Measuring Long-Range Structure in the Voynich Manuscript

[quimqu]

I did some comparing tests today, that show something intresting (I will try to explain it in my own English this time). 

I wanted to compare the behaviour of the mutual information of the characters. Remember that it is sort of "having the character c, how does it affect the predictability of a character d spaces away). I have limited d to 50 and removed spaces (as the effect I will try to explain is shown better) (note that with spaces the effect is very simmilar). I compared Voynich A, B and full with Torsten Timm's generated text, naibe cipher text and several natural languages (including Vietnamese). I compared them full text and with words shuffled.

Here are the plots:

   
   

I think it is interesting to compare the differences between the raw text and the shuffled text. We can see that all natural languages (including Naibe cipher) tend to the same MI at d=50. You can see that shuffling the words collapses the text into that MI very fast. 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). For example, If we look at Alchemical Herbal or Culpeppers's lines (full and shuffled) the area within both lines is the effect of the natural language that we loose shuffling the words:

       

Let's call the area between both plots once the MI is converged as text meaning area.

What is interesting is what happens to Torsten Timm's text. We know it is a generated text that depends much on the previous word. But look how the MI at long distances do not converge. The MI falls to an evident gap. This can mean that shuffing the words, we have broken the link thay have during their generation.There is also one more point to observe: both curves (full and shuffled) seem to have the same form, just moved in the vertical axis. If we force the MI at long d to converge, we see that the lines have almost the same shape:

       

So... no text meaning area at all. Shuffling the words we loose "only" the links between them (MI converges at a lower rate), but it may have no meaning at all. Let's call the vertical difference between full text and shuffled text the generative area.

So what happens to the Voynich? Let's divide it in Voynich A and Voynich B. This is how they look like (full text versus shuffled text):

       

We see both of them have some generative area, not as much as Torsten Timm plots, but more then the natural languages. Do they have text meaning area? Welll. take a look:

       

Only Voynich B seems to have a small amount of text meaning area. From the natural languages analyzed in this work, only Ambrosius Medionalensis In Psalmum David CXVIII Expositio has similar behaviour in terms of text meaning area, but it has (almost) no generative area:

   

Well, these results raise questions rather than answer them. Whether the observed patterns reflect linguistic organization, generative constraints, or something else entirely remains an open problem.