The Brevity Law as a Scaling Law, and a Possible Origin of Zipf's Law for Word Frequencies

Low Literacy Levels Among U.S. Adults and Difficult Ballot Propositions

High-level literacy skills are required for full participation in the democratic process through voting. Consequently, adults with low-level literacy skills are at a disadvantage. This work investigated the disparity between the readability of U.S. ballot propositions for year 2022 state elections and grade level reading estimates (≤eighth grade) for adults. Educational attainment was also examined. Propositions (n = 140) from 38 states were included. Mean readability was 18 (range 7.0-64.0). Only four measures (3%) fell within range of national estimates for adult reading ability. Thirty-nine percent of adults completed high school or less, yet 74% of ballots were written well above a high school reading level. There is a discrepancy between the literacy skills of the average voter and the readability of most propositions. The findings of this study have important implications for individuals with learning disabilities. Policy changes and educational support efforts should be initiated.

Background check: cross-cultural differences in the spatial context of comic scenes

Cognitive research points towards cultural differences in the way people perceive and express scenes. Whereas people from Western cultures focus more on focal objects, those from East Asia have been shown to focus on the surrounding context. This paper examines whether these cultural differences are expressed in complex multimodal media such as comics. We compared annotated panels across comics from six countries to examine how backgrounds convey contextual information of scenes in explicit or implicit ways. Compared to Western comics from the United States and Spain, East Asian comics from Japan and China expressed the context of scenes more implicitly. In addition, Nigerian comics moderately emulated American comics in background use, while Russian comics emulated Japanese manga, consistent with their visual styles. The six countries grouped together based on whether they employed more explicit strategies such as detailed, depicted backgrounds, or implicit strategies such as leaving the background empty. These cultural differences in background use can be attributed to both cognitive patterns of attention and comics' graphic styles. Altogether, this study provides support for cultural differences in attention manifesting in visual narratives, and elucidates how spatial relationships are depicted in visual narratives across cultures.

Compression principle and Zipf's Law of brevity in infochemical communication

Compression has been presented as a general principle of animal communication. Zipf's Law of brevity is a manifestation of this postulate and can be generalized as the tendency of more frequent communicative elements to be shorter. Previous works supported this claim, showing evidence of Zipf's Law of brevity in animal acoustical communication and human language. However, a significant part of the communicative effort in biological systems is carried out in other transmission channels, such as those based on infochemicals. To fill this gap, we seek, for the first time, evidence of this principle in infochemical communication by analysing the statistical tendency of more frequent infochemicals to be chemically shorter and lighter. We analyse data from the largest and most comprehensive open-access infochemical database known as Pherobase, recovering Zipf's Law of brevity in interspecific communication (allelochemicals) but not in intraspecific communication (pheromones). Moreover, these results are robust even when addressing different magnitudes of study or mathematical approaches. Therefore, different dynamics from the compression principle would dominate intraspecific chemical communication, defying the universality of Zipf's Law of brevity. To conclude, we discuss the exception found for pheromones in the light of other potential communicative paradigms such as pressures on successful communication or the Handicap principle.

Popularity of Video Games and Collective Memory

Describing the permanence of cultural objects is an important step in understanding societal trends. A relatively novel cultural object is the video game, which is an interactive media, that is, the player is an active contributor to the overall experience. This article aims to investigate video game permanence in collective memory using their popularity as a proxy, employing data based on the Steam platform from July 2012 to December 2020. The objectives include characterizing the database; studying the growth of players, games, and game categories; providing a model for the relative popularity distribution; and applying this model in three strata, global, major categories, and among categories. We detected linear growth trends in the number of players and the number of categories, and an exponential trend in the number of games released. Furthermore, we verified that lognormal distributions, emerging from multiplicative processes, provide a first approximation for the popularity in all strata. In addition, we proposed an improvement via Box–Cox transformations with similar parameters (from −0.12 (95% CI: −0.18, −0.07) to −0.04 (95% CI: −0.08, 0)). We were able to justify this improved model by interpreting the magnitude of each Box–Cox parameter as a measure of memory effects.

Lognormals, power laws and double power laws in the distribution of frequencies of harmonic codewords from classical music

Zipf's law is a paradigm describing the importance of different elements in communication systems, especially in linguistics. Despite the complexity of the hierarchical structure of language, music has in some sense an even more complex structure, due to its multidimensional character (melody, harmony, rhythm, timbre, etc.). Thus, the relevance of Zipf's law in music is still an open question. Using discrete codewords representing harmonic content obtained from a large-scale analysis of classical composers, we show that a nearly universal Zipf-like law holds at a qualitative level. However, in an in-depth quantitative analysis, where we introduce the double power-law distribution as a new player in the classical debate between the superiority of Zipf's (power) law and that of the lognormal distribution, we conclude not only that universality does not hold, but also that there is not a unique probability distribution that best describes the usage of the different codewords by each composer.

