Difference between revisions of "Change in language"
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'''1. Problem and history'''
 
'''1. Problem and history'''
  
−
Everything in language changes. The complete complex of causes can not be ascertained; we are interested in the general processes of change and its course, whatever the entity con¬cerned. There are four aspects treated in this volume, for which models could be set up:
+
Everything in language changes. The complete complex of causes can not be ascertained; we are interested in the general processes of change and its course, whatever the entity concerned. There are four aspects treated in this volume, for which models could be set up:
 
 
 
Qualitative change
 
Qualitative change
Line 15: Line 15:
 
(iv) lexicon decay or glottochronology (<math>\rightarrow</math>)
 
(iv) lexicon decay or glottochronology (<math>\rightarrow</math>)
  
−
The research in quantitative form most probably began with different hypotheses of G. K. Zipf concerning age and frequency, age and length, etc. (1946, 1947, 1949, cf. Prün 1985). Measurement concerning individual phenomena can be found in Piotrowski (1960), Graudina (1964), Lazard (1965), whose results have been empirically fitted by Piotrovskaja, Piotrowski (1974) using an arctangent function. The theoretical derivation has been performed by Beö¬thy, Altmann (1982), Altmann, von Buttlar, Rott, Strauß (1983) combining Piotrowski´s find¬ings with an assumption of Weinreich, Labov, Herzog (1968). Altmann (1983) derived the three possible variants of the law shown below. A number of corroborations was brought by Best (1983), Best, Kohlhase (1983, 1983a), Imsiepen (1983), Kohlhase (1983), Müller-Hase¬mann (1983), Best, Altmann (1986), Kroch (1989a,b, 2001), Best, Beöthy, Altmann (1990), Tuldava (1998), Best (2001), Bresnan, Dingare, Manning (2001), Vulanović (2003). The law is called Piotrowski law or Piotrowski-Altmann law and is used for modelling phenomena like the increase of the number of borrowings, changes in morphology, etc.  
+
The research in quantitative form most probably began with different hypotheses of G. K. Zipf concerning age and frequency, age and length, etc. (1946, 1947, 1949, cf. Prün 1985). Measurement concerning individual phenomena can be found in Piotrowski (1960), Graudina (1964), Lazard (1965), whose results have been empirically fitted by Piotrovskaja, Piotrowski (1974) using an arctangent function. The theoretical derivation has been performed by Beöthy, Altmann (1982), Altmann, von Buttlar, Rott, Strauß (1983) combining Piotrowski´s findings with an assumption of Weinreich, Labov, Herzog (1968). Altmann (1983) derived the three possible variants of the law shown below. A number of corroborations was brought by Best (1983), Best, Kohlhase (1983, 1983a), Imsiepen (1983), Kohlhase (1983), Müller-Hasemann (1983), Best, Altmann (1986), Kroch (1989a,b, 2001), Best, Beöthy, Altmann (1990), Tuldava (1998), Best (2001), Bresnan, Dingare, Manning (2001), Best (2006), Vulanović (2007), Vulanović, Baayen (2007). The law is called Piotrowski law or Piotrowski-Altmann law and is used for modelling phenomena like the increase of the number of borrowings, changes in morphology, etc.  
  
 
 
Line 32: Line 32:
 
(1) <math>dp_t=k_tp_t(C-p_t)dt\quad\quad</math>,
 
(1) <math>dp_t=k_tp_t(C-p_t)dt\quad\quad</math>,
  
−
<math>p_t</math> = proportion of new forms
+
where
  
−
<math>pk_t</math> = a function of time (can also be a constant)
+
<math>p_t</math> = proportion of new forms,
  
−
C = limit of change
+
<math>pk_t</math> = a function of time (can also be a constant),
  
−
t > 0, time
+
<math>C</math> =  limit of change,
  
−
<math>dp_t</math> = change of the proportion
+
<math>t > 0</math>, time,
  
 +
and
  
−
telling that the change of the proportion of new forms is proportional to the interaction of new and old forms. The solution yields three variants:
+
<math>dp_t</math>  = change in the proportion.
  
