Menzerath's Law Research Articles

Scale in Language.

A central concern of the cognitive science of language since its origins has been the concept of the linguistic system. Recent approaches to the system concept in language point to the exceedingly complex relations that hold between many kinds of interdependent systems, but it can be difficult to know how to proceed when "everything is connected." This paper offers a framework for tackling that challenge by identifying *scale* as a conceptual mooring for the interdisciplinary study of language systems. The paper begins by defining the scale concept-simply, the possibility for a measure to be larger or smaller in different instances of a system, such as a phonemic inventory, a word's frequency value in a corpus, or a speaker population. We review sites of scale difference in and across linguistic subsystems, drawing on findings from linguistic typology, grammatical description, morphosyntactic theory, psycholinguistics, computational corpus work, and social network demography. We consider possible explanations for scaling differences and constraints in language. We then turn to the question of *dependencies between* sites of scale difference in language, reviewing four sample domains of scale dependency: in phonological systems, across levels of grammatical structure (Menzerath's Law), in corpora (Zipf's Law and related issues), and in speaker population size. Finally, we consider the implications of the review, including the utility of a scale framework for generating new questions and inspiring methodological innovations and interdisciplinary collaborations in cognitive-scientific research on language.

Variable expression of linguistic laws in ape gesture: a case study from chimpanzee sexual solicitation.

Two language laws have been identified as consistent patterns shaping animal behaviour, both acting on the organizational level of communicative systems. Zipf's law of brevity describes a negative relationship between behavioural length and frequency. Menzerath's law defines a negative correlation between the number of behaviours in a sequence and average length of the behaviour composing it. Both laws have been linked with the information-theoretic principle of compression, which tends to minimize code length. We investigated their presence in a case study of male chimpanzee sexual solicitation gesture. We failed to find evidence supporting Zipf's law of brevity, but solicitation gestures followed Menzerath's law: longer sequences had shorter average gesture duration. Our results extend previous findings suggesting gesturing may be limited by individual energetic constraints. However, such patterns may only emerge in sufficiently large datasets. Chimpanzee gestural repertoires do not appear to manifest a consistent principle of compression previously described in many other close-range systems of communication. Importantly, the same signallers and signals were previously shown to adhere to these laws in subsets of the repertoire when used in play; highlighting that, in addition to selection on the signal repertoire, ape gestural expression appears shaped by factors in the immediate socio-ecological context.

Can Menzerath's law be a criterion of complexity in communication?

Menzerath's law is a quantitative linguistic law which states that, on average, the longer is a linguistic construct, the shorter are its constituents. In contrast, Menzerath-Altmann's law (MAL) is a precise mathematical power-law-exponential formula which expresses the expected length of the linguistic construct conditioned on the number of its constituents. In this paper, we investigate the anatomy of MAL for constructs being word tokens and constituents being syllables, measuring its length in graphemes. First, we derive the exact form of MAL for texts generated by the memoryless source with three emitted symbols, which can be interpreted as a monkey typing model or a null model. We show that this null model complies with Menzerath's law, revealing that Menzerath's law itself can hardly be a criterion of complexity in communication. This observation does not apply to the more precise Menzerath-Altmann's law, which predicts an inverted regime for sufficiently range constructs, i.e., the longer is a word, the longer are its syllables. To support this claim, we analyze MAL on data from 21 languages, consisting of texts from the Standardized Project Gutenberg. We show the presence of the inverted regime, not exhibited by the null model, and we demonstrate robustness of our results. We also report the complicated distribution of syllable sizes with respect to their position in the word, which might be related with the emerging MAL. Altogether, our results indicate that Menzerath's law-in terms of correlations-is a spurious observation, while complex patterns and efficiency dynamics should be rather attributed to specific forms of Menzerath-Altmann's law.

