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

TL;DR

This paper introduces the concept of a Fundamental Scale of descriptions, a set of symbols that minimizes entropy in language and music texts, providing a new tool for analyzing the structure of complex communication systems.

Contribution

It proposes a novel method to identify the Fundamental Scale of languages and music, moving beyond preconceived symbol sets to better understand their intrinsic structure.

Findings

Successfully identified the Fundamental Scale in English and MIDI music texts.

Demonstrated that the Fundamental Scale minimizes system entropy.

Showed potential for analyzing language and complex systems using this approach.

Abstract

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.