Abstract
The complexity of the description of a system is a function of the entropy of its symbolic description. Prior to computing the entropy of the system’s description, an observation scale has to be assumed. In texts written in artificial and natural languages, typical scales are binary, characters, and words. However, considering languages as structures built around certain preconceived set of symbols, like words or characters, limits the level of complexity that can be revealed analytically. This study introduces the notion of the fundamental description scale to analyze the essence of the structure of a language. The concept of Fundamental Scale is tested for English and musical instrument digital interface (MIDI) music texts using an algorithm developed to split a text in a collection of sets of symbols that minimizes the observed entropy of the system. This Fundamental Scale reflects more details of the complexity of the language than using bits, characters or words. Results show that this Fundamental Scale allows to compare completely different languages, such as English and MIDI coded music regarding its structural entropy. This comparative power facilitates the study of the complexity of the structure of different communication systems.
Highlights
The understanding of systems and their complexity requires accounting for their entropy
The entropies calculated at the scales of characters and words were 0.81 and 0.90 respectively, the entropy at the fundamental scale was 0.76; an important reduction of the information required to describe the same message
The results clearly showed the calculus of the entropy content of a communication system varies in important ways, depending on the scale of analysis
Summary
The understanding of systems and their complexity requires accounting for their entropy. Gell-Mann sees both randomness and order as manifestations of regularity, and quantities that offer the possibility for reducing the length of a description and the computed complexity of a system. These complexity concepts are all evaluated using arbitrarily selected symbol scales. They explored the effects of multivariate distributions and calculate the entropy associated to several 2D patterns. All these studies share the same direction; assume a space for a domain and a scale and compute the entropy. This representation of the components may convey a description of a system and its structural essence
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