Kustaanheimo’s proposal—I reproduce here in rough outline the excellent presentation of his proposal in Welti (1987: 487–521), which is far more accessible than the original work—is based on the following line of reasoning. A standard model for the classical axiomatic theory of Euclidean geometry consists of the cartesian product of the real numbers with itself. Or, as it is usually formulated, a point in the plane is mapped onto a couple of real numbers, its coordinates. The real numbers have the mathematical structure of an infinite field. But finite fields exist as well. So why not replace the infinite real number field with a finite field, a so-called Galois field?