  
−
'''(a) Complete change''' if C = 1 and <math>k_t = b</math> is constant
+
This means that the change of the proportion of new forms is proportional to the interaction of new and old forms. The solution yields three variants.
  
−
(2) <math>p=\frac{1}{1+ae^{-bt}}</math>     
 
  
−
where a is the integration constant. The result in (2) represents the so-called logistic curve used in different disciplines  for modeling growth phenomena.
+
'''(a) Complete change''' if <math>C = 1</math> and <math>k_t = b</math> is constant
  
−
'''Example'''. Since years represent large numbers hindering the fitting, one usually transforms the time intervals in a time variable beginning with t = 1. Often the cumulative frequencies are changed to cumulative proportions, or the proportions are ascertained from the occurrence of rival forms.
+
(2) <math>p=\frac{1}{1+ae^{-bt}}</math>,      
−
Complete change: The replacement of –{t} by –{st} in German 2nd person singular indicative present time with the verb “wollen”, shown by Best (2003a). The result of fitting is presented in Table 1 and Fig. 1. Here ft is the relative frequency of –{st}, pt is the computed relative frequency according to (2).
 
  
 +
where <math>a</math> is the integration constant. The result in (2) represents the so-called logistic curve used in different disciplines  for modeling growth phenomena.
  
−
<div align="center">[[Image:Figur1_CiL.jpg]]</div>
+
'''Example'''. Since years represent large numbers hindering the fitting, one usually transforms the time intervals in a time variable beginning with <math>t = 1</math>. Often, the cumulative frequencies are changed to cumulative proportions, or the proportions are ascertained from the occurrence of rival forms.
 +
Complete change: The replacement of –{t} by –{st} in German 2nd person singular indicative present tense of the verb “wollen”, shown by Best (2003a). The result of fitting is presented in Table 1 and Fig. 1. Here <math>f_t</math> is the relative frequency of –{st} and <math>p_t</math> is the computed relative frequency according to (2).
 +
 
 +
 
 +
<div align="center">[[Image:Figur11_CiL.jpg]]</div>
  
 
The fitting is excellent. The curve was fitted to the proportion of –{st} found in the sources.
 
The fitting is excellent. The curve was fitted to the proportion of –{st} found in the sources.
Line 66: Line 70:
  
  
−
(b) '''Partial change''' if <math>k-t = b</math>  is constant, C is the asymptote
+
(b) '''Partial change''' if <math>k-t = b</math>  is constant, <math>C</math> is the asymptote
  
 
(3) <math>p=\frac{C}{1+ae^{-bt}}</math>       
 
(3) <math>p=\frac{C}{1+ae^{-bt}}</math>       
  
−
and a is the integration constant.
+
and <math>a</math> is the integration constant.
  
−
Example. Partial change: Borrowings from Latin in  Hungarian
+
Example. Partial change: Borrowings from Latin in  Hungarian.
 
Beöthy and Altmann examined the borrowing from different langugages in Hungarian. The fate of Latin words is shown in Table 2 and Fig. 2. The fitting was performed for the cumulative values.
 
Beöthy and Altmann examined the borrowing from different langugages in Hungarian. The fate of Latin words is shown in Table 2 and Fig. 2. The fitting was performed for the cumulative values.
  
−
<div align="center">[[Image:Figur2_CiL.jpg]]</div>
+
<div align="center">[[Image:Figur22_CiL.jpg]]</div>
  
 
<div align="center">[[Image:Grafik2_CiL.jpg]]</div>
 
<div align="center">[[Image:Grafik2_CiL.jpg]]</div>
Line 81: Line 85:
  
  
−
(c) '''Reversible change''' if <math>k_t</math> = a´ - b´t, C = constant
+
(c) '''Reversible change''' if <math>k_t = A - Bt</math>, <math>C</math> = constant
  
−
(4)<math>p_t=\frac{C}{1+ae^{-bt+ct^2}}</math>
+
(4) <math>p_t=\frac{C}{1+ae^{-bt+ct^2}}</math>
  
−
where a, b, c are simple functions of a´, b´and C.
+
where <math>a, b</math> and <math>c</math> depend on <math>A, B</math> and <math>C</math>.
  
