Towards a mathematical theory of meaningful communication

Meaning has been left outside most theoretical approaches to information in biology. Functional responses based on an appropriate interpretation of signals have been replaced by a probabilistic description of correlations between emitted and received symbols. This assumption leads to potential paradoxes, such as the presence of a maximum information associated to a channel that creates completely wrong interpretations of the signals. Game-theoretic models of language evolution and other studies considering embodied communicating agents show that the correct (meaningful) match resulting from agent-agent exchanges is always achieved and natural systems obviously solve the problem correctly. Inspired by the concept of duality of the communicative sign stated by the swiss linguist Ferdinand de Saussure, here we present a complete description of the minimal system necessary to measure the amount of information that is consistently decoded. Several consequences of our developments are investigated, such as the uselessness of a certain amount of information properly transmitted for communication among autonomous agents.We thank Kepa Ruiz-Mirazo, Álvaro Corral and the members of the CSL for useful discussions. This work was supported by the Fundación Botin, the Santa Fe Institute (R.V.S.), the Austrian Fonds zur Förderung der Wissenschaftlichen Forschung project “Quantifying socioeconomic multiplex networks in a massive multiplayer online game” KPP23378FW (B.C.-M.) and the Secretary for Universities and Research of the Ministry of Economy and Knowledge of the Government of Catalonia and the Cofund programme of the Marie Curie Actions of the 7th R&D Framework Programme of the European Union, and the research projects 2009SGR1079, FFI201123356 (J.F.)