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
September 2001
Math Anxiety and Math Competence,
how are they related? A study by Mark Ashcraft and Elizabeth Kirk, of Cleveland
State University, picked up in a piece by B. Bower in the June 30, 2001
Science News, describes experiments giving
evidence that math anxiety can be a cause of low math competence
and not just
a consequence. The most
striking experiments show that math-anxious students who can perform
as well as their peers on pencil-and-paper tests fall behind on
mental arithmetic tasks, especially those involving the ``carrying''
operation. The authors explain the lower performance in terms
of ``working memory:'' ``We propose that there is an on-line
reduction in the available working-memory capacity of
high-math-anxiety individuals when their anxiety is
aroused.'' Full text of the Ashcraft-Kirk article is
available online.
What is Math about? The
question comes up in a ``Words'' piece by John Casti (Technical University
of Vienna) in the May 31, 2001 Nature. Casti's piece is titled
``Formally speaking'' and deals mostly with the mathematical process
of formalizing the informal (``...`rational' decision-making and game
theory, `closeness' and topology, `infinity' and calculus''). But it
includes his interesting take on Gödel's incompleteness theorem:
``... Gödel's incompleteness theorem shows that there is an
irreducible semantic component to mathematics. It is not just a game
of shuffling meaningless strings of symbols about in accordance
with a set of transformation rules.'' Or, as he puts it elsewhere,
``... one must always remember that number theory is about numbers.''
Tying and untying molecular knots. A report in the June 14, 2001 Nature describes a synthetic
oligomer which can be chemically directed to knot itself, to unknot and
to reknot. The work, by a six-person team (Henry Adams, Eleanor Ashorth,
Gloria Breault, Jun Guo, Christopher Hunter, Paul Mayers)
based in Britain, involves
creating a string of three rigid ``linkers'' joined by two ``ligands.''
When zinc perchlorate is added to the solution, the linkers assemble
themselves in an octahedron-like cluster about a zinc ion, and as a
result the ligand-linker chain becomes knotted.
| The clustering of the linkers about the zinc ion forces the linker-ligand molecule to become knotted. Image adapted from image in Nature. |
Wiles at the Olympiad.
Andrew Wiles was ``greeted like a rock star by the current
generation of young math stars at the close of their global
competition.'' This from the lead paragraph of ``Young Math Competitors Pay Tribute to Their Hero'' in the July 14, 2001 New York Times.
Wiles addressed the International Mathematical
Olympiad, hosted in Washington D.C. this year. ``You can tell by the
response here that he is a hero among the math community,'' said silver
medalist Oaz Nir, 17. Mr. Nir, David Shin (silver) and Reid Barton,
Gabriel Carroll, Ian Le and Tiankai Liu (all gold medalists) made
up the U.S. team, which tied with Russia for second place. First
place went to China. Barton, who is 18, won a gold medal for the
fourth time. He and Carroll had perfect scores on the examination.
Is pi normal?
Which means, do all digit sequences of the same length appear
with the same frequency in its decimal expansion? Statistical
evidence favors normality. For example, in the first 200 of the 206 billion
digits recently computed by Yasumasa Kanada et al. at the University of
Tokyo, 7 occurred 19,999,967,594 times. This information is from
a piece by Ivars Peterson in the September 1, 2001 Science News.
It seems sort of obvious that
there should be no incestuous relationship between pi and 10, but
establishing a proof is another matter. Recent progress has been made,
however. It builds on a 1995 discovery by David Bailey (Lawrence
Berkeley National Lab), Peter Borwein (Simon Fraser)
and Simon Plouffe (University of Quebec at Montreal),
who ``unexpectedly found a simple formula that
enables one to calculate isolated digits of pi --say, the trillionth
digit-- without computing and keeping track of all the preceding digits.''
This formula only works for the base 2 and base 16 expansions,
not the decimal, but it seems like a step towards determining the
normality of pi in those bases. Now Bailey and Richard Crandall (Reed)
have proved the equivalence between the base-2 normality of pi (and ln 2)
and the equidistribution property for the orbit of certain self-maps
of the interval. Peterson tells us which map works for ln 2:
xn = 2xn-1 + 1/n (mod 1), and relates
the pessimistic opinion of Jeff Lagarias (AT&T labs), that the
new problem may be as intractable as the old. As usual, pi brings
out the puns: Peterson called his piece ``Pi à la mode,''
while the Nature comment was titled
``Pi shared fairly.''
-Tony Phillips
Stony Brook
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