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Universal and Particular

Poet Yves Bonnefoy (b 1923) is one of France's greatest living poets. And Bonnefoy's university studies included mathematics. I read recently of Bonnefoy in the *Wall Street Journal Bookshelf* posting for 11 February 2012 by Micah Mattix entitled "The Pursuit of Presence." This reminder sent me to my bookshelf to review the poet's work with mathematics in mind. I found a bit of *attitude* toward the subject in a prose poem entitled "Devotion" when he used the phrase "stern mathematics." And Section 1 of "Trial by Ordeal" (offered below) ends with the word "proof."
Mattix opened his Bonnefoy article with a quote: *If I had to sum up in a sentence the impression Shakespeare makes upon me," the poet Yves Bonnefoy wrote in an early essay, "I should say that, in his work, I see no opposition between the universal and the particular."* This universal-particular pairing (evident in Bonnefoy, as in Shakespeare) led my thoughts to the mathematical pairing, *global-local*, which I explore briefly following Bonnefoy's poem.*
** Trial By Ordeal** by Yves Bonnefoy
** I )**
I was the one who walks out of care
For a final troubled water. The day
Was beautiful, brightest summer. It was night
Always, without end, and forever.
In the clay of the seas
The foam's chrysanthemum, and there was always
The same stale earthy smell of November
When I trod the black garden of the dead.
There was
A voice that called for belief, and always
Turned against itself and always
Made of its own fading its grandeur, its proof.
"Devotion and "Trial by Ordeal" are found in the bilingual collection *Yves Bonnefoy Early Poems 1947-1957*, translated from the French by Galway Kinnell and Richard Pevear (Ohio University Press, 1991).
*As in Shakespeare, the universal and the particular are intimately paired in mathematics; one such pairing occurs in considertion of "global" and "local" properties. For example, the hyperbola given by the equation *y = 1/x* is **locally** continuous (near each point on the graph, there are no breaks in the curve) but *not ***globally** continuous (the graph-as-a-whole is in two disconnected sections since *y = 1/x* has no computable value when *x = 0*).
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