February 12, 2003
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Diamond Life
(Von Neumann’s Song, Part II)
A reader of yesterday’s entry “St. John von Neumann’s Song” suggested the relevance of little Dougie Hofstadter‘s book Gödel, Escher, Bach: An Eternal Golden Braid. While the title of this work does continue the “golden” theme of my last three entries, Dougie is not playing in von Neumann’s league. The nature of this league is suggested by yesterday’s citation of
For work that is more in von Neumann’s league than in Hofstadter’s, see the following
VECTOR-VALUED EXTENSIONS
OF SOME CLASSICAL THEOREMS
IN HARMONIC ANALYSIS
Abstract:
…. The approach used combines methods from Fourier analysis and the geometry of Banach spaces, such as R-boundedness.
A related paper by the same authors:
CRITERIA FOR R-BOUNDEDNESS
OF OPERATOR FAMILIES
Abstract:
…smooth operator-valued functions have a R-bounded range, where the degree of smoothness depends on the geometry of the Banach space.
Those who would like to make a connection to music in the charmingly childlike manner of Hofstadter are invited to sing a few choruses of “How do you solve a problem like Maria?“
Personally, I prefer the following lyrics:
Diamond life, lover boy;
We move in space with minimum waste and maximum joy.
City lights and business nights
When you require streetcar desire for higher heights.
No place for beginners or sensitive hearts
When sentiment is left to chance.
No place to be ending but somewhere to start.
No need to ask.
He’s a smooth operator….
Words and Music: Sade Adu and Ray St. John
Some may wish to alter the last five syllables of these lyrics in accordance with yesterday’s entry on another St. John.
