Are there fractal structures in language? Units of measurement and dimensions in linguistics*

Abstract

There is an increasing interest in questions of determining units in linguistics and musicology which can be used for measuring quantitative properties such as length, frequency, and complexity. Up to now, however, their discussion has been restricted to problems of the definition of basic elements in the particular field of research, of their features, of methods for their identification and segmentation in texts, etc. The present contribution considers the question of linguistic units of measurement. Is the kind of formula as used in quantitative linguistics incomplete and incorrect just as a large part of the equations in physics would be if the units (e.g., meter, kilogram, hour, newton, or farad) were omitted? If not, all linguistic quantities introduced so far would be dimensionless, and hence every dependence investigated and every law would be. We will show that this is the case and consider the consequences of this result for relations between elements on different levels of linguistic analysis (such as the Menzerath‐Altmann law). In particular, Hfebi'cek's hypothesis on “the fractal nature of language”; is affected.