# Piotrowski law

In general linguistics, Piotrowski's law is a common name for the language change law of quantitative linguistics , named after the Saint Petersburg linguist Rajmund G. Piotrowski (Marchuk 2003), who apparently was the first to attempt a mathematical modeling of language change processes together with A. A. Piotrowskaja. This suggestion was made by Altmann (1983) et al. a. criticized and developed. The Piotrowski law is an application of the logistic function and makes a statement about the course of language change ; it is one of the central achievements of quantitative linguistics.

## On the form of the Piotrowski law

The basic idea is based on the assumption that a change in language begins somewhere in an individual and - if it is adopted by others - initially spreads very gradually. The greater the number of people who join the innovation, the faster it will spread. At some point a turning point will be reached, from which the speed of the spread slows down until it finally comes to a standstill. The pattern for this course is therefore: slow start - acceleration - turning point - decrease in the speed of propagation - stop of the propagation. In some cases the spread of a linguistic innovation completely replaces an old form (= complete language change); in other cases a linguistically new appearance can only assert itself to a certain extent (= incomplete language change).

• Form of the Piotrowski law for complete language change:
${\ displaystyle p (t) = {\ frac {1} {1 + a \ cdot e ^ {- b \ cdot t}}}}$

a and b are the parameters of the model; t stands for time. Such a case is in the replacement of the word form darft (second person singular present indicative of the verb may ) by valid botanical form allowed to in frühneuhochdeutscher time:

Period t - {t} - {st} Share - {st} observed Share - {st} calculated
1426-1447 1 7th 3 0.3000 0.2646
1448-1469 2 10 8th 0.4444 0.4242
1470-1491 3 35 40 0.5395 0.6013
1492-1513 4th 19th 47 0.7121 0.7554
1514-1535 5 11 120 0.9160 0.8634
1536-1557 6th 0 105 1.0000 0.9283

Adjusting the formula for complete language change results in a coefficient of determination of D = 0.96, where D is considered good if it is greater than or equal to 0.80; it cannot be greater than D = 1.00. The replacement of the older form by the newer one thus proceeds according to Piotrowski's law. (For more detailed explanations, please refer to the literature given.)

• Form of the Piotrowski law for incomplete language change:
${\ displaystyle p (t) = {\ frac {c} {1 + a \ cdot e ^ {- b \ cdot t}}}}$

Parameter c represents the value towards which the observed language change strives. Such a case is shown in the article Sprachwandelgesetz using the example of the spread of Arabic borrowings in German.

As a further case for this type of language change, reference can be made to the adoption of computer vocabulary in dictionaries aimed at the general public:

year t source Proportion observed Proportion calculated
1952 1 Mackensen, New German Dictionary 0 1.34
1953 2 The big Brockhaus 1 1.62
1954 3 Duden. Spelling 14th edition 0 1.95
1955 4th The great herder 1 2.34
1956 5 The big Brockhaus 1 2.82
1961 10 Duden. Spelling 15th edition 4th 7.05
1966 15th Truly. The great German dictionary 22nd 17.20
1977 26th Mackensen. German dictionary 9th edition 77 91.04
1980 29 Truly. German dictionary 146 124.74
1983 32 Duden. German universal dictionary 157 158.15
1986 35 Duden. Spelling 19th edition 169 186.67
1989 38 Duden. German universal dictionary 2nd edition 218 208.09

Adjusting the formula for incomplete language change results in a coefficient of determination of D = 0.99.

The difference between these dictionaries for the general public and a technical lexicon is striking: According to the blurb, such a work, which was published in 1990, contains "over 4000 terms that are used again and again when dealing with the computer."

As a special feature, it can sometimes be observed that a linguistic innovation initially spreads and at some point loses ground again. Such cases of a reversible language change occur, for example, when choosing first names that follow conspicuous fashions. A reversible course of the use of a word could also be demonstrated using the example of a fighting dog .

