Measuring Long-Range Structure in the Voynich Manuscript

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The next step was obvious.

If the gap can be produced by mixing different systems, then what happens if we isolate Voynich A and Voynich B?

Using Currier transliteration, I measured the tail gap separately.

Subset Tail gap
Voynich A only ≈ 0.00084
Voynich B only ≈ 0.00080
A + B concatenated ≈ 0.00255
A + B interleaved ≈ 0.00046

This clarifies several things.

First, A and B are statistically distinct. When concatenated in blocks, the gap rises sharply. When interleaved word by word, it drops. This is exactly what we expect from mixing two differentiated systems.

But here is the important part: A alone and B alone still show a non-zero gap.

So the Voynich effect is not simply “two languages glued together”. Each variant already contains internal non-stationarity.

To probe deeper, I clustered pages automatically using bigram statistics. The clustering cleanly recovered A vs B without being told anything about Currier classification. That confirms the distinction is real and structural.

Then I measured the gap inside each cluster:
Cluster Tail gap
A cluster ≈ 0.00083
B cluster ≈ 0.00082

Again, the same pattern. The difference between A and B explains part of the global gap, but not all of it.

Finally, I tested whether the gap inside A might just be an ordering issue. By permuting page order freely, the gap dropped from about 0.00084 to about 0.00034. When I restricted reordering to physically plausible moves (only swapping entire quires), the reduction was much smaller, down to about 0.00065.

That tells us something important.

Part of the signal behaves like block-level drift. But part of it is intrinsic to the internal structure of the text. Even within a single Currier variant, the manuscript is not statistically stationary.

Putting everything together:
– The Voynich gap is not caused by punctuation.
– It is not generated inside lines or paragraphs.
– It is not solely explained by the A/B split.
– It behaves like structured heterogeneity across coherent blocks.

Compared to natural language mixtures, the magnitude of differentiation inside Voynich is stronger than dialectal variation, weaker than completely unrelated languages, and present even within single variants.

At this point, the manuscript looks less like a homogeneous language and more like a system with layered statistical regimes.

The (old) question is what kind of generative process produces this kind of multi-level structure.