A mathematical approach to double words, conditional logic and the missing pages

[Vuk88]

This is an important point. Consider the possibility that Voynichese is a natural language with some encoding that maps each distinct word type to the same distinct word type [...] Then a "doublet" is not an interesting category for analysis.
[...]
Thus I think you should
- focus on specific doublets, like "daiin daiin", rather than "doublets" in general

Dear Professor Stolfi,  
I would like to reply by combining the extraordinary insights you provided in both of your messages (posts #25 and #27), offering you the empirical data I have just calculated.

1. (Post #25) Finding your orthographic speculations very interesting, I mathematically verified their impact. I modified my algorithm so that it would apply to the LSI corpus (36,364 words cleaned of notes and markers) a restrictive set of substitutions based exclusively on your indications: global substitution of m with iin, of Ih/ITh/IKh to Ch/CTh/CKh, and conditional substitution of the endings -ir and -iir to -iin and -iiin (only at the end of a word).
   

  Judge the result for yourself:

• A full 206 Hapax Legomena (rare words appearing only once in the corpus) vanished, assimilated into more common roots; essentially, you have provided an important key to drastically reducing the vocabulary's entropy, cleaning it from transliteration errors!
  
• The total number of doublets rose from 301 to 328 (revealing hidden repetitions like daiir daiin).
  
• The syntactic correlation remained nothing short of "robust"... the qoteedy trigger continued to predict the presence of doublets in 38 cases out of 38.
  

(To definitively rule out the hypothesis that this precision was a statistical artifact linked to high frequency, I ran a randomization test by randomly shuffling the order of all 36,364 tokens. In the randomized text, the predictive capacity of qoteedy plummeted from 100% to 39.3%, proving that the pairing in the real text is intentional and positional).

1. The "Mississippi / Singing" analogy (Post #27) Your analogy regarding the English trigraph doublets is, in my opinion, methodologically rigorous. Indeed, treating all doublets as a single indistinguishable bucket risks creating a statistical "soup". It is for this reason that I have just conducted a disaggregated analysis specifically on the repetition typologies for the top 5 triggers of the manuscript.
   

Globally, the most frequent doublet in the book is daiin daiin (9.8% of all doublets). But look what happens to the specific distribution when the text is "activated" by the triggers:

• In the presence of qoteedy: daiin daiin suffers a drastic collapse (2.7%). In its place, the repetition qokeedy qokeedy (11%) and the short syllable ol ol (4.8%) emerge anomalously.
  
• In the presence of olkeey: daiin daiin is almost totally inhibited (1.0%). In its place, ol ol dominates (7.1%).
  
• In the presence of qokeedy: daiin daiin drops to 3.4%. The syllable ar ar emerges (4.5%).
  
• In the presence of qokedy: daiin daiin halves to 4.7%.
  
• In the presence of shedy: daiin daiin drops to 4.2%.
  

This "extreme level of active suppression" exactly corroborates your thesis: we are not looking at a generic propensity to duplicate words, but rather we are observing triggers that "call" only specific roots or targeted monosyllables (inhibiting the other, more common options). Whether it is a monosyllabic language or operative commands, the conditional rigidity of this syntactic structure appears amply supported by the evidence.

Lastly, I enthusiastically accept your methodological recommendations for the next steps. Abandoning the "page" as a geographical unit to test the algorithm on single paragraphs (in the Herbal section) or on sliding windows of k-tokens (in the Bio section) to measure the correlation based on distance will be the focus of my next analysis session.
Thank you again for the time dedicated to this research.
With profound esteem,
Alfredo