What are numbers? Are some numbers more real than others? More rational? Just … better? No, of course not! You reply. It is absurd to make a moral or quasi-moral judgment about or classification of numbers. Numbers are just … numbers. Numbers are simply sums or aggregates. Each is a very short way of saying something about a collection of things, events, or people, as in the perfectly comprehensible sentence, "a number of people were hurt in the accident." There is no need to make heavy water out of this. But then, why do categories of numbers have the strange and sometimes stigmatizing names they do? Some numbers are called “irrational,” in contrast to the “rational.” Others are called “imaginary,” in contrast to the “real.” What is irrational about the former or unreal about the latter? It is a tricky question. But it is worth unravelling this knot. It is worth so even if you took no pleasure in mathematics at school, or since, and even if you are co...