💻 computer science

A Quantitative Confirmation of the Currier Language Distinction

This paper provides quantitative evidence supporting the validity of Currier's A/B language distinction in the Voynich manuscript by demonstrating that a Beta-Binomial mixture model can recover the split without prior labels and a supervised classifier can predict folio identities with 89.2% accuracy.

Original authors: Christophe Parisel

Published 2026-04-30

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Christophe Parisel

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Voynich Manuscript as a mysterious, ancient book written in a code no one has ever cracked. For decades, a cryptographer named Prescott Currier had a hunch: this book isn't written in just one "language." He thought it was actually a mix of two distinct dialects, which he called Language A and Language B.

For years, this was just a theory based on a gut feeling about word patterns. But in this new paper, the author, Christophe Parisel, decides to put that hunch to the test using math, not just guesswork. Think of this study as a forensic audit of the book's DNA.

Here is the breakdown of what they did and what they found, using simple analogies:

1. The Detective's Tool: "Character Pairs"

Instead of trying to read the words (which is impossible), the researchers looked at how the author chose between visually similar letters.

The Analogy: Imagine you are writing a story. Sometimes you use the word "color," and sometimes "colour." If you switch between them randomly, it's just a quirk. But if you always use "color" in the first half of the book and always use "colour" in the second half, that suggests two different writers or two different rules.
The Study: They picked 11 pairs of letters that look alike in the Voynich script (like d vs. l, or or vs. ar). They counted how often each letter in the pair was used on every single page (folio).

2. The Big Question: Is it Real or Just a Coincidence?

The researchers asked three tough questions:

Is it just random noise? Could the differences happen by chance in a single language?
Is it a trick of the binding? Currier's original split happened to line up with where the book was physically stitched together (the "quires"). Maybe the book just changed style because the scribe changed, not because the language changed.
Can we predict it? If we hide the labels (A or B) and let a computer guess, can it figure out which "language" a page is in just by looking at the letter counts?

3. The Results: The "Two-Language" Theory Holds Up

The study used a sophisticated statistical model (a Beta-Binomial mixture) which acts like a smart sorter. It looked at the raw numbers without knowing which page was A or B.

The "Magic" Sort: Even without being told the answers, the computer naturally sorted the pages into two distinct groups. It matched Currier's original A/B split with about 38% accuracy (which is a huge deal in statistics for this kind of data) and was 90% confident on over 100 pages.
The "Blind" Test: When they trained a computer to recognize the patterns on half the book and then asked it to guess the language of the other half, it got it right 89.2% of the time.
Ruling Out the "Binding" Theory: They found that when the language changed inside a single stitched section (a quire), the letter patterns jumped sharply. This proves the change isn't just about who stitched the book; it's about the text itself.

4. The Three "Personality Types" of Letters

The study discovered that the letter pairs don't all behave the same way. They fall into three groups, like different types of employees in a company:

The "Switchers" (Categorical): These letters are strict. If the page is Language A, they use one letter. If it's Language B, they switch to the other. They are the "ID cards" that prove the two languages exist.
The "Leaning" (Intermediate): These letters have a preference but aren't strict. They lean toward one style or the other, acting like a subtle signal.
The "Free Spirits" (Free Variation): These letters don't care about the language at all. They change randomly, regardless of whether it's page A or B.

5. The "Surprise" Anomaly

One pair of letters (e/ch) was weird. It didn't help sort the pages into A or B, but it was the best at spotting the exact moment the language switched from one to the other. It's like a smoke detector that doesn't tell you what room the fire is in, but screams the second the fire starts.

The Bottom Line

The paper concludes that Currier was right. The Voynich Manuscript isn't a single, uniform text. It contains a genuine, structural split between two distinct "languages" (or writing regimes).

It's not random: The patterns are too strong to be a fluke.
It's not a physical trick: The change happens even within the same physical section of the book.
It's predictable: A computer can look at the letter stats and guess the language with high accuracy.

However, the study also notes that the "A vs. B" split only explains about 29% of the differences in the text. This means there is still a lot of hidden complexity and structure in the book that we haven't figured out yet, but the "Two-Language" theory is definitely a real, measurable fact, not just a myth.

1. Problem Statement

The paper addresses the validity of Prescott Currier's 1976 hypothesis that the Voynich Manuscript contains two distinct "languages" (designated Currier A and Currier B). While widely cited, this distinction has historically lacked rigorous quantitative validation against explicit null hypotheses. The study seeks to resolve three specific challenges:

Statistical Fluctuation: Determining if observed differences are merely random noise within a single homogeneous text.
Codicological Confounds: Verifying if the distinction is a genuine linguistic property or an artifact of the manuscript's physical structure (e.g., quire boundaries), as Currier's original assignment correlates with these physical divisions.
Intrinsic Predictability: Establishing whether the A/B distinction is an intrinsic statistical property discoverable without prior labels and capable of predicting unseen text behavior.

2. Methodology

The authors employed a multi-faceted quantitative approach using the Takahashi EVA transcription (32,693 word tokens across 185 folios).

