💬 NLP

Evidence of Layered Positional and Directional Constraints in the Voynich Manuscript: Implications for Cipher-Like Structure

This paper identifies unique directional constraints in the Voynich Manuscript's grapheme sequences that distinguish it from natural languages and demonstrates that neither parametric slot-based nor Cardan grille generators can fully reproduce its structural signatures, suggesting the text possesses complex cipher-like properties that resist simple generative models.

Original authors: Christophe Parisel

Published 2026-04-23

📖 6 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, locked box found in a dusty attic. For centuries, linguists and code-breakers have tried to crack it, but the text inside looks like gibberish. It has its own unique alphabet, strange pictures, and words that don't match any known language.

This paper is like a new set of X-ray glasses that doesn't try to translate the words, but instead looks at the shape and structure of the writing itself. The author, Christophe Parisel, asks: "If this isn't a normal language, what kind of machine or rule created it?"

Here is the story of the findings, broken down with simple analogies.

1. The Two-Layer Puzzle (The "Backwards-Forwards" Trick)

Most languages are consistent. If you write English, you read left-to-right, and the words flow left-to-right. If you write Hebrew, you read right-to-left, and the words flow right-to-left.

The Voynich Manuscript is weird because it has two different rules happening at the same time:

Inside the words: If you look at the letters inside a single word, they make the most sense if you read them Right-to-Left (like Hebrew).
Between the words: But if you look at how one word connects to the next, they flow Left-to-Right (like English).

The Analogy: Imagine a train. The individual train cars (the words) are built so that if you walk backwards through them, they fit together perfectly. However, the train itself is moving forwards down the track. It's a "backwards-inside, forwards-outside" structure that no normal language does.

2. The "Magic" vs. The "Machine"

The author tested a very clever idea: Is this weird "backwards-inside, forwards-outside" pattern a sign of a secret code, or is it just a side effect of how the words are built?

He built a robot simulator (a Markov chain) that didn't know any rules. It just took real Voynich words and shuffled them around randomly, like a child playing with a deck of cards.

The Result: The robot accidentally recreated the "backwards-inside, forwards-outside" pattern perfectly.
The Lesson: This specific pattern isn't a secret code. It's just a natural consequence of the fact that the words themselves are built in a specific way. It's like how a pile of bricks naturally forms a wall; you don't need a secret blueprint to explain the wall, just the shape of the bricks.

3. The Four "Fingerprints" That Don't Match

Once the author realized the "direction trick" was just a side effect, he looked deeper. He found four specific fingerprints that the Voynich Manuscript has, which normal languages (English, French, Hebrew, Arabic) do not have.

Think of these as four locks on a door. To prove the Voynich Manuscript is a normal language (or a simple fake), a generator would have to be able to open all four locks at once.

The "End-to-Start" Lock: In normal languages, the last letter of a word and the first letter of the next word are somewhat random. In Voynich, there is a rigid rule: 80% of the time, a word must end with a "Type A" letter and the next word must start with a "Type B" letter. It's like a dance where partners always switch roles in a specific way.
The "Extreme" Lock: In normal languages, some letters only appear at the start (like 'Q' in English) or the end (like 'S' in English). In Voynich, this extreme behavior happens on both sides with equal intensity, and there are no obvious reasons (like "final letter forms" in Hebrew) to explain it.
The "Zipfian" Lock: In normal languages, the frequency of letters at the start and end of words looks like a flat table (a plateau). In Voynich, it looks like a steep slide (a power law/Zipfian curve). It's a completely different mathematical shape.
The "Secret Connection" Lock: The words in Voynich are highly connected to each other. If you know the end of one word, you can predict the start of the next one much better than in any normal language.

4. The Failed Experiments (The "Bad Copies")

The author then tried to build a machine that could create a fake Voynich Manuscript. He tried two famous theories:

The "Slot Machine" Theory: Imagine building words by picking a "prefix" from one bucket and a "suffix" from another.
The "Cardan Grille" Theory: Imagine a secret code where you look through holes in a piece of cardboard to reveal letters.

He ran these machines thousands of times, tweaking every knob and setting.

The Result: None of them worked.
- The "Slot Machine" could get the "End-to-Start" rule right, but it failed the "Secret Connection" rule.
- The "Cardan Grille" could get the "Secret Connection" right, but it failed the "End-to-Start" rule.
- It was like trying to build a car that is both a Ferrari and a Tractor. The machines could be a Ferrari or a Tractor, but never both at the same time.

