Saturday, August 28, 2010

Set Theory in Pembrokeshire

Red wine was coursing round my system. My nerves felt like they were on fire and yet were somehow slowly dropping off to sleep. The mathematics continued:

(x)(y)(yx)

"So this states (it's an axiom really) that there exists a set x for all y, such that y is not a member of x. It vacuously proves the existence of the empty set..."

Now then. I'm on holiday. The sun had already dipped into a golden sky over the sparkling sea, and the whitest of moons had joined Venus in the fading sky. What on Earth was I doing then, learning the basic principles of Set Theory? This, I reasoned, is what happens when you go on holiday and stay with a brilliant mathematician who is also an atheist.

I was wondering, quite nervously, whether he was beguiling me like an ingenious barrister. There is an empty set... There can't logically be a set that contains every other set... Therefore... a universal, omniscient deity can't logically exist... what do you think about that, Slighty-Tipsy-God-boy?

Thankfully, there was no such cliff-edge in the conversation, and no sheer drop into the chasm of metaphysics or theology. Clive simply cycled through his new tee-shirt designs, explaining as he went. His favourite proofs seem to describe ways of determining the mathematical constant pi (π)... which appears in sums and integrals and other complicated looking formulae, inscribed on mugs, bathroom tiles, the front door, and yes, several dozen custom-made tee-shirts. In case you're interested, if you square π and divide it by 6, you get the same number as you would by adding together the reciprocals of all the squares of all the real positive numbers. And if you're not, well - I doubt you're alone.

I love mathematicians. In essence they're like mountain-bikers. They get excited by thrills that most of us would find terrifying. They love talking about the tools they use, the problems they had to solve and the awesomeness of finding yourself exactly where you wanted to be; still alive, if a little-shaken up by what you've been through, and desperate to tell anyone who will listen. Exhilaration comes in strange forms for the math-boffins. They relive their calculations through the Nth dimension, the scree-laden slope of a discontinuous function, and the possibilities and probabilities that perhaps no-one else thinks about. They ride rough-shod over primes, googolplexes, equations and singularities, gripping the handlebars given them by Euler and Euclid and Gauss, like there's no 'TODAY+1'. This morning, for example, I was more than a little astonished to discover that there are different orders of infinity. In other words, some infinities are bigger than others. I jest not. But who knew?

-

I'm reluctant to let you into a secret. Here it is though: Wales is beautiful. I guess, my reluctancy stems from the fact that this part of the country is often completely ignored - and this enhances its lonely desperate beauty. Today, I stood completely alone on the top of a grassy mountain in the Preseli hills. The wind was rushing through my hair, warm and salty as it blew in from the Atlantic. In the distance, the ocean stretched away, cool and blue, deep and mysterious. Great and ancient hills rose up around me, bathed in the rolling, changing shadows cast by low clouds and cheery sunlight. It was breathtakingly peaceful. And with no phone, no facebook, no email, nothing to connect me to the other world, I felt completely free and alone with God.


The God who thought up π and made it the exact ratio of a circle's circumference and diameter. The God who invented gravity and chuckled when Isaac Newton cottoned-on to the way it works. The God who positioned Venus exactly where it is, so that one-day, in a little village in Pembrokeshire, a confused former physics graduate could spot it sparkling next to the moon and smile while the sun dipped majestically below the horizon.


I love that God; even when I'm slightly inebriated and confused by Set Theory.

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