The S-Shaped Curve
It goes without saying that language change in real time can best be traced by using corpora that cover a long timespan. In a way, it is a paradox that we have learnt a great deal about language change from sociolinguists, who have not had access to historical data. The first chapters of Labov (1994) raise many issues concerning the character of historical linguistics and, nevertheless, the time depth in the real-time replications in that book hardly exceeds 20 years, a period which in our research is regarded as the basic unit of contemporaneous writing. Differences like this are indicative of the divergent perspectives between the sociolinguistic research into the present-day spoken idiom and the study of past language forms. The latter inevitably focuses on general trends and large-scale developments instead of minute details. However, this does not exclude micro-level observations on the linguistic behaviour of individuals who lived long ago.
An important sociolinguistic contribution to the description of the time course of language change is the S-shaped curve. This model, borrowed from studies of the diffusion of innovations among populations (e.g. Cooper 1982), has become a stock-in-trade for sociolinguists describing the spread of linguistic innovations. It refers to a pattern with a slow initial spread, a rapid middle stage and a slower final phase (Figure 4.1). According to Labov (1994: 65-66), the motivation for this process lies in the frequency of contact between users of the new and the old forms and the subsequent adoption of the new form. At the beginning of the change, those who use the old form are rarely exposed to the innovation, and so only a small amount of transfer takes place. The rate of change is greatest at midpoint, when contact between the speakers is greatest. According to Labov (1994: 66), the nature of linguistic change explains the slow last phase. There is only a slight pressure to change, which leads to a slight shift at each speech contact. The rate of change falls, since the number of speech events where the shift can occur diminishes. We must not forget that there may be linguistic environments that resist a given change and hence slow down its operation in the final stages.
Figure 4.1. The S-shaped curve.
Figure 4.1 gives the abstract shape of the S-curve generated from the cumulative frequencies of the binomial distribution, and, as Labov (1994: 65) mentions, there are other functions which produce curves of this shape. We have found it sufficient for our purposes to use S-curves based on raw data without further mathematical elaboration.
The idea of the S-curve has been developed by Aitchison (1981: 100), who introduces a model of successive overlapping small S-curves, which form a cumulative S-shaped curve (Figure 4.2). Her model is especially suited to the description of changes that proceed from one linguistic environment to another in a regular manner. Owing to our focus on the nonlinguistic constraints, we mainly discuss the cumulative curves, but the existence of the overlapping S-curves can be assumed for most changes.1
Although there may be diverging opinions about the mechanism that lies behind the functioning of the S-shaped curve and especially its slow tailing off (e.g. Denison 2003), we find the concept a useful descriptive tool. It seems to us that, in addition to the frequency of contacts, accommodation theory and audience design might provide explanations for its operation (see Chapters 3, 9 and 10).2
Furthermore, we have found it useful to divide ongoing changes into five stages, covering different areas on the slope of the S-curve. In Labov's system (1994: 67, 79- 83), these stages include incipient, new and vigorous, mid-range, nearly completed and completed phases. We have applied the following classification in terms of the proportion of incoming forms:
Figure 4.2. Overlapping S-curves (after Aitchison 1981: 100).
Incipient below 15 per cent
New and vigorous between 15 and 35 per cent
Mid-range between 36 and 65 per cent
Nearing completion between 66 and 85 per cent
Completed over 85 per cent
Sociolinguists have introduced two ways of carrying out real-time studies (Labov 1994: 76-77). Trend study replicates an earlier study with the same population and the same methodology in sampling and analysis. It is, however, unlikely that the same individuals would be interviewed in both studies. In order to obtain reliable results on language change, the researcher should make sure that the community has remained unchanged between the two studies. Panel study, on the other hand, means that the same individuals whose language has been studied are located at a later date, and a new study is carried out.
Our model resembles trend study, since we use a socially representative corpus from successive periods. The condition that the community should remain unchanged is, however, inapplicable to historical linguistics. As pointed out in Chapter 3, societies inevitably change in the long run. The only way of tackling this question is through qualitative interpretation. Social change has to be analysed and assessed at the same time as language change is reported.
Some CEEC informants have provided letters from several decades with the consequence that their material has been divided between different subperiods. In this way these people's input complies with the idea of panel study, the same individuals contributing research data for successive periods.