Measuring Long-Range Structure in the Voynich Manuscript

[nablator]

To myself (and this is full my theroy), we could say that the area between the full text and the shuffled text is the effect that the word ordening has to the MI (so how the natural language links words and characters in a long term).

I am trying to understand the asymptotic behavior: your MI(d) curves seem to converge to a different value in word-shuffled texts than in "raw" (original) texts, right? (But the Ambrosius text does not, the curves are very close.) If so, it seems very counterintuitive: there should be no predictability at all at large distances. For the "raw" texts because obviously words are preferentially followed by other words, but this fact tells you nothing about the words on the next page or 10 pages later. For the word-shuffled texts it is often characters of the same word that are picked together at low distances so there can be some predictability, it diminishes with distance and goes down to zero as soon as the distance exceeds the length of the longest word.

The explanation must be in the way MI(d) is calculated or displayed. Pardon the very basic question: how is it defined? Is it this formula?

The mutual information of two jointly discrete random variables X and Y is calculated as a double sum:
   

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