−
Example 3. Reversible change: Epithesis with strong verbs in German. Imsiepen (1983) observed that the epithesis of /e/ with strong verbs (1st and 3rd person sg. Past tense) is a reversible process in German. Altmann (1983) has shown some estimation procedures for this curve, but since several observed values are very unreliable, Best, Beöthy and Altmann (1990) considered smoothed values (moving average of 7 values) and obtained the data in Table 3. They took the value of C into consideration and used formula (4).
+
Example 3. Reversible change: Epithesis with strong verbs in German. Imsiepen (1983) observed that the epithesis of /e/ with strong verbs (1st and 3rd person sg. past tense) is a reversible process in German. Altmann (1983) has shown some estimation procedures for this curve, but since several observed values are very unreliable, Best, Beöthy and Altmann (1990) considered smoothed values (moving average of 7 values) and obtained the data in Table 3. They took the value of <math>C</math> into consideration and used formula (4).
  
−
<div align="center">[[Image:Grafik3_CiL.jpg]]</div>
+
<div align="center">[[Image:Tabelle33_CiL.jpg]]</div>
  
 
The fitting is very good.
 
The fitting is very good.
Line 97: Line 101:
  
  
−
'''4. Author:''' G. Altmann
+
'''4. Authors:''' U. Strauss, G. Altmann
  
  
Line 114: Line 118:
 
'''Bailey, Ch.J.N.''' (1973). ''Variation and linguistic theory.'' Arlington: Center for Applied Lin-guistics.
 
'''Bailey, Ch.J.N.''' (1973). ''Variation and linguistic theory.'' Arlington: Center for Applied Lin-guistics.
  
−
'''Beöthy, E., Altmann, G.''' (1982). Das Piotrowski-Gesetz und der Lehnwort¬schatz. ''Zs. für Sprachwissenschaft 1, 171-178.''
+
'''Beöthy, E., Altmann, G.''' (1982). Das Piotrowski-Gesetz und der Lehnwortschatz. ''Zs. für Sprachwissenschaft 1, 171-178.''
  
 
'''Best, K.-H.''' (1983). Zum morphologischen Wandel einiger deutscher Verben. In: Best, Kohlhase (eds.) 1983: 107-118.
 
'''Best, K.-H.''' (1983). Zum morphologischen Wandel einiger deutscher Verben. In: Best, Kohlhase (eds.) 1983: 107-118.
Line 126: Line 130:
 
'''Best, K.H.''' (2003a). “Spracherwerb, Sprachwandel und Wortschatzwachstum in Texten. Zur Reichweite des Piotrowski-Gesetzes.” ''Glottometrics 6, 9-34.''
 
'''Best, K.H.''' (2003a). “Spracherwerb, Sprachwandel und Wortschatzwachstum in Texten. Zur Reichweite des Piotrowski-Gesetzes.” ''Glottometrics 6, 9-34.''
  
−
'''Best, K.-H.''' (2003b). Wie verläuft Sprachwandel? ''Naukovij Visnik Černivec´kogo Univeristetu 155, 86-94.''
+
'''Best, K.-H.''' (2003b). Wie verläuft Sprachwandel? ''Naukovyj Visnyk Černivec´koho Universytetu 155, 86-94.''
  
−
'''Best, K.-H.''' (2003c). “Spracherwerb, Sprachwandel und Wortschatzwachstum in Texten. Zur Reichweite des Piotrowski-Gesetzes.” ''Glottometrics 6, 9-34.''  
+
'''Best, K.-H.''' (2003c). Spracherwerb, Sprachwandel und Wortschatzwachstum in Texten. Zur Reichweite des Piotrowski-Gesetzes. ''Glottometrics 6, 9-34.''  
  
 
'''Best, K.-H.''' (2003d). Zum Wandel von Idiolekten. ''Naukovyj Visnyk Černivec’koho Universytetu, Vypusk 165-166, 36-43.''
 
'''Best, K.-H.''' (2003d). Zum Wandel von Idiolekten. ''Naukovyj Visnyk Černivec’koho Universytetu, Vypusk 165-166, 36-43.''
  
