February 2000
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.
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