[Blog Post] Ruminations on the Voynich Manuscript

[MarcoP]

   
This is something I posted in a comment on Patrick's blog.

In "§ 5 Patterns of Similarity and Repetition", Patrick shows the two lines that appear in the top plot of the image. The plot is about word similarity in Voynichese paragraph text: the whole text is processed as a single long sequence of words.
Patrick's description of the plot and some of his discussion of it:

Measurement of average similarity between words n and n+x for x in the range 1-20.  Blue: comma breaks disregarded (= fewer but longer words).  Orange: comma breaks treated as real word breaks (= more but shorter words). 

... 

There’s a sharp peak at n+2, which shows that horizontal pairs of words separated by one intervening word are actually more similar on average than words that are immediately next to each other.  This is followed by a periodic rise and fall at an interval close to the average length of a line.  Such a period would be consistent with vertically patterned word similarity within lines

What I did in the lower part of the image was adding more plots based on crudely filtering out words according to their position in lines. I used a slightly different similarity measure  (Levenshtein ratio, instead of the custom measure that Patrick discusses). My dark-blue and red lines correspond to Patrick's: these are close enough to show that the different similarity measure does not have a great impact.

The purple and light-blue lines show what happens if all the first and last words in lines are removed. Some of the observable effects:

• similarity is increased;
  
• the "periodic rise and fall" at 9/18 (dark blue) and 10/19 (orange/red) disappears;
  
• the N+2 peak is amplified.
  

This possibly shows that the vertical patterns pointed out by Patrick are due to line-initial and line-final words being "special": roughly, each of the three sets of words (line-initial, inside-line, line-final) is made of relatively homogeneous words which differ from the words of the other two sets. By removing line-initial and line-final words, only inside-line words are left and this results in greater overall similarity.

The yellow and green line show the result of removing the fourth word from lines containing at least seven words (i.e. an inside-line word is removed). Effects:

• similarity is decreased;
  
• I would have expected the periodic peaks to still be observable, but it seems this is only the case with the green line (since one word was removed, the peak shifts from position 10 to position 9);
  
• the N+2 peak is still visible, though attenuated, in the green line (i.e. when uncertain spaces are considered); it disappears in the yellow lines (uncertain spaces ignored).
  

Hacking lines like I did is certainly brutal. I guess that the less smooth behaviour of the resulting plots when compared with the dark-blue and red lines is due to this. It would be nice to come up with a method of analysis that further investigates the details without altering the nature of the text.

The feature that I am mostly curious about is the N+2 peak. Something similar was pointed out by Torsten in his paper about "Co-Occurrence Patterns in the Voynich Manuscript": in Table 2 he showed that identical words are more likely to occur at a distance of 2 (1.07%), rather than immediately next to each other (0.96%).