Change in language

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).

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

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.

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).

The fitting is very good.

4. Authors: U. Strauss, G. Altmann

5. References

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