Even if surprising for many mathematicians, quite a large number of the distances described in the Encyclopedia of distances, are not metric distances, i.e., they do not comply with some or other of the metric axioms which appear to be so natural or even unexpendable to those who tackle this multifaceted geometric and topological notion. Using examples taken from linguistics and word strings, we argue that the notion of distance is so rich and fruitful that the metric axioms in some cases risk to be an unreasonably narrow cage.
