A few years ago, I read Simon Singh’s wonderful book Fermat’s Enigma. I was an undergraduate at the time, and had recently written a paper about Doctor Faustus. “Lines, circles, letters, characters” – Faustus’s desire of these made me think not just of his necromantic ambitions, but of a sense of a power in geometrical metaphors to define oneself up to an invented boundary, and then to redefine oneself not as what is contained within, but as the infinite without.
Singh’s book introduced me to Euclid’s proof of the irrationality of the square root of two. It may seem a small thing to those who understand mathematics better than I do, but I found it dazzling for two main reasons. The first was that I’d never heard of a proof by contradiction before: the idea that you could prove something by considering the consequences of it not being true was a profound revelation. The second was the idea of irrationality itself. The proof by infinite descent seemed to suggest a curious notion of numbers tumbling into an indefinable and infinite void, always falling, never settling on perfect definition. To me it was poignant – tragic in being unimaginable, receding endlessly from view.
I first learned statistics during my maths A Level, though I didn’t learn it well. I didn’t take any time to build up an intuitive foundation, and the result was that I manipulated numbers with no understanding of why, and therefore no ability to do it well. I’m rectifying this as I develop the skills I’ll need for data analysis in my MSc dissertation, and something interesting is happening as a result.
I always viewed statistics as one of those branches of mathematics that holds no philosophical interest, but learning about p-values proved me wrong. Here, again, was the excitement of considering the consequences of something not being true. I felt a sense that the vast and unknowable world of chance and uncertainty could be known better – the bounded sample seemed to turn itself around and contain – like Faustus – the infinite without.