# Menzerath's law

Menzerath's law, or Menzerath–Altmann law (named after Paul Menzerath and Gabriel Altmann), is a linguistic law according to which the increase of a linguistic construct results in a decrease of its constituents, and vice versa [1] .[2]

E.g., the longer a sentence (measured in terms of the number of clauses) the shorter the clauses (measured in terms of the number of words), or: the longer a word (in syllables or morphs) the shorter the syllables or words in sounds.

According to Altmann (1980),[3] it can be mathematically stated as:

$y=a \cdot x^{-b} \cdot e^{-c x}$

where:

• $y$ is the constituent size (e.g. syllable length)
• $x$ size of the linguistic construct that is being inspected (e.g. number of syllables per word)
• $a$, $b$, $c$ are the parameters

Beyond quantitative linguistics, Menzerath's law can be discussed in any multi-level complex systems. Given three levels, $x$ is the number of middle-level units contained in a high-level unit, $y$ is the averaged number of low-level units contained in middle-level units, Menzerath's law claims a negative correlation between $y$ and $x$. Menzerath's law is shown to be true for both the base-exon-gene levels in the human genome ,[4] and base-chromosome-genome levels in genomes from a collection of species .[5]

## References

1. ^ Gabriel Altmann, Michael H. Schwibbe (1989). Das Menzerathsche Gesetz in informationsverarbeitenden Systemen. Hildesheim/Zürich/New York: Olms. ISBN 3-487-09144-5.
2. ^ Luděk Hřebíček (1995). Text Levels. Language Constructs, Constituents and the Menzerath-Altmann Law. Wissenschaftlicher Verlag Trier. ISBN 3-88476-179-X.
3. ^ Gabriel Altmann (1980). "Prolegomena to Menzerath's law". Glottometrika 2: pp. 1–10.
4. ^ Wentian Li (2012). "Menzerath's law at the gene-exon level in the human genome". Complexity 17 (4): 49–53. doi:10.1002/cplx.20398.
5. ^ Ramon Ferrer-I-Cancho, Núria Forns (2009). "The self-organization of genomes". Complexity 15 (5): 34–36. doi:10.1002/cplx.20296.