Why the Voynich Manuscript Might Not Be a Real Language

[quimqu]

But please, please, please people: the character entropy is a property of the encoding.  Not of the language, not of the text.  IIff yyoouu  jjuusstt  wwrriittee  eevveerryy  lleetttteerr  ttwwiiccee, the average per-character entropy will be halved.  iF yOU raNdOmLY cAPitAliZe eACh lEtTer, you will add 1 to the average per-character entropy. If you insert two random capital letters after each letter, lMTiGUkSHeWP tNNhLOiZQsDB, you will add at leasr 3 to the per-character entropy.

You're absolutely right — and thank you for bringing this up.

Yes, perplexity is a function of next-character entropy, and that entropy is deeply tied to how a language is encoded as a symbol stream. The examples you give (doubling characters, random capitalization) show how drastically entropy can shift depending on the structure of the encoding — not necessarily the language itself.

To show it clearly to everybody, I ran a character-level perplexity analysis on a Latin philosophical text (De Docta Ignorantia). Then I created two variants:

1. Doubled every character (ddee  ddooccttaa...)
   
2. Randomly capitalized letters (dE DocTA iGNorANTiA)
   

Here are the results (perplexity across n-grams from 1 to 9):



So while random capitalization increased the perplexity dramatically, doubling the characters actually reduced it — especially for higher-order n-grams. This is because repetition makes the sequence far more predictable: once you see a d, you know the next character is another d, and so on.

This highlights a subtle but important distinction:

• Entropy and perplexity depend on how information is distributed in the symbol stream, not just the richness or structure of the language itself.
  
• A more "redundant" encoding lowers perplexity, because it’s easier to guess what’s coming next — even if the underlying content hasn't changed at all.
  

So when we see low perplexity in something like Voynichese, it may reflect a repetitive or inefficient encoding system, rather than an inherently simple or transparent language. Given that Voynichese was created centuries before modern linguistic or cryptographic theory, this is entirely plausible.

Thanks again for the insightful comment — it's an important reminder not to overinterpret statistical measures without considering encoding effects.