It is provable and was in fact proved in 2019 for all discrete systems by Greg Warr and myself after a ten year battle. The solution appears on the boundary between statistical mechanics and Information theory. The full proof is freely available at Royal Society Open Science, https://doi.org/10.1098/rsos.191101 (https://doi.org/10.1098/rsos.191101)
Zipf's law appears naturally in this paper under the title homogeneous distribution. There is a second related distribution called a heterogeneous distribution which predicts word length in letters as in your article and also the lengths of computer functions in programming tokens as well as the lengths of proteins in amino acids.
The full implications of this appear in a book “Exposing Nature’s Bias: the hidden clockwork behind society, life and the universe (2022)”. Its an emergent property of all discrete systems traceable back to the appearance of alphabets in ancient Egypt and all the way forward where its footprint is all over the genome and the entire known proteome. Contact me if you would like more info.
It is provable and was in fact proved in 2019 for all discrete systems by Greg Warr and myself after a ten year battle. The solution appears on the boundary between statistical mechanics and Information theory. The full proof is freely available at Royal Society Open Science,
https://doi.org/10.1098/rsos.191101 (https://doi.org/10.1098/rsos.191101)
Zipf's law appears naturally in this paper under the title homogeneous distribution. There is a second related distribution called a heterogeneous distribution which predicts word length in letters as in your article and also the lengths of computer functions in programming tokens as well as the lengths of proteins in amino acids.
The full implications of this appear in a book “Exposing Nature’s Bias: the hidden clockwork behind society, life and the universe (2022)”. Its an emergent property of all discrete systems traceable back to the appearance of alphabets in ancient Egypt and all the way forward where its footprint is all over the genome and the entire known proteome. Contact me if you would like more info.