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July 10, 1999
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A Song About Pi
At the age of 82, Irving Kaplansky remains actively engaged in mathematical research.
Now Director Emeritus of the Mathematical Sciences Research Institute (MSRI) in Berkeley, Calif., Kaplansky spends much of his time in the library, poking into various nooks and crannies of mathematical history. Tidying up loose ends and filling in unaccountable gaps in the mathematical literature, he patiently works through mathematical arguments, proves theorems, and prepares papers for publication. His remarkably wide-ranging efforts belie the oft-repeated notion that mathematicians are most productive when they are young.
A distinguished mathematician who has made major contributions to algebra and other fields, Kaplansky was born in Toronto, Ontario, several years after his parents had emigrated from Poland. In the beginning, his parents thought that he was going to become a concert pianist. By the time he was 5 years old, he was taking piano lessons. That lasted for about 11 years, until he finally realized that he was never going to be a pianist of distinction.
Nonetheless, Kaplansky loved playing the piano, and music has remained one of his hobbies. "I sometimes say that God intended me to be the perfect accompanistthe perfect rehearsal pianist might be a better way of saying it," he says. "I play loud, I play in time, but I don't play very well."
While in high school, Kaplansky started to play in dance bands. During his graduate studies at Harvard, he was a member of a small combo that performed in local night clubs. For a while, he hosted a regular radio program, where he played imitations of popular artists of the day and commented on their music. A little later, when Kaplansky became a math instructor at Harvard, one of his students was Tom Lehrer, later to become famous for his witty ditties about science and math. Lehrer is now at the University of California, Santa Cruz.
In 1945, Kaplansky moved to the University of Chicago, where he remained until he retired in 1984. Subsequently he became MSRI director.
Songs have always interested him, particularly those of the period from 1920 to 1950. These songs tended to have a particular structure: the form AABA, where the A theme is repeated, followed by a contrasting B theme, then a return to the original A theme.
Early on, Kaplansky noticed that certain songs have a more subtle, complex structure. This alternative form can be described as AA'BAA'(B/2)A", where A is a four-bar phrase, A' and A" are variants, and B is a contrasting eight-bar phrase. "I don't think anyone had noticed that before," he says. Kaplansky's discovery is noted in a book about the American musical by Chicago film scholar Gerald Mast.
Kaplansky argues that the second structure is really a superior form for songs. To demonstrate his point, he once used it to turn an unpromising source of thematic materialthe first 14 decimal digits of piinto a passable tune. In essence, each note of the song's chorus corresponds to a particular decimal digit. When Chicago colleague Enid Rieser heard the melody at Kaplansky's debut lecture on the subject in 1971, she was inspired to write lyrics for the chorus.
A SONG ABOUT PI
In all the bygone ages,
The chorus is in the key of C major, and the musical note C corresponds to 1, D to 2, and so on, in the decimal digits of pi (see also Prime Listening, June 20, 1998, and A Passion for Pi, Aug. 2, 1997).
The music and lyrics are unpublished. However, if you ever get a chance to hear a performance by singer-songwriter Lucy Kaplansky (Irving Kaplansky's daughter), you might very well get a rendition of "The Song About Pi" as part of the program. A club headliner, recording artist, and former psychologist, Lucy Kaplansky has her own distinctive style but doesn't mind occasionally showcasing her father's old-fashioned tunemanship.
In 1993, Irving Kaplansky wrote new lyrics for the venerable song "That's Entertainment" to celebrate his enthusiasm for mathematics. He dedicated the verses to Tom Lehrer.
The fun when two parallels meet
With Lagrange everyone of us swears
Comments are welcome. Please send messages to Ivars Peterson at firstname.lastname@example.org.
Ivars Peterson is the mathematics/computer writer and online editor at Science News (http://www.sciencenews.org). He is the author of The Mathematical Tourist, Islands of Truth, Newton's Clock, Fatal Defect, and The Jungles of Randomness. He and his wife, Nancy Henderson, have just completed Math Trek: Adventures in the MathZone, a book for children of middle-school age to be published in the fall by Wiley.
Ivars Peterson is presently serving as journalist in residence at the Mathematical Sciences Research Institute in Berkeley, Calif. (http://www.msri.org/people/members/ivars).
MATHEMUSEMENTS: Look for math-related articles by Ivars Peterson every month in the children's general-interest magazine Muse (http://www.musemag.com) from the publishers of Cricket and Smithsonian magazine.
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