The origins of Zipf's meaning‐frequency law

Abstract

In his pioneering research, G.K. Zipf observed that more frequent words tend to have more meanings, and showed that the number of meanings of a word grows as the square root of its frequency. He derived this relationship from two assumptions: that words follow Zipf's law for word frequencies (a power law dependency between frequency and rank) and Zipf's law of meaning distribution (a power law dependency between number of meanings and rank). Here we show that a single assumption on the joint probability of a word and a meaning suffices to infer Zipf's meaning‐frequency law or relaxed versions. Interestingly, this assumption can be justified as the outcome of a biased random walk in the process of mental exploration.

Polysemy and brevity versus frequency in language

“…Our analyses have shown the robustness of these Zipfian patterns from the standpoint of a correlation analysis. Such robustness provides support to Zipf's hypothesis that these laws originate from abstract principles, e.g., functional pressures (least effort as he would put it), that are consistent with modern formalizations as a compression principle for the law of abbreviation [12,40] or a biased random walk over the mapping words into meanings for the origins of Zipf's meaning frequency law [13]. This theoretical approaches strongly suggest that it might be possible to provide a coherent and parsimonious explanation for the laws we have examined in this article and other laws such as Zipf's law for word frequencies [44] or Menzerath's law [45].…”

“…The analysis of the two measures of frequency versus the three measures of length are in Tables C. 13 and C.14 in English, Tables C. 15 and C.16 in Dutch, and Tables C. 17 and C.18 in Spanish in the Appendix C. In this case, the results show a more compact behavior, since all correlations are significant and negative both for children and for adults.…”

“…These laws are regarded as universal although the only evidence of their universality is that they hold in every language where they have been tested so far [11]. Because of their generality, these laws have triggered modeling efforts that attempt to explain their origin and support their presumable universality with the help of abstract mechanisms or communication principles [12,13], or exploring directly from voice those statistical patterns in levels under the phoneme scale [14]. Therefore, investigating the experimental conditions under which these laws surface is crucial.…”

Optimization Models of Natural Communication

“…Recent research has shown that models of that family are able to shed light on at least four apparently universal tendencies in world languages (Ferrer-i-Cancho, 2017;Ferrer-i-Cancho & Vitevitch, 2017;Ferrer-i-Cancho, 2016a). First, the principle of contrast, namely that "every two forms contrast in meaning" (Clark, 1987).…”

“…In this article, a family of models (Ferrer-i-Cancho & Solé, 2003;Ferrer-i-Cancho, 2005a;Ferreri-Cancho, 2014;Ferrer-i-Cancho, 2017;Ferrer-i-Cancho & Vitevitch, 2017) that is able to shed light on these four patterns of language will be reviewed. It is worth mentioning that bidirectional optimality theory provides complementary accounts of diachronically stable and cognitively optimal form-meaning pairs that goes beyond the scope of the present article (Benz & Mattausch, 2011).…”