Linguistic laws in biology

Linguistic laws, the common statistical patterns of human language, have been investigated by quantitative linguists for nearly a century. Recently, biologists from a range of disciplines have started to explore the prevalence of these laws beyond language, finding patterns consistent with linguistic laws across multiple levels of biological organisation, from molecular (genomes, genes, and proteins) to organismal (animal behaviour) to ecological (populations and ecosystems). We propose a new conceptual framework for the study of linguistic laws in biology, comprising and integrating distinct levels of analysis, from description to prediction to theory building. Adopting this framework will provide critical new insights into the fundamental rules of organisation underpinning natural systems, unifying linguistic laws and core theory in biology.

Zipf's laws of meaning in Catalan

In his pioneering research, G. K. Zipf formulated a couple of statistical laws on the relationship between the frequency of a word with its number of meanings: the law of meaning distribution, relating the frequency of a word and its frequency rank, and the meaning-frequency law, relating the frequency of a word with its number of meanings. Although these laws were formulated more than half a century ago, they have been only investigated in a few languages. Here we present the first study of these laws in Catalan. We verify these laws in Catalan via the relationship among their exponents and that of the rank-frequency law. We present a new protocol for the analysis of these Zipfian laws that can be extended to other languages. We report the first evidence of two marked regimes for these laws in written language and speech, paralleling the two regimes in Zipf's rank-frequency law in large multi-author corpora discovered in early 2000s. Finally, the implications of these two regimes will be discussed.

Entropy Estimation Using a Linguistic Zipf-Mandelbrot-Li Model for Natural Sequences

Entropy estimation faces numerous challenges when applied to various real-world problems. Our interest is in divergence and entropy estimation algorithms which are capable of rapid estimation for natural sequence data such as human and synthetic languages. This typically requires a large amount of data; however, we propose a new approach which is based on a new rank-based analytic Zipf–Mandelbrot–Li probabilistic model. Unlike previous approaches, which do not consider the nature of the probability distribution in relation to language; here, we introduce a novel analytic Zipfian model which includes linguistic constraints. This provides more accurate distributions for natural sequences such as natural or synthetic emergent languages. Results are given which indicates the performance of the proposed ZML model. We derive an entropy estimation method which incorporates the linguistic constraint-based Zipf–Mandelbrot–Li into a new non-equiprobable coincidence counting algorithm which is shown to be effective for tasks such as entropy rate estimation with limited data.

Principle of Least Effort and Sentence Length in Public Speaking

The analysis of sentence lengths in the inaugural speeches of US presidents and the annual speeches of UK party leaders is carried out. Transcripts of the speeches are used, rather than the oral production. It is discovered that the average sentence length in these speeches decreases linearly with time, with the slope of 0.13 ± 0.03 words/year. It is shown that among the analyzed distributions (log-normal, folded and half normal, Weibull, generalized Pareto, Rayleigh) the Weibull is the best distribution for describing sentence length. These two results can be considered a consequence of the principle of least effort. The connection of this principle with the well-known principles of maximum and minimum entropy production is discussed.

Distinct flavors of Zipf's law and its maximum likelihood fitting: Rank-size and size-distribution representations

In recent years, researchers have realized the difficulties of fitting power-law distributions properly. These difficulties are higher in Zipfian systems, due to the discreteness of the variables and to the existence of two representations for these systems, i.e., two versions depending on the random variable to fit: rank or size. The discreteness implies that a power law in one of the representations is not a power law in the other, and vice versa. We generate synthetic power laws in both representations and apply a state-of-the-art fitting method to each of the two random variables. The method (based on maximum likelihood plus a goodness-of-fit test) does not fit the whole distribution but the tail, understood as the part of a distribution above a cutoff that separates non-power-law behavior from power-law behavior. We find that, no matter which random variable is power-law distributed, using the rank as the random variable is problematic for fitting, in general (although it may work in some limit cases). One of the difficulties comes from recovering the "hidden" true ranks from the empirical ranks. On the contrary, the representation in terms of the distribution of sizes allows one to recover the true exponent (with some small bias when the underlying size distribution is a power law only asymptotically).