I just read with peculiar attention the seventh chapter of Complexity: A Guided Tour, by Melanie Mitchell (Defining and measuring complexity, pages 94 to 111). She works with the Santa Fe Institute which is a major institution regarding research on complex systems. She gives a convincing outlook of this field. Still, I did not read anything on the question of language as a complex adaptive system, although there are researchers who focus on this topic (e.g. in Santa Fe).

According to her, there are different sciences of complexity with different notions of what complexity means. The notion of complexity is itself complex. She chooses to refer to three questions coined by Seth Lloyd in 2001 to approach the complexity of a system:

  1. How hard is it to describe ?
  2. How hard is it to create ?
  3. What is its degree of organization ?

Then she details a few definitions which can be seen as sides of the problem. Beginning with a selection from a larger list by Seth Lloyd, she tries to explain where or if these approaches are used. Thus, according to her, these are possible definitions of complexity:

  • Size
  • Entropy
  • Algorithmic information content – Murray Gell-Mann speaks of « effective complexity »
  • Logical depth (a theory by Charles Bennett). She mentions there is no practical way of using it
  • Thermodynamic depth, a similar definition. It states that more complex objects are harder to construct, but requires to list all the events of an evolution
  • Computational capacity (Stephen Wolfram), but she writes this is rarely a good measure of complexity.
  • Statistical complexity (Jim Crutchfield & Karl Young). The minimum amount of information to optimally predict the behaviour of a system (Peter Grassberger speaks of « effective measure complexity »).
  • Fractal dimension
  • Degree of hierarchy (Herbert Simon), based on the ideas of subsystems, hierarchy and near-decomposibility

This classification provides an interesting outlook of research on complex systems but only a few approaches could be used to tackle the issue of linguistic complexity, that might be the reason why Mitchell does not mention studies about language.

Here are a few quoted works (which I am currently reading, I may write a review on them later): - M. Mitchell, Complexity: A Guided Tour, Oxford, New York: Oxford University Press, 2009. - S. Lloyd, “Measures of Complexity : a non-exhaustive list”, Department of Mechanical Engineering, Massachusetts Institute of Technology, 2001. - M. Gell-Mann, “What is complexity ?”, Complexity, vol. 1, iss. 1, 1995. - H. A. Simon, “The Architecture of Complexity”, Proceedings of the American Philosophical Society, vol. 106, iss. 6, pp. 467-482, 1962.