The Parameters of the Altmann-Menzerath Law

Cramer, Irene M.

doi:10.1080/09296170500055301

Cited by 39 publications

(31 citation statements)

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“…To conclude, the minimization of K can be viewed as a general principle of compression, shedding light on the origins of both Zipf's law of abbreviation and Menzerath's law. This provides theoretical support for the intuition that Menzerath's law is an effect of compression (14,23,25). Indeed, one can also conclude that minimization of K and a negative correlation between the weight of a unit and its magnitude (Zipf's law of abbreviation, Menzerath's law) are intimately related, based upon previous arguments for L (11).…”

Section: V) Is Intercall Interval Duration Negatively Correlated Withmentioning

confidence: 50%

“…Finally, our demonstration of how a generalized principle of compression produces Menzerath's law, in conjunction with our previous work indicating that Zipf's law of abbreviation also reflects this principle (5), suggests that compression may underpin biological information systems in a broad sense. Compression exists not only at different levels of the chemistry of life-codons (63), proteins (23), genes (22), and entire genomes (18)-but also in multiple forms of animal behavior, from elementary patterns of behavior (7) to vocal communication in nonhumans (8,10) and human language (4,6,25).…”

Section: Resultsmentioning

confidence: 99%

“…Although a connection between Menzerath's law and compression has been suggested various times (14,25), it has not been formally investigated. Here, to our knowledge, we provide the first mathematical demonstration of the connection between compression and Menzerath's law.…”

Section: Discussionmentioning

confidence: 99%

“…We then extend our analyses to explore the silences between calls (intercall intervals) testing whether (v) Menzerath's law also holds for silences, such that intercall intervals are shorter in sequences with more calls, and (vi) durations of intercall intervals become shorter later in sequences. Finally, as a link between Menzerath's law and the principle of compression has previously been proposed (14,25), but not systematically established, we (vii) use a Fig. 1.…”

Section: Significancementioning

confidence: 99%

“…Although Menzerath's law was originally induced as a linguistic law, it has since been applied to a wide range of systems beyond human language: a negative correlation between construct and constituent size has been found in domains such as music (16) and at the molecular level, with species that have a larger number of chromosomes tending to have a smaller mean chromosome size (4,(17)(18)(19)(20), genes that have a higher number of exons having shorter exons on average (21,22), and proteins with a higher number of domains having on average shorter domains (23). This broad adherence to Menzerath's law can be interpreted as a manifestation of self-organization (24) and compression of information (14,25), and suggests that these processes may be widespread in shaping multilevel systems as diverse as macromolecules, language, and music.…”

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Gelada vocal sequences follow Menzerath’s linguistic law

Gustison

Semple

Ferrer-i-Cancho

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

140

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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.communication | language | primate | Menzerath | Zipf

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Section: V) Is Intercall Interval Duration Negatively Correlated Withmentioning

confidence: 50%

Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Significancementioning

confidence: 99%

mentioning

confidence: 99%

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Gelada vocal sequences follow Menzerath’s linguistic law

Gustison

Semple

Ferrer-i-Cancho

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

140

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Stereotactic radiosurgery (SRS)

Combs

Widmer

Thilmann

et al. 2005

Cancer

184

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

Ferrer-i-Cancho

Forns²,

Hernández-Fernández

et al. 2012

Complexity

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The 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 18: [11][12][13][14][15][16][17] 2013 Key Words: statistical laws; language; genomes; music; non-coding DNA; Menzerath's law INTRODUCTIONA ttempts to demonstrate that statistical patterns of language have a trivial explanation have a long history that goes back at least to the research by G. A. Miller and collaborators questioning the relevance of Zipf's law for word frequencies around 1960 [1-3]. Zipf's law states that the curve that relates the frequency of a word f and its rank r (the most frequent word having rank 1, the second most frequent word having rank 2, and so on) should follow f $ r 2a [4]. Miller argued that if monkeys were chained ''to typewriters until they had produced some very long and random sequence of characters'' one would find ''exactly the same 'Zipf curves' for the monkeys as for the human authors '' [3]. Under his view, Zipf's law would be an inevitable consequence of the fact that words are made of units, e.g., letters or phonemes. The typewriter argument has been revived many times since then [5][6][7][8]. However, rigorous analyses indicate that the curves do not really look the same and the parameters of this random typing model giving a good fit to real word frequencies are not forthcoming [9,10] claim that the finding of another statistical pattern of language, Menzerath's law, is also inevitable [11]. P. Menzerath hypothesized that ''the greater the whole, the smaller its constituents'' (''Je größer das Ganze, desto kleiner die Teile'') in the context of language [12] (pp. 101). Converging research in music and genomes [13][14][15][16] suggests that Menzerath's law is a general law of natural and humanmade systems. In this article, we leave the term Menzerath-Altmann law for referring to the exact mathematical dependency that has been proposed by the quantitative linguistics traditi...

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The Parameters of the Altmann-Menzerath Law

Cited by 39 publications

References 0 publications

Gelada vocal sequences follow Menzerath’s linguistic law

Gelada vocal sequences follow Menzerath’s linguistic law

Stereotactic radiosurgery (SRS)

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

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