Monday 26 November 2007

as long as a piece of string

Looking ahead to Advent, which I’m going through this year with Maggi Dawn’s reflections Beginnings and Endings, the cover and blurb drew me into thinking about time; time (chronos — how long), and time (kairos — opportunity). And what about the context of both: beyond time what? — eternity? Infinity? world without end?

We can use a bit of Maths here. How long is the coastline of Britain? There’s an AA Road Atlas answer, which is good enough for most purposes, but there’s also a completely different Mathematical answer, which you could express by breaking down every line and mapping it as a set of points in a complex plane to form a fractal. Here’s a Mandelbrot set (not the coast of Britain). If the final frame were the width of your screen, the whole fractal would be larger than the known universe — it’s an interesting image to pray with... world without end?


BanjoVicar said...

Fractals are amazing. Do you know about the Peano Snowflake - a simple shape that one can readily prove has a finite area but an infinite perimeter? Like the coastline of Britain, I suppose.

Bishop Alan Wilson said...

Many thanks, Steve. I've never quite understood how the classic snowflake shape works. I'm interested by the finite/infinite implications of the deal you mention — intinite perimeter, finite area. When I'd overcome the temptation to pronounce Peano like Beano (something else) I found a website which unpacked it a bit.

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