27-02-2026, 01:45 PM
One obvious question is whether the Voynich gap could simply be the result of mixing different linguistic systems inside the same manuscript.
To test this, I ran the same long-range tail gap calculation on mixtures of real natural texts. Each text alone has essentially zero gap. Then I concatenated them and measured the effect.
Here is the comparison (tail gap = MI(raw) − MI(word shuffle), d = 60–100):
A few things stand out.
Mixing two Latin texts produces almost no gap. Mixing two related but distinct languages (Catalan and Latin) produces a moderate gap. Mixing very different languages (English and Latin) produces a large one.
The Voynich sits between these cases. Its internal heterogeneity is clearly stronger than what we see between closely related natural languages, but weaker than what we see between very distant ones.
So the long-range gap does not require anything exotic. Strong non-stationarity alone can create it. But the magnitude in Voynich suggests that its internal blocks are statistically more differentiated than simple stylistic or dialectal variation within a single language.
That gives us a useful scale. We are no longer asking whether there is a gap, but how large it is compared to known linguistic differences.
To test this, I ran the same long-range tail gap calculation on mixtures of real natural texts. Each text alone has essentially zero gap. Then I concatenated them and measured the effect.
Here is the comparison (tail gap = MI(raw) − MI(word shuffle), d = 60–100):
| Text combination | Tail gap |
|---|---|
| Latin + Latin (Plato + Alchemical) | ≈ 0.00014 |
| Catalan + Latin (Tirant + Ambrosius) | ≈ 0.00123 |
| English + Latin | ≈ 0.00585 |
| Voynich (Currier) | ≈ 0.00246 |
A few things stand out.
Mixing two Latin texts produces almost no gap. Mixing two related but distinct languages (Catalan and Latin) produces a moderate gap. Mixing very different languages (English and Latin) produces a large one.
The Voynich sits between these cases. Its internal heterogeneity is clearly stronger than what we see between closely related natural languages, but weaker than what we see between very distant ones.
So the long-range gap does not require anything exotic. Strong non-stationarity alone can create it. But the magnitude in Voynich suggests that its internal blocks are statistically more differentiated than simple stylistic or dialectal variation within a single language.
That gives us a useful scale. We are no longer asking whether there is a gap, but how large it is compared to known linguistic differences.