Math Digest
Summaries of Media Coverage of Math
Edited by Allyn Jackson, AMS
Contributors: Mike Breen (AMS), Claudia Clark (freelance science writer), Lisa DeKeukelaere (2004 AMS Media Fellow), Annette Emerson (AMS), Brie Finegold (University of California, Santa Barbara), Adriana Salerno (University of Texas, Austin)

October 2008
 Articles on deciphering the opening chord of the Beatles' "A Hard Day's Night", October, November, and December 2008
 Articles about Marcus du Sautoy, October and November 2008
 Articles about AMS Notices study of girls in highlevel math competitions, October 2008
 "TierneyLab: A Beautiful Math," New York Times, 28 October 2008
 "It's all in the numbers: Math art subject of exhibit," Shreveport Times, 26 October 2008
 "And the winner is...", New Scientist, 25 October 2008
 "Disputed Definitions," Nature, 23 October 2008
 "Master talent at the top," Sowetan, 20 October 2008
 "Berkeley woman among 80 trailblazers in Oprah's magazine", Oakland Tribune, 18 October 2008
 "Knot or not?", New Scientist, 18 October 2008
 "Counting Fish," Nature, 16 October 2008
 "Exhausted jugglers find opportunity in becoming mathematicians," Irish Times, 15 October 2008;
"Stratocaster helps explain magic of maths," Irish Times, 16 October 2008
 "Q & A with Donald Saari about election math," Independent Weekly, 15 October 15 2008
 "Divide and conquer, and get the chicken," Boston Globe, 13 October 2008
 "Feeling Financial Pain? First, Blame All the Scientists," USA Today, 13 October 2008
 "Artificial Intelligence Prize Goes to Chatty Computer", National Public Radio, 14 October 2008;
"Test explores if robots can think", BBC News, 12 October 2008
 "ChaosMathematical and Financial," ABCNews.com, 5 October 2008
 "Sexy maths: Primes of passion," The Times Online, 1 October 2008
 "Outcalculating the Competition," Scientific American, October 2008
"A Hard Day's Night," by Chris Lambie. The Chronicle Herald (Halifax), 28 October 2008.
"How a Professor Unraveled the 'Hard Day's Night' Mystery," by Eliot Van Buskirk. Wired News, 31 October 2008.
"A piano gave uniqueness to the Beatles' Hard Day's Night's opening chord," by Ani. Fresh News, 3 November 2008.
"'Hard Day's Night': A Mathematical Mystery Tour," by Keith Devlin and Scott Simon. NPR: Weekend Edition, 27 December 2008.
"Professor Uses Mathematics to Decode Beatles Tunes," by Easha Anand. The Wall Street Journal, 30 January 2009.

Dalhousie mathematics professor and Beatles fan Jason Brown worked for months to decipher the first chord in a Hard Day's Night, which has remained a mystery to the public since the song was recorded. Using Fourier transforms, Brown finally identified the frequencies of those first few notes. In his article for Guitar Player magazine he speculated that both piano and guitar were used to form the opening chord. "I'm a mathematician so people think I should be clinical. But I'm always attracted to the esthetic," says Brown, who studies combinatorics and plays guitar. Brown's new book, Our Days Are Numbered, contains a chapter in which he discusses the relationships between popular music and mathematics. He continues looking for patterns, and wants to solve the mystery of who wrote In My Life, another Beatles hit. (Photo by Danny Abriel.)
 Brie Finegold

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Articles about Marcus du Sautoy, October and November 2008.

