of the most important unsolved problems in mathematics. It is just one case of Thurston's geometrization conjecture." Thurston received a Fields Medal in part for his proof of a large portion of the geometrization conjecture. Grigory Perelman proved the conjecture in full generality in 2003 (and famously declined to accept the Fields Medal; see an item on Perelman below). Lamb quotes Benson Farb, one of Thurston's PhD students, as saying that Thurston "changed the way geometers/topologists think about mathematics. He changed our idea of what it means to 'encounter' and 'interact with' a geometric object. The geometry that came before almost looks like pure symbol pushing in comparison." Photo of Thurston receiving the Steele Prize for Seminal Contribution to Research at the 2012 Joint Mathematics Meetings, by E. David Luria.
--- Allyn Jackson
"Searching for Russia's Reclusive Math Genius," by Brett Forrest. The Daily Telegraph, 22 August 2012.
Grigori Perelman: the man who proved the Poincaré conjecture, the first person to turn down the Fields Medal, and possessor of perhaps the longest fingernails in mathematics. But who is he? In this most exclusive of exclusives, intrepid reporter Brett Forrest stakes out the Perelmans' apartment in St. Petersburg for three days, and succeeds in exchanging real words with the man and his mother. An admirer of Perelman - he rhapsodizes, "his will was free, his result pure, and therein lay his glory" - Forrest paints a sympathetic portrait of the person behind Poincaré. In his youth, in addition to competitive mathematics, Perelman enjoyed ping-pong and trips to the opera. He prefers women, says his closest friend Sergei Rushkin, but was never motivated enough to act on his inclination: "If Grisha ever looked upon anything with loving eyes," says Rushkin, "it was on the blackboard." More recently, Perelman has been notoriously disinterested in socializing. According to Sergei Kislyakov, head of St. Petersburg's Steklov Institute of Mathematics, and Perelman's mentor since his days in the Mathematical Olympiad, "Perelman talks to no one. But he particularly hates journalists."
Despite this, Forrest's persistence and his apparently excellent Russian win him a walk and talk with Perelman and the one person he does talk to - his mother Lyubov, whose prodigious mathematical talent was a casualty of sexism. Lyubov wears thick glasses and has a "cheery face," and Grigori Yakovlevich speaks in a "high-toned, bird-like voice." Despite some eccentric behavior, Perelman comes off as tolerant, considerate, and emphatically human. He does a lot of shrugging and looking at the sky, but that may have to do with his dislike for reporters, and Forrest's instinctual attempts to move their conversation into interview territory. But I will do no more to spoil this interview that is not an interview, and I encourage you to read for yourself about the future of Perelman's mathematical career (could it be a mother-son collaboration?), the current status of his ping-pong game, and all that Perelman himself knows about where his life goes from here. If you're hungry for more, you can read more about Perelman in his entry at the Encyclopedia of World Biography, as well as in this recent book review.
--- Ben Polletta
"Wert von x ein fü alle Mal auf 5 festgesetzt (Value of x determined once and for all to be 5)". Der Postillon, 21 August 2012.
This satirical article says that the Max-Planck-Institut für Mathematik has announced that the value of the variable x is exactly 5, resulting in a huge savings of labor by students. In fact, the MPI has collected many thousands of computations over the past 100 years and found that the average value of x is actually 5.14929131. However, "because this is such a complicated number, we have rounded it off to 5," fictional mathematician Hanno Schmidt is quoted as saying. As a result of this advance, school math classes throughout Germany are to be shortened, and mathematicians worry about keeping their jobs.
--- Allyn Jackson
"A new approach to math," interview with Danica McKellar. Morning Joe, MSNBC, 13 August 2012;
"Actress Danica McKellar Helps 'Girls Get Curves'," interview with Danica McKellar. Science Friday, NPR, 17 August 2012.
You may know actress Danica McKellar from her roles in TV series such as The Wonder Years, The West Wing, and NCIS. What you may not know is that McKellar is also a mathematician who has written four math books that help girls learn math and build confidence. During the MSNBC interview, McKellar pointed out that girls do just as well as boys at math. The difference is in how girls perceive their abilities: if they do well, they often downplay their abilities; if they do poorly, they typically see it as evidence that they don’t belong in this field. Girls are told that it's important to be pretty, she notes, but it's important for them to find the confidence that comes from feeling smart. Her first book, Math Doesn’t Suck: How to Survive Middle School Math Without Losing Your Mind or Breaking a Nail, was written for ages 9-12. In her latest book, Girls Get Curves: Geometry Takes Shape, McKellar combines math with testimonials of women who used to be afraid of math but who now use math in careers that they love. On Science Friday, McKellar talked about her books and how she got interested in math.
