Redundancy Ratio: An Invariant Property of the Consonant Inventories of the World’s Languages

Proceedings of the 45th Annual Meeting of the Association of Computational Linguistics, pages 104–111, Prague, Czech Republic, June 2007. c⃝2007 Association for Computational Linguistics Redundancy Ratio: An Invariant Property of the Consonant Inventories of the World’s Languages Animesh Mukherjee, Monojit Choudhury, Anupam Basu, Niloy Ganguly Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur {animeshm,monojit,anupam,niloy}@cse.iitkgp.ernet.in Abstract In this paper, we put forward an information theoretic definition of the redundancy that is observed across the sound inventories of the world’s languages. Through rigorous statis- tical analysis, we find that this redundancy is an invariant property of the consonant in- ventories. The statistical analysis further un- folds that the vowel inventories do not ex- hibit any such property, which in turn points to the fact that the organizing principles of the vowel and the consonant inventories are quite different in nature. 1 Introduction Redundancy is a strikingly common phenomenon that is observed across many natural systems. This redundancy is present mainly to reduce the risk of the complete loss of information that might oc- cur due to accidental errors (Krakauer and Plotkin, 2002). Moreover, redundancy is found in every level of granularity of a system. For instance, in biologi- cal systems we find redundancy in the codons (Lesk, 2002), in the genes (Woollard, 2005) and as well in the proteins (Gatlin, 1974). A linguistic system is also not an exception. There is for example, a num- ber of words with the same meaning (synonyms) in almost every language of the world. Similarly, the basic unit of language, the human speech sounds or the phonemes, is also expected to exhibit some sort of a redundancy in the information that it encodes. In this work, we attempt to mathematically cap- ture the redundancy observed across the sound (more specifically the consonant) inventories of the world’s languages. For this purpose, we present an information theoretic definition of redun- dancy, which is calculated based on the set of fea- tures1 (Trubetzkoy, 1931) that are used to express the consonants. An interesting observation is that this quantitative feature-based measure of redun- dancy is almost an invariance over the consonant inventories of the world’s languages. The observa- tion is important since it can shed enough light on the organization of the consonant inventories, which unlike the vowel inventories, lack a complete and holistic explanation. The invariance of our measure implies that every inventory tries to be similar in terms of the measure, which leads us to argue that redundancy plays a very important role in shaping the structure of the consonant inventories. In order to validate this argument we determine the possibil- ity of observing such an invariance if the consonant inventories had evolved by random chance. We find that the redundancy observed across the randomly generated inventories is substantially different from their real counterparts, which leads us to conclude that the invariance is not just “by-chance” and the measure that we define, indeed, largely governs the organizing principles of the consonant inventories. 1In phonology, features …

Content truncated to 500 words