Marcus du Sautoy is professor of mathematics at Oxford University and has been named Oxford University's new Charles Simonyi Professor of the Public Understanding of Science. He is wellknown in the U.K. for his articles in the Times, the Daily Telegraph, and the Independent, and for his regular column in the Times called "Sexy Maths". Two of his recent books, The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics, and Finding Moonshine: a Mathematician's Journey Through Symmetry, received positive reviews worldwide (link to reviews). In 2008 he wrote and presented a fourpart series for the BBC called The Story of Maths. Upon his appointment as Simonyi professor the Guardian published three articles about Marcus du Sautoy: "Popular face of maths to succeed godless Dawkins," by Alok Jha (29 October 2008); "Lessons in Science," by Tim Radford (3 November 2008); and "A mathematician who's in his prime," by Robin McKie (2 November 2008). Each provides a profile of du Sautoy and presents the challenges he faces in popularizing mathematics and science. He notes in the Jah article, "For me, science is about discovery but it is also about communication. A scientific discovery barely exists until it is communicated and brought to life in the minds of others. Our next generation of scientists depends on people broadening out and not just talking to those in the ivory towers." (Photo by Niall McDiarmid.)
 Annette Emerson

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"Study finds culture a factor in female math achievement Nurturing climate produces more elite competitors", by Carolyn Y. Johnson. Boston Globe, 10 October 2008.
"Making Math Uncool is Hurting America, report says," by Maggie Fox. Reuters news service, 10 October 2008.
"Math Skills Suffer in U.S., Study Finds", by Sara Rimer. New York Times, 10 October 2008, page 17.
"Numbers Don't Add Up for U.S. Girls", by Davide Castelvecchi. Science News, 10 October 2008.
"US culture is to blame for girls' indifference to maths, says expert." Newstrack India, (ANI news service story), 11 October 2008.
"Girls and Math: It Doesn't Add Up", by Jeannine Stein. Los Angeles Times, 13 October 2008.
"Mädchen können in Mathe brillieren (Young girls can shine in mathematics)", by Kathrin MeierRust. Neue Zürcher Zeitung, 19 October 2008.
"Math in school should be cool," by A.C. Grayling. New Scientist, 25 October 2008, page 48.
"Math is Hard, Barbie Said," by Sharon Begley. Newsweek, 27 October 2008.
These articles report on a study that appeared in the November 2008 issue of the AMS Notices. The study, "CrossCultural Analysis of Students with Exceptional Talent in Mathematical Problem Solving", which brings together decades of data from several extremely highlevel mathematics competitions for young people. These data show that there exist many females with profound intrinsic ability in mathematics. What is more, whether this ability is identified and nurtured is highly dependent on sociocultural, educational, or other environmental factors. In the United States, these factors keep many boys as well as most girls from developing their mathematical talents to the fullest. Even some relatively small countries, such as Bulgaria and Romania, can field highly successful IMO teams. "[W]hat most of these countries [that excel in the IMO] have in common are rigorous national mathematics curricula along with cultures and educational systems that value, encourage, and support students who excel in mathematics," the study says. Since 1974, the highlyranked Bulgarian, East German/German, and USSR/Russian IMO teams have included 9, 10, and 13 different girls, respectively. By contrast, during that same time period, the US teams included just 3 girls. News stories about the report appeared around the world.
 Allyn Jackson
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"TierneyLab: A Beautiful Math," by John Tierney. New York Times, 28 October 2008.

In his TierneyLab blog, journalist John Tierney describes and praises the recentlyaired NOVA program Hunting the Hidden Dimension, a documentary about the development of fractal geometry and its applications. "It's hard enough to make modern mathematics comprehensible in print, so I'm especially impressed to see anyone try to do it on television," he writes. The documentary provides the general viewer with an introduction to fractals and the work of mathematician Benoît Mandelbrot. The use of fractals to develop cellphone antennas, create realistic images of nature, diagnose cancer earlier, and approximate how much carbon dioxide a rainforest can absorb are a few of the applications presented. Of course, the program is filled with images of fractals in nature, as well as computergenerated images of fractals, particularly the Mandelbrot set.
You can watch the program, view an interview with Benoît Mandelbrot, learn more about the Mandelbrot set, or zoom in on an image of the Mandelbrot set to a magnification of 250,000,000x by going to the website. (At left, image based on fractals, created by Jos Leys. See more images on the Mathematical Imagery page.)
 Claudia Clark

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"It's all in the numbers: Math art subject of exhibit," by RoseMarie Lillian. Shreveport Times, 26 October 2008.

