Measuring Long-Range Structure in the Voynich Manuscript

[quimqu]

I ran a very simple experiment to see where the character-level structure of the Voynich text actually lives.
The figure shows raw mutual information between characters at distance d under four conditions:

- Original text
- Tokens shuffled (words preserved internally, but reordered)
- Lines shuffled
- Full character shuffle

   

The character shuffle behaves as expected: the curve collapses almost completely. This confirms that the signal depends on ordering, not just on character frequencies.

The key comparison is between the original text and the token shuffle. When tokens are randomly reordered, the curve drops sharply and stabilizes close to the character-shuffle baseline after short distances. Internal word structure is still present in this condition, so what disappears is the structure between tokens.

Line shuffling sits in between: it preserves structure within lines but weakens longer-range continuity across lines.
The ordering is consistent:

Original > Line shuffle > Token shuffle > Character shuffle.

From this figure alone, it seems clear that the Voynich manuscript contains statistical dependencies that extend beyond individual tokens. The structure is not purely internal to word-like units.

This does not imply syntax or natural language. It simply shows that cross-token ordering contributes significantly to the long-range signal