Math in the Media
Highlights of math news from science literature and the current media
Math in the Media
Highlights of math news from science literature and the current media
April 2001
Math in The Lancet.
The February 17, 2001 issue of the #1 medical journal features a review
by Seamus Sweeney of ``The mystery of the aleph: mathematics, the Kabbalah,
and the search for infinity" by Amir D Aczel (New York: Four Walls Eight
Windows, 2000), a book about Georg Cantor's life and his discoveries in
the theory of sets. Perhaps the profession's interest was sparked by
Poincaré's judgment, quoted in the first sentence of the review,
that Cantor's work was "a malady, a perverse illness from which
someday mathematics will be cured." Sweeney gives the book a careful and
sympathetic review, including a presentation of Cantor's famous
diagonal argument establishing the uncountability of the real numbers.
He does get a bit carried away: ``Reading of the dizzying orders of infinity that Cantor explored, one feels perhaps that maths and music are the closest humanity can get to any sense of the divine." This must sound odd to the
M.D.s, many of whom confront transcendent problems on a daily basis.
Sweeney concludes: ``Indeed the rarefied world of infinity and its relationship with the divine is perhaps the most beguiling seductress mathematics can rely on to persuade the reflex numerophobes conditioned to see mathematics as dry, soulless, and worst of all, boring."
As other accessible introductions to the world of pure mathematics he
recommends Paul Hoffman's ``The man who loved only numbers" (New York : Hyperion, 1998) and
John D Barrow's ``Pi in the sky" (Oxford : Clarendon Press ; New York : Oxford University Press, 1992.)
Solitons in matter. Solitons,
or solitary waves, were first discovered as surface waves in canals. They
manifest solutions of the non-linear wave equation which have the
remarkable property of maintaining their form unchanged as they
propagate. Eran Sharon,
Gil Cohen and Jay Fineberg, three members of the Racah Institute of Physics
in Jerusalem, have a
``Letter to Nature" in the March 1, 2001 issue where
they show how perturbations to a crack front in a brittle material result
in long-lived and highly localized waves (`front waves') with many of the
properties of solitons. They conclude that (presumably novel) nonlinear
focussing processes, ``perhaps analogous to processes that occur in
classical soliton formation, are at play."
Teenager finds new triangle theorem. The March 3, 2001 Atlanta
Constitution ran a piece entitled "Theoretically, teen's a geometry whiz," by
Kirk Kicklighter. It tells the story of Josh Klehr who on May 8, 1999, his last day of eighth grade,
discovered a new concurrence theorem for triangles. In retrospect, it is the
circumcenter theorem in the Minkowski metric
ds2 = dx2 - dy2, but no one had ever noticed it
before. Congratulations, Josh! The theorem is now known as the Klehr-Bliss Theorem.
If we call the Minkowski perpendicular bisector of a segment with slope
a
the line through its midpoint with slope 1/a (the two lines are
orthogonal in the Minkowski metric),
the Klehr-Bliss theorem says that the Minkowski
perpendicular bisectors of the three sides of a triangle are concurrent. The proof
follows the usual proof: any point on the Minkowski perpendicular bisector of
a segment is Minkowski equidistant from the two ends. For the proof of a
more general statement, see Floor von Lamoen, Morley related triangles
on the nine-point circle, Amer. Math. Monthly 107, 941-945.
God, Steve Wolfram, etc.
What has Stephen Wolfram, alumnus
of Eton and Oxford, veteran of Argonne, CalTech, and the Institute for
Advanced Study, MacArthur Fellow at age 21, been doing since his release
of Mathematica (``the most popular scientific software ever made")
in 1988? He has been planning the
complete mathematization of science, and the overhaul of mathematics
itself, through his work on cellular automata. This from
a long essay by Michael S. Malone, in the online
Forbes ASAP for
November 27, 2000, entitled ``God, Steve Wolfram, and Everything Else."
Cellular automata go back
to Von Neumann, but gained wide fame through John Conway's game ``Life"
(try Alan Hensel's Java
implementation online).
How will Wolfram bring about his revolution?
To a mathematician the article does not
offer any useful clues.
The one specific example given, the pattern of
markings on a Textile Cone Shell, fits into perfectly conventional science,
but it is not clear whether this example is to be taken literally
or not, i.e. whether this remark is relevant.
A piece apearing in Forbes, and
containing statements like ``Everything from cars to cartoons, from
farms to pharmaceuticals, may reflect the richness of the natural world
as seen through Wolfram's cellular automata" and "Within 50 years, more
pieces of technology will be created on the basis of my science than on
the basis of traditional science," inevitably sounds more like the
publicity for an IPO than the presentation of news about current scientific
research.
The beautiful and moving initial
image (the 2-billion-tile rose generated from black and white squares
laid according to "half a dozen ... abitrary rules") typifies the essay.
We do not know if the rose is fact or metaphor. We have no way of
judging if the
tremendous technical developments hinted at are fact or science fiction.
``A New Kind of Science," Wolfram's magnum opus on the topic, is
promised for sometime this year.
Calculus with Mother Hen.
The March 30, 2001 edition of The Chronicle of Higher Education
tells the story of ``Operation Mother Hen," a Web-based teaching tool for
students who are ``chicken about calculus," and a new approach
to the perennial problem of high drop-out and failure rates.
Mother Hen is the nom de plume of Ann Piech,
a Buffalo mathematics professor and calculus teacher. Each of her
lectures is broken down into six concepts and accompanying problems,
and each of the six segments is posted as a separate video clip on the Web:
``at any hour of the day or night a student who is having
trouble with, say, polar coordinates or improper
integrals can get a mini-tutorial in the subject with
a mere click of the mouse." Check it out at
http://motherhen.eng.buffalo.edu.
-Tony Phillips
Stony Brook
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