Paul Sisson is a mathematics professor at Louisiana State University, Shreveport. He is also an artist. In the "Math Meets Art" exhibit at the East Bank Gallery in Bossier City, Sisson and a dozen of his former students showed some of their artwork, inspired by and created through mathematics. Sisson says that the process of making the images involves having a computer track the behavior of a complex number after repeatedly acting on it by a given complexvalued function. Each number is assigned a color, and subsequent iterations of the function modify the colors. Combining the computations for about 10,000,000 points on the complex plane would give an image like the ones in the collection. He created a class in which students got to play around with parameters, determine the colors, and even use their favorite function. Sandy Watkins, one of the artists/students, described the process as "really addictive." Sisson says that even though most people would not think of mathematics and art as being related, "to a mathematician the connection is apparent and beautiful... it is my hope, with this artwork, to communicate the joy of both mathematics and art just a little bit." (Photo: Jim Hudelson/Shreveport Times.)
 Adriana Salerno

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"And the winner is...", by Jim Giles. New Scientist, 25 October 2008, pages 1213.
Appearing shortly before the US presidential election, this article discusses statistical approaches to forecasting such elections. Some of these approaches rely on statistics about historical trends in past elections. For example, one researcher found that in the past every percentage point of increase in the disposable income of voters during a presidential term translated into a 3.6 percentage point advantage for the party of the president in office. Generally this kind of forecasting does not rely on polling data, though such data can be useful to forecasters as the election draws near. One novel method of forecasting creates a "market" for the election by buying and selling shares whose price depends on the outcome of the election. If, for example, McCain won the election with 51 percent of the vote, McCain shares would pay out 51 cents. Assuming that buyers and sellers are well informed, the article says, "the market will integrate all forecasts to produce the best possible prediction." At the time the article was written, most forecasts were predicting a win for Barack Obama. "[I]f McCain takes this election," the article says, "he will have beaten not only Obama, but a lot of mathematicians too."
 Allyn Jackson
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"Disputed Definitions." Nature, 23 October 2008.
The definition of "complexity" is complex in itself; even researchers focused on complexity and complex systems cannot seem to agree on a single explanation for the oftused term. "Significant" faces a similar quandary; although the term has a formal statistical definition, it is often inappropriately attached to study results and is easily confused with subjective, qualitative judgments. This Nature article (a series of short pieces by different authors) examines these terms, as well as others such as "consciousness" and "paradigm shift," to determine causes for the disputes and similarities within the pools of definition for each term. "Complexity," for example, may be more easily defined for its subcategories, such as computational complexity and algebraic complexity. In general, however, complex systems are independent agents that are continuously interacting with each other. The "significance" of a result is technically defined in relation to the probability of observing a set of data, such as a clinical trial result, if the result, such as a drug being ineffective, is accurate. Labeling a cancer drug as "significantly" prolonging life by one month, however, may mean little to a cancer patient who views a single month as a qualitatively insignificant amount of time. The "Complexity" piece is by M. Mitchell Waldrop, and "Significant" is by Geoff Brumfiel.
 Lisa DeKeukelaere
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"Master talent at the top," by Don Makatile. Sowetan, 20 October 2008.
Professor Loyiso Nongxa is ViceChancellor of the University of the Witwatersrand (Wits University), Johannesburg, South Africa. He chose a career path in mathematics over medicine and along the way mentored several outstanding black mathematicians: Themba Dube (professor of mathematics at the University of Zululand), Thandwa Mthembu (vice chancellor, Central University of Technology in Bloemfontein), Duma Malaza (chief executive of the Association of Unviersities), and Siswe Mabizela (deputy vice chancellor at Rhoades University). Nongxa goes on to list several other young mathematicians, some at Wits now, others in their early careers, and notes the challenges of increasing enrollment of students of African ancestry and including African women in senior level staff positions. The article concludes, "When he leaves Wits, it will be to go out in search of such smart kids from disadvantaged backgrounds, children with potential to do well in scarce skillsmaths, science and accounting."
 Annette Emerson
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"Berkeley woman among 80 trailblazers in Oprah's magazine", by Kristin Bender. Oakland Tribune, 18 October 2008.

