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Ferrer i Cancho, Ramon

Hidden communication aspects in the exponent of Zipf's law

Here we focus on communication systems following Zipf's law. We study the relationship between the properties of those communication systems and the exponent of the law. We describe the properties of communication systems using quantitative measures of the semantic vagueness and the cost of word use. We try to reduce the precision and the economy of a communication system to a func­tion of the exponent of Zipf's law and the size of the communication system. Taking the exponent of the frequency spectrum, we show that semantic precision grows with the exponent whereas the cost of word use reaches a global minimum between 1.5 and 2 if the size of the communication system re­mains constant. We show that the exponent of Zipf's law is a key aspect for knowing about the num­ber of stimuli handled by a communication system and determining which of two systems is less vague or less expensive. We argue that the ideal exponent of Zipf's law should be very slightly above 2.

Glottometrics, RAM-Verlag

Volume: 11, 09/2005
Pages: 98-119

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