−
'''Best, K.-H.''' (2004). Kürzungstendenzen im Deutschen aus der Sicht der Quantitativen Linguistik. In: Bär, J. A., Roelcke, T., & Steinhauer, A. (Hrsg.), ''Sprachliche Kürze. Konzeptuelle, strukturelle und pragmatische Aspekte.'' Berlin/ New York: de Gruyter. (Im Druck)
+
'''Best, K.-H.'''(2003e). Zur Entwicklung von Wortschatz und Redefähigkeit bei Kindern. ''Göttinger Beiträge zur Sprachwissenschaft 9, 7-20.''
 +
 
 +
'''Best, K.-H.''' (2006a). Zum Computerwortschatz im Deutschen. ''Naukovyj Visnyk Cernivec’koho Universytetu: Hermans’ka filolohija. Vypusk 289, 10-24.''
 +
 
 +
'''Best, K.-H.'''(2006b). Italianismen im Deutschen. ''Göttinger Beiträge zur Sprachwissenschaft 13, 77-86.''
 +
 
 +
'''Best, K.-H.'''(2006c). ''Quantitative Linguistik - Eine Annäherung.'' 3., stark überarbeitete und ergänzte Auflage. Göttingen: Peust & Gutschmidt.
 +
 
 +
'''Best, K.-H.'''(2006d). Quantitative Untersuchungen zu den Jiddismen im Deutschen. ''Jiddistik-Mitteilungen 36, 1-14.''
 +
 
 +
'''Best, K.-H.'''(2006e). Wortlängen im Deutschen. ''Göttinger Beiträge zur Sprachwissenschaft 13, 23-49.''
 +
 
 +
'''Best, K.-H.''' (2007a). Zur Entwicklung des Wortschatzes der Elektrotechnik, Informationstechnik und Elektrophysik im Deutschen. ''Glottometrics 15, 24-27.''
 +
 
 +
'''Best, K.-H.''' (2007b). Kürzungstendenzen im Deutschen aus der Sicht der Quantitativen Linguistik. In: Bär, J. A., Roelcke, T., & Steinhauer, A. (Hrsg.), ''Sprachliche Kürze. Konzeptuelle, strukturelle und pragmatische Aspekte.'' Berlin/ New York: de Gruyter, S. 45-62.
  
−
'''Best, K.-H., Altmann, G.''' (1986). Untersuchungen zur Gesetzmäßigkeit von Entlehnungs¬prozessen im Deutschen. ''Folia Linguistica Historica 31-41.''
+
'''Best, K.-H., Altmann, G.''' (1986). Untersuchungen zur Gesetzmäßigkeit von Entlehnungsprozessen im Deutschen. ''Folia Linguistica Historica 31-41.''
  
 
'''Best, K.-H., Beöthy, E., Altmann, G.''' (1990). Ein methodischer Beitrag zum Piotrowski-Gesetz. ''Glottometrika 12, 115-124.''
 
'''Best, K.-H., Beöthy, E., Altmann, G.''' (1990). Ein methodischer Beitrag zum Piotrowski-Gesetz. ''Glottometrika 12, 115-124.''
Line 141: Line 159:
  
 
'''Best, K.-H., Kohlhase, J.''' (1983a). Der Wandel von ''ward'' zu ''wurde''. In: Best, Kohlhase (eds.) 1983: 91-102.
 
'''Best, K.-H., Kohlhase, J.''' (1983a). Der Wandel von ''ward'' zu ''wurde''. In: Best, Kohlhase (eds.) 1983: 91-102.
 +
 +
'''Best, K.-H., Zhu, Jinyang''' (2006). Sprachwandel im Chinesischen. ''Archiv orientální 74, 203-214.''
  
 
'''Brainerd, B.''' (1983). A stochastic model for language change. In: Brainerd, B. (ed.): ''Historical linguistics: 25-49''. Bochum: Brockmeyer.
 
