Unzipping Zipf’s law

Abstract

In spite of decades of theorizing, the origins of Zipf’s law remain elusive. I propose that a Zipfian distribution straightforwardly follows from the interaction of syntax (word classes differing in class size) and semantics (words having to be sufficiently specific to be distinctive and sufficiently general to be reusable). These factors are independently motivated and well-established ingredients of a natural-language system. Using a computational model, it is shown that neither of these ingredients suffices to produce a Zipfian distribution on its own and that the results deviate from the Zipfian ideal only in the same way as natural language itself does.

Dynamical analogues of rank distributions

“…Fig 1 exemplifies four such types of distributions. Over the years, [1–7] interest has been mostly placed on ranked data that exhibits power-law behavior even if this is not observed over the entire collection of records since this suggests a possible relationship with the famous empirical Zipf’s law [8, 9]. Less attention has been placed to the comprehensive study of a wider range of types of rank distributions with the purpose of uncovering the broad-spectrum physics, if there is one, behind rank distributions.…”

“…Originally [9], Zipf law referred to the number of occurrences of words in texts and since then it has been assigned also to the number of occurrences of other items and more freely to magnitudes or sizes of other entities. A large number of studies on the subject have been developed since and general considerations made, a taster is given in Refs [1–7]. Here we refer only to ranked magnitude or size data.…”

Advancing rational analysis to the algorithmic level

“…The target article sketches the promise of combining rational principles and cognitive constraints to understand human cognition, and singles out linguistics as one domain for work along those lines. While it touches on aspects of language rooted in individual cognition like the principle of least effort (Lestrade 2017;Zipf 1949), I want to probe the limits of the resource-rational framework by looking beyond individual minds to interactive language use, the primary ecology of human cognition (Böckler et al 2010;Waldron & Cegala 1992). Here, under the relentless pressures of rapid-fire turn-taking (Levinson 2016) and always-on inferential processes (Enfield 2013;Goffman 1967), language provides a window onto how social rational agents deal with resource limitations in a noisy and uncertain environment.…”

Scaling Laws for Phonotactic Complexity in Spoken English Language Data

“…Third, it was argued that Zipf's law may be a consequence of multiple underlying and interacting processes, which in isolation would not necessarily give rise to power-law distributions (Aitchison et al, 2016). On the lexical level, it was argued by Lestrade (2017) on computational grounds that an interaction of syntactic and semantic factors provides a better explanation of Zipf's law in the lexicon than each of these two domains in isolation. Clearly, phonotactics is influenced by various linguistic domains as well: sound sequences are brought about through concatenating phonemes within morphemes (i.e., lexical phonotactics in the narrow sense), through morphology (e.g., affixation, ablaut), or through syntax (across word boundaries).…”