A bizarre set of of 8-dimensional numbers could explain how to handle string-theory's extra dimensions, why elementary particles come in families of three... and maybe even how spacetime emerges in four dimensions.

Mathematician and physicist John Baez declares himself fascinated by exceptions in mathematics. This interest has led him to study the octonions, and, through them, to find out more about the origins of complex numbers and quaternions. In the second of two articles, he talks about the characters of the different dimensions, beauty and utility in mathematics, and just why he likes dimension 8 so much.