'''Brainerd, B.''' (1983). A stochastic model for language change. In: Brainerd, B. (ed.): ''Historical linguistics: 25-49''. Bochum: Brockmeyer.
Line 168: Line 188:
 
'''Körner, H.''' (2004). Zur Entwicklung des deutschen (Lehn)Wortschatzes. ''Glottometrics 7, 25-49.''
 
'''Körner, H.''' (2004). Zur Entwicklung des deutschen (Lehn)Wortschatzes. ''Glottometrics 7, 25-49.''
  
−
'''Kroch, A.S.''' (1989a). Function and grammar in the history of English: periphrastic do. In: Fasold, R.W., Schiffrin, D. (eds.), Language change and variation: 133-172. Amsterdam: Benjamins.
+
'''Kroch, A.S.''' (1989a). Function and grammar in the history of English: periphrastic ''do''. In: Fasold, R.W., Schiffrin, D. (eds.), Language change and variation: 133-172. Amsterdam: Benjamins.
  
 
'''Kroch, A.S.''' (1989b). Reflexes of grammar in patterns of language change. In: Fasold, R.W., Schiffrin, D. (eds.), ''Language change and variation: 199-244''. Amsterdam: Benjamins.
 
'''Kroch, A.S.''' (1989b). Reflexes of grammar in patterns of language change. In: Fasold, R.W., Schiffrin, D. (eds.), ''Language change and variation: 199-244''. Amsterdam: Benjamins.
Line 175: Line 195:
  
 
'''Lazard, G.''' (1965). Les empruntes arabes dans la prose persane du X-e au XII-e siècle : aperçu statistique. ''Revue de l´Ecole National des language orientales 2, 53-67''.
 
'''Lazard, G.''' (1965). Les empruntes arabes dans la prose persane du X-e au XII-e siècle : aperçu statistique. ''Revue de l´Ecole National des language orientales 2, 53-67''.
 +
 +
'''Lehfeldt, W., Altmann, G.''' (2003). The process of fall of the reduced vowels in Old Russian in the lingth of the Piotrovskij law. ''Russian Linguistics 27, 141-149.''
  
 
'''Leopold, E.''' (1998). ''Stochastische Modellierung lexikalischer Evolutionsprozesse''. Hamburg: Kovač.
 
'''Leopold, E.''' (1998). ''Stochastische Modellierung lexikalischer Evolutionsprozesse''. Hamburg: Kovač.
  
−
'''Leopold, E.''' (2005). Das Piotrowski-Gesetz. In: Altmann, G., Köhler, R., Piotrowski, R. (Hg.), ''Quantitative Linguistik – Quantitative Linguistics. Ein internationales Handbuch: 627-633.'' Berlin/ N.Y.: de Gruyter.
+
'''Leopold, E.''' (2005). Das Piotrowski-Gesetz. In: Köhler, R., Altmann, G., Piotrowski, R. (Hg.), ''Quantitative Linguistik – Quantitative Linguistics. Ein internationales Handbuch: 627-633.'' Berlin/ N.Y.: de Gruyter.
  
 
'''Müller-Hasemann, W.''' (1983). Das Eindringen englischer Wörter ins Deutsche ab 1945. In: Best, Kohlhase (eds.) 1983: 143-160.
 
'''Müller-Hasemann, W.''' (1983). Das Eindringen englischer Wörter ins Deutsche ab 1945. In: Best, Kohlhase (eds.) 1983: 143-160.
Line 206: Line 228:
 
'''Sankoff, D.''' (1969). ''Historical linguistics as stochastic process.'' Montreal. Diss., McGill Univ., Montreal.
 
'''Sankoff, D.''' (1969). ''Historical linguistics as stochastic process.'' Montreal. Diss., McGill Univ., Montreal.
  
−
'''Sankoff, D.''' (1971). Stochastic models for glottochronology. In: Hodson, F.R. et al. (eds.),  ''Anglo-Romanian Conference on Mathematics in the Archaeological and Historical Sciences. Mamaia, Romania, 1970.'' Edinburgh: Edinburgh Univ. Press, 1971. S.381-386.
+
'''Sankoff, D.''' (1971). Stochastic models for glottochronology. In: Hodson, F.R. et al. (eds.),  ''Anglo-Romanian Conference on Mathematics in the Archaeological and Historical Sciences. Mamaia, Romania, 1970: 381-386.'' Edinburgh: Edinburgh Univ. Press.
 