Data Representation: The study focused on 11 pairs of visually similar EVA characters (e.g., k/t, d/l, or/ar). For each folio, the ratio $r = \frac{\text{count}(a)}{\text{count}(a) + \text{count}(b)}$ was calculated for every pair, provided a minimum threshold of 20 combined occurrences was met.
Simulation Baselines: To test null hypotheses, three models were generated:
- Label Shuffle: Real text with randomized A/B labels.
- Single Markov: Synthetic text from a single homogeneous Markov model.
- Split Markov: Synthetic text from separate A and B Markov models (positive control).
Unsupervised Recovery: Clustering algorithms (K-means, GMM, etc.) were applied to the folio $\times$ pair ratio matrix without access to Currier's labels to see if the data naturally partitions into two groups.
Generative Modeling: A Beta-Binomial mixture model was fitted to raw character counts. This model assumes folio counts are drawn from a binomial distribution where the success probability follows a Beta distribution specific to a latent regime. The model was fitted via Expectation-Maximization (EM) to determine the optimal number of regimes ( $k$ ).
Predictive Validation: A supervised Beta-Binomial classifier was trained on a subset of folios to predict the A/B identity of held-out folios. Validation included cross-validation, spatial splits (early vs. late manuscript), and permutation tests.
Boundary Analysis: Transitions between folios were categorized (Same, Quire-only, Language-only, Both) to measure the magnitude of ratio jumps at language boundaries versus physical book boundaries.

3. Key Contributions

Unsupervised Discovery: Demonstrated that a generative model fitted to raw counts without access to Currier's labels independently recovers the A/B split (ARI = 0.383), proving the distinction is intrinsic to the data structure.
Functional Taxonomy: Identified that character pairs do not behave uniformly but separate into three distinct functional regimes: Categorical, Intermediate, and Free Variation.
Decoupling from Codicology: Provided statistical evidence that language transitions within the same quire produce significantly larger statistical jumps than physical quire boundaries, ruling out the physical structure as the primary cause of the variation.
Predictive Power: Established that knowing the A/B label allows for the prediction of character-pair statistics on unseen folios with high accuracy, moving beyond mere description to prediction.

4. Key Results

Statistical Robustness

Cramér's V: Six of the eleven character pairs showed Cramér's V values exceeding all 1,000 random label permutations. The mean Cramér's V (0.136) was significantly higher than the shuffled baseline (0.025).
Simulation Rejection:
- The Single Markov model failed to reproduce the observed inter-folio variance or boundary effects (0/200 simulations matched).
- The Split Markov model matched aggregate statistics but failed to reproduce the high folio-level variance and boundary sharpness of the real manuscript.

Unsupervised & Generative Recovery

Clustering: K-means clustering on the ratio matrix yielded an Adjusted Rand Index (ARI) of 0.208 (significant, $p < 0.001$ ). Removing "noisy" pairs increased ARI to 0.456.
Beta-Binomial Mixture: The model selected $k=2$ as the optimal number of components based on the Bayesian Information Criterion (BIC).
- The model assigned 113 of 185 folios (61%) with >90% posterior confidence to one of the two regimes.
- The recovered partition aligned with Currier's manual assignment (ARI = 0.383).

Predictive Validation

Accuracy: The supervised classifier achieved 89.2% accuracy in predicting held-out folio labels (Cross-Validated).
Significance: Zero of 500 label permutations achieved comparable accuracy ( $p < 0.002$ ).
Variance Explained: The A/B label explained 29.3% of the variance in character-pair ratios on unseen folios ( $R^2 = 0.293$ ).
Spatial Asymmetry: Forward spatial splits (early $\to$ late) performed well (79.6%), while backward splits (late $\to$ early) failed (41.3%) due to class imbalance (late folios are predominantly B), confirming the signal is real but sensitive to training set composition.

Character Pair Regimes

The study categorized the 11 pairs into three regimes:

Categorical (e.g., d/l, or/ar): Near-binary switches between regimes; essential for clustering.
Intermediate (e.g., ol/al, k/t): Moderate preference shifts; carry boundary signals.
Free Variation (e.g., o/a, ch/sh): Near-zero dependence on the A/B regime; likely represent allographic variation.

Note on Anomaly: The e/ch pair had near-zero global correlation but the strongest local boundary effect, suggesting its variation is conditioned by factors other than the binary regime (e.g., word position).

5. Significance

This paper provides the first rigorous, quantitative confirmation that the Currier A/B distinction is a genuine, intrinsic, and predictive property of the Voynich Manuscript, rather than an artifact of physical structure or random noise.

Implications for Decipherment: Any theory of the Voynich writing system must account for a dual-regime structure where specific character pairs switch categorically between regimes while others vary freely.
Nature of the Text: The results suggest the manuscript is not a single homogeneous text but contains a complex structure where the binary A/B split is the primary axis of variation, though it only explains ~29% of the total variance, implying further sub-regimes or gradients exist.
Methodological Advance: The study demonstrates the efficacy of Beta-Binomial mixture models and unsupervised learning in cryptanalysis, offering a framework to validate linguistic hypotheses in undeciphered scripts without relying on manual labeling.