Wednesday, 2 December 2015

Contemplation for Mathematicians

I came across this wonderful passage recently in Jordan Ellenberg's How Not To Be Wrong, a fascinating foray into the world of contemporary mathematics. Not your thing? Try these couple of paragraphs before you make up your mind. He's discussing a mathematical problem known as Buffon's Needle (though you don't need to know the details).
Outsiders sometimes have an impression that mathematics consists of applying more and more powerful tools to dig deeper and deeper into the unknown, like tunnelers blasting through the rock with ever more powerful explosives. And that's one way to do it. But Grothendieck, who remade much of pure mathematics in his own image in the 1960s and '70s, had a different view: "The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration ... the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it ... yet it finally surrounds the resistant substance.
The unknown is a stone in the sea, which obstructs our progress. We can try to pack dynamite in the crevices of rock, detonate it, and repeat until the rock breaks apart, as Buffon did with his complicated computations in calculus. Or you can take a more contemplative approach, allowing your level of understanding gradually and gently to rise, until after a time what appeared as an obstacle is overtopped by the calm water, and is gone.
Mathematics as currently practiced is a delicate interplay between monastic contemplation and blowing stuff up with dynamite.
Replace "Mathematics" in that last line with "Theology and Church governance" and you get a a perceptive summary of contemporary Anglican life ...!

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