Applying chaos and complexity theory to language variation analysis

2. Applying chaos and complexity theory to language variation analysis Neil Wick, York University

3. 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

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

7. Chaos Not “randomness” but the precursor to order Sensitive dependence on initial conditions Catastrophe Small changes produce big and non-linear outcomes “the straw that broke the camel’s back”

8. 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

9. 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

11. 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

12. 4 cuspoids • Fold 1 control factor • Cusp 2 control factors • Swallowtail 3 control factors • Butterfly 4 control factors

13. The fold

14. The cusp

15. Hysteresis

17. 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

18. Question #/Desc. Canadian variant Can US Diff. 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% 35: Lever [eaver] (vs. [ever]) 66% 16% 50%

32. Hysteresis on the Fold

33. Stability: Stable Semi-stable Unstable

34. 4 regions included: 1991-92 Golden Horseshoe 1997 Ottawa Valley 1994 Quebec City 1998-99 Montreal

49. Attractors • Features tend to go towards stable positions called attractors • Example: tongue heights of vowels

50. 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