Colloquium Nijmegen, May 24, Arjen P. Versloot Crazy Rules: Self-Organization and Chaos Theory Crazy Rules Self-Organization and Chaotic behaviour in a Deterministic System

Colloquium Nijmegen, May 24, Arjen P. Versloot Crazy Rules: Self-Organization and Chaos Theory Is language just a dialect with an army? Icelandic: taka heiði augu

Colloquium Nijmegen, May 24, Arjen P. Versloot Crazy Rules: Self-Organization and Chaos Theory Speaker population and sounds p (2 tailed) = 0.014

Colloquium Nijmegen, May 24, Arjen P. Versloot Crazy Rules: Self-Organization and Chaos Theory Archaic dialects in the Swiss Alps snîdan‘to cut’ heftan‘to attatch’ machôn‘to make’ losên‘to losen’..\..\..\..\All Users\Bureaublad\ILWIS 3.3 Academic.lnk CH.xlsx

Colloquium Nijmegen, May 24, Arjen P. Versloot Crazy Rules: Self-Organization and Chaos Theory Components of Human Language Data Storage and retrieval in the brain (Neural Darwinism ⇒ Frequencies) Acoustics Semantics (from idiosyncratic to systematic: “two dogs”)

Colloquium Nijmegen, May 24, Arjen P. Versloot Crazy Rules: Self-Organization and Chaos Theory The Bidirectional Table Speakers are probabilistic learners, guided by: –Memory and Common Practice –Perceptual Reliability / Avoiding Semantic Biases Large scale individual behaviour can be modelled with stochastic approximations  “Ideal Speaker”

Colloquium Nijmegen, May 24, Arjen P. Versloot Crazy Rules: Self-Organization and Chaos Theory The working of the bidirectional table: Middle Frisian hab, habbe & habba Middle Frisian hab, habbe & habba ‘to have’, ø production sg %37%2% inf 01390%3%97% 100%97%5% 61% (63%)36% (37%)0% 3%95% 0% 93% (100%) perception

Colloquium Nijmegen, May 24, Arjen P. Versloot Crazy Rules: Self-Organization and Chaos Theory If language is deterministic and developing towards equilibria: where do the changes come from? Example: Old English: -3 vowel system in unstressed syllables -Stable for 200 years, followed by change -Learning not based on unlimited dataset Stability and Instability

Colloquium Nijmegen, May 24, Arjen P. Versloot Crazy Rules: Self-Organization and Chaos Theory Balancing Powers General phonetic centralization tendency /u/ 28% /a/ 41% [ə][ə] 31% /e/ 10% 8% 9% Distributional proportions based on Old English text Noise levels based on modern vowel duration contrast Equilibrium/a//e//u/ Full85%87%86% Schwa15%13%14%

Colloquium Nijmegen, May 24, Arjen P. Versloot Crazy Rules: Self-Organization and Chaos Theory..\Language Fractal\modelcalc.xls..\Proefskrift\Afr-a\matrixcalcul.xls

Colloquium Nijmegen, May 24, Arjen P. Versloot Crazy Rules: Self-Organization and Chaos Theory /e/ and the equilibrium /e/ > / ə / /a/ > / ə / equil. The equilibrium is only preserved in a narrow strip in the proportion – noise area!

Colloquium Nijmegen, May 24, Arjen P. Versloot Crazy Rules: Self-Organization and Chaos Theory /a/ and the equilibrium /a/ > / ə / /u/>/ ə / equil. The threshold of /u/ > / ə / shows CHAOTIC behaviour!

Colloquium Nijmegen, May 24, Arjen P. Versloot Crazy Rules: Self-Organization and Chaos Theory Chance and resolution (I) Large scale individual behaviour can be modelled with stochastic behaviour Only true for sample size (n) ⇒ ∞ p = observed proportion for phenomenon x P = statistical chance for x to appear n x = number of observations with x n t = total number of observations n x /n t = p ≈ P

Colloquium Nijmegen, May 24, Arjen P. Versloot Crazy Rules: Self-Organization and Chaos Theory Chance and resolution (II) Throw a die 10 times Chance for ‘6’ = 1/6 1/6 * 10 = 1,67 ‘best match’ = 2 times ‘6’ (2-1,67)/1,67 = 20% deviation

Colloquium Nijmegen, May 24, Arjen P. Versloot Crazy Rules: Self-Organization and Chaos Theory Chance and resolution (III) drunkards walk.xlsx

Colloquium Nijmegen, May 24, Arjen P. Versloot Crazy Rules: Self-Organization and Chaos Theory Consequences for system stability /a/ > / ə / /u/>/ ə / equil. /a/ > / ə / /u/>/ ə / equil.

Colloquium Nijmegen, May 24, Arjen P. Versloot Crazy Rules: Self-Organization and Chaos Theory Consequences for system stability Smaller sample sets broaden the equilibrium zone: robust for chance variation. Smaller sample sets increase unpredictable threshold behaviour: chaotic character. /a/ > / ə / /u/>/ ə / equil.

Colloquium Nijmegen, May 24, Arjen P. Versloot Crazy Rules: Self-Organization and Chaos Theory Conclusion The Bidirectional Table models the interaction of memory (frequency), acoustics (noise levels) and semantics (functional contrasts) It predicts and explains e.g.: stability of sound or lexical contrasts structural differences depending on population size both equilibrium situations and chaotic disturbances

Tank foar jo omtinken! Arjen Versloot UvA/Fryske Akademy: Frisian Language Database: Colloquium Nijmegen, May 24, Arjen P. Versloot Crazy Rules: Self-Organization and Chaos Theory