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Crazy Rules

Crazy Rules. Self-Organization and Chaotic behaviour in a Deterministic System. Is language just a dialect with an army? Icelandic: tak a heið i aug u. Speaker population and sounds. p (2 tailed) = 0.014. Archaic dialects in the Swiss Alps snîd a n ‘to cut’ heft a n ‘to attatch’

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Crazy Rules

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  1. Crazy Rules: Self-Organization and Chaos Theory Crazy Rules Self-Organization and Chaotic behaviour in a Deterministic System

  2. Crazy Rules: Self-Organization and Chaos Theory Is language just a dialect with an army?Icelandic:takaheiðiaugu

  3. Crazy Rules: Self-Organization and Chaos Theory Speaker population and sounds p (2 tailed) = 0.014

  4. 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

  5. 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: “twodogs”)

  6. 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”

  7. Crazy Rules: Self-Organization and Chaos Theory The working of the bidirectional table:Middle Frisian hab, habbe & habba

  8. Crazy Rules: Self-Organization and Chaos Theory Stability and Instability • 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

  9. Crazy Rules: Self-Organization and Chaos Theory Balancing PowersGeneral phonetic centralization tendency 31% /e/ /u/ 28% [ə] 9% 10% Distributional proportions based on Old English text Noise levels based on modern vowel duration contrast 8% /a/ 41%

  10. Crazy Rules: Self-Organization and Chaos Theory ..\Language Fractal\modelcalc.xls ..\Proefskrift\Afr-a\matrixcalcul.xls

  11. Crazy Rules: Self-Organization and Chaos Theory /e/ and the equilibrium The equilibrium is only preserved in a narrow strip in the proportion – noise area! /e/ > /ə / equil. /a/ > /ə /

  12. Crazy Rules: Self-Organization and Chaos Theory /a/ and the equilibrium The threshold of /u/ > /ə/ shows CHAOTIC behaviour! /a/ > /ə / equil. /u/>/ə /

  13. 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 nx = number of observations with x nt = total number of observations nx/nt = p ≈ P

  14. 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

  15. Crazy Rules: Self-Organization and Chaos Theory Chance and resolution (III) drunkards walk.xlsx

  16. Crazy Rules: Self-Organization and Chaos Theory Consequences for system stability /a/ > /ə / /a/ > /ə / equil. equil. /u/>/ə / /u/>/ə /

  17. 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 / equil. /u/>/ə /

  18. 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

  19. Crazy Rules: Self-Organization and Chaos Theory Tank foar jo omtinken! Arjen Versloot UvA/Fryske Akademy: aversloot@fryske-akademy.nl http://www.fryske-akademy.nl/Members/arjen/arjen-p-versloot Frisian Language Database: www.fryske-akademy.nl/tdb

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