Peplow writes about mathematician Cliff Reiter of Lafayette College, who is using cellular automata to create snowflakes. Reiter uses cellular automata because he found that models that use differential equations weren't "aesthetically pleasing." His research is published in "A local cellular model for snow crystal growth" in the February (2005) issue of Chaos, Solitons & Fractals (Vol, 23, Issue 4, pages 1111-1119). Videos showing the growth of Reiter's snowflakes can be viewed online.
--- Mike Breen
"How math enriches our lives," by Arthur Michelson. The Providence Journal, 30 December 2004.
Michelson, a middle school teacher in Menlo Park CA, bemoans the fact that many American students and adults don't think math is important. Why do I need math in "real life"? Michelson notes that math is not just about computation, geometric proofs, and balancing a checkbook. He offers that math "has intrinsic value. It is about discipline, precision, thoroughness and meticulous analysis. It helps you see patterns, develops your logic skills, teaches you to concentrate and to separate truth from falsehood. These are abilities and qualities that distinguish successful people." He goes on to show a few examples of how math helps one make financial decisions, evaluate false claims, and determine risk.
--- Annette Emerson
"Taming the Hyperbolic Jungle by Pruning Its Unruly Edges," by Dana Mackenzie. Science, 24 December 2004, pages 2182-2183.
"The Return of a Beautiful Mind": Interview with John Nash. Interviewed by Michael Brooks. New Scientist, 18 December 2004, pages 46-49.
In this fascinating interview, John Nash reflects on his fame and his bouts with mental illness, which in recent years has taken the form of caring for his mentally ill son, also a mathematician. Asked whether the Nobel Prize changed his life, he replied: "It changed everything for me." But in fact some things have not changed: He said he is still living in the same house in Princeton. "I still don't have enough money to buy a mansion," he said.
--- Allyn Jackson
"Gödel and Einstein: Friendship and Relativity," by Palle Yourgrau. The Chronicle of Higher Education, 17 December 2004, pages A9-A10.
"The Mathematician's Literary Companion." NetWatch. Science, 17 December 2004, page 2009.
"The Designated Hitter as Moral Hazard," by Daniel H. Pink, and "Sabermetrics for Football," by Paul Campos and Jonathan Chait. New York Times Magazine, 12 December 2004, page 63 and pages 91-92 (respectively).
These two short articles, involving mathematical analyses of sports, are from the Fourth Annual Year in Ideas issue of the New York Times Magazine. The first idea is from a paper presented by John-Charles Bradbury and Doug Drinen (University of the South) at the Joint Mathematics Meetings in Phoenix last January. The paper examined the reason for a higher rate of hit-batsmen in baseball's American League (AL) when compared to the National League. The pair examined many factors and concluded that the AL's designated hitter rule, which effectively keeps AL pitchers from batting, accounts for a large part, if not all, of the difference. Sabermetrics, the subject of the second idea, employs statistical analysis to coaching or managerial decisions. Very popular in baseball, sabermetrics is now starting to come into use in football as well. Two analyses cited here are David Rowe's (University of California, Berkeley) on "going for it" on fourth down and Harold Sackrowitz' on two-point conversions. Bill Belichick and the New England Patriots, winners of two of the past three Super Bowls, used the advice from both.
--- Mike Breen
Po-Ling Loh, a senior at James Madison Memorial High School in Madison, Wisconsin, won second place in the 2004-05 Siemens-Westinghouse Competition in Math, Science and Technology. Her total prize money from the national and local competitions was US$54,000 in college scholarships. Loh's project was Closure Properties of D2p in Finite Groups. She was advised by Michael Ashbacher at Cal Tech who said, 'Very few people can cope with the abstraction and rigor that are necessary to do creative mathematics, ... Po-Ling has that kind of ability...' Loh's interest in that area of number theory came from a number theory class she took from Martin Isaacs (University of Wisconsin). The article concludes with Isaacs' assessment of Loh's future: "'She will make a real contribution to mathematical research,' he said, adding that he wouldn't be 'surprised if she will eventually be one of the great mathematicians of the 21st century.'"
--- Mike Breen
"Parallel Worlds": Review of János Bolyai, Non-Euclidean Geometry, and the Nature of Space by Jeremy J. Gray. Reviewed by Fernando Q. Gouvêa. Science, 10 December 2004, pages 1893-1894.
This book is the first in a series from the Burndy Library in which facsimiles of resources from the library are published, so that they can be available to a wider audience. This book contains Bolyai's original Latin publication from 1932 on non-Euclidean geometry, an 1896 translation by George B. Halsted, and a lengthy 'preface' by Jeremy Gray. The reviewer calls Gray's preface a "delight," and writes that Gray gives "a very full account of the story of the Parallel Postulate, the discovery of non-Euclidean geometry, and the impact of these ideas from the mid-19th to the early 20th century."
