The degree of union resulting from reaction points expressed in a diatopic table. An application to a Catalan verb morphology database

Abstract For describing a particular area from a geolinguistic perspective, the basic procedure is to create a two-dimensional table with an axis showing forms or phenomena and another axis showing localities. In this table, observing the specific reaction in every cell will allow us to develop both co-occurrence and coefficient matrixes, as well as clustering and multivariate interpretation graphs. In this table, which is the starting point for multivariate analyses of geolinguistic data, certain convergences and divergences of the reaction points are revealed. Our interest is in a quantitative evaluation of the degree of convergence and divergence that takes the form of a rectangular linkage of the reacted points; that is to say, an analysis of the state of their continuity set out in rectangular plots. In order to evaluate properly the absolute values in numbers of unions (U) it is necessary to develop a mathematical function that will return the maximum number of unions (Umax) in a parameter with the number of reactions (n): Umax (n). Once the Umax function has been established, the desirable “Degree of Binding” will be formulated through the division of U by Umax(n). The aim of this paper is to put into practice this method with the data from La flexió verbal en els dialectes catalans (‘Verbal Flexion’) (1929-1932), by Antoni M. Alcover, previously analysed in Perea & Ueda (2010). The calculation of the Degree of Binding is applied to the data in both its forms: the original data and the patternized distribution of data (see Perea & Ueda 2010: 103-111). The result of our calculations gives rise to a new multivariate perspective of “isoglosses” for overcoming the problems of mismatched lines on the linguistic maps.