   
 
   
 
'''Sankoff, D.''' (1972). Lexical replacement processes. ''Computer Studies in the Humanities and Verbal Behaviour 4, 208-212.''
 
'''Sankoff, D.''' (1972). Lexical replacement processes. ''Computer Studies in the Humanities and Verbal Behaviour 4, 208-212.''
Line 212: Line 234:
 
'''Tuldava, J.''' (1998). ''Probleme und Methoden der quantitativ-systemischen Lexikologie''. Trier: WVT.
 
'''Tuldava, J.''' (1998). ''Probleme und Methoden der quantitativ-systemischen Lexikologie''. Trier: WVT.
  
−
'''Vulanović, R.''' (2003). Fitting periphrastic do in affirmative declaratives. QUALICO 2003, Atlanta.
+
'''Vulanović, R.''' (2007). Fitting periphrastic ''do'' in affirmative declaratives. ''Journal of quantitative linguistics 14, 111-126''.
 +
 
 +
'''Vulanović, R., Baayen, H.''' (2007). Fitting the development of periphrastic do in all sentence types. In: Grzybek, P., Köhler, R. (eds.),
 +
''Exact Methods in the Study of Language and Text: 679-688.'' Berlin/New York: Mouton de Gruyter.
  
 
'''Weinreich, U., Labov, W., Herzog, M.E.''' (1968). Empirical foundations for a theory of language change. In: Lehmann, W.P., Malkiel, Y. (eds.), ''Directions for historical linguistics: 95-188.'' Austin: University of Texas Press.
 
'''Weinreich, U., Labov, W., Herzog, M.E.''' (1968). Empirical foundations for a theory of language change. In: Lehmann, W.P., Malkiel, Y. (eds.), ''Directions for historical linguistics: 95-188.'' Austin: University of Texas Press.
  
−
'''Winter, W.''' (1971). Formal frequency and linguistic change. Some preliminary comments. ''Folia Linguistica 5, 55-61''.
+
'''Winter, W.''' (1971). Formal frequency and linguistic change. Some preliminary comments. ''Folia linguistica 5, 55-61''.
 
   
 
   
 
'''Zipf, G.K.''' (1946). Cultural-chronological strata in speech. ''Journal of abnormal and social psychology 41, 351-355.''
 
'''Zipf, G.K.''' (1946). Cultural-chronological strata in speech. ''Journal of abnormal and social psychology 41, 351-355.''

Latest revision as of 11:24, 10 June 2009

1. Problem and history

Everything in language changes. The complete complex of causes can not be ascertained; we are interested in the general processes of change and its course, whatever the entity concerned. There are four aspects treated in this volume, for which models could be set up:

Qualitative change

(i) change of individual entities, which is the object of this chapter

(ii) sound change (\rightarrow)

Volume change

(iii) lexicon growth (\rightarrow)

(iv) lexicon decay or glottochronology (\rightarrow)

The research in quantitative form most probably began with different hypotheses of G. K. Zipf concerning age and frequency, age and length, etc. (1946, 1947, 1949, cf. Prün 1985). Measurement concerning individual phenomena can be found in Piotrowski (1960), Graudina (1964), Lazard (1965), whose results have been empirically fitted by Piotrovskaja, Piotrowski (1974) using an arctangent function. The theoretical derivation has been performed by Beöthy, Altmann (1982), Altmann, von Buttlar, Rott, Strauß (1983) combining Piotrowski´s findings with an assumption of Weinreich, Labov, Herzog (1968). Altmann (1983) derived the three possible variants of the law shown below. A number of corroborations was brought by Best (1983), Best, Kohlhase (1983, 1983a), Imsiepen (1983), Kohlhase (1983), Müller-Hasemann (1983), Best, Altmann (1986), Kroch (1989a,b, 2001), Best, Beöthy, Altmann (1990), Tuldava (1998), Best (2001), Bresnan, Dingare, Manning (2001), Best (2006), Vulanović (2007), Vulanović, Baayen (2007). The law is called Piotrowski law or Piotrowski-Altmann law and is used for modelling phenomena like the increase of the number of borrowings, changes in morphology, etc.