--- Claudia Clark
As McKellar made her way through the TV talk show and radio interview circuit to promote her new book, she was able to communicate her main points about how girls can be discouraged from liking and pursuing math, and how to address that. She had more success in some outlets than in others.
But many of the hosts were uncomfortable talking about math, deflecting the conversation to another topic, and freely admitting a dislike and lack of knowledge of math themselves.
--- Annette Emerson
"Simulation helps forecast fighting in Afghanistan," by Rachel Ehrenberg. Science News, 11 August 2012, pages 5-6.
This issue of Science News reports on how mathematical simulations can be used to predict the intensity and whereabouts of future insurgent activity. Computer scientist Guido Sanguinetti of the University of Edinburgh and his research associates used secret U.S. military logs detailing the Afghan war and methods typically used by epidemiologists to predict the spread of a virus outbreak to estimate future levels of insurgent activity. The model also estimates the probability that its predictions are correct, illuminating areas where it’s really hard to predict future activity. "It delivers best guesses with honest estimates of how good those guesses are so you don’t have to be dogmatic," says statistical epidemiologist Peter Diggle of Lancaster University and the University of Liverpool, both in England. "This is a very nice and imaginative application of this modeling approach. It’s a good piece of work." Image (that accompanied the article): Three-dimensional map of total violence in Afghanistan by 20 km grid cells and by year. The view from the north is from a view angle perspective of 30°. The density estimate calculation uses an isotropic Gaussian smoothing kernel with a standard deviation of 20 km to estimate the intensity of the point process that generated the observed conflict-event data. Image reprinted from Eurasian Geography and Economics, Vol. 51, No. 4, p. 483 with permission of Bellwether Publishing, Ltd. ("Peering into the Fog of War: The Geography of the WikiLeaks Afghanistan War Logs, 2004–2009," John O’Loughlin, et al)
--- Baldur Hedinsson
"Olympics: are the fastest and strongest reaching their mathematical limits?" by Daniel Tammet. Guardian, 11 August 2012.
In this article, Daniel Tammet explores the all-important "precise measurement of achievement" that is a hallmark of the modern Games. Today’s fraction-of-a-second margins that make the difference between earning a gold or silver medal—or earning a medal at all—would have been "unthinkable" to the ancient Greeks because "victory was always visible [and] incontrovertible," accurate measurements were not taken, and "no single standard was upheld." All of that changed with the first modern Games, held in Athens in 1896. For example, competitors in the modern pentathlon, first held in 1912, were ranked objectively by points. However, this "quantification of accomplishment" has led us to believe that we can objectively compare athletes' abilities when, in fact, these precise numbers do not take into account "the stark differences in, say, nutrition, financial incentive or lane position." Furthermore, sports philosopher Sigmund Loland critiques what he refers to as "'the cult of abstract entities' in which a race is turned into 'a quest for objective knowledge similar to what we find in a scientific experiment.'" Attention has turned away from the "peculiar stories and rivalries" of athletes to "empirical research questions" like "How fast can a human being run? How quickly can she swim?"
Finally, the motto of the Games may be "Citius, altius, fortius, but human performance cannot continue to improve indefinitely, Tammet argues, no matter how much more precise the measurements may be. And "why reduce performance to a number at all?" he asks. "Every sport and sportsman and sportswoman is unique. Consider, in place of abstract records, a renewed focus on the human drama and infinite variety of the match."
--- Claudia Clark
"Mathematicians grow an 11-set Venn diagram rose," by Ian Steadman. Wired.Co.UK, 10 August 2012.
Drawing Venn diagrams in an easy way to represent the relationship between sets of data. You're probably familiar with a Venn diagram of two sets, maybe even three, but with four or more sets things tend to become unwieldy. Khalegh Mamakani and Frank Ruskey, from the University of Victoria in British Columbia, have generated a host of Venn diagrams using a computer simulation and found an 11-set Venn diagram that isn't too hard to understand (see picture above). The different colors represent the different overlapping areas and the white line that runs along one curve delineates the boundary of one of the sets. A New Rose : The First Simple Symmetric 11-Venn Diagram is available on the arXiv. More details about the diagram have been posted by the authors. Image created by Khalegh Mamakani, courtesy of Frank Ruskey.
