Colloquium Nijmegen, May 24, Arjen P. Versloot Crazy Rules: Self-Organization and Chaos Theory Crazy...
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Transcript of Colloquium Nijmegen, May 24, Arjen P. Versloot Crazy Rules: Self-Organization and Chaos Theory Crazy...
![Page 1: Colloquium Nijmegen, May 24, Arjen P. Versloot Crazy Rules: Self-Organization and Chaos Theory Crazy Rules Self-Organization and Chaotic behaviour in a.](https://reader030.fdocuments.us/reader030/viewer/2022032707/56649e555503460f94b4d08e/html5/thumbnails/1.jpg)
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
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Colloquium Nijmegen, May 24, Arjen P. Versloot
Crazy Rules: Self-Organization and Chaos Theory
Is language just a dialect with an army?
Icelandic:takaheiðiaugu
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Colloquium Nijmegen, May 24, Arjen P. Versloot
Crazy Rules: Self-Organization and Chaos Theory
Speaker population and sounds
p (2 tailed) = 0.014
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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
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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”)
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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”
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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
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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
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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%
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Colloquium Nijmegen, May 24, Arjen P. Versloot
Crazy Rules: Self-Organization and Chaos Theory
..\Language Fractal\modelcalc.xls
..\Proefskrift\Afr-a\matrixcalcul.xls
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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!
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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!
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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
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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
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Colloquium Nijmegen, May 24, Arjen P. Versloot
Crazy Rules: Self-Organization and Chaos Theory
Chance and resolution (III)
drunkards walk.xlsx
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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.
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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.
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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
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Tank foar jo omtinken!
Arjen VerslootUvA/Fryske Akademy: [email protected]://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