Measuring Long-Range Structure in the Voynich Manuscript

[quimqu]

To check whether the gap is simply caused by different pages having different letter frequencies, I built a very simple artificial model. For each page (or paragraph), I kept the same letter proportions but generated the text randomly inside the block. No word structure, no internal rules. Just random letters with the right frequencies. This is an i.i.d. block model.

Here is the comparison:

Text	Real tail gap	Block i.i.d. gap (mean)
Voynich (Currier)	0.00246	0.00407 (page) / 0.00498 (para)
Torsten Timm	0.00270	0.00221–0.00234
Natural texts	≈ 0	clearly larger than real
Nibe cipher	≈ 0.00004	≈ 0.00013–0.00016

Now the picture is clearer.

For natural language, the real gap is basically zero. When we force artificial block differences, the gap increases. That means natural texts are fairly stable across pages.

For Torsten Timm, the real gap is very close to the artificial block model. That suggests his generator behaves largely like a simple mixture of statistically different blocks.

The Nibe cipher behaves like natural language. Its real gap is essentially zero. The artificial block-mixture model produces a slightly larger value, but still very small. This shows that simply encrypting natural language does not create the long-range gap seen in Voynich. That comparison is important. It means the Voynich effect is not just a by-product of symbol substitution or reduced alphabet size. A cipher of natural text does not reproduce it.

For Voynich Currier, the artificial block model produces a much larger gap than the real manuscript. This matters. It means the Voynich is not just a loose mixture of pages with different letter frequencies. There is internal structure inside the blocks that moderates the effect.

So the long-range gap in Voynich cannot be explained by block-level frequency drift alone. It reflects a system that combines large-scale segmentation with internal constraints that are not captured by a purely random block model.