You don’t have to be playing a Sembl or Hipbone game to make a great Sembl move — you just have to see a rich semblance between two concepts in (previously) widely separated fields of thought. Thus Pierre Deligne of Princeton’s Institute for Advanced Study, who won the Abel Prize in mathematics this year, did so by working on a rich Sembl-style insight from André Weil. As Scientific American reports today:
Deligne’s most spectacular results are on the interface of two areas of mathematics: number theory and geometry. At first glance, the two subjects appear to be light-years apart. As the name suggests, number theory is the study of numbers, such as the familiar natural numbers (1, 2, 3, and so on) and fractions, or more exotic ones, such as the square root of two. Geometry, on the other hand, studies shapes, such as the sphere or the surface of a donut. But French mathematician André Weil had a penetrating insight that the two subjects are in fact closely related. In 1940, while Weil was imprisoned for refusing to serve in the army during World War II, he sent a letter to his sister Simone Weil, a noted philosopher, in which he articulated his vision of a mathematical Rosetta stone. Weil suggested that sentences written in the language of number theory could be translated into the language of geometry, and vice versa. “Nothing is more fertile than these illicit liaisons,” he wrote to his sister about the unexpected links he uncovered between the two subjects; “nothing gives more pleasure to the connoisseur.”
While I was still a schoolboy, my favorite place to visit on vacation was the great Abbaye St. Pierre de Solesmes, celebrated for its central part in the renewal of Catholic liturgy and of the Gregorian Chant in particular. Two of my fondest memories are of the terrific bowls of coffee served in the monastic refectory at breakfast, and of my opportunity to take a class in chant under the chironomic hand of Dom Joseph Gajard, then Choirmaster at Solesmes. The liturgy and the chant were sublime.
I was an Anglican (“Episcopalian”) at the time, and just a wee bit concerned that the monks might want to convert me to the One Holy [Roman] Catholic and Apostolic version of the faith — but when I expressed my concern to one of the monks, I was reassured: they had had an earlier guest at the abbey, one Simone Weil, and she too had been unready to convert, though deeply moved by the liturgy…
When I read the catechism of the Council of Trent, it seems as though I had nothing in common with the religion there set forth. When I read the New Testament, the mystics, the liturgy, when I watch the celebration of the mass, I feel with a sort of conviction that this faith is mine or, to be more precise, would be mine without the distance placed between it and me by my imperfection.
I love her for that — and I love, too, that her brother should make such a splendid Sembl move.
I suppose I’d better post my reading of Wiles’ Proof of Fermat’s Last Theorem viewed as a Glass Bead Game as a follow up.