I can easily draw the diagonal of a square, but I cannot express its length in numbers – I cannot count the number of dots it contains. The point-to-point correspondence between arithmetic and geometry has broken down – and with it the universe of number-shapes. It is said that the Pythagoreans kept the discovery of irrational numbers – they called them arrhe¯tos, unspeakable – a secret, and that Hippasos, the disciple who let the scandal leak out, was put to death.