The Big Conclusion

The paper doesn't say "We solved the Voynich Manuscript!" Instead, it says: "We found the exact shape of the puzzle piece that is missing."

What we know: The Voynich Manuscript has a very specific, complex structure that is different from any normal language and different from simple "gibberish" generators.
What we don't know: We don't know what created it. It could be a very complex cipher, a lost language with weird grammar, or a hoax made by a genius who understood these rules better than anyone else.
The Takeaway: Any future theory about the Voynich Manuscript must be able to explain all four of those fingerprints at the same time. If a theory can't explain them all, it's probably wrong.

In short: The Voynich Manuscript isn't just random noise, and it isn't a simple code. It's a highly structured puzzle that has stumped every machine we've tried to build so far. The author has just handed us the blueprint of the puzzle, so we know exactly what the solution needs to look like.

1. Problem Statement

The Voynich Manuscript (VMS) remains one of history's most enduring cryptographic and linguistic mysteries. Three dominant hypotheses exist: it is meaningless gibberish, a natural/constructed language, or a ciphertext. A critical, under-explored aspect is the directionality of the script. While the physical manuscript is written left-to-right (LTR), previous work suggested the underlying character stream is optimized for right-to-left (RTL) reading.

However, a paradox exists:

Character-level: The VMS shows RTL optimization (lower perplexity when read RTL).
Word-boundary level: Natural languages typically show asymmetric grapheme distributions at word boundaries (e.g., specific letters appear more often at the start or end). Standard metrics for detecting directionality at boundaries fail for the VMS because its boundary distributions follow a Zipfian (power-law) curve rather than the plateau-shaped curves of natural languages.

The paper aims to resolve this directional dissociation, quantify the unique positional constraints of the VMS, and test whether these constraints can be reproduced by known generative models (slot-based or cipher-based).

2. Methodology

Data and Corpora

The study compares the VMS (37,016 words from the EVA transcription) against four natural languages:

LTR: English (Moby Dick), French (Le Comte de Monte Cristo).
RTL: Hebrew (Wikipedia), Arabic (Big Corpus).
Note: The authors explicitly state these four languages are a convenience sample; claims of "difference" apply only to this set, not all natural languages.

Analytical Framework

The authors employ a multi-layered approach:

Directionality Metrics:
- Character-stream Perplexity ( $\Delta$ ): Measures if the text is more predictable LTR or RTL.
- Cross-Boundary Directionality ( $\Delta_{CB}$ ): Measures conditional entropy and Mutual Information (MI) between the end of one word and the start of the next.
- Markov Simulation: A word-level Markov chain (order 1 and 2) is trained on the VMS to generate synthetic text. This tests if the observed directional dissociation is a surface-level statistical artifact of word sequences rather than a deep structural feature.
Positional Diagnostics:
- Polarization: Classifies graphemes as "start-preferring," "end-preferring," or "ambiguous" based on a 2:1 occurrence ratio.
- MI Decomposition: Breaks down cross-boundary MI into:
  - $MI_{class}$ : Information carried by positional class labels (e.g., "start" vs. "end").
  - $MI_{within}$ : Residual information carried by specific grapheme identities within those classes.
- Four-Signature Joint Criterion: To "pass" as a plausible VMS generator, a model must simultaneously satisfy:
  1. Sig1: End-to-Start (E→S) transition rate between 70–95%.
  2. Sig2: Bilateral positional extremity (extreme ratios >100:1 in both start and end classes).
  3. Sig3: Cross-boundary MI > 0.10 bits.
  4. Sig4: Zipfian boundary distribution shape ( $R^2 > 0.85$ ).
Generative Model Testing:
Two classes of generators were tested across full parameter spaces:
- Slot-based Generator: A parametric model building words from ordered prefix/suffix slots with tunable Zipf exponents and Markov sparsity.
- Cardan Grille Generator: Implements Rugg's (2004) gibberish hypothesis, using a mask over a table of graphemes. Includes "honest" configurations (no pre-separated pools) and "circular" configurations (pre-separated pools).
- Naibbe Cipher: A specific cipher hypothesis (Greshko, 2025) tested as a structured generator.

