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Frontiers of Engineering Reports on Leading-Edge Engineering from the 2005 Symposium (2006) / Chapter Skim
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Population Dynamics of Human Language: A Complex System
Pages 89-98

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From page 89...
... The study of language and grammar dates back to classical India and Greece. In the eighteenth century, the discovery of the Indo-European language family led to the surprising realization that very different languages may be related to each other; this was the beginning of historical linguistics.
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From page 90...
... Various approaches to these questions have been suggested, including viewing language as a complex adaptive system (Steels, 2000)
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From page 91...
... Discovering properties of universal grammar and particular human learning algorithms requires the empirical study of neurobiological and cognitive functions of the human brain involved in language acquisition. Some aspects of universal grammar, however, might be revealed by studying common features of existing human languages.
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From page 92...
... The learner has a mechanism to evaluate input sentences and to choose one of the candidate grammars in his search space. A MATHEMATICAL FORMULATION OF LANGUAGE EVOLUTION Our approach differs from many others in that we use mathematical, analytical tools to address questions of language origins and evolution (Komarova and Nowak, 2001a,b, 2003; Komarova et al., 2001; Nowak and Komarova, 2001; Nowak et al., 2001, 2002)
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From page 93...
... Another biological concept based on the theory of Darwinian evolution is variability. The "mutation rates" are defined as follows: denote by Qij the probability that a child learning from a parent with grammar Gi will end up speaking grammar Gj.
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From page 94...
... . It was found that the low-coherence delocalized solution undergoes a transcritical bifurcation for the value Q = -Îwhere Î is the identity matrix defined by the entries of the matrix Â.
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From page 95...
... We have formulated a mathematical theory for the population dynamics of grammar acquisition. The key result here is a "coherence threshold" that relates the maximum complexity of the search space to the amount of linguistic input available to the learner and the performance of the learning procedure.
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From page 96...
... New York: Cambridge University Press. Batali, J
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From page 97...
... New York: Oxford University Press. Mitchener, W.G.
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Key Terms

  • human language
  • population dynamics
  • language acquisition
  • coherence threshold
  • complex adaptive

  • search space
  • language theory
  • language evolution
  • learning theory
  • cultural evolution

  • candidate grammars
  • language disorder
  • formal language
  • human languages
  • grammatical coherence

  • evolutionary biology
  • evolutionary dynamics
  • natural selection
  • learning algorithms
  • human brain

  • grammar acquisition
  • darwinian evolution
  • identity matrix
  • grammatical sentences
  • learning procedure

  • grammatical rules
  • restricted set
  • critical period
  • individual using
  • universality property


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