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Emergence of Zipf’s law in the evolution of communication

Bernat Corominas-Murtra1,4, Jordi Fortuny2, and Ricard V. Solé3,4

  • 1ICREA-Complex Systems Lab, Universitat Pompeu Fabra -Parc de Recerca Biomèdica de Barcelona (PRBB). Dr Aiguader 88, E-08003 Barcelona, Spain
  • 2Centre de Lingüística Teòrica (CLT), Facultat de Lletres, Edifici B, Universitat Autònoma de Barcelona, E-08193 Bellaterra (Barcelona), Spain
  • 3Santa Fe Institute, 1399 Hyde Park Road, New Mexico 87501, USA
  • 4Institut de Biologia Evolutiva. CSIC-UPF. Passeig Marítim de la Barceloneta, 37-49, E-08003 Barcelona, Spain

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Phys. Rev. E 83, 036115 – Published 28 March, 2011

DOI: https://doi.org/10.1103/PhysRevE.83.036115

Abstract

Zipf’s law seems to be ubiquitous in human languages and appears to be a universal property of complex communicating systems. Following the early proposal made by Zipf concerning the presence of a tension between the efforts of speaker and hearer in a communication system, we introduce evolution by means of a variational approach to the problem based on Kullback’s Minimum Discrimination of Information Principle. Therefore, using a formalism fully embedded in the framework of information theory, we demonstrate that Zipf’s law is the only expected outcome of an evolving communicative system under a rigorous definition of the communicative tension described by Zipf.

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References (25)

  1. F. Auerbach, Patermanns Geographische Mitteilungen 59, 74 (1913).
  2. G. K. Zipf, The Psycho-Biology of Language (Routledge, London, 1936).
  3. G. K. Zipf, Human Behavior and the Principle of Least Effort (Addison-Wesley, Reading, 1949).
  4. P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987).
  5. X. Gabaix, The Quarterly Journal of Economics 114, 739 (1999).
  6. M. E. J. Newman, Contemp. Phys. 46, (2005).
  7. V. Pareto, Cours d’Economie Politique (Droz, Geneva, 1896).
  8. H. A. Simon, Biometrika 42, 425 (1955).
  9. W. Li, IEEE Trans. Inf. Theory 38, 1842 (1992).
  10. P. Harremoës and F. Topsœ, Entropy 3, 191 (2001).
  11. R. Ferrer-i-Cancho and R. V. Solé, Proc. Natl. Acad. Sci. USA 100, 788 (2003).
  12. B. Corominas-Murtra and R. V. Solé, Phys. Rev. E 82, 011102 (2010).
  13. P. Vogt, in I. J. Pollack, M. Bedau, P. Husbands, T. Ikegami, and R. A. WatsonArtificial Life IX Proceedings of the Ninth International Conference on the Simulation and Synthesis of Living Systems, edited by (MIT Press, Cambridge, 2004).
  14. T. Maillart, D. Sornette, S. Spaeth, and G. von Krogh, Phys. Rev. Lett. 101, 218701 (2008).
  15. S. N. Dorogovtsev and J. F. F. Mendes, Evolution of Networks (Oxford University Press, New York, 2003).
  16. E. T. Jaynes, Phys. Rev. 106, 620 (1957).
  17. S. Kullback, Information Theory and Statistics (John Wiley and Sons, New York, 1959).
  18. A. R. Plastino, H. G. Miller, and A. Plastino, Phys. Rev. E 56, 3927 (1997).
  19. J. Hurford, Lingua 77, 187 (1989).
  20. M. A. Nowak and D. Krakauer, Proc. Nat. Acad. Sci. USA 96, 8028 (1999).
  21. N. L. Komarova and P. Niyogi, Art. Int. 154, 1 (2004).
  22. T. M. Cover and J. A. Thomas, Elements of Information Theory (John Wiley and Sons, New York, 1991).
  23. M. Abramowitz and S. I. (editors), Handbook of Mathematical Functions, Vol. 55 of NBS, Appl. Math. Ser. (US Government Printing office, Washington, D. C., 1965).
  24. I. Kanter and D. A. Kessler, Phys. Rev. Lett. 74, 4559 (1995).
  25. D. Avnir, O. Biham, D. Lidar, and O. Malcai, Science 279, 39 (1998).

Outline

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Phys. Rev. E 83, 036115– Published 28 March, 2011
  • Received 30 July 2010

©2011 American Physical Society

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