2. Hypothesis

Everything in language changes as a result of interaction between old forms and new forms.

The independent variable is time, given usually in form of a transformed time index. The dependent variable is the proportion of new forms.


3. Derivation

The interaction can be presented in the form

(1) dp_t=k_tp_t(C-p_t)dt\quad\quad,

where

p_t = proportion of new forms,

pk_t = a function of time (can also be a constant),

C = limit of change,

t > 0, time,

and

dp_t = change in the proportion.


This means that the change of the proportion of new forms is proportional to the interaction of new and old forms. The solution yields three variants.


(a) Complete change if C = 1 and k_t = b is constant

(2) p=\frac{1}{1+ae^{-bt}},

where a is the integration constant. The result in (2) represents the so-called logistic curve used in different disciplines for modeling growth phenomena.

Example. Since years represent large numbers hindering the fitting, one usually transforms the time intervals in a time variable beginning with t = 1. Often, the cumulative frequencies are changed to cumulative proportions, or the proportions are ascertained from the occurrence of rival forms. Complete change: The replacement of –{t} by –{st} in German 2nd person singular indicative present tense of the verb “wollen”, shown by Best (2003a). The result of fitting is presented in Table 1 and Fig. 1. Here f_t is the relative frequency of –{st} and p_t is the computed relative frequency according to (2).


Figur11 CiL.jpg

The fitting is excellent. The curve was fitted to the proportion of –{st} found in the sources.


Grafik1 CiL.jpg
Fig. 1. The result presented in Table 1


(b) Partial change if k-t = b is constant, C is the asymptote

(3) p=\frac{C}{1+ae^{-bt}}

and a is the integration constant.

Example. Partial change: Borrowings from Latin in Hungarian. Beöthy and Altmann examined the borrowing from different langugages in Hungarian. The fate of Latin words is shown in Table 2 and Fig. 2. The fitting was performed for the cumulative values.

Figur22 CiL.jpg
Grafik2 CiL.jpg
Fig. 2. Fitting formula (3) to data in Table 2


(c) Reversible change if k_t = A - Bt, C = constant

(4) p_t=\frac{C}{1+ae^{-bt+ct^2}}

where a, b and c depend on A, B and C.

Example 3. Reversible change: Epithesis with strong verbs in German. Imsiepen (1983) observed that the epithesis of /e/ with strong verbs (1st and 3rd person sg. past tense) is a reversible process in German. Altmann (1983) has shown some estimation procedures for this curve, but since several observed values are very unreliable, Best, Beöthy and Altmann (1990) considered smoothed values (moving average of 7 values) and obtained the data in Table 3. They took the value of C into consideration and used formula (4).

Tabelle33 CiL.jpg

The fitting is very good.

Grafik4 CiL.jpg


4. Authors: U. Strauss, G. Altmann


5. References

Altmann, G. (1983a). Das Piotrowski-Gesetz und seine Verallgemeinerungen. In: Best, K.-H., Kohlhase, J. (Hrsg.), Exakte Sprachwandelforschung: 54-90. Göttingen: Herodot.

Altmann, G. (1985). On the Dynamic Approach to Language. In: Ballmer, T. T. (ed.), Linguistic Dynamics: 181-189. Berlin/ New York: de Gruyter.

Altmann, G. (1992). Piotrowski’s Law of Language Change. In: Saukkonen, P. (ed.), What is Language Synergetics? 34-35. Oulu: Acta Universitatis Ouluensis, Series B: Humaniora, 16.

Altmann, G., Bagheri, D., Goebl, H., Köhler, R., Prün, C. (2002). Einführung in die quantitative Lexikologie. Götingen: Peust & Gutschmidt.

Altmann, G., v. Buttlar, H., Rott, W., Strauß, U. (1983). A law of change in language. In: Brainerd, B. (ed.), Historical linguistics: 104-115. Bochum: Brockmeyer.

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