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Chaos and language.

W Garrett Mitchener¹, Martin A Nowak

¹Institute for Advanced Study, Princeton University, New Jersey, USA. wgm@math.duke.edu

Proceedings. Biological Sciences

|June 24, 2004

Summary

This summary is machine-generated.

Mathematical models reveal that language evolution can exhibit unpredictable, chaotic changes over time. This complexity arises from game dynamics and learning, mirroring real-world language shifts.

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Area of Science:

Linguistics
Mathematical Biology
Evolutionary Game Theory

Background:

Human language is a complex system with vast expressibility.
Children acquire native languages through exposure.
Languages evolve unpredictably over historical timescales.

Purpose of the Study:

To investigate the mathematical modeling of language acquisition and evolution.
To demonstrate complex dynamics in language evolution models.
To explore the role of learning in language change.

Main Methods:

Utilizing game dynamical equations with learning.
Analyzing simple examples of these equations.
Applying concepts from evolutionary game theory.

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Main Results:

Simple language dynamical equations can exhibit complex limit cycles and chaos.
These models effectively mimic unpredictable language changes.
Imperfect learning can lead to chaotic switching between equilibria.

Conclusions:

Mathematical models based on game dynamics can capture the complexity of language evolution.
Chaotic dynamics are a potential feature of language change.
Learning mechanisms significantly influence the evolutionary trajectory of languages.