A Fundamental Scale of Descriptions for Analyzing Information Content of Communication Systems

The complexity of a system description is a function of the entropy of its symbolic description. Prior to computing the entropy of the system description, an observation scale has to be assumed. In natural language texts, typical scales are binary, characters, and words. However, considering languages as structures built around certain preconceived set of symbols, like words or characters, is only a presumption. This study depicts the notion of the Description Fundamental Scale as a set of symbols which serves to analyze the essence a language structure. The concept of Fundamental Scale is tested using English and MIDI music texts by means of an algorithm developed to search for a set of symbols, which minimizes the system observed entropy, and therefore best expresses the fundamental scale of the language employed. Test results show that it is possible to find the Fundamental Scale of some languages. The concept of Fundamental Scale, and the method for its determination, emerges as an interesting tool to facilitate the study of languages and complex systems.Comment: 29 pages, 2 Tables, 5 Figure