A beautiful movie. The screen adaptation of Sylvia Nasar's story of the John Nash saga is now playing nationwide and has been widely reviewed. According to A. O. Scott (New York Times, December 21 2001, ``From Math to Madness and Back'') A Beautiful Mind is ``elegant, but wrong,'' in a (mis-)quotation from the script. According to Anthony Lane (The New Yorker, January 7 2002, ``Game Boy'') ``The book is far superior to the film; ...'' According to Dr. Jonathan David Farley (Time Sampler, January 5 2002, ``American Pi'' -ouch!) ``It betrays the prize-winning book of the same name on which it is based.'' These reviewers seem to have expected, as I originally did, that the film could bring Nasar's book to life. In fact the movie is dual to the book. Where the book patiently accumulates fact upon fact about the outside of Nash, the film manages with a few brilliant cinematic metaphors to make us imagine what it might have been like inside the head of the mathematical genius and the psychiatric patient. It goes a little syrupy at the end but Richard Schickel, in the January 7 2002 Time, gets it right: ``mainstream moviemaking at its highest, most satisfying level.''
Tiny computer factors 15. The December 20/27 2001 Nature ran a ``letter to Nature'' from an IBM Almaden/Stanford University team describing their implementation of Peter Shor's quantum factoring algorithm using a molecule as quantum computer. (Ancillary details appear in an IBM Research News item: IBM's Test-tube Quantum Computer Makes History.) It takes 7 ``qubits" to factor 15; Isaac Chuang and his team-mates custom synthesized a special molecule to accomodate and process them.
The experiment depends crucially on properties of this special molecule, e.g.: ``All seven spins in this molecule are remarkably well separated in frequency.'' But `` the demands of Shor's algorithm clearly push the limits of the current molecule, despite its exceptional properties.'' And in fact the IBM News release concedes that ``... it will be very difficult to develop and synthesize molecules with many more than seven qubits.'' This is still significant as the first physical realization of Shor's algorithm. The answer, 3 times 5, was obtained in about 720ms.
"Knot Possible" is Ivars Peterson's cover story in the December 8, 2001 Science News. Peterson gives a quick tour of the basics of knot theory, including Reidemeister moves, and focuses on the problem of algorithmic identification of the unknot. This includes Wolfgang Haken's 1961 algorithm, the recent estimate by Joel Hass and Jeffrey Lagarias of a bound on the number of Reidemeister moves required, and even more recent work by Joan Birman and collaborators on a new algorithm using braid theory. He ends promising that knot theory will ``keep mathematicians tied up for many years to come.''
A mathematician backstage. MIT's Daniel Kleitman participated in Good Will Hunting, and now Barnard College's Dave Bayer served as ``mathematical help'' for A Beautiful Mind. The story appears in the December 2001 SIAM News. Bayer reviewed Proof for the Notices; director Ron Howard read the review and invited Bayer to help with the mathematical authenticity of his John Nash project. Bayer wound up being Russell Crowe's hand double: their hands look alike and so does their handwriting. That blackboard crammed with math that appears late in the movie is pure Bayer.
Waves of measles. An article in the December 13, 2001 Nature applies wavelets to the study of measles epidemics. In ``Travelling waves and spatial hierarchies in measles epidemics,'' Bryan Grenfell (Cambridge), Ottar Bjørnstad (Cambridge, Penn State) and Jens Kappey (Penn State) ``use wavelet phase analysis'' to ``demonstrate recurrent epidemic travelling waves in an exhaustive spatio-temporal data set for England and Wales.'' One of their observations is that the increase in the vaccinated population from 1968 to the late 1980s generates a progressive increase in the period of this wave phenomenon.
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