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Decoding least effort and scaling in signal frequency distributions

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  • Ferrer i Cancho, Ramon

Abstract

Here, assuming a general communication model where objects map to signals, a power function for the distribution of signal frequencies is derived. The model relies on the satisfaction of the receiver (hearer) communicative needs when the entropy of the number of objects per signal is maximized. Evidence of power distributions in a linguistic context (some of them with exponents clearly different from the typical β≈2 of Zipf's law) is reviewed and expanded. We support the view that Zipf's law reflects some sort of optimization but following a novel realistic approach where signals (e.g. words) are used according to the objects (e.g. meanings) they are linked to. Our results strongly suggest that many systems in nature use non-trivial strategies for easing the interpretation of a signal. Interestingly, constraining just the number of interpretations of signals does not lead to scaling.

Suggested Citation

  • Ferrer i Cancho, Ramon, 2005. "Decoding least effort and scaling in signal frequency distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 345(1), pages 275-284.
    • Handle: RePEc:eee:phsmap:v:345:y:2005:i:1:p:275-284
    DOI: 10.1016/j.physa.2004.06.158
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    1. Pietronero, L. & Tosatti, E. & Tosatti, V. & Vespignani, A., 2001. "Explaining the uneven distribution of numbers in nature: the laws of Benford and Zipf," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 293(1), pages 297-304.
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