This book was also reviewed by Brian Hayes in American Scientist, May-June 2005, pages 275-276.
--- Mike Breen
Maor enjoyed this book, which is mostly about "curiosities associated with π." One included curiosity is the value of π to 100,000 places. Another is that the world record for memorizing digits of π belongs to Hiroyuki Goto, who has memorized over 42,000 digits of π. Maor would have enjoyed the book more had it had fewer typos; he hopes that a future edition will be edited more thoroughly.
--- Mike Breen
Temple University professor of mathematics, John Allen Paulos, considers 3 examples of "misleading, dubious or uncertain numbers" that appear in today's news.
The first example considers the current proposal to cut the average American's Social Security contribution from 6.2% to 4.2% of his income, the balance to be placed in private investments. While typically-and erroneously-reported as a diversion of 2% of Social Security funds into private investments, this in fact represents a more significant 32% diversion of social security funds.
Paulos then considers the figures given for the number of people illegally crossing the U.S.-Mexican border. U.S. border agents note that they apprehend about 1 million people every year attempting to cross the border, and estimate that 3 times as many make it across. But freelance journalist Ben Winograd has noted a few problems with these numbers. First, the "1 million" figure represents the number of apprehensions, not the number of people: Winograd notes that many people repeatedly attempt the crossing. Secondly, he asks, how can one estimate the number of people not apprehended when they haven't been caught?
For the final example, Paulos looks at the estimates given for the number of Iraqi civilians killed in the current war. He gives some reasons-including small sample size, not quite random sampling of the population, and less than certain assumptions-to be "skeptical (but not dismissive)" of the figure of 100,000 reported in a study recently appearing in the Lancet. While this may be too large, he notes that the 15,000 figure given by Iraqi Body Count may be too small: the reality, Paulos guesses, lies somewhere in between.
--- Claudia Clark
Klarreich writes about random- and pseudorandom-number generators, which are used in expected settings such as shuffling a virtual deck of cards at an online poker site, and in unexpected ones such as an archaeologist choosing which quadrants to survey at a big dig. Billions of random numbers are needed each day, so good random-number generators are in demand. Bias in a random-number generator can lead to unwanted consequences: For example, a website's online transactions might no longer be secure if a hacker could exploit the bias. Klarreich describes effective random-number generators and the faults of some others.
--- Mike Breen
"Shiing-Shen Chern, 93." Milestones, Time, 20 December 2004.
"Students Show Mixed Science, Math Scores," by Ben Feller. Newsday, 15 December 2004;
Results of two international tests in math and science were released recently. The 2003 Trends in International Mathematics and Science Study (TIMSS) released its statistics based on tests given to fourth and eighth graders last year. In the TIMSS math rankings, Singapore students from both grades finished first, of 44 countries participating. U.S. fourth graders finished 12th, while eighth graders finished 15th. The study showed improvement in the math scores of U.S. minority students. The TIMSS webpage has all results from 2003 and earlier years. In a study of how well students apply their knowledge - the Program for International Student Assessment (PISA) - Hong Kong students finished first, while U.S. students finished 24th. The PISA test was given to 270,000 15-year olds in 41 countries, also in 2003. More information is at the organization's website. The third article is reaction to the poor U.S. scores on the latter test. Two sample questions from the test are included in a sidebar. McNeil's thesis is that "In all but the most arcane specialties (like teaching math), the need for math has atrophied." After making his case, McNeil quotes others' reaction to his thesis. He concludes with a quote from his daughter's math teacher: "...kids don't study poetry just because they're going to grow up to be poets. It's about a habit of mind. Your mind doesn't think abstractly unless it's asked to - and it needs to be asked to from a relatively young age. The rigor and logic that goes into math is a good way for your brain to be trained."
--- Mike Breen
In the early 1800s, Uranus was thought to be the outermost planet yet scientists could not reconcile its observed orbit with theoretical predictions based on Newton's laws of gravity and motion. In 1846 French mathematician Urbain Jean Joseph Le Verrier stated that another planet---now named Neptune---must exist, affecting Uranus' orbit, and indicated where to look for it. This led to the discovery of Neptune a few months later. One year before Le Verrier's prediction, Englishman John Couch Adams had done calculations about a hypothetical planet and left a sheet of paper about his work at the home of George Biddell Airy. Adams has shared credit with LeVerrier for the discovery of Neptune but historians of science have been unable to examine the paper since the 1960s. The crucial document has recently become available. Based on their examination of the paper and other related documents, the authors conclude that "Adams does not deserve equal credit with Le Verrier for the discovery of Neptune. ... The achievement was Le Verrier's alone."
--- Mike Breen
"Optics and Realism in Renaissance Art," by David G. Stork. Scientific American, December 2004, pages 76-83.
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