Menzerath’s Law in the Syntax of Languages Compared with Random Sentences

The Menzerath law is considered to show an aspect of the complexity underlying natural language. This law suggests that, for a linguistic unit, the size (y) of a linguistic construct decreases as the number (x) of constructs in the unit increases. This article investigates this property syntactically, with x as the number of constituents modifying the main predicate of a sentence and y as the size of those constituents in terms of the number of words. Following previous articles that demonstrated that the Menzerath property held for dependency corpora, such as in Czech and Ukrainian, this article first examines how well the property applies across languages by using the entire Universal Dependency dataset ver. 2.3, including 76 languages over 129 corpora and the Penn Treebank (PTB). The results show that the law holds reasonably well for . Then, for comparison, the property is investigated with syntactically randomized sentences generated from the PTB. These results show that the property is almost reproducible even from simple random data. Further analysis of the property highlights more detailed characteristics of natural language.

Phylogeny and mechanisms of shared hierarchical patterns in birdsong

Organizational patterns can be shared across biological systems, and revealing the factors shaping common patterns can provide insight into fundamental biological mechanisms. The behavioral pattern that elements with more constituents tend to consist of shorter constituents (Menzerath's law [ML]) was described first in speech and language (e.g., words with more syllables consist of shorter syllables) and subsequently in music and animal communication. Menzerath's law is hypothesized to reflect efficiency in information transfer, but biases and constraints in motor production can also lead to this pattern. We investigated the evolutionary breadth of ML and the contribution of production mechanisms to ML in the songs of 15 songbird species. Negative relationships between the number and duration of constituents (e.g., syllables in phrases) were observed in all 15 species. However, negative relationships were also observed in null models in which constituents were randomly allocated into observed element durations, and the observed negative relationship for numerous species did not differ from the null model; consequently, ML in these species could simply reflect production constraints and not communicative efficiency. By contrast, ML was significantly different from the null model for more than half the cases, suggesting additional organizational rules are imposed onto birdsongs. Production mechanisms are also underscored by the finding that canaries and zebra finches reared without auditory experiences that guide vocal development produced songs with nearly identical ML patterning as typically reared birds. These analyses highlight the breadth with which production mechanisms contribute to this prevalent organizational pattern in behavior.

Adherence to Menzerath's Law is the exception (not the rule) in three duetting primate species.

Across diverse systems including language, music and genomes, there is a tendency for longer sequences to contain shorter constituents; this phenomenon is known as Menzerath's Law. Whether Menzerath's Law is a universal in biological systems, is the result of compression (wherein shortest possible strings represent the maximum amount of information) or emerges from an inevitable relationship between sequence and constituent length remains a topic of debate. In non-human primates, the vocalizations of geladas, male gibbons and chimpanzees exhibit patterns consistent with Menzerath's Law. Here, we use existing datasets of three duetting primate species (tarsiers, titi monkeys and gibbons) to examine the wide-scale applicability of Menzerath's Law. Primate duets provide a useful comparative model to test for the broad-scale applicability of Menzerath's Law, as they evolved independently under presumably similar selection pressures and are emitted under the same context(s) across taxa. Only four out of the eight call types we examined were consistent with Menzerath's Law. Two of these call types exhibited a negative relationship between the position of the note in the call and note duration, indicating that adherence to Menzerath's Law in these call types may be related to breathing constraints. Exceptions to Menzerath's Law occur when notes are relatively homogeneous, or when species-specific call structure leads to a deterministic decrease in note duration. We show that adherence to Menzerath's Law is the exception rather than the rule in duetting primates. It is possible that selection pressures for long-range signals that can travel effectively over large distances was stronger than that of compression in primate duets. Future studies investigating adherence to Menzerath's Law across the vocal repertoires of these species will help us better elucidate the pressures that shape both short- and long-distance acoustic signals.

An exploration of Menzerath's law in wild mountain gorilla vocal sequences.