Picking a career may seem like a multiplechoice problem, but young minority women participating in the Infinite Possibilities Conference founded by Tanya Moore are encouraged to think otherwise. The November issue of O, The Oprah Magazine profiles Dr. Moore, who is codirector of the Chronic Disease Program for the city of Berkeley's Public Health Department, under the heading "The Science Rock Stars." In 2002, the year Dr. Moore earned her Ph.D. in Biostatistics from UC Berkeley, less than one percent of all mathematical science doctorates in the U.S. were awarded to AfricanAmerican women. To help others navigate the obstacles that she overcame in order to pursue a career in math, Dr. Moore helped design a conference that fosters interaction between female mathematicians and students from high school to graduate school. And Dr. Moore got a chance to interact with 79 other powerful women last summer at a leadership training conference partially funded by O, The Oprah Magazine, for which 3,000 applications were received. More information about The Infinite Possibilities Conference which will be held at UCLA in 2010, is online. (Photo courtesy of Tanya Moore.)
 Brie Finegold

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"Knot or not?", by Richard Elwes. New Scientist, 18 October 2008, pages 3235.
Knot design by Rob Scharein, just one of the thousands of decorative knots included with KnotPlot software. See the KnotPlot website at http://www.knotplot.com/.

This article discusses developments in the mathematical theory of knots. A mathematical knot is a loop of string with under and overcrossings of the stringan example is given in the accompanying picture. Mathematicians have searched for a long time for a foolproof way of distinguishing knots. A big advance came in the 1990s, when Vaughan Jones came up with a surprising new formula. The formula is an "invariant", meaning that for a particular knot the formula does not change no matter how you manipulate the knot by moving the crossings around or folding the string over. Jones's formula was an improvement over other invariants that had come before, but it still could not be used to distinguish knots: Two different knots could have the same Jones invariant. Victor Vassiliev and Mikhail Goussarov took a different tack, resulting in what are known as "finitetype" invariants. Vassiliev conjectured that if two knots are really different, then at least one of their finitetype invariants will differ. Vassiliev's conjecture remains unproved. Taking yet a different approach, Mikhail Khovanov revisited Jones's invariant and tried to find a way to make it a special case in a larger theory, through the notion of "categorification". Categorification involves setting the invariants in a higherlevel structural context and regarding the invariants as "shadows" of larger components in the structure. And there is more. "[S]ome researchers think they have spotted a tantalizing hint that whole chunks of mathematical physics are just shadows of larger categorical structures."
 Allyn Jackson

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"Counting Fish," by Karen Kaplan. Nature, 16 October 2008.

"The Fisheries Service of the U.S. National Oceanic and Atmospheric Administration (NOAA) is looking for a few good fish counters." So beings this brief article in the Career View section of Nature. Scientists with a background in mathematics, computer science, and/or conservation are neededand are in short supplyto fulfill positions as "stockassessment scientists." Reports say that U.S. institutions will graduate only 160 such scientists to fill at least 340 positions. Stock assessment scientists "gather data on species populations, on the basis of catches and aerial surveys. The data inform mathematical models that help design monitoring programs and predict populations under different managemant scenarios. This in turn helps regulators to set quotas." One such scientist, Larry Alade, says "he's now in a job he lovescontributing to sustainability."
 Annette Emerson

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"Exhausted jugglers find opportunity in becoming mathematicians," by Mary Minihan. Irish Times, 15 October 2008.
"Stratocaster helps explain magic of maths," by Mary Minihan. Irish Times, 16 October 2008.
Minihan covers the many events celebrating "Maths Week" in Ireland, including mathematicians who juggled, offered magic shows, discussed beautiful geometric patterns on mosaics, described how computers have improved weather prediction, and presented a daily logic puzzle. The "Stratocaster" article features David Acheson (Jesus College Oxford), who "wields his red Stratocaster to demonstrate one of physics' most important rules, the wave equation, used to describe the vibration of a stretched string among other things," and Brendan McCann (Waterford Institute of Technology), who explains Pythagorean Theorem, "the most widelyused piece of intellectual property ever created."
 Annette Emerson
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"Q & A with Donald Saari about election math," by Fiona Morgan. Independent Weekly, 15 October 15 2008.

