- Line breaks in the VM do not act like line breaks in a natural text, in that they do not provide evidence of whether the text runs left-to-right or right-to-left.
- Word breaks in Currier A act like word breaks in a natural text, but in Currier B they do not.
- Since my analysis of F81R as a poem was based on the assumption that line breaks and word breaks were natural, yet they turn out not to be natural at all, there remains nothing to support the idea that this page contains a poem.
Sunday, September 19, 2021
Thursday, September 16, 2021
In the Latin ISE corpus, the word 'in' is the second most frequent word, and it would be surprising if this word was not among the top ten words of any Latin text of significant length. The word 'in' also has the property that it is rarely followed by another high-frequency word. The reason for this is that 'in' is a preposition, and is therefore usually followed by a noun with high semantic content, and those words are generally lower in frequency than function words.
Despite the fact that it is rarely followed by another high-frequency word, 'in' is commonly preceded by another high-frequency word, particularly 'et', 'est' or 'ut'. This can be seen in the frequencies by which the top ten most frequent words appear together:
Wednesday, September 15, 2021
In this post I'll look at similarities between high-frequency qok- words in Currier B and high-frequency qu- words in Latin.
1. Textual Frequency
The prefix qu- is the most frequent two-letter prefix in the Latin ISE corpus, and the prefix qok- is the most frequent three-letter prefix in Currier B.
2. Zipf Rank
The most frequent qok- words in Currier B occupy similar Zipf ranks to the most frequent qu- words in Latin (though the Currier B words have a tendency to have lower Zipf ranks).
Some of the qu- words in Latin may be reduplicated, as may some of the qok- words in Currier B:
Sunday, September 12, 2021
Currier B has the high-frequency words qokeedy, qokain, qokedy, qokeey and qokain which raises the textual frequency of the prefix qo- relative to its lexical frequency.
Tuesday, September 7, 2021
My efforts to get a copy of The Curse of the Voynich are themselves apparently cursed. The first time I tried to order this book I was at a vacation rental for a month, and discovered that the postal service would not deliver it because the rental had no mailbox. The second time my order was canceled because the book was out of stock. I am hopeful that my third effort will meet with a better outcome.
While I wait for it to arrive, however, I've been looking at one of Nick Pelling's ideas. Did the Voynich cipher employ contraction and abbreviation as part of its process? If so, it seems like this could explain the relatively low amount of information conveyed by Voynichese words. It would be a lossy compression process similar to the removal of vowels, but perhaps more culturally appropriate to the 15th century.
I looked at the 1901 German translation of Adriano Cappelli's Lexicon abbreviaturarum, and it seems that conventions for contraction and abbreviation evolved over time such that by the 14th or 15th centuries scribes were using a number of methods in conjunction, including the use of a small set of symbols borrowed from Tironian notes. In order to understand these processes better, I took thirty random entries from the lexicon and looked at what the scribes chose to keep from the full written word and what they felt they were able to do away with. In general, I found that words could be divided into three parts:
Prefix: The prefix is made of consecutive letters from the start of the word, including at minimum the first letter. In my samples, the prefix is one character long about 53% of the time, two characters about 23% of the time, three characters about 6% of the time.
Infix: The infix is made of of letters that are generally not consecutive, chosen from the middle of the word. Presumably these are letters that differentiate between one contracted word and another. There is roughly 12% chance that a given letter from the middle of the word will appear in the infix.
Suffix: The suffix is made of consecutive letters from the end of the word, except the -m of accusative endings, which is sometimes dropped. The last letter was included in the suffix about 63% of the time, the second-to-last about 30% of the time, the third-to-last about 6% of the time.
What is interesting about this, to me, is that the first letter of each word is always retained. That means, if the Voynich cipher employs abbreviations and/or contractions, and the subsequent steps are only forms of substitution (and not, for example, transposition), then it might be possible to crack the first letters of Voynichese words.
It would be hard to know if you had gotten it right, though!
Thursday, August 26, 2021
I've just read an article titled The Linguistics of the Voynich Manuscript by Claire L. Bowern and Luke Lindemann, which summarizes previous scholarship on the manuscript and concludes that "the character-level metrics show Voynichese to be unusual, while the word- and line-level metrics show it to be regular natural language."
