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+---- Thread: A mathematical approach to double words, conditional logic and the missing pages (/thread-5861.html)
A mathematical approach to double words, conditional logic and the missing pages - Vuk88 - 30-06-2026
Hi everyone,
I'm Alfredo. My background is actually in social science data analysis, but like many of you, the Voynich Manuscript has been a long-time obsession of mine. I recently had an intuition regarding its structure that I really wanted to test out.
I started wondering if the manuscript is less like standard prose and more like a highly structured technical manual or data ledger. I know that's not a brand-new concept, but I wanted to see if I could find hard statistical proof of its internal grammar. Building on the Latent Semantic Analysis (LSA) research by Bowern, Layfield, and Davis (which the mods here kindly shared!), I decided to run some computational models on the EVA transliteration to hunt for deterministic rules.
I specifically focused on one of the most famous statistical anomalies: the "double repetitions" (like chol chol). While it's common to dismiss these as dittography or scribal copying errors, I hypothesized something different. What if, in a highly structured document with zero punctuation, these consecutive repetitions actually act as mechanical syntactic markers? Essentially, logic gates or section delimiters.
To test this, I applied Machine Learning algorithms (Logistic Regression and LSA) to analyze the words that heavily co-occur on the same pages as these doubles, looking for a mathematical correlation.
The dependency turned out to be massive. These double words aren't isolated or random; they are strictly bound to specific associated words. I've attached a clustering graph below (voynich_syntax_constellation_en.png) where you can see a distinct separation.
The blue and red dots represent two entirely separate grammatical families. The t-SNE algorithm segregated the vocabulary into two distinct functional 'clouds', showing a strong structural dependency. This rigid separation is the fingerprint of a highly structured system that rigorously distinguishes between different functional categories of words
To find out exactly which words do this, I looked at the Logistic Regression coefficients. In the attached bar chart logistic_bar_chart_en.png, you can see these specific "syntactic triggers" isolated. The red bars highlight the exact words that heavily co-occur on the exact same pages as the double sequences, while the blue bars show the ones that mathematically inhibit them (they almost never appear together).
To prove this wasn't just a coincidence, I ran a Monte Carlo Permutation Test with 1,000 iterations. Basically, I had the script completely scramble the text 1,000 times. This destroys the original word order, but keeps the raw word counts exactly the same. As you can see in the second attached graph (permutation_violin_en.png) , the randomly shuffled text completely failed to recreate the pattern (p-value = 0.0010). This proves the manuscript follows rigid conditional rules.
But here is the part with the biggest codicological implications. By mapping the spatial density of these syntactic markers across the whole manuscript (see the attached graph: voynich_all_missing_density.png) , a striking coincidence emerges: the absolute highest peaks of density are concentrated exactly on the pages right next to the codicological gaps—the 14 missing folios (f12, f59-f64, f74, f91-f98, f109-f110). see the attached graph: voynich_all_missing_density.png
- A quick note on the attached graph (lsa_vs_syntax.png): This chart visually summarizes the intersection between semantic and syntactic data. The X-axis represents the manuscript folios (timeline from f1 to f116). The colored background blocks show the different thematic sections identified by the LSA algorithm (Herbal, Astronomical, etc.), separated by vertical dashed lines indicating where the topic abruptly changes. The red line represents my data: the density of the double words. As you can clearly see, almost every time there is a semantic transition (a change in topic), there is a massive red spike in syntactic double words. They act as physical boundaries between sections.
I recently published the full paper, the dataset, and the Python framework I used for the analysis. You can check everything out here: You are not allowed to view links. Register or Login to view.
I would love for the experts here to take a close look, test the Python framework, and offer some constructive criticism. I'm really curious to hear your thoughts on how we might use this syntactic mapping moving forward.
Thanks for your time!
P.S. For those who prefer a less technical read, I have also attached a simplified, non-academic summary of the theory below in PDF format.
RE: A mathematical approach to double words, conditional logic and the missing pages - Mauro - 30-06-2026
RE: A mathematical approach to double words, conditional logic and the missing pages - nablator - 30-06-2026
RE: A mathematical approach to double words, conditional logic and the missing pages - Vuk88 - 30-06-2026
RE: A mathematical approach to double words, conditional logic and the missing pages - Vuk88 - 30-06-2026
RE: A mathematical approach to double words, conditional logic and the missing pages - Mauro - 30-06-2026
RE: A mathematical approach to double words, conditional logic and the missing pages - Vuk88 - 30-06-2026
RE: A mathematical approach to double words, conditional logic and the missing pages - asteckley - 01-07-2026
RE: A mathematical approach to double words, conditional logic and the missing pages - Mauro - 01-07-2026
RE: A mathematical approach to double words, conditional logic and the missing pages - Linda - 01-07-2026