Menzerath's law, traditionally framed as a negative relationship between the size of a structure and its constituent parts (e.g. sentences with more clauses have shorter clauses), is widespread across information-coding systems ranging from human language and the vocal and gestural sequences of primates and birds, to the building blocks of DNA, genes and proteins. Here, we analysed an extensive dataset of 'close-call' sequences produced by wild mountain gorillas (Gorilla beringei beringei, no. individuals = 10, no. sequences = 2189) to determine whether, in accordance with Menzerath's law, a negative relationship existed between the number of vocal units in a sequence and the duration of its constituent units. We initially found positive evidence for this but, on closer inspection, the negative relationship was driven entirely by the difference between single- and multi-unit (two to six unit) sequences. Once single-unit sequences were excluded from the analysis, we identified a relationship in the opposite direction, with longer sequences generally composed of longer units. The close-call sequences of mountain gorillas therefore represent an intriguing example of a non-human vocal system that only partially conforms to the predictions of Menzerath's law.

Brevity is not a universal in animal communication: evidence for compression depends on the unit of analysis in small ape vocalizations.

Evidence for compression, or minimization of code length, has been found across biological systems from genomes to human language and music. Two linguistic laws—Menzerath's Law (which states that longer sequences consist of shorter constituents) and Zipf's Law of abbreviation (a negative relationship between signal length and frequency of use)—are predictions of compression. It has been proposed that compression is a universal in animal communication, but there have been mixed results, particularly in reference to Zipf's Law of abbreviation. Like songbirds, male gibbons (Hylobates muelleri) engage in long solo bouts with unique combinations of notes which combine into phrases. We found strong support for Menzerath's Law as the longer a phrase, the shorter the notes. To identify phrase types, we used state-of-the-art affinity propagation clustering, and were able to predict phrase types using support vector machines with a mean accuracy of 74%. Based on unsupervised phrase type classification, we did not find support for Zipf's Law of abbreviation. Our results indicate that adherence to linguistic laws in male gibbon solos depends on the unit of analysis. We conclude that principles of compression are applicable outside of human language, but may act differently across levels of organization in biological systems.

Male gibbon loud morning calls conform to Zipf's law of brevity and Menzerath's law: insights into the origin of human language

The study of vocal communication in nonhuman primates, especially apes, offers critical insight into the origins of human language. Although human language represents a highly derived and complex form of communication, researchers have found that the organization of language follows a series of common statistical patterns, known as ‘linguistic laws’. Zipf's law of brevity and Menzerath's law are pervasive across human languages, and these laws have been identified in the communication of a small number of primate species. What remains less clear is whether these two laws also affect long-distance vocal communication in primates. Here, we provide evidence that the long-distance morning calls of male gibbons (cao vit gibbon, Nomascus nasutus, and western black-crested gibbon, Nomascus concolor ) follow both Zipf's law of brevity and Menzerath's law. We found that notes of male gibbon calls conform to Zipf's law of brevity, with the most common notes being shortest in duration. Similarly, longer sequences are made up of shorter calls on average, consistent with Menzerath's law; we also found a shortening of specific note type duration and an increase in proportion of shorter call types in longer sequences, which may underpin the emergence of this law. Our findings support the generality of these two linguistic laws beyond human language and provide evidence for compression at two levels of organizations (how frequently different note types are used, and how vocal sequences are constructed) in a long-range communication system. • Male gibbon morning calls conform to Zipf's law of brevity and Menzerath's law. • The most common notes being shortest in duration. • Longer sequences are made up of shorter calls on average.

Linguistic laws in chimpanzee gestural communication.

Studies testing linguistic laws outside language have provided important insights into the organization of biological systems. For example, patterns consistent with Zipf's law of abbreviation (which predicts a negative relationship between word length and frequency of use) have been found in the vocal and non-vocal behaviour of a range of animals, and patterns consistent with Menzerath's law (according to which longer sequences are made up of shorter constituents) have been found in primate vocal sequences, and in genes, proteins and genomes. Both laws have been linked to compression-the information theoretic principle of minimizing code length. Here, we present the first test of these laws in animal gestural communication. We initially did not find the negative relationship between gesture duration and frequency of use predicted by Zipf's law of abbreviation, but this relationship was seen in specific subsets of the repertoire. Furthermore, a pattern opposite to that predicted was seen in one subset of gestures-whole body signals. We found a negative correlation between number and mean duration of gestures in sequences, in line with Menzerath's law. These results provide the first evidence that compression underpins animal gestural communication, and highlight an important commonality between primate gesturing and language.

