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

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 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 T i the text degraded at step i. We then segmented T i into words. We found that rank and frequency were not independent and approximately verified the relationship:The coefficient b i 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 H i and the amount of effort E i of the various degraded texts T i . 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

Compression principle and Zipf’s Law of brevity in infochemical communication

“…In some noisy or adverse domains, selection pressures have maximized transmission through redundancy in opposite to efficiency or energy saving, as it happens in acoustic long-distance calls [52,57,58]. This could be happening in the case of intraspecific pheromone communication, and it is consistent with the unrevealed Shannon entropy, significantly higher when comparing pheromones to other allelochemicals [36,59].…”