Reading the article reminded me to finish this post, which I started several weeks ago. Here, I'll outline a cipher using ideas from my previous posts, which I believe a late medieval or early Renaissance scholar might plausibly have created, which I think would produce some of the features of the Voynich manuscript.
I'll walk through the cipher steps with an English phrase and a Latin phrase: Can you read these words? Potesne legere haec verba?
Step 1: Remove the vowels from all of the words. This is what causes the words of the cipher text to carry less information than they would in the source language. In this example I'm treating the letter v as a vowel in Latin, but w as a consonant in English, because these are the historical conventions in these languages.
English; cn y rd ths wrds?
Latin: ptsn lgr hc rb?
It is an open question for me whether it is feasible to reverse this step in Latin. In English I know it is reasonable if you are familiar with the general content of the text, because a similar approach was used to create mnemonics describing Masonic ceremonies:
Step 2: Encipher each word using a substitution cipher that replaces each letter with a syllable, with special syllables reserved for the last letters in each word, to create the appearance of an inflected language. This is what creates the low second-order character entropy.
In this case, I have created the key using the first and last syllables from polysyllabic words at the beginning of Virgil's Aeneid. I haven't bothered to create a complete key, it only covers the letters needed for this example.
English: viam tum prono vepria liprocaa?
Latin: favelaam otrogus prirum proma?
One of the neat things about this cipher approach is that one could hypothetically train oneself to speak the cipher.
Step 3: Write the cipher in a secret alphabet. This changes very little about the cipher, and might be considered more of a cultural requirement of the era.
To be clear, I don't think the Voynich cipher worked in exactly this way. For example, the frequency of daiin in the Currier A pages is nearly exactly the frequency of t (representing et, ut, te, tu, etc.) in a long devoweled Latin Text, but it isn't clear how daiin could be used to encode initial, medial or final t in other longer words. If the underlying language of the VM is Latin, and it is encoded using a system like this, then it is likely that there is some additional complexity in step 2. For example, there might be a set of words (like daiin, chol, chor) that encode single letters, then another set of prefixes and suffixes to encode letters in longer words.
Friday, August 6, 2021
In my last two posts, I first suggested that Voynich Manuscript 81R might contain a poem in Latin dactylic hexameter, but then I argued that the lines only convey about half of the information necessary to encode such a poem. In this post I'll try to reconcile those two arguments by showing that a late medieval/early Renaissance cipher system could have produced this effect.
The pages of the VM have been carbon-dated to between 1404 and 1438. If the text is not a hoax, and it was written within a century or so of the production of the vellum, then what cryptographic techniques might the author plausibly have known, and how would they impact the total bits per line of an enciphered poem?
According to David Kahn's The Code-Breakers, the following methods might have been available to someone in Europe during that period. For most of these, I have created simulations using the Aeneid as a plain text, and measured the effect on bits per line using the formula for Pbc from my last post.
- Writing backwards (0.2% increase)
- Substituting dots for vowels (28.5% decrease)
- Foreign alphabets (little or no change, depending on how well the foreign alphabet maps to the plaintext alphabet)
- Simple substitution (no change)
- Writing in consonants only (45.6% - 49% decrease, depending on whether v and j are treated as vowels)
- Figurate expressions (impractical to test, but likely to increase bits per line)
- Exotic alphabets (no change, same as simple substitution)
- Shorthand (impractical to test, but likely to decrease bits per line)
- Abbreviations (impractical to test, but certain to decrease bits per line)
- Word substitutions (did not test, but likely to cause moderate increase or decrease to bits per line)
- Homophones for vowels (increase bits per line, but the exact difference depends on the number of homophones per vowel. With two homophones for each vowel, there was a 19.5% increase)
- Nulls (increase bits per line, but the exact difference depends on the number of distinct nulls used and the number of nulls inserted per line)
- Homophones for consonants (increase bits per line, but the exact difference depends on the number of homophones per consonant)
- Nomenclators (impact depends on the type of nomenclator. I tested with a large nomenclator and got a 44.5% decrease in bits per line)
- Writing in consonants only
- Using a large nomenclator