• Form of the Piotrowski law for the reversible (i.e. first increasing and then decreasing or vice versa) language change:
${\ displaystyle p (t) = {\ frac {1} {1 + a \ cdot e ^ {- b \ cdot t + c \ cdot t ^ {2}}}}}$

Another example of such a reversible language change can be found in the article sentence length in the section "Development of sentence length".

The vast majority of cases of language change observed so far show an astonishingly “smooth” course with only minor deviations from a calculated ideal line. If this is not the case, there can be two causes:

1. It can be a problem simply due to a lack of data.
2. But it can also be a language phenomenon whose "irregular" course has systematic reasons that have to be included in the modeling.

## Areas of application

An abundance of studies on morphological and syntactic change as well as on loan processes and changes in orthographic habits shows that this approach is suitable for modeling the course of language change processes. The development of the vocabulary of languages ​​is also subject to this law. This applies to both the loss and the expansion of vocabulary. Even individual words develop accordingly, as the example of globalization shows. The same model has also proven itself as a language acquisition law : the acquisition of the vocabulary of the mother tongue and a number of other learning processes take place in this way.

## Forecasting in Linguistics

If one looks at well-researched processes of language change, one can ask how these will develop in the future. The problem is discussed in Best (2009) using the example of borrowings from Latin and English into German. It is crucial that, on the basis of the Piotrowski law, prognoses are also possible in linguistics if there is sufficient data on the course of a language change.

## literature

• Gabriel Altmann : The Piotrowski law and its generalizations. In: Karl-Heinz Best, Jörg Kohlhase (Ed.): Exact language change research. Theoretical contributions, statistical analyzes and work reports (= Göttinger Schriften zur Sprach- und Literaturwissenschaft. Vol. 2). edition herodot, Göttingen 1983, ISBN 3-88694-024-1 , pp. 54-90.
• Gabriel Altmann, Haro von Buttlar, Walter Rott, Udo Strauß: A law of change in language. In: Barron Brainerd (Ed.): Historical linguistics (= Quantitative Linguistics. Vol. 18). Brockmeyer, Bochum 1983, ISBN 3-88339-305-3 , pp. 104-115.
• Gabriel Altmann, Dariusch Bagheri, Hans Goebl, Reinhard Köhler , Claudia Prün: Introduction to quantitative lexicology (= Göttingen linguistic treatises. Vol. 5). Peust & Gutschmidt, Göttingen 2002, pages 160–166, ISBN 3-933043-09-3 .
• Karl-Heinz Best : Language acquisition, language change and vocabulary growth in texts. On the scope of the Piotrowski law. In: Glottometrics Vol. 6, 2003, , pp. 9-34. (PDF full text )
• Karl-Heinz Best: Shortening tendencies in German from the point of view of quantitative linguistics. In: Jochen A. Bär, Thorsten Roelcke, Anja Steinhauer (eds.): Linguistic brevity. Conceptual, structural and pragmatic aspects (= linguistics - impulses & tendencies. Vol. 27). de Gruyter, Berlin et al. 2007, ISBN 978-3-11-017542-4 , pp. 45–62 (The article models the course of various types of shortening tendencies in German as a process that follows the Piotrowski law ).
• Karl-Heinz Best, Emmerich Kelih (editor): Borrowings and foreign words: Quantitative aspects. RAM-Verlag, Lüdenscheid 2014. ISBN 978-3-942303-23-1 .
• Festschrift in honor of Professor Raijmund G. Piotrowski. In: Journal of Quantitative Linguistics. Vol. 10, Issue 2, 2003, , pp. 79-211, and Issue 3, pp. 215-292.
• Emmerich Kelih, Ján Mačutek: Problems of modeling loan relationships (using the example of Serbo-Croatian in Slovenian). In: Emmerich Kelih, Róisín Knigth, Ján Mačutek, Andrew Wilson: Issues in Quantitative Linguistics 4. Dedicated to Reinhard Köhler on the occasion of his 65th birthday. RAM-Verlag, Lüdenscheid 2016. ISBN 978-3-942303-44-6 , pages 260-272.
• Edda Leopold: Stochastic modeling of lexical evolutionary processes. Publishing house Dr. Kovač, Hamburg 1998. ISBN 3-86064-856-X . (= Dissertation, Trier 1998.)
• Edda Leopold: The Piotrowski law. In: Reinhard Köhler, Gabriel Altmann, Rajmund G. Piotrowski (eds.): Quantitative Linguistics. An international manual. = Quantitative Linguistics (= handbooks for linguistics and communication studies. Vol. 27). de Gruyter, Berlin et al. 2005, ISBN 3-11-015578-8 , pp. 627-633.
• Yurii N. Marchuk: The Burdens and Blessings of Blazing the Trail . In: Journal of Quantitative Linguistics. Vol. 10, Issue 2, 2003, pp. 81-85, doi: 10.1076 / jqul.10.2.81.16713 .
• Rajmond G. Piotrowski, Kaldybaj B. Bektaev, Anna A. Piotrowskaja: Mathematical Linguistics (= Quantitative Linguistics. Vol. 27). Brockmeyer, Bochum 1985, ISBN 3-88339-453-X .
• Piotrowskaja, AA, Rajmond G. Piotrowski: Matematičeskie modeli diachronii i tekstoobrazovanija . In: Statistica reči i avtomatičeskij analiz teksta , Leningrad: Nauka 1974, 361-400. This contribution is the starting point for the development of the Piotrowski law.

