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 Complex boundaries between two stable states Attractors: differing degrees of stability

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

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 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

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 Fold1 control factor Cusp2 control factors Swallowtail3 control factors Butterfly4 control factors

The fold

The cusp

Hysteresis

AgeCanadaU.S over 8078 Grand Total93580 Age distribution in the Golden Horseshoe data

39: Athletic shoesrunn- (vs. sneak-)91%0%91% 43: Shone[a] (vs. [o])85%2%83% 5: Garden knobtap (vs. faucet)89%6%83% 4: Sink knobtap (vs. faucet)84%5%79% 58: Antitee (vs. tie)86%16%70% 8: Vaseause/ays (vs. ace)76%7%69% 57: Semime (vs. my)89%25%64% 62: Zzed (vs. zee)64%5%59% 6: Cloth for facefacecloth (vs. washcloth)66%11%55% 40: wants (to go) outout (vs. to go out)61%8%53% 37: Asphalt has [sh]sh (vs. z)80%27%53% Question #/Desc.Canadian variantCan US Diff. 35: Lever[eaver] (vs. [ever])66%16%50%

Hysteresis on the Fold

Stability: -Stable -Semi-stable -Unstable

4 regions included: Golden Horseshoe 1997Ottawa Valley 1994Quebec City Montreal

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-Germanicno /y,  / Pre-historic OE /y,  / emerged through i-umlaut During OE periodmerged with /i, e/ During MEre-emerged Late southern MElost again Modern Englishincreasingly common