applying chaos and complexity theory to language variation analysis
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Applying chaos and complexity theory to language variation analysis. Neil 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 - PowerPoint PPT PresentationTRANSCRIPT
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Applying chaos Applying chaos and complexity and complexity
theory to theory to language language
variation analysisvariation analysisNeil Wick, York University
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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
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The search for patterns is of fundamental importance, but what constitutes a pattern?
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Chesterfield vs. Couch in the Golden Horseshoe
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over 80 70-79 60-69 50-59 40-49 30-39 20-29 14-19
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A[]phalt in Quebec City by Age
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Age (apparent time)
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Quebec City
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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
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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
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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
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1 2 3
4 5
6 7 8
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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
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4 cuspoids
• Fold 1 control factor• Cusp 2 control factors• Swallowtail 3 control factors• Butterfly 4 control factors
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The fold
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The cusp
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Hysteresis
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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
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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%
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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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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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E5 E4 E3 E2 E1 S1 S2 S3 S4 S5 NY1 NY2
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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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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
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Canada/U.S. Shibboleths averaged
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Hysteresis on the Fold
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Stability:
-Stable-Semi-stable-Unstable
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4 regions included:
1991-92 Golden Horseshoe
1997 Ottawa Valley1994 Quebec City1998-99 Montreal
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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
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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
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A[]phalt in Quebec City by Age
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40%
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60%
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100%
70+ 60-69 50-59 40-49 30-39 20-29 14-19
Age (apparent time)
% [ ]
Quebec City
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A[]phalt in Quebec Province by LUI
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70+ 60-69 50-59 40-49 30-39 20-29 14-19
Age (apparent time)
% [ ]
LUI>1 LUI<=1
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A[sh]phalt in Quebec Province by Education
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70+ 60-69 50-59 40-49 30-39 20-29 14-19
Age (apparent time)
% [
sh
]Primary/Secondary Post-secondary
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A[sh]phalt in Quebec Province by RI
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40%
50%
60%
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70+ 60-69 50-59 40-49 30-39 20-29 14-19
Age (apparent time)
% [
sh
]RI <= 2 RI > 2
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A[]phalt in Quebec Province by sex
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40%
50%
60%
70%
80%
90%
100%
70+ 60-69 50-59 40-49 30-39 20-29 14-19
Age (apparent time)
% [ ]
Male Female
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A[]phalt in Ontario and Quebec by LUI
0%
20%
40%
60%
80%
100%
70+ 60-69 50-59 40-49 30-39 20-29 14-19
Age (apparent time)
% [
]Ont. LUI > 1 (Bilingual) Ont. LUI <= 1 (Anglophone)
Que. LUI > 1 (Bilingual) Que. LUI <=1 (Anglophone)
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Ottawa Valley: Asphalt with [], Cat wants out
0%
20%
40%
60%
80%
100%
70+ 60-69 50-59 40-49 30-39 20-29 14-19
Age (apparent time)
% y
es
asphalt with [sh] cat wants out.
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Attractors
• Features tend to go towards stable positions called attractors
• Example: tongue heights of vowels
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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
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Saddle
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Limit Cycle
Attracting type- Any point starting near the limit cycle will move towards it
Repelling type also exists- Nearby points will move away
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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
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Canada/U.S. Shibboleths across the Niagara River
0%
10%
20%
30%
40%
50%
60%
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90%
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
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Guarantee in Québec & Golden Horseshoe
50%
over 80
14-19
over 80
14-19QC
GH
100% care"
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