Divergent acoustic properties of gelada and baboon vocalizations and their implications for the evolution of human speech.

Human speech has many complex spectral and temporal features traditionally thought to be absent in the vocalizations of other primates. Recent explorations of the vocal capabilities of non-human primates are challenging this view. Here, we continue this trend by exploring the spectro-temporal properties of gelada (Theropithecus gelada) vocalizations. First, we made cross-species comparisons of geladas, chacma baboons, and human vowel space area. We found that adult male and female gelada exhaled grunts-a call type shared with baboons-have formant profiles that overlap more with human vowel space than do baboon grunts. These gelada grunts also contained more modulation of fundamental and formant frequencies than did baboon grunts. Second, we compared formant profiles and modulation of exhaled grunts to the derived call types (those not shared with baboons) produced by gelada males. These derived calls contained divergent formant profiles, and a subset of them, notably wobbles and vocalized yawns, were more modulated than grunts. Third, we investigated the rhythmic patterns of wobbles, a call type shown previously to contain cycles that match the 3-8 Hz tempo of speech. We use a larger dataset to show that the wobble rhythm overlaps more with speech rhythm than previously thought. We also found that variation in cycle duration depends on the production modality; specifically, exhaled wobbles were produced at a slower tempo than inhaled wobbles. Moreover, the variability in cycle duration within wobbles aligns with a linguistic property known as 'Menzerath's law' in that there was a negative association between cycle duration and wobble size (i.e. the number of cycles). Taken together, our results add to growing evidence that non-human primates are anatomically capable of producing modulated sounds. Our results also support and expand on current hypotheses of speech evolution, including the 'neural hypothesis' and the 'bimodal speech rhythm hypothesis'.

Gelada vocal sequences follow Menzerath’s linguistic law

Identifying universal principles underpinning diverse natural systems is a key goal of the life sciences. A powerful approach in addressing this goal has been to test whether patterns consistent with linguistic laws are found in nonhuman animals. Menzerath's law is a linguistic law that states that, the larger the construct, the smaller the size of its constituents. Here, to our knowledge, we present the first evidence that Menzerath's law holds in the vocal communication of a nonhuman species. We show that, in vocal sequences of wild male geladas (Theropithecus gelada), construct size (sequence size in number of calls) is negatively correlated with constituent size (duration of calls). Call duration does not vary significantly with position in the sequence, but call sequence composition does change with sequence size and most call types are abbreviated in larger sequences. We also find that intercall intervals follow the same relationship with sequence size as do calls. Finally, we provide formal mathematical support for the idea that Menzerath's law reflects compression-the principle of minimizing the expected length of a code. Our findings suggest that a common principle underpins human and gelada vocal communication, highlighting the value of exploring the applicability of linguistic laws in vocal systems outside the realm of language.

When is Menzerath-Altmann law mathematically trivial? A new approach.

Menzerath's law, the tendency of Z (the mean size of the parts) to decrease as X (the number of parts) increases, is found in language, music and genomes. Recently, it has been argued that the presence of the law in genomes is an inevitable consequence of the fact that Z=Y/X, which would imply that Z scales with X as Z ∼ 1/X. That scaling is a very particular case of Menzerath-Altmann law that has been rejected by means of a correlation test between X and Y in genomes, being X the number of chromosomes of a species, Y its genome size in bases and Z the mean chromosome size. Here we review the statistical foundations of that test and consider three non-parametric tests based upon different correlation metrics and one parametric test to evaluate if Z ∼ 1/X in genomes. The most powerful test is a new non-parametric one based upon the correlation ratio, which is able to reject Z ∼ 1/X in nine out of 11 taxonomic groups and detect a borderline group. Rather than a fact, Z ∼ 1/X is a baseline that real genomes do not meet. The view of Menzerath-Altmann law as inevitable is seriously flawed.

