Applying chaos Applying chaos and complexity and complexity

theory to theory to language language

variation analysisvariation analysisNeil Wick, York University

Outline

New ways of looking at sociolinguistic data

Key concepts demonstrated with quantitative linguistic data

Non-linearity: small changes in initial conditions can have large effects

Complex boundaries between two stable states

Attractors: differing degrees of stability

The search for patterns is of fundamental importance, but what constitutes a pattern?

Chesterfield vs. Couch in the Golden Horseshoe

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A[]phalt in Quebec City by Age

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Chaos

Not “randomness” but the precursor to order

Sensitive dependence on initial conditions

Small changes produce big and non-linear outcomes

“the straw that broke the camel’s back”

Catastrophe

Cellular Automata

• Invented in the 1940’s• More manageable with computers• Conway’s Game of Life (1968)

– “Mathematical Games” column by Martin Gardner in Scientific American

– A cell dies with <2 or >3 neighbours– A cell with exactly 3 neighbours is

reborn

Stochastic algorithm

• In a dialect simulation, each cell tends to talk like its neighbours

• The more neighbours that differ from a given cell, the more likely it will adopt that variant

1 2 3

4 5

6 7 8

Thom’s 7 elementary catastrophes

• Thom’s classification theorem 1965

• All the structurally stable ways to change discontinuously with up to 4 control factors

• 2-dimensional to 6-dimensional

4 cuspoids

• Fold 1 control factor• Cusp 2 control factors• Swallowtail 3 control factors• Butterfly 4 control factors

The fold

The cusp

Hysteresis

Age Canada U.S.

14-19 64 33

20-29 297 31

30-39 166 2

40-49 151 2

50-59 106 5

60-69 37 5

70-79 36 2

over 80 78  

Grand Total 935 80

Age distribution in the Golden Horseshoe data

39: Athletic shoes runn- (vs. sneak-) 91% 0% 91%

43: Shone [a] (vs. [o]) 85% 2% 83%

5: Garden knob tap (vs. faucet) 89% 6% 83%

4: Sink knob tap (vs. faucet) 84% 5% 79%

58: Anti tee (vs. tie) 86% 16% 70%

8: Vase ause/ays (vs. ace) 76% 7% 69%

57: Semi me (vs. my) 89% 25% 64%

62: Z zed (vs. zee) 64% 5% 59%

6: Cloth for face facecloth (vs. washcloth) 66% 11% 55%

40: wants (to go) out out (vs. to go out) 61% 8% 53%

37: Asphalt has [sh] sh (vs. z) 80% 27% 53%

Question #/Desc. Canadian variant Can US Diff.

35: Lever [eaver] (vs. [ever]) 66% 16% 50%

39: "Exercise shoes" around the Golden Horseshoe

runners/running shoes

[sneakers]

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43: "Shone" around the Golden Horseshoe

1. John [ohn]

2. Joan [oan]

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5: "Garden knob" around the Golden Horseshoe

1.[tap]

2.[faucet]

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4: "Sink knob" around the Golden Horseshoe

1.[tap]

2.[faucet]

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58: "Anti" around the Golden Horseshoe

2. [tee]

1. [tie]

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8: "Vase" around the Golden Horseshoe

3.[ause]

2.[ays]

1.[ace]

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57: "Semi" around the Golden Horseshoe

2. [me]

1. [my]

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62: "Z" around the Golden Horseshoe

2. [zed]

1. [zee]

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6: "Face cloth" around the Golden Horseshoe

2.[face cloth]

1.[w ash cloth]

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40: "Cat wants (to go) out" around the GH

2. the cat w ants out.

1. The cat w ants to go out.

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37: "Asphalt has sh" around the Golden Horseshoe

1. yes [sh]

2. no [z]

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Canada/U.S. Shibboleths across the Niagara River

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l[i]ver

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Hysteresis on the Fold

Stability:

-Stable-Semi-stable-Unstable

4 regions included:

1991-92 Golden Horseshoe

1997 Ottawa Valley1994 Quebec City1998-99 Montreal

Divergence of a[]phalt in Ontario and Quebec

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Quebec English Ontario English

Polynomial trendline Polynomial trendline

Divergence of a[]phalt in Ontario and Quebec

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Quebec English Ontario English

Polynomial trendline Polynomial trendline

A[]phalt in Quebec City by Age

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A[]phalt in Quebec Province by LUI

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LUI>1 LUI<=1

A[sh]phalt in Quebec Province by Education

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sh

]Primary/Secondary Post-secondary

A[sh]phalt in Quebec Province by RI

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A[]phalt in Quebec Province by sex

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A[]phalt in Ontario and Quebec by LUI

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]Ont. LUI > 1 (Bilingual) Ont. LUI <= 1 (Anglophone)

Que. LUI > 1 (Bilingual) Que. LUI <=1 (Anglophone)

Ottawa Valley: Asphalt with [], Cat wants out

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es

asphalt with [sh] cat wants out.

Attractors

• Features tend to go towards stable positions called attractors

• Example: tongue heights of vowels

4 types of behaviour

• Sink – stable point, attracts nearby objects

• Source – unstable point, repels nearby objects

• Saddle – stable in one direction, unstable in the other

• Limit cycle – forms a closed loop

Saddle

Limit Cycle

Attracting type- Any point starting near the limit cycle will move towards it

Repelling type also exists- Nearby points will move away

Front rounding in English

Proto-Germanic no Pre-historic OE emerged

through i-umlautDuring OE period merged with During ME re-emergedLate southern ME lost againModern English increasingly

common

Canada/U.S. Shibboleths across the Niagara River

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wants out

a[sh]phalt

l[i]ver

Guarantee in Québec & Golden Horseshoe

50%

over 80

14-19

over 80

14-19QC

GH

100% care"