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

[Vuk88]

You used a clever method, but I rather agree with asteckley here (You are not allowed to view links. Register or Login to view.).

I'd feel much more comfortable with a reshuffling test done along the lines of my You are not allowed to view links. Register or Login to view.. If after the reshufflings the plots come out significantly different from the original, then that would be something.

@asteckley and @Mauro.
I read your comments regarding the physical permutation test. In reality, setting up the analysis with those rules would result in a structural error... applying a physical shuffle to a Bag-of-Words model triggers a macroscopic homogenization bias, and it is obvious to expect results that would artificially favor the algorithm even more.
Out of pure scientific curiosity and to see exactly how the algorithm would run, I tried running it with your rules. As expected I got exactly the result I imagined, the algorithm proved me even more right by returning an accuracy of 63.3% compared to the 54% of the real text. But accepting this result would be a mistake for a very specific reason…If you physically shuffle the words in an entire section you completely destroy the natural variance of the manuscript. The original text is clustered, the author grouped specific words in specific places. When we scramble them we create a homogeneous soup.
 I empirically measured this phenomenon and the vocabulary variance between pages drops by 40% after the shuffle. To explain it simply, let's think about the initial part of the Voynich where there are many drawings and very little text. If we physically shuffle the words of that section, we take the words from the dense pages and spread them over those with the drawings. We end up homogenizing the text, making the empty pages equal to the text-rich ones, irreparably altering the sophisticated and rigid structure of the manuscript's distribution. By doing so, we would end up feeding the model artificial and too “perfect” data... The algorithm has an incredibly easy job when it works with homogeneous data, and that is why the accuracy increases, but it is a trick, a bias.
 It was precisely to avoid this error the reason why the Y-Scrambling algorithm I used is better for this task. Instead of touching the text, Y-Scrambling leaves the complex manuscript 100% intact exactly as it was written. It only randomizes the target labels, namely the doublets. This forces the model to work on the real and unaltered text, taking into maximum consideration the variance and complexity of the manuscript that the physical test instead destroys.
To guarantee maximum transparency, I will write down the logical steps with which I fed the algorithm for the physical shuffling test so that you can verify its setup. Logical Pipeline of the Physical Shuffling Test :

1. Section Isolation: 
   The manuscript was divided into thematic quires (Herbal, Astro, Balneo, Pharm, Recipes). Words never crossed the section boundaries.
   
2. Extraction and Locking: 
   For each section, the length of each page and the exact positions of the original doublets were locked. All other single words were inserted into a section shuffling pool.
   
3. Shuffling: 
   The pool of single words was randomly shuffled for 1000 iterations.
   
4. Reconstruction: 
   The pages were reconstructed by filling the empty spaces with the words from the shuffled pool. I added a rule to prevent the creation of new accidental doublets. If a word drawn from the pool was identical to the one just inserted, the algorithm discarded it and drew a different one.
   
5. Evaluation: 
   The shuffled pages were evaluated by the same Logistic Regression model. I thank you for suggesting this test. Observing how the model reacts to homogenized data was very instructive for understanding the underlying structure of the manuscript. If you believe there are logical errors in this pipeline or that the algorithm needs modifications, I am absolutely ready to listen and discuss them.Alfredo