Safety in Numbers

An extract from Euclid's Elements

I'm reading "Pythagorean Murders" by Tefkros Michailidis at the moment. It is set in the 1920s, where a mathematician is trying to find out who murdered his friend (a maths teacher). As his friend didn't get out much, this is a bit of a mystery, but it may be that the novel's interludes, which talk about the Pythagoreans thousands of years ago keeping quiet about a terrible secret, have something to do with it.

The Pythagoreans were a little bit odd. They believed in reincarnation, and so did not eat meat, since it was possible that the animal would turn out to be one of their long deceased relatives. They also did not eat beans. I read somewhere years ago that this was because it was also possible that you were reincarnated as a bean.

Pythagoras (top left) with some of his followers.

So far in the book, one of these ancient Greeks has discovered something awful. They don't have enough numbers. They've got numbers like 1,2,3,4, and so on. They also have numbers like 1/2, 78/96, and so on. There are infinitely many of these, so what's the problem?

The problem is that a new recruit to the sect has realised that if he draws a square, say, 1 metre by 1 metre, he can't work out the length of the diagonal. It's none of the numbers I've mentioned. In fact, it's irrational.

This can't be the reason that our guy gets bumped off in the 20s, because even Plato knew about irrational numbers. These aren't numbers that need to see a shrink, or female numbers, or numbers which are odder than odd numbers. They are numbers which can't be written as fractions.

Some of these irrational numbers are transcendental (don't ask). These have nothing to do with Doctor Who, or Oriental Meditation. If I draw a circle, say, 1 metre in diameter, then the circumference will be a transcendental number of metres long.

We also have complex numbers, each of which is part real, and part imaginary. Funnily enough, these are used by engineers, who you'd have thought wouldn't have much imagination. Some groups of numbers are friendly, others amicable or sociable, and a special few are perfect.

I still can't think (imagine?) why someone killed the novel's victim. Maybe it was an irate neighbour, complaining about the smell. He probably ate too many beans and stank out his block of flats. Come to think of it, the Pythagoreans may not have been completely crazy...