--- Baldur Hedinsson
"UNH professor connects math with wonders of digital world," by Gretyl Macalester. Union Leader, 5 August 2012.
University of New Hampshire mathematics professor Kevin Short (left) has combined a classroom focus on real-world applications with real-world success in music and business, including a Grammy Award and two companies. Using math, Short reconstructed a 1949 bootleg Woody Guthrie recording to win the prestigious music awards. [Hear Short talk about this work.] His company, Groove Mobile, offered the first music download capability for U.S. cell phones, and his current venture, Setem Technologies, aims to improve the capability of hearing aids to identify and filter background noise. Short, who studied string theory at the Imperial College of Science and Technology MIT in the UK, explains that his diverse successes were driven by his desire to find and attack "cooler, harder problems." He channels his focus on applications into the classroom as well, using exercises to demonstrate that math forms the foundation of the video games many students love. Photo by Lisa Nugent, UNH Photo Services.
--- Lisa DeKeukeleare
"History as science," by Laura Spinney. Nature, 2 August 2012, pages 24-26;
"Mathematicians Predict the Future With Data From the Past," by Klint Finley. Wired, 10 April 2013.
Science marches onward! This time, into history. In this fascinating article on the new science of cliodynamics - named for the Greek muse of history, Clio - Laura Spinney tells how nonlinear dynamics and big data, the two-person SWAT team of modern science, have begun crashing through the windows of history's bunker and leveling their sights at the large-scale trends in social unrest, violence, and religious fervor. In their exploration of violent social upheaval, former population ecologist Peter Turchin and his humanities colleagues Sergey Nefedov and Andrey Korotayev have focused on the large-scale rhythms and interrelationships between four variables - population numbers, social structure, state strength, and political instability. What they've found are two remarkable, interacting cycles that fit patterns of instability across thousands of years - from the 5th century BC onwards - in European and Asian history. The first of these cycles has a period of one or two centuries, and relates to levels of inequality, as labor outstrips demand, and society proceeds from egalitarian to highly unequal. The second, with a period of only 50 years, fits recent U.S. history precisely. It has been dubbed the "fathers-and-sons" cycle: one generation reacts violently to social injustice, while its children reap the unpleasant rewards of this upheaval, and abstain from violent rebellion. Turchin's efforts contrast sharply with those of contemporary academic historians, who "have abandoned the belief in general laws" after the demise of the grand theories of the past century, and rely on detailed narratives of individual events, painstakingly reconstructed from the patchy historical record, to draw larger conclusions. While statistics are common in historical studies, the search for large-scale patterns, and the mathematical analysis of the interactions between variables, are not. To get around history's patchiness, Turchin and his colleagues search widely for proxies of their four main variables, chosen both for their relevance and for the ease with which they can be recovered.
Besides discovering the exact period history repeats at, Turchin's team has also examined the spread of religion, finding that its growth is exponential, like a contagious disease, rather than linear, which would reflect a constant rate of revelation. Whether by infection or revelation, Turchin is being joined by others, such as "computer social scientist" Claudio Cioffi-Revilla - who uses agent-based modeling to capture the effects of climate change on the drought-ridden societies of East Africa's Rift Valley - and anthropologist Harvey Whitehouse - who is constructing a huge database about rituals, social structure, and conflict, and hopes to illuminate the small-scale dynamics of political violence, such as the role of violent rituals in political groups. These psychohistorians' prognosis for our own society is not good - "inequality is almost always a bad thing for societies", says Turchin - with the next eruption of violent unrest predicted to peak in 2020 if decisive action to reduce inequality and joblessness is not taken. Turchin began formulating cliodynamics after coming to the conclusion that all the major questions in population dynamics had been resolved. Perhaps ironically, his penchant for both academic controversy and history come to Turchin through his father, computer scientist Valentin Turchin, who was exiled from the Soviet Union for theorizing about the origins of totalitarianism. Perhaps we had better forestall the violent outbursts of academic historians, who are still deeply skeptical of cliodynamics, and rephrase that opening sentence: Human understanding is on the march! That's something we can all get fired up about (in a good way).
The Wired article updates Turchin's work, explainis how he got into cliodynamics, and notes that the availability of digital historical data has made a lot of his work possible.
--- Ben Polletta
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