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

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:takaheiðiaugu

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 & habbaMiddle Frisian hab, habbe & habba ‘to have’, 1430-1460

ø <e> <a> production

sg 50 30 2 61% 37% 2%

inf 0 1 39 0% 3% 97%

  100% 97% 5%61%

(63%)36%

(37%) 0%

  0% 3% 95% 0% 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 PowersGeneral phonetic centralization tendency

/u/ 28%

/a/ 41%

[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/

Full 85% 87%

86%

Schwa 15% 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.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.equil.

The threshold of /u/ > /ə/ showsCHAOTICbehaviour!

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 xP = statistical chance for x to appearnx = number of observations with x

nt = total number of observations

nx/nt = 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.equil.

/a/ > /ə /

/u/>/ə /

equil.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.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 VerslootUvA/Fryske Akademy: aversloot@fryske-akademy.nlhttp://www.fryske-akademy.nl/Members/arjen/arjen-p-versloot

Frisian Language Database: www.fryske-akademy.nl/tdb

Colloquium Nijmegen, May 24, Arjen P. Versloot

Crazy Rules: Self-Organization and Chaos Theory