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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Quebec City
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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E5 E4 E3 E2 E1 S1 S2 S3 S4 S5 NY1 NY2
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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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E5 E4 E3 E2 E1 S1 S2 S3 S4 S5 NY1 NY2
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8: "Vase" around the Golden Horseshoe
3.[ause]
2.[ays]
1.[ace]
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E5 E4 E3 E2 E1 S1 S2 S3 S4 S5 NY1 NY2
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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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E5 E4 E3 E2 E1 S1 S2 S3 S4 S5 NY1 NY2
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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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E5 E4 E3 E2 E1 S1 S2 S3 S4 S5 NY1 NY2
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%
37: "Asphalt has sh" around the Golden Horseshoe
1. yes [sh]
2. no [z]
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E5 E4 E3 E2 E1 S1 S2 S3 S4 S5 NY1 NY2
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Canada/U.S. Shibboleths across the Niagara River
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% o
f in
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an
ts a
ge
d 1
4-2
9
runn-
sh[a]ne
tap
ant[i]
va[z]e
sem[i]
zed
facecloth
wants out
a[sh]phalt
l[i]ver
Canada/U.S. Shibboleths averaged
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Region
% o
f in
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an
ts a
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d 1
4-2
9
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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over 80 70-79 60-69 50-59 40-49 30-39 20-29 14-19
Age (apparent time)
%
Quebec English Ontario English
Polynomial trendline Polynomial trendline
Divergence of a[]phalt in Ontario and Quebec
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over 80 70-79 60-69 50-59 40-49 30-39 20-29 14-19
Age (apparent time)
%
Quebec English Ontario English
Polynomial trendline Polynomial trendline
A[]phalt in Quebec City by Age
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Quebec City
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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sh
]RI <= 2 RI > 2
A[]phalt in Quebec Province by sex
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Male Female
A[]phalt in Ontario and Quebec by LUI
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70+ 60-69 50-59 40-49 30-39 20-29 14-19
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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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70+ 60-69 50-59 40-49 30-39 20-29 14-19
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% y
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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100%
E5 E3 E1 S2 S4 NY1
Region
% o
f in
form
an
ts a
ge
d 1
4-2
9
runn-
sh[a]ne
tap
ant[i]
va[z]e
sem[i]
zed
facecloth
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"
