Computer simulations of language change notes

This website collects my personal notes on Computer simulations of language change. These notes are provided to bring full transparency to my research process. Of course, since they are only notes, they do not reflect my final thoughts on a topic, and should not be interpreted as such. To read finished papers, please consult my website. Do not use these notes as a basis for your own scientific research. Start from high-quality, peer-reviewed scientific literature instead.

Motives for language change

p. 54

Log(ist)ic and simplistic S-curves

David Denison

Introduction

topic at hand

why the S-curve?

p. 55

How change occurs

1. slow change

After the first occurrence, the curve slowly climbs through single-figure percentages until the innovation is being used on maybe 20–25 per cent of the available occasions.

2. speed-up

All the time its rate of increase is increasing – the curve is getting steeper – and after a while its progress is very rapid!

3. final increase (theoretically)

rate goes on increasing until the remaining pool of unchanged words is altogether used up

diffusion is possible like this, but it doesn’t work in this way

p. 56

4. final increase (realistically)

after the phase when the new form gains ascendancy rather rapidly, the process of change slows down again as the last remnants of the older state linger on

The whole thing can last hundreds of years altogether, indeed may never be wholly completed, but the bulk of the change is located within a much narrower slice of time where the slope is steeper.

p. 57

Examples of the passive progressive, which was first prevalent in its old form (a road was building), then suddenly received a new form (a road was being built). The new form became popular quickly, but the old form continued to exist for a while, though sporadically.

p. 58

Why an S-shaped curve?

Stages of the S-curve

1. innovation

change requires variation → the existence of an alternative way of saying (roughly) the same thing

There must be some sort of advantage for using the new form (be it structural or social).

At the same time, inertia and the need to communicate with older generations mean that the old form has a reason to continue to exist.

2. propagation

“the change proper gets going if the new form acquires a social value (Croft 2000: 185–6)”

Speakers reproduce approximately what they hear, including variation, and even apparently including the rough proportions of variant usage they hear around them.₃ However, if there is some slight advantage in the new form over the old, the proportions may adjust slightly in favour of the new.

₃ Labov talks of probability matching (1994: 580–6, also cf. 1994: 65–6, 595), an interesting concept which I cannot go into here.

form advantage

shakes up the status quo → frequencies not reproduced perfectly
speaker has made a slightly different choice

Explaining the shape

[The] effect of choice is greatest when the two variants are both there to choose from. In the very early stages of a change, so the argument runs, the new form is rare, so the pressures of choice are relatively weak and the rate of change is slow. In the late stages of a change, the old form is rare, so that the selective effect of having two forms to compare and choose between is again weak, and once again the rate of change is slow. Only in the middle period, when there are substantial numbers of each form in competition, does the rate of change speed up. Hence the S-curve.

Mathematics

logistic function

best mathematical model for modelling an S-curve

p. 59

The axes of the graph

Y-axis

traditional

⇒ percentage of all speech events in a language during a period (theoretically)
⇒ percentages or relevant linguistic contexts in a corpus

lexical diffusion

changes spread word by word through the relevant lexemes of a language
⇒ proportion of relevant words which have succumbed to a change at a given time

Words that are particularly salient, or maybe especially frequent or infrequent, or of a particular form, might resist the change for reasons which had not applied – or at least did not apply so strongly – to those words which had succumbed early on.

syntactic change

change through particular construction types
(difficult to graph, since constructions are, by definition, infinite)

p. 61

orderly heterogeneity

a strict free variation in the same speaker

p. 62

social network diffusion

Milroy & Milroy diffusion via weak and strong ties
percentage shows percentage of community using a particular form

X-axis

What to plot on the horizontal scale?

1. time of composition

you plot it when it is uttered / written

2. time of birth of the writer

you plot when the author was born

↳ depends on viewpoint: does language change during adulthood of speakers?

Syntactic illustrations

p. 65

Variables and variants

1. sound changes and S-curves

phonological level: possibility of continuous variation → no two competitors!
can be solved using feature analysis to a quantised, abstract interpretation

2. more than two choices

at any time, there are probably more than two competing forms

p. 66

3. completely new form

if a completely new form arises, there is no competition with anything

p. 67

Conflation of S-curves: the shape of English

p. 68

Concluding remark

The S-curve is neither as simple nor as uniform a phenomenon as is sometimes assumed. Given too the simplistic picture of variation it sometimes reflects (and requires), the S-curve should not be seized on too readily as the general shape of language change.

Computer simulations of language change notes