The deconstruction of a text: the permanence of the generalized Zipf law- the inter-textual relationship between entropy and effort amount
Résumé
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 = constantVarious 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 ap- proach, 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 explana- tions, 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:〖rank〗^(β_i ) * frequency = constant[ 1]
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