Interchangeable ch/sh and k/t characters

[Jorge_Stolfi]

The problem with Voynich solutions is that solvers* do not explain how their target language has such a low entropy when written in the Voynich script and would presumably in its usual script have a higher entropy.

If a proposed solution is a simple one-to-one letter substitution cipher, the frequency distributions of glyphs (D1) and of digraphs (D2) of the encrypted text should be the the same as those of the plaintext, modulo the substitution.   (The zero-order entropy H0 is determined by D1 and the first-order entropy H1 is determined by D2, so looking at D1 and D2 should be more revealing than looking at H0 and H1 alone.)

But this is not the case if the claimed solution is anything more complicated than a one-to-one substitution cipher.   Then the D's (and H's) of the encrypted text may be quite uninformative.  One can easily construct a deterministic lossless encryption method that will take typical English prose text and produce an encrypted text with arbitrarily low H0 and H1 entropies. Or with H0 and H1 equal to the limit of log2(26) = 4.7 bits per letter.

Therefore, if one intends to use the distributions D1 and D2 (or the entropies H0 and H1) to test the validity of the solution, one should instead compute them on the decoded plaintext.  The result would be the same in the simplest case, but would be meaningful for any deterministic lossless cipher, even a codebook (nomenclator) one.

However, what should we conclude if the decoded plaintext is claimed to be (say) Latin, but its D's turn out to be very different from the typical Latin prose text?  If the decoded text turns out to be "phares genuit hesron hesron genuit ram ram genuit aminadab aminadab genuit nahasson nahasson genuit salmon salmon genuit booz booz genuit obed obed genuit isai isai genuit david" -- can we say that the solution is wrong because this text has weird D1 and D2?  Can we demand that the person proposing the solution provide an explanation for these anomalous statistics?

Well, no; we can only say that, statistically, the plaintext of the VMS happens to be a rathe atypical Latin prose text.   

In fact, if the proposed solution produces this text when fed lines f1r.1-5, it would be hard to argue that the solution is wrong.

But you say:

In most cases, I would imagine they cannot explain, because their solution is actually not just a simple substitution system but a product of multiple, diverse, and fatally inconsistent decisions to add or remove letters in order to match Voynichese words with their target language, and none of this can be formalised and reproduced.

So the issue is how to refute solutions that postulate a lossy encryption method -- whose decoding must involve guesses.  But looking at the D's (or H's) of the encrypted text will not help.  If the encryption is not a simple one-to-one substitution, these statistics of the encrypted text will be hard to relate to the statistics of the decoded plaintext; and anyway these would not tell us whether the solution is valid or not (see the example above).

I can't think of any mathemagical way to decide whether a non-deterministic decryption method is valid.  The question is basically whether the encryption method is "effectively" invertible: that is, if Alice encrypts a secret -- but meaningful and plausible -- plaintext T in the alleged language, and Bob decodes the encrypted text E, whether he will reliably obtain a text T' that is sufficiently close to T.  But Bob must allowed to chose the guesses any way he can, including You are not allowed to view links. Register or Login to view. or unlimited trial and error until he obtains a text that seems plausible to him.

So I think that the most (only?) reliable way to evaluate a proposed solution is to perform this challenge test.  Statistics seem pretty useless for that purpose.

All the best, --stolfi