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A monthly survey of math news
This doughnut universe. The top half of the front page of the New York Times Science section for March 11, 2003 was given over to illustrations for "Universe as Doughnut: New Data, New Debate" a substantial article by Dennis Overbye. The new data come from NASA's Wilkinson Microwave Anisotropy Probe, whose first results were released last month. The Probe is designed for precise measurement of the background microwave radiation permeating the universe; the anisotropy it examines is, as Overbye explains, the manifestation of sound waves expressing microscopic fluctuations ("lumps in the cosmic gravy") during the first instant of time. Overbye quotes Max Tegmark, a cosmologist at Penn: "There's a hint in the data that if you traveled far and fast in the direction of the constellation Virgo, you'd return to Earth from the opposite direction." The hint referred to by Tegmark comes from the spectrum of those waves: "If the universe were a guitar string, it would be missing its deepest notes, the ones with the longest wavelength, perhaps because it is not big enough to sustain them." The somewhat speculative conclusion is that the universe is finite, at least in certain directions. One section of the article is devoted to the topological implications of finiteness; it mentions William Thurston and Jeffrey Weeks as mathematicians who "have speculated about universes composed of various polyhedrons glued together in various ways." The article includes directions for making a torus out of a flat sheet of material. Don't try this at home.
Knots in the Washington Post. The March 9 2003 Washington Post rana review of a math book: Alexei Sossinsky's "Knots: Mathematics with aTwist" (Harvard University Press). The reviewer,John Derbyshire, describes "Knots" as "an account of mathematical knot theory, aimed at a nonspecialist reader" and, as pop-math books go, "at the high end of the range of difficulty for readers who are not mathematicians."But he adds: "Once you have grasped three or four basic ideas, and got into the knotty way of thinking, it is easy to expand your understanding."Derbyshire runs through the basic examples of knot theory: the unknot,the trefoil, explains knot equivalence, and introduces the idea of aninvariant: "some characteristic mathematical object that is left unchanged by manipulations of the slide-but-don't-cut type.""I think the Jones polynomial ... will be the pons asinorum of the book for non-mathematicians. It is worth persevering with, though, for after 10 pages a very beautiful result is obtained ..."
Sossinsky's "Knots" had been reviewed, by Andrzej Stasiak, in the January 30 2003 Nature. He also singled out the calculationof the Jones polynomial: "This experience alone, if you're willing to putin the effort, makes the book worth reading."
Anthrax: the math. Results from a simulation using a mathematical model of an airborne anthrax attack (on a city the size of New York) were described in the March 18 2003 Chronicle of Higher Education. The article, "Death Toll in Airborne Anthrax Attack Could Exceed 100,000, Mathematical Model Finds" by Lila Guterman, cites a study just published in the Proceedings of the National Academy of Sciences, by Lawrence Wein (Stanford), Edward Kaplan (Yale) and David Craft, a graduate student at MIT. Wein is an expert in queuing theory: the thrust of the article is that if people have to wait in line for vaccination, in the case of a massive attack, many will die. The simulation showed, on the other hand, that "By simply eliminating the lines for antibiotics, the numbers of deaths can be nearly halved." Guterman quotes Wein: "Everything has to be measured in hours, not days ... We have to be very, very aggressive." Better yet, according to Wein, would be to distribute appropriate antibiotics beforehand to the entire population. In a statement quoted on the Stanford website he recommends: "Give it to the people now so that they can just turn on CNN and wait for Secretary Ridge to tell the people in their region to take their Cipro now."