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A monthly survey of math news
Math Snow Sculpture Wins Prize at Breckenridge. A team from Macalester College, representing Minnesota, and sponsored by Wolfram Research won Second Prize at the Breckenridge International Snow Sculpture Competition, held from January 18-23, 2000. Their entry was a model of the Enneper Surface, a minimal surface with ``tremendous symmetry'' and huge overhangs. More pictures and details at the SnowSculpting2000 website. Third prize went to Switzerland.
Bubbles can sink in stout. A nice application of Computational Fluid Dynamics was announced in December and picked up in the New York Times for January 11, 2000: ``Analyzing the Tempest in a Pot of Stout'' by Larry Fountain. The computation resulted in a simulation you can see at the website of Fluent Incorporated, the people who made the software. Barflies apparently had thought they were seeing things (``an artifact of the drinking process'' as one of Fountain's sources described it) when they witnessed bubbles moving downward inside pint draughts of Guiness Stout. Not so. The simulation reveals that the upward motion of large bubbles dislodged from the center of the bottom of the mug sets up a kind of convection pattern that drags down small bubbles near the edge. The high viscosity of this liquid is said to help.
More on Parrando's Paradox. This time the Nature piece we saw last month was picked up by Sandra Blakeslee in the January 25, 2000 New York Times: ``Paradox in Game Theory: Losing Strategy that Wins.'' Blakeslee got Derek Abbott, one of the original authors, to expound on the concept of ratchets (important in understanding this phenomenon). ``Any child knows that when you shake a bag of mixed nuts, the Brazil nuts rise to the top. This is because smaller nuts block downward movement of larger nuts.''
``DNA Computer is created and does Complex Calculations'' was an AP release published in the January 13, 2000 New York Times. The release picks up an article in that day's Nature, ``DNA Computing on Surfaces,'' by a University of Wisconsin team. The article describes the solution of a case of the ``3-SAT''-problem, in this case determining whether the Boolean expression:
(W or X or Y) and (W or Y' or Z) and (X' or Y) and (W' or Y')(where X' = not X, etc.) can be satisfied: Does there exist an assignment of T ``true'' and F ``false'' to the variables X,Y,Z,W so that the whole expression computes out to be ``true''? The ``3'' refers to the fact that the expression can be written as an and of ors (this can be done for any expression) in such a way that no or involves more than three variables. The 3-SAT problem is known to be NP-complete.
More Chimp Math? The latest is reported in the January 6, 2000 Nature: Cognition: Numerical memory span in a chimpanzee, by Nobuyuki Kawai and Tetsuro Matsuzawa of the Kyoto University Primate Research Institute. Their chimpanzee's name is Ai. She can recognize arabic numbers (from 0 to 9) as corresponding to to the correct cardinalities, and in particular can order any set of them by size. If five numbers are displayed (in random positions) on a screen she can therefore point to them in increasing order, but she can also do this if, after she has pointed to the lowest number, the others are all masked by opaque squares. There is clearly some high-order processing going on.
``The Curl of Agnesi'' is the proper name for the curve x2=a2(a - y) associated with the Italian mathematician Maria Gaetana Agnesi (1718-1799). Agnesi and several of her colleagues are remembered in a piece ``The Women Scientists of Bologna'' by Maria Cieslak-Golonka and Bruno Morten in the American Scientist for January-February 2000. In the 18th century universities were generally off-limits to women; Italian universities were the exception, a consequence, the story goes, of the ``old Roman spirit of freedom of which the Italians were the natural inheritors.'' In any case, the University of Bologna led the way and was rewarded by the great fame that several of its alumnae attained. Agnesi was perhaps the most brilliant of all of them. She wrote a very widely read book, the Instituzioni Analitiche, which ``set a standard for academic mathematical treatises'' and apparently influenced the mathematical vocabulary and style of Lagrange himself. Only her sex kept her out of the Académie des Sciences, as they informed her. It turns out, we are told, she was doing it all to keep her father (a mathematics professor) happy, and after he died she dropped her research and devoted the rest of her life to her first loves: good works and religion.
SUNY at Stony Brook