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PETER D. LAX, New York US
LINDA and ANDREW PAPANICOLAOU, California US

ABOUT THE HAIKU AND HAIGA

Do mathematics and haiku mix? From the very beginnings of our serious study of haiku, we learn to avoid abstraction, and if you enter "mathematical haiku" into a search engine, for the most part what you will get back is pseudo-haiku. A haijin's response to the above question, therefore, may well be "No!"

Years of living with mathematicians, however, have taught me that it's all in the point of view. For mathematicians, their chosen pursuit is a language that describes the natural world in a way that is precise, economical and aesthetic—somewhat like the aesthetic of haiku, in fact.

The mathematical haiku that I've used in this haigarefers to important work that Peter and one of his students had done to analyze "what happens to solutions of dispersive systems when dispersion tends to zero." The concept is difficult to explain in layman's terms, so for a report to the American Philosophical Society he cast it in haiku form (interview in the NY Times, 29 March 2005). The poem was widely publicized when he won the Abel Prize, and I learned of the poem when my husband gave it to me and said "Peter's written a haiku."

"Lovely, but strictly speaking it's not a haiku," I replied. That quickly, however, as some poems will do, the elegance of its language got into my head. I went back to read it again, and again. Soon the idea took hold of using it in a haiga and I found myself deep (well, deep for a layman) into the subjet of solitary waves. The story of solitons, as they're now called, is an Aha! moment if ever there was one. They were discovered in 1834 by John Scott Russell, a naval engineer who noticed a wave of water roll forward from a barge that had broken its tow rope on a canal near Edinburgh. The bargemen must have seen such phenomena many times, but the scientific study began when Russell jumped on a horse and pursued this wave up the canal until it dispersed. Solitons occur in tsunamis, tidal bores and cloud formations and the theory of them lies at the heart of pure and applied mathematics with applications in quantum field theory, solid state physics, biological systems and telecommunications (Helge Holden, Peter D. Lax: Elements from his Contributions to Mathematics, Trondheim 2005; online at www.abelprisen.no).

I had begun with the notion of finding a graph relaltive to Peter's work for the haiga, but as I read about solitary waves I became drawn more to their natural occurrences. The photograph I finally chose was taken by my son Andrew (who, appropriately enough, is a surfer whenever he is not studying math in graduate school). The wave in the haiga is not really a soliton, but by now I was back to where I had begun, working in personal response to Peter's poem rather than simply illustrating it. For me, the language of line 3 is about where ideas come from, how you may be walking on the beach and one will swell up and tug at you until it achieves realization.

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