In this timely article, writer Fiona Morgan interviews University of California, Irvine, professor of mathematics and economics Donald Saari about how we elect our public officials. According to Saari, the most heinous form of voter disenfranchisement is the voting system we use: plurality voting, a system in which each person votes for a single candidate and the candidate with the most votes wins. The problem with this system arises when more than two candidates are running for the same office, particularly in a closely contested race. As an example, assume that 15 people who are planning a party rate three beveragesmilk, wine, and beerby order of preference. Six of these people choose milk first, wine second, and beer last; five choose beer first, wine second, and milk last; and four choose wine first, beer second, and milk last. Using plurality voting, milk gets the most votes, 6, and therefore wins, while beer comes in second with 5 votes, and wine is in last place with 4 votes. However, looking at all of the choices reveals some interesting information: nine of the 15 people actually preferred wine to milk, nine of the 15 preferred beer to milk, and ten of the 15 preferred wine to beer.
The system that Saari thinks best reflects what voters want is the Borda count, named after 18th century French mathematician JeanCharles de Borda. Borda proposed the following system for electing candidates to the French Academy of Sciences: if there are three candidates, your first choice gets two points, your second choice gets one point, and your last choice gets zero points.
 Claudia Clark

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"Divide and conquer, and get the chicken," by Johnny Diaz. The Boston Globe, 13 October 2008.
(Photo by Dick Quinn.)

Zhaoning Nancy Wang, Edward Newkirk, Williams College Professor Steven Miller (holding the brown chicken, affectionately named "Cluck"), Middlebury College Professor Peter Schumer, Shengen Zhai, Victor Larsen, Ying (Daisy) Zhuo. (Not pictured : Nick Arnosti and Brian Li, from the Williams team, and Chaoyi Chai, from the Middlebury team.) (Photo courtesy of the Williams Math Department.)

"The Green Chicken," pictured above, is a trophy in an annual math competition between students at Williams and Middlebury Colleges. Says Victor Larsen, a math major at Middlebury, "It's an honor to win the competition but maybe not an honor to have that trophy stick around your office for a year." The trophy's history backs up Larsen's assessment: Middlebury College math professor Bob Martin gave the trophy, when it was still just a casserole dish, to his sister as a wedding present. Later she gave it back to him as a housewarming present. In 1978, the regifting stopped and the dish became the prize in the math competition. Says Martin, "The big question we had to wrestle with is: Who should get it, the winners or the losers?" The annual competition is made up of six questions. The winning school is the one with the highest total among its top four scorers. Williams held the trophy from 2003 to 2007, but Middlebury won the 2008 competition on November 1.
 Mike Breen
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"Feeling Financial Pain? First, Blame All the Scientists," by Dan Vergano. USA Today, 13 October 2008.

Amid the fingerpointing that follows from the recent financial crisis, some have suggested that the mathematicians and physicists who created some of the models used in the financial industry are to blame. Several mathematicians argue, however, that the real problem lies with financial analysts who used the models. First, the analysts didn't build the models to include the possibility of extreme risk and realworld catastrophe. Second, some analysts exploited flaws in the creditrating agencies' models in order to develop securities that would earn undeservedly high ratings. One of the mathematicians also points out that the "fancy math" of today was not around during previous financial tumbles like the Great Depression, a situation just as dire but without the scientific scapegoat.
This article was prompted in part by a segment on 60 Minutes, "A Look at Wall Street's Shadow Market," (aired on October 5, 2008).
 Lisa DeKeukelaere