## bibliography

• Karl-Heinz Best : Bibliography - Piotrowski's law . In: Glottotheory 7, Issue 1, 2016, pages 89–93.

Wiktionary: Piotrowski law  - explanations of meanings, word origins, synonyms, translations

## Individual evidence

1. Acknowledgment: Archived copy ( memento of the original from February 20, 2015 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. .
2. ^ All three formulas according to Altmann 1983.
3. ^ Karl-Heinz Best: Quantitative Linguistics. An approximation . 3rd, heavily revised and expanded edition. Peust & Gutschmidt, Göttingen 2006, ISBN 3-933043-17-4 , page 109.
4. ^ Karl-Heinz Best: To the computer vocabulary in German. In: Naukovyj Visnyk Černivec'koho Universitetu. Vypusk 289, 2006, , pages 10-24; Example on page 12.
5. Thomas Kaltenbach, Udo Reetz, Hartmut Woerrlein: The large computer encyclopedia. Current terms from Ada to Zuse. Fischer Taschenbuch Verlag, Frankfurt / Main 1990, ISBN 3-596-10219-7 .
6. ^ Gerhard Koß: Name research. An introduction to onomastics (= Germanistic workbooks 34). Niemeyer, Tübingen 1990, ISBN 3-484-25134-4 , p. 88. Koß outlines the reversible development of the first names Peter and Andreas from the 1940s to the 1970s.
7. On the use of the term in the period 1994-2004: Karl-Heinz Best: On the use of "Kampfhund" in German. In: Glottotheory. Vol. 2, No. 2, 2009, , pp. 15-18.
8. Archived copy ( memento of the original from July 19, 2011 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.
9. ^ Katharina Ternes: Developments in the German vocabulary. In: Glottometrics. Vol. 21, 2011, pages 25–53 (PDF full text ).
10. Karl-Heinz Best: On the development of the vocabulary of everyday German , in: Glottometrics 20, 2010, pp. 34–37 (PDF full text ).
11. ^ Karl-Heinz Best: On the spread of "globalization" in German. In: Göttingen Contributions to Linguistics 16, 2008 [published 2010], pages 17–20.
12. ^ Karl-Heinz Best: Laws of first language acquisition. In: Glottometrics Vol. 12, 2006, pages 39-54 (PDF full text ).
13. Karl-Heinz Best: Are prognoses possible in linguistics? In: Tilo Weber, Gerd Antos (Hrsg.): Types of knowledge. Conceptual differentiation and characteristics in the practice of knowledge transfer (= transfer sciences. Vol. 7). Peter Lang, Frankfurt am Main et al. 2009, ISBN 978-3-631-57109-5 , pp. 164-175.