We put forward two mathematical tools, called the rank distance and the bubble distance, to compare the ordinal structure of natural languages. Traditionally, ordinal structures have only been studied in a very basic and “abstract” context, as for example, the six idealised arrangements for the subject-verb-object sequence. Our tools allow one to get an overall picture of the ordinal distance between a text and its translation. Thinking of future work, availability of web resources will make it possible to conduct large-scale experiments, which will account for the difficulties experienced by simultaneous interpreters, say between Italian and German, or even more so between Italian and Turkish. However, if one wants to get a realistic picture of these differences, one has to abandon the traditional approach to mathematics, based on binary logics (true vs. false, black vs. white), and introduce the grey nuances made available by soft logic; in other words one has to relinquish the esprit de géometrie and adopt the esprit de finesse which is typical of soft computing. It is no coincidence that soft logic has been largely inspired by the flexible logical structures which are possessed by natural languages, rather than those of “hard” mathematics. A crisp mathematical approach will do for simple and abstract structures such as subject-verb-object, but it is wholly insufficient if one moves to the overall word order in actual texts.
