# P-values, Faustus, and making something out of nothing

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*.