geoffreycaveney's Judaeo-Greek theory

[geoffreycaveney]

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Your table actually seems to cause a slight increase in conditional entropy: character sequences are more unpredictable. In Greek (as in basically all languages) vowels and consonants tend to alternate. Your process removes some vowels and has characters that can function as both vowels and consonants: the result is more unpredictability i.e. higher conditional entropy. Even if your table slightly reduces the size of the alphabet, the ambiguation process results in only a small decrease in character entropy. In other words, the transformed text has entropy values close to those of Greek, with a conditional entropy that is marginally higher than the original Greek and much higher than Voynichese.

For instance, the Iliad fragment you considered You are not allowed to view links. Register or Login to view. has
character entropy: 4.10
conditional entropy: 2.45

A Voynich fragment of the same length:
character entropy: 3.77
conditional entropy: 1.68 (much lower than Greek)

If you transform the Iliad fragment according to your table you get something like this (one of an almost infinite number of possible outcomes):

Sisir eor kC li dCye koa kZey rtrdy
ZitsZi qiray prS sSkoeo kiray k
i liS q okC SaSN Zrol paril aldelatolae
roZ SeS lai SayZay Zr triy pkCkd yZae
e s tS eqs CtSC dCrCl y pasrCka iaCaN
dreZo Soi qry oyZro di kardN Z Sde edS
ayas eka ta l dto siry kSsaCa qitoiC

(where C stands for "ch", N for 'iin', S and Z for open/closed "sh")

Entropy values are now:
character entropy: 3.95
conditional entropy: 2.54 (just higher than Greek, much higher than the VMS)

This is the second part of my reply to Marco's post. Here I want to focus on this issue of the entropy values of the text, character entropy and conditional entropy.

We must distinguish between two very different steps of the encryption process: 

1) First there is the compression of the alphabet, whereby each group of phonetically related letters is merged into a single letter each. 
Thus 
"t"/"th"/"d" all > [k]
"k"/"kh"/"g" all > [t]
"p"/"ph"/"b" all > [d]  (in the majority of the text where [p] and [f] are not used)
"s"/"z" both > [y]
"m"/"n" both > [l]
"l"/"r" both > [r]
(The vowels unfortunately overlap somewhat and thus are not quite this simple; I consider this a result of the role of the Hebrew alphabet, or a similar writing system, at some stage of the encryption process.)

This is actually the most complicating step and creates the most actual difficulties in reading and interpreting the text. When I refer to the "ambiguation" of the text, I am referring to this step of compressing the alphabet. That is because the resulting characters are ambiguous: [k] could represent "t" or "th" or "d", [r] could represent "r" or "l", etc. 

2) The following step, although it obscures the text on the surface, is actually simpler in principle, and much easier to account for when reading and interpreting the text, once one has figured out the encryption method correctly. It is the classic cryptographic method of "homophonic substitution", which by the way was already known to have been used in northern Italy at the beginning of the 15th century, and so is not anachronistic as applied to the Voynich MS. In this step, for each of the above single cipher characters, the author then created one or more alternate cipher characters that mean the same thing:

[k] > [k] or [s] or [sh] with open loop
[t] > [t] or [q]  ("g" pronounced as a "y" glide in Greek is a separate special case)
[d] > [d] or [p] or [f]  (here only considering the original consonants)
(Note: I believe in the actual composition of the MS that in fact [d] was a substitute for [p] and [f], not the other way around. But it makes no difference in the end result of the final MS text, as long as the author could still recognize which [d]'s were "consonantal" and only (optionally) replace some of them with [p] or [f] in first lines of paragraphs.)
[y] > [y] or [m] or [g]
[l] > [l] or [sh] with closed loop or final [(i)in]
(Again, I am only describing the original consonants in this summary so that it is easier for the reader to follow and understand the basic process.)

I describe this second step as "obfuscation" rather than "ambiguation". It is a classic cryptographic method designed to make letter frequencies harder to recognize. But once such a step is discovered and the encryption method understood, it can be deciphered readily and no longer presents a difficulty in reading and interpreting the text.

Now here is the key point to grasp in terms of the effect of these two distinct steps on the entropy of the text:

The second step, the "homophonic substitution" or "obfuscation" step of the encryption, can be carried out by the author in a very great variety of complicated ways. But the author doesn't have to use such a great variety of complicated ways to carry out this step. An author whose aim is to achieve maximum cryptographic complexity and obfuscation of the resulting cipher text, will choose a very complicated way to perform this step. I believe that Marco did just such a thing in his example of the application of this whole encryption system to the given passage from the Iliad. 

But the author is not and was not obligated to make the actual application of this step of the process so complicated and obscure. In fact, I conclude that the Voynich MS author actually chose a rather simple and for the most part regular method to carry out this step, with particular alternate characters occurring in particular parts of words and lines, and before or after particular neighboring characters.

The point is, the author's choice of how to carry out this homophonic substitution step, will have a very significant effect on the entropy values of the resulting text. Marco chose to perform this step in a way that created a resulting text with rather high entropy values. But one could just as well carry out this step in a more predictable, regular, systematic way, with the same substitutions being performed in the same parts of words and lines, and before or after the same neighboring characters. This different approach and application of the same encryption system would create a resulting text with much lower entropy values. And this in fact is what I conclude that the Voynich MS author actually did.

This explains why the encryption system that I propose, which could create a resulting text with rather high entropy values, as Marco demonstrates, still at the same time could also create a resulting text with much lower entropy values, such as the Voynich MS text itself. It all depends upon the free choice of the author with respect to how to carry out this homophonic substitution step of the encryption process.

Geoffrey