Day-to-day judgments in soil systematics that are usually made intuitively can now be made automatically and consistently using numerical methods. Nevertheless, intuition is still required to choose suitable methods. This paper recommends those that can be represented geometrically, and describes them as means of examining a character space in which each soil specimen, profile, or site is represented by a point. The estimation of likeness, classification, ordination, allocation, and the optimisation of classifications are discussed in turn.