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"Artificial Intelligence Prize Goes to Chatty Computer." Morning Edition. National Public Radio, 14 October 2008.
"Test explores if robots can think." BBC News, 12 October 2008.
The latest Turing Test (named after British mathematician Alan Turing) was held at the University of Reading (U.K.). Five computers were tested to see if they could hold a textbased conversation with humans. Some computers used humor, argued, or offered opinions. The annual Loebner Artificial Intelligence Prize went to a program called Elbot. No machine has ever passed the Turing Test, "which requires the robot to fool 30% of its human interrogators", but "Elbot came close by reaching 5% below the pass mark," the BBC reported. The test results were covered by media in the U.K. (BBC, Guardian, New Scientist, Times Online), India (NDTV), Australia, Croatia, and U.S. (NPR, Chronicle of Higher Education, Discover Magazine, TechNewsWorld), among others, 1214 October.
 Annette Emerson
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"ChaosMathematical and Financial," by John Allen Paulos. ABCNews.com, 5 October 2008.
The fate of the current economic crisis after the recent US$700 billion bailout is uncertain, and John Allen Paulos posits in this column that it is likely to stay that way for a long time. He compares the economy (and other nonlinear dynamical systems)`[ to a modified game of pool. Imagine a pool table with 30 round obstacles fixed randomly on its surface. An expert pool player is asked to place a ball anywhere on the table, shoot it toward the obstacles and predict its trajectory on the table. The player will probably guess the first three or four bounces, but minuscule errors and miscalculations will continually be magnified every time the ball hits a new obstacle, and eventually the ball will do nothing like the player initially predicted. The economy has a myriad of complicated, interacting factors that act much like the obstacles on the pool table, which makes the whole system very resistant to trustworthy longrange forecasts. Paulos also suggests the ideas for managing the economy and the bailout might be found in chaos theory. In the end, he says, when trying to understand a complex system like the economy one "should act with a certain humble dubiousness, not with an unblinking rashness."
 Adriana Salerno
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"Sexy maths: Primes of passion," by Marcus du Sautoy. The Times Online, 1 October 2008.
The Times Online has recently unveiled a new column by Marcus du Sautoy, in which he will "explore the human side of maths." This first installment is devoted to one of the great enigmas of mathematics (albeit not a "human" one): the prime numbers. Really large primes are essential for encoding data and are really hard to come by. Their existence isn't an issue, since the Greeks proved 2000 years ago that there are infinitely many primes, and so we can find arbitrarily large ones. The problem is coming up with specific numbers or finding a pattern to predict the next big prime (one such pattern is predicted by the Riemann hypothesis.) Companies are giving prizes to whoever can find really big primes, the latest being a US$150,000 prize for a prime with 100 million digits, and there is still US$1 million for whoever proves the Riemann hypothesis (posed almost 150 years ago.) But the motivation for mathematicians doesn't come from these incentives (as Sautoy points out, "who does mathematics for money?"), but rather from the desire to understand some of the most basic and fundamental objects in mathematics.
Other recent "Sexy Maths" columns by mathematician du Sautoy include "Why the taxman has your number," (22 October 2008); "A calculating approach to love," (15 October 2008); and "Happy (birthday) coincidences" (8 October 2008).
 Adriana Salerno
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"Outcalculating the Competition," by Heather Wax. Scientific American, October 2008, pages 9699.
Wax writes about Martin A. Nowak and his work in evolutionary dynamics, a term he coined to describe the field of modeling how populations change over time. In 2003, Nowak became the first person at Harvard University to receive a joint appointment in mathematics and biology. Now he is trying to model the origin of life, attempting to capture "the transition from no life to life." Nowak was trained as a biochemist but believes that mathematics is the "true language of science," which will help uncover secrets of the past. He encodes monomersthe first building blocks of lifeas binary strings in a chemical system and allows the strings to combine randomly, hoping that they will develop the ability to replicate. Nowak thinks that his models will help guide experiments: "Mathematics is the proper language of evolution. I don't know what the 'ultimate understanding' of biology will look like, but one thing is clear: It's all about getting the equations right."
 Mike Breen
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