The global minima of the communicative energy of natural communication systems

Until recently, models of communication have explicitly or implicitly assumed that the goal of a communication system is just maximizing the information transfer between signals and 'meanings'. Recently, it has been argued that a natural communication system not only has to maximize this quantity but also has to minimize the entropy of signals, which is a measure of the cognitive cost of using a word. The interplay between these two factors, i.e. maximization of the information transfer and minimization of the entropy, has been addressed previously using a Monte Carlo minimization procedure at zero temperature. Here we derive analytically the globally optimal communication systems that result from the interaction between these factors. We discuss the implications of our results for previous studies within this framework. In particular we prove that the emergence of Zipf's law using a Monte Carlo technique at zero temperature in previous studies indicates that the system had not reached the global optimum.

[1]  Claude E. Shannon,et al.  The mathematical theory of communication , 1950 .

[2]  George Kingsley Zipf,et al.  Human Behaviour and the Principle of Least Effort: an Introduction to Human Ecology , 2012 .

[3]  L. Goddard.  Information Theory , 1962, Nature.

[4]  A Wingfield,et al.  Response Latencies in Naming Objects , 1965, The Quarterly journal of experimental psychology.

[5]  R. Kirk.  CONVENTION: A PHILOSOPHICAL STUDY , 1970 .

[6]  Adrian Akmajian,et al.  Linguistics: An Introduction to Language and Communication , 1979 .

[7]  W. Strange.  Evolution of language. , 1984, JAMA.

[8]  James R. Hurford,et al.  Biological evolution of the Saussurean sign as a component of the language acquisition device , 1989 .

[9]  J. Mullennix,et al.  Word familiarity and frequency in visual and auditory word recognition. , 1990, Journal of experimental psychology. Learning, memory, and cognition.

[10]  Alan S. Brown,et al.  A review of the tip-of-the-tongue experience. , 1991, Psychological bulletin.

[11]  LAURANCE R. DOYLE,et al.  Quantitative tools for comparing animal communication systems: information theory applied to bottlenose dolphin whistle repertoires , 1999, Animal Behaviour.

[12]  M A Nowak,et al.  An error limit for the evolution of language , 1999, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[13]  M A Nowak,et al.  Evolutionary biology of language. , 2000, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[14]  Martin A. Nowak,et al.  The evolution of syntactic communication , 2000, Nature.

[15]  Martin A. Nowak,et al.  Major Transitions in Language Evolution , 2001, Entropy.

[16]  M A Nowak,et al.  The evolutionary dynamics of the lexical matrix , 2001, Bulletin of mathematical biology.

[17]  R. Shillcock,et al.  Rethinking the Word Frequency Effect: The Neglected Role of Distributional Information in Lexical Processing , 2001, Language and speech.

[18]  F. Pulvermüller.  Brain reflections of words and their meaning , 2001, Trends in Cognitive Sciences.

[19]  Luc Steels,et al.  Language games for autonomous robots , 2001 .

[20]  S. Hanser,et al.  Using information theory to assess the diversity, complexity, and development of communicative repertoires. , 2002, Journal of comparative psychology.

[21]  Ricard V. Solé,et al.  Least effort and the origins of scaling in human language , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[22]  R. Baayen,et al.  Putting the bits together: an information theoretical perspective on morphological processing , 2004, Cognition.

[23]  Partha Niyogi,et al.  Optimizing the mutual intelligibility of linguistic agents in a shared world , 2004, Artif. Intell..

[24]  Béla Bollobás,et al.  The consequences of Zipf's law for syntax and symbolic reference , 2005, Proceedings of the Royal Society B: Biological Sciences.

[25]  R. Ferrer i Cancho,et al.  Zipf's law from a communicative phase transition , 2005 .

[26]  J. M. Jenkins,et al.  The appropriate use of Zipf's law in animal communication studies , 2005, Animal Behaviour.

[27]  Ramon Ferrer-i-Cancho,et al.  Hidden communication aspects in the exponent of Zipf's law , 2005, Glottometrics.

[28]  Ramon Ferrer i Cancho,et al.  Decoding least effort and scaling in signal frequency distributions , 2005 .

[29]  R. Ferrer i Cancho,et al.  The variation of Zipf's law in human language , 2005 .

[30]  John R. Buck,et al.  The use of Zipf's law in animal communication analysis , 2005, Animal Behaviour.

[31]  Ramon Ferrer i Cancho,et al.  When language breaks into pieces. A conflict between communication through isolated signals and language. , 2006, Bio Systems.

[32]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[33]  Ramon Ferrer-i-Cancho,et al.  On the universality of Zipf's law for word frequencies , 2007, Exact Methods in the Study of Language and Text.