The deconstruction of a text: the permanence of the generalized Zipf law—the inter-textual relationship between entropy and effort amount.

Autor/inn/en	Lafouge, Thierry; Agouzal, Abdellatif; Lallich, Genevieve
Titel	The deconstruction of a text: the permanence of the generalized Zipf law—the inter-textual relationship between entropy and effort amount.
Quelle	In: Scientometrics, (2015) 1, S.193-217 PDF als Volltext Verfügbarkeit
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0138-9130
DOI	10.1007/s11192-015-1600-z
Schlagwörter	Zipf’s law; Signal theory; Entropy; Text
Abstract	Abstract Zipf’s law has intrigued people for a long time. This distribution models a certain type of statistical regularity observed in a text. George K. Zipf showed that, if a word is characterised by its frequency, then, rank and frequency are not independent and approximately verify the relationship: Rank×frequency≈constant$${\text{Rank }} \times {\text{ frequency}} \approx {\text{constant}}$$Various explanations have been advanced to explain this law. In this article, we talk about the Mandelbrot process, which includes two very different approaches. In the first approach, Mandelbrot studies language generation as the transmission of a signal and bases it on information theory, using the entropy concept. In the second, geometric approach, he draws a parallel with the fractal theory, where each word of the text is a sequence of characters framed by two separators, meaning a simple geometric pattern. This leads us to hypothesise that, since the statistical regularities observed have several possible explanations, Zipf’s law carries other patterns. To verify this hypothesis, we chose a text, which we modified and degraded in several successive stages. We called Ti the text degraded at step i. We then segmented Ti into words. We found that rank and frequency were not independent and approximately verified the relationship: Rankβi×frequency≈constantβi>1$${\text{Rank}}\,\beta_{i} \, \times {\text{ frequency}} \approx {\text{constant}}\quad \beta_{i} \, > 1$$The coefficient βi increases with each step i. We call Eq. (1) the generalized Zipf law. We found statistical regularities in the deconstruction of the text. We notably observed a linear relationship between the entropy Hi and the amount of effort Ei of the various degraded texts Ti. To verify our assumptions, we degraded a text of approximately 200 pages. At each step, we calculated various parameters such as entropy, the amount of effort, and the coefficient. We observed an inter-textual relationship between entropy and the amount of effort. This paper therefore provides a proof of this relationship.
Erfasst von	OLC
Update	2023/2/05