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 Tony Phillips' Take on Math in the MediaA monthly survey of math news |
February 2001
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| Plimpton 322, George A. Plimpton Collection, Rare Book and Manuscript Library, Columbia University. Click for larger image. |
Rereading Plimpton 322. Plimpton
322, the tiny dark star of Columbia University's Rare Book Library, is probably
the world's best known piece of Mesopotamian mathematics. A clay tablet, about
5 inches long and 3.5 inches wide, with 4 columns and 15 rows of cuneiform hexadecimal
numbers, it is usually dated 1900-1600 BC. Sir Christopher Zeeman lectured on
it in San Antonio in 1995 AD, calls it ``the oldest preserved document on number
theory," and gives a mathematical argument for its interpretation as a set of
pythagorean triples. Lectures available online.
The January 27 2001 Science News has a piece by Ivars Peterson describing
a recent reevaluation of the mathematical content of the tablet. The work is due
to Eleanor Robson (Oriental Institute, Oxford) and is presented as an example
of ``new scholarly approaches to Mesopotamian mathematics" which ``combine historical,
linguistic and mathematical techniques." Dr Robson pins down the date of the tablet
to 1800 +/- 40 BC, and gives an alternative explanation of the tablet's purpose:
it ``served as a guide for a teacher preparing exercises involving squares and
reciprocals." Despite this downgrading from number theory to arithmetic, Robson
considers Plimpton 322 ``the epitome of Mesopotamian mathematical culture at its
best. ... It's a well-organized, well-executed, beautiful piece of mathematics."
"Loving Math Infinitely" is the
title of a piece by Josephina Alvarez, professor of mathematics at New Mexico
State University at Las Cruces, that ran in the Chronicle Review section of
the January 19, 2001 Chronicle of Higher Education. Prof. Alvarez describes
her experiences teaching ``a course on mathematics appreciation for nonscience
majors." This is a rich piece, with many valuable ideas for mathematics teachers
at any level. She finds that in order to reach her students, she has to ``look
into their training and interests. I need to learn to use their language. My
challenge is to extract the mathematical ideas in music, philosophy, art, and
other seemingly nonmathematical fields." She elaborates on ``As soon as I knew
what I should be looking for, I started to see mathematics in unexpected places."
with many examples, and concludes: ``Interestingly enough, once we saw mathematics
as firmly rooted in human need and experience, it seemed easy to depart on a
tour of increasing abstraction." To summarize her article in two sentences:
``Mathematics appreciation is more than a course. It is an attitude that we
should cultivate in every mathematics course."
How do fish swim? ``The dynamics
of swimming fish and flapping flags involves a complicated interaction of their
deformable shapes with the surrounding fluid flow." This is the beginning of
a ``letter to Nature" (14 December 2000) from a Courant Institute/Rockefeller
University team headed by Jun Zhang. Their research used flexible filaments
in a flowing soap film 3-4 microns thick. In particular they report that beyond
a certain critical length the system becomes bi-stable, with both a ``stretched-straight
state" and a ``stable flapping state" possible.
|
| A snapshot of the flapping state. Note that the end of the filament is near the center of the image. Image from NYU Wetlab, used with permission. Click for larger image. |
.
Here, y(x, t) is the horizontal displacement of the filament from
the centre-line,
measured at a vertical distance x from the fixed point for time t.
f(x) is a spatial
envelope function (increasing monotonically from the fixed point),
nu is the flapping frequency and lambda the wavelength."
An interesting final point: ``Swimming offers alternatives comparable to the bistability of our filament. The stretched-straight state is the analogue of a glide, whereas the flapping state is analogous to swimming. Efficient propulsion uses the natural oscillations of the swimmer, which in the filament is a property mediated by stiffness." A web presentation of this research is available.
Digital Archimedes. The thousand-year-old
palimpsest
that turned up on the front pages in 1998 is undergoing a thoroughly modern
analysis. A report entitled ``Through the Layers, a Glimmer of Archimedes" by
Lawrence Biemiller (The Chronicle of Higher Education, January 26, 2001)
describes this treasure: a precious euchologion, a 10th century Greek
prayer book, was written on parchment that had previously been used for a collection
of works by the great Archimedes. Even though the pages had been scraped clear
of the original text, enough remained for the Danish scholar Johan Ludvig Heiberg
to recognize. The discovery (published in 1907) was sensational: among other
works the manuscript contained a copy of ``The Method," an important work of
Archimedes that had been thought completely lost. Biemiller tells the story
of how this item came to be sold at Christies' in 1998 (for $2 million) and
how the present owner has agreed to pay for the Walters Art Gallery in Baltimore
to take over the conservation of the manuscript and the computer-aided digital
imaging of its pages. Two teams, one from Johns Hopkins and one from the Rochester
Institute of Technology, are collaborating with the Walters. They predict a
much more complete transcription of the text and, quite important, access to
the original drawings. The project should take four years.
Math teachers are nerds ... not.
John Dunford, a math teacher himself (and general secretary of the somewhat
ominously named Secondary Heads Association) takes issue with a survey of 12-year-old
schoolchildren's ``impressions of their maths teachers." In a piece in the January
4, 2001 Guardian he defends the profession from the merciless gaze of
the young: ``Fat, bald nerds with glasses and beards apparently predominate
at the front of maths classrooms. These sad figures are apparently seen as unmarried
and unstylish, wrinkled from all the hard thinking that they have had to do
in order to solve maths problems throughout their lives." Not so, says Dunford.
Speaking of his colleagues over the years: ``I cannot really recall anyone who
might have been described as a nerd. ... family people mostly, with a good range
of interests from swimming and badminton to reading and cooking." But wait!
``There could be an age factor too. I may not find my colleagues nerdish, but
I do recall my own maths teachers at school as coming into that category." The
piece is available online.
Math and Fiction. Incompatible careers? Not
if you ask Manil Suri, expert in partial differential equations, Professor of
Mathematics at the University of Maryland Baltimore County, and author of a
New Yorker short story (``The Seven Circles," February 14, 2000) and
a novel ``The Death of Vishnu" (Norton, January 2001). Suri was interviewed
by Ivar Stakgold in the January-February 2001 SIAM News. The interview
ranges over many topics, but keeps returning to the similarities and differences
between doing math and writing fiction. Suri: ``What's a little eerie is how
similar the thought processes can be for the two activities. Suppose I am trying
to decide whether a mathematical entity X is bounded. I might try to
think of varous ways that X might try to misbehave ... . Fiction presents
a similar scenario -- perhaps X is now a character in a certain situation.
To find out what happens next, I would try to put myself in X's place,
looking for all the ways I could proceed, maneuvering around any of the story's
imposed constraints, and choosing the most interesting path." He mentions a
reading at MSRI after which a colleague told him ``It's all about Fourier series,"
i.e. that ``all fiction is composed of the same Fourier modes: love, death,
marriage, sex and so on, and one gets different stories by assembling different
combinations of these basis functions." Prof. Suri knows how to milk a metaphor:
``Certainly a key strategy to getting fiction published is to orthogonalize
to what has been written before."
-Tony Phillips
Stony Brook
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Comments: webmaster@ams.org |