3. Key Results

A. The Directional Dissociation (Surface-Level)

Observation: The VMS exhibits RTL optimization at the character level but LTR optimization at word boundaries. This is the only text in the comparison set with opposite-direction signals.
Markov Simulation: A simple word-level Markov chain (using real VMS words) reproduced this exact dissociation in 10/10 runs.
Implication: The directional dissociation is a surface-level consequence of VMS word-internal structure and word-to-word transition probabilities. It is not a diagnostic for a specific generative mechanism (like a cipher) but rather a statistical artifact of how VMS words are sequenced.

B. Positional Signatures (Deep Structure)

Unlike the directional dissociation, the following four properties are not reproducible by surface resampling and differ significantly from the comparison languages:

High Boundary Concentration: The VMS has an 80.6% rate of end-class graphemes followed by start-class graphemes. Comparison languages range from 19.8% to 35.5%.
Bilateral Positional Extremity: The VMS contains extreme positional ratios (>100:1) in both start-preferring (e.g., 'q') and end-preferring (e.g., 'iin') classes. In natural languages, such extremes are usually confined to one class or explained by orthography (e.g., Hebrew final forms).
Zipfian Boundary Distributions: VMS boundary grapheme frequencies follow a power-law curve, unlike the plateau shapes of natural languages.
High Structural MI: The VMS has the highest total cross-boundary MI (0.230 bits) and retains the most MI (21%) after word-order shuffling, indicating strong order-independent structural regularity.

C. Generative Model Failure Modes

No tested generator achieved all four signatures simultaneously:

Slot-based Generator: Could achieve Sig1, Sig2, and Sig3, but failed Sig4 (Zipfian shape). Conversely, tuning for Sig4 (high Zipf exponent) collapsed Sig3 (MI). The trade-off is mechanistic: high frequency concentration creates Zipfian shapes but destroys sequential diversity.
Cardan Grille (Honest): Could achieve Sig4 but failed Sig1 (E→S rate) and Sig3. High column skew created Zipfian shapes but eliminated positional asymmetry.
Cardan Grille (Circular/Split): Could achieve Sig3 and Sig4 but failed Sig1.
Naibbe Cipher: Scored 1/4, failing Sig1, Sig3, and Sig4 due to its independent card-draw mechanism, which destroys sequential dependencies and dilutes positional concentration.

4. Key Contributions

Resolution of Directionality: The paper clarifies that the VMS's "opposite-direction" signal is a reducible surface statistic, shifting the focus of cryptanalysis to the non-reducible positional constraints.
Quantitative Benchmarks: It establishes the first rigorous, four-signature joint criterion for evaluating VMS generative models.
Mechanistic Constraints: It demonstrates that two prominent structural hypotheses (slot-based composition and Cardan grille) are structurally incompatible with the VMS's joint profile. Specifically, the VMS requires a mechanism where positional alternation (E→S) and Zipfian frequency concentration are controlled by independent mechanisms, whereas current models couple them.
MI Decomposition: It reveals that 97% of the VMS's cross-boundary information lies in specific grapheme transitions within positional classes, not in the class labels themselves, suggesting a complex internal grammar or cipher logic.

5. Significance and Implications

For Cryptanalysis: The results suggest that simple frequency-based or positional-slot models are insufficient. Any successful cipher hypothesis must explain how the VMS achieves high E→S alternation and Zipfian boundary distributions simultaneously, a combination that breaks current generative models.
For Linguistic Analysis: The findings do not rule out the VMS being a natural language, but they imply that if it is, it possesses a morphological structure with extreme positional constraints and bilateral extremity not seen in the four tested languages.
For Gibberish Hypotheses: The high structural MI and specific Zipfian constraints make the "random gibberish" hypothesis unlikely, as random generation fails to reproduce the joint profile.
Future Work: The paper identifies a critical gap: the need to test generators where positional pool structure and frequency concentration are independently tunable. It also highlights the need for testing against morphologically richer languages (e.g., agglutinative or templatic languages) to see if the "bilateral extremity" is unique to the VMS or a feature of untested language families.

In conclusion, the VMS exhibits a cipher-like structural constraint that is difficult to reproduce from simple positional or frequency-based mechanisms alone. The manuscript's structure is defined by a rigid, high-information interplay between word boundaries and internal grapheme sequences that current standard models cannot replicate.