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A monthly survey of math news
This month's topics:
Last December 2, the New York Times Magazine printed a portfolio of seven full-page black-and-white photographs by Hiroshi Sugimoto. Sugimoto's subjects were plaster mathematical models from the University of Tokyo's collection, but it was a set that many schools acquired long ago and that many still have on display. The models have been superseded by computer graphics as aids to visualization, and by now most live on inconspicuously in their dusty display cases. Sugimoto brings out their latent beauty: he shoots them lovingly cleaned, perhaps repainted for the occasion, dramatically lit against a black background like intergalactic objects in deep space. The roughish texture of the plaster becomes a photographic asset. And they come with their generating equations, e.g.:
You can read about it in the New York Times. The portfolio is available as a slide show online.The math behind "Intelligent Design"
H. Allen Orr's "Devolution," subtitled "Why intelligent design isn't," ran in the May 30 2005 New Yorker under their Annals of Science rubric. Orr, Professor of Biology at the University of Rochester, examines the most recent instars of the Intelligent Design (I.D.) argument. In particular he mentions the claim that "recent mathematical findings cast doubt on the power of natural selection." This claim, Orr tells us, has been put forward by William A. Dembski, who "holds a Ph.D. in mathematics, another in philosophy, and a master of divinity in theology." Dembski, once on the faculty at Baylor University and now a member of the Center for Science and Theology at Southern Baptist Theological Seminary, uses the "so-called No Free Lunch, or N.F.L. theorems" to attack natural selection. These theorems analyze the efficiency of search algorithms. "Roughly, the N.F.L. theorems prove the surprising fact that, averaged over all possible terrains, no search algorithm is better than any other." Therefore the search algorithm posited by Darwinism (random mutation plus natural selection), looking for the best in the landscape of all possible adaptations, "is no better than blind search, a process of utterly random change unaided by any guiding force like natural selection." So runs the argument. "Since we don't expect blind change to build elaborate machines showing an exquisite coördination of parts, we have no right to expect Darwinism to do so, either." As Orr reports, "Dembski's arguments have been met with tremendous enthusiasm in the I.D. movement. In part, that's because an innumerate public is easily impressed by a bit of mathematics." But Orr mentions recent work showing that the N.F.L theorems "don't hold in the case of co-evolution, when two or more species evolve in response to one another. And most evolution is surely co-evolution. Organisms ... are perpetually challenged by, and adapting to, a rapidly changing suite of viruses, parasites, predators and prey. A theorem that doesn't apply to these situations is a theorem whose relevance to biology is unclear." He ends this discussion by quoting David Wolpert, one of the authors of the N.F.L. theorems, on Dembski's use of those theorems: "fatally informal and imprecise." Wolpert's paper, joint work with William Macready, is available online, as is Wolpert's critique of Dembski's argument.Archimedes palimpsest update
Capsule history: A 10th-century parchment containing several works of Archimedes (one of them known to us only by its title) was partially erased sometime between the 12th and 14th century and reused as a religious text. The new book, carefully preserved in monasteries, was found in 1906 by J. L. Heiberg, a scholar who recognized the subtext and was able to decipher and publish most of it. The book went out of sight and resurfaced in 1998 when it was sold at auction for $2 million. The collector who bought it has loaned it until 2008 to the Walters Art Museum in Baltimore. There modern techniques (X-ray fluorescence, optical character recognition and multi-spectral imaging) are being used to tease out the maximum possible of Archimedes' barely legible text. The update: Scholars in Baltimore were stymied by four pages which a 20th-century forger had overpainted with pseudo-medieval imagery, presumably to make the book more valuable. One of them, hearing that the ancient ink was iron-based, thought to take those pages to the Stanford Synchrotron Radiation Laboratory, where high-energy X-rays could make the hidden iron atoms fluoresce and give up their information. The result is four superimposed images (both texts, both sides of the parchment) but the message, which deals with floating bodies and the equilibrium of planes, is there for deciphering. This material is taken from a Stanford University news release posted online by Science Daily on May 22 2005. The release was picked up in the May 19 2005 Nature ("Eureka moment as X-rays slice through forgery"). The Nature item shows one of the forged overpaintings and gives a glimpse of the SSRL radiograph.