The challenges of statistical patterns of language: The case of Menzerath's law in genomes

AbstractThe importance of statistical patterns of language has been debated over decades. Although Zipf's law is perhaps the most popular case, recently, Menzerath's law has begun to be involved. Menzerath's law manifests in language, music and genomes as a tendency of the mean size of the parts to decrease as the number of parts increases in many situations. This statistical regularity emerges also in the context of genomes, for instance, as a tendency of species with more chromosomes to have a smaller mean chromosome size. It has been argued that the instantiation of this law in genomes is not indicative of any parallel between language and genomes because (a) the law is inevitable and (b) noncoding DNA dominates genomes. Here mathematical, statistical, and conceptual challenges of these criticisms are discussed. Two major conclusions are drawn: the law is not inevitable and languages also have a correlate of noncoding DNA. However, the wide range of manifestations of the law in and outside genomes suggests that the striking similarities between noncoding DNA and certain linguistics units could be anecdotal for understanding the recurrence of that statistical law. © 2012 Wiley Periodicals, Inc. Complexity, 2012

Menzerath's law at the gene‐exon level in the human genome

AbstractA previous discussion of a linguistic law called Menzerath's law (the longer a word, the shorter the syllables) in the genomic context was focused on the genome‐chromosome‐base level (the more number of chromosomes in a genome, the smaller the chromosome size). We apply this linguistic metaphor to more appropriate levels of gene, exon, and base. Using the human gene data, we found that the Menzerath's law at these levels holds true: the more number of exons in a gene, the shorted the averaged exon size. Since this negative correlation can be a trivial consequence of the constant size of the messenger RNA coded by the gene, we also exclude this possibility by showing that messenger RNA size increases with the number of exons. This increase of messenger RNA size is however not fast enough for genes with large number of exons to maintain a constant exon size. © 2011 Wiley Periodicals, Inc. Complexity, 2011.

On Hilberg's law and its links with Guiraud's law*

Hilberg (1990) supposed that finite-order excess entropy of a random human text is proportional to the square root of the text length. Assuming that Hilberg's hypothesis is true, we derive Guiraud's law, which states that the number of word types in a text is greater than proportional to the square root of the text length. Our derivation is based on some mathematical conjecture in coding theory and on several experiments suggesting that words can be defined approximately as the nonterminals of the shortest context-free grammar for the text. Such operational definition of words can be applied even to texts deprived of spaces, which do not allow for Mandelbrot's “intermittent silence” explanation of Zipf's and Guiraud's laws. In contrast to Mandelbrot's, our model assumes some probabilistic long-memory effects in human narration and might be capable of explaining Menzerath's law.

The Parameters of the Altmann-Menzerath Law

This investigation deals with statistical analysis of the empirical results published in different papers on Menzerath's law. The comparison of the published results collected on different linguistic levels and in various languages revealed that there might be additional not yet discovered correlations. Therefore, the aim is to find out whether the parameters formalized by Altmann show characteristic values depending on the level of linguistic analysis. The type of functional correlation between the parameters in the equations established by Altmann (1980) is an interesting aspect to be investigated as well as the question if there are clusters forming

The Fall of the Reduced Vowels in the Light of P. Menzerath's Law

The Fall of the Reduced Vowels in the Light of P. Menzerath's Law

Graphemic and Syllabic length of words in text and vocabulary*

Word length is investigated in terms of grapheme and syllable number with respect to their distribution in Russian text and vocabulary. The results are discussed in connection with Menzerath's law.

Some remarks on the relation between word length and morpheme length

Abstract Against the background of the synergetic approach to language some hypotheses about the relation between word length and morpheme length are discussed. First of all, Menzerath's law on the word‐morpheme level is given. On the basis of this law, a function is derived which reflects the dependence of the number of graphemes of a word on its number of morphemes. Furthermore, the influence of morpheme length on the number of graphemes of words containing morphemes of this length is analysed. It is shown that this relation is not just proportional. The results of statistical tests which were realised with the help of the CELEX lexical database are given. They show that all of these hypotheses can for the present be accepted as valid for the languages English, German and Dutch.