Thursday, December 15, 2005

Thursday December 15, 2005

Filed under: General — m759 @ 3:48 PM
In honor of Freeman Dyson’s birthday:

Dance of the Numbers

“Mahlburg likens his approach to an analogous one for deciding whether a dance party has an even or odd number of attendees. Instead of counting all the participants, a quicker method is to see whether everyone has a partner—in effect making groups that are divisible by 2.

In Mahlburg’s work, the partition numbers play the role of the dance participants, and the crank splits them not into couples but into groups of a size divisible by the prime number in question. The total number of partitions is, therefore, also divisible by that prime.

Mahlburg’s work ‘has effectively written the final chapter on Ramanujan congruences,’ Ono says.

‘Each step in the story is a work of art,’ Dyson says, ‘and the story as a whole is a sequence of episodes of rare beauty, a drama built out of nothing but numbers and imagination.'”

Erica Klarreich in Science News Online, week of June 18, 2005

This would seem to meet the criteria set by Fritz Leiber for “a story that works.” (See previous entry.)  Whether the muse of dance (played in “Xanadu” by a granddaughter of physicist Max Born– see recent entries) has a role in the Dyson story is debatable.

Born Dec. 11, 1882, Breslau, Germany.

Died Jan. 5, 1970, Göttingen,
West Germany.

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Max Born

Those who prefer less abstract stories may enjoy a mythic tale by Robert Graves, Watch the North Wind Rise, or a Christian tale by George MacDonald, At the Back of the North Wind.

Related material:

“The valley spirit never dies. It’s named the mystic woman.”

Tao Te Ching

For an image of a particular
incarnation of the mystic woman
(whether as muse, as goddess,
or as the White Witch of Narnia,
I do not know) see Julie Taymor.

“Down in the valley,
 valley so low,
 hang your head over,
 hear the wind blow.”

Folk song

“Which is the sound of the land
Full of the same wind
That is blowing in
    the same bare place

For the listener,
    who listens in the snow,
And, nothing himself, beholds
Nothing that is not there
    and the nothing that is.”

Wallace Stevens

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