Duodecimal?

Research 30 June, text

Test case

Still on page 70v of the Voynich Manuscript (VMS), image 127 in the collection of the Yale University, the ‘word’ or code “otolal”, otolal. My conjecture is that it encodes ‘pisces’, via the Vulgate Bible in Latin. If that is really so, how does the encoding work?

Grammar

According to Stolfi’s word grammar, the VMS ‘word’ “otolal” consists of a Core element ot, followed by two CrustSuffixes, -ol- and -al. In order to unambiguously identify a Latin word from the Vulgate, we would need: book, chapter, letter, and word count. That’s four elements, but in “otolal”, otolal, I see only three. So one must have the default value. I assume it’s the letter.

That eliminates a fundamental difficulty I’m still having: so far I haven’t been able to find an online Vulgate Bible that indicates the letters within the chapters, that the Saint-Cher Concordance uses. For an exact word count, you need to know exactly where the chapter divisions start. Just saying a chapter is divided into seven roughly equal parts, clearly isn’t enough. By assuming the letter is the default, ‘a’, I can count from the beginning of the chapter. Easy.

A Core consists of OGallows, perhaps following by OE, but clearly not here. OGallows can be Gallows, possibly preceded by an ‘o’, as is the case here, or by a ‘y’. If the element G isn’t surrounded by c and h, it can be t, p, k or f. Four possibilities. Perhaps those stand for the four Gospels? With the preceding ‘o’ or ‘y’ or nothing assumed to represent the Old or New Testament, or the Apocrypha.

Perhaps only four books of the Pentateuch are used, excluding Numbers, which contains a lot of names and numbers, that are not very useful for the purpose of encoding the Latin words of a secret text.

That leaves the elements -ol-al of “ot-ol-al” for encoding chapter and word count.

Search by elimination

I'll put that hard-to-read concordance aside for now, and being the spoiled modern computer user that I am, I use the grep search utility on downloaded text versions of the Vulgate books. Of the Pentateuch only Genesis 9:2 qualifies. Not Exodus 7, because the two occurrences are both to far into the chapter, so wouldn’t have ‘a’ as their letter, in the assumed concordance-based location encoding.

Of the Gospels, Matthew 7, 14 and 15, and Mark 6 cannot be right: also too far into the chapter to have an ‘a’. Luke 9:13 maybe? Luke 9 has 62 verses, that’s almost 63 or 7 times 9, so verse 13 is probably in section ‘b’ of the chapter, not ‘a’. That leaves John 6:9 as the only possibility in the Gospels.

Now let’s see if we can find a plausible structure of the counters -ol-al of “ot-ol-al”, otolal, for the remaining candidates Genesis 9:2 and John 6:9.

A CrustSuffix without an OptOFinal is CrS. Here CrS is OR.OR. OR can be R, O.R or O.O.R, and here is clearly O.R. R stands for one of the six letters d, l, r, s, n and x. O can be o, a or y, or be missing entirely. It seems likely that this letter is only there if a number higher than six is to be encoded. So that excludes John 6:9, because then the VMS ‘word’ should have been ot.l.al, with the l meaning 6, and nothing else needed for the chapter number.

So it can only be Genesis 9:2. (OK, that is if all my assumptions were right, and there were many of them. But you have to start somewhere.) The “ol” in “otolal” in a hexal number system means ‘one time six, plus 3, makes 9’, and that is indeed the chapter number.

If all of this is correct, the final element -al must mean 15 for the word count: a = 2*6, and l = 3. Now it’s really getting exciting! Maybe I should insert a cliff-hanger here. Well no, let’s just keep going. Is ‘pisces’ really the 15th word of Genesis 9? I almost could not get myself to look. But I did.

No, it’s not. In both text versions I have, from Fourmilab and from the Vatican (the two are not exactly the same!), ‘pisces’ is the 39th word!

So that’s the end of it. I’m on the wrong track with all my baseless and silly conjectures. Sorry for having wasted your time.

Bingo!

Then suddenly that afternoon of 30 June, after a nice short family bicycle tour, which often helps ease the mind and smoothen the thinking, I had this flash of genius (said he):

Those six letters, like the ‘l’ representing 6, when used as a word counter, can not only encode digits 1 thru 6, but also 7 thru 12, by adding some as yet unknown element after it. See Stolfi’s word grammar. So instead of the hexal number system used for the chapter numbers, the word counts are encoded in a duodecimal system. If ‘o’ = 1, ‘a’ can be 3, ‘l’ is still 3, and 3*12+3 equals … tada … 39!!! Isn’t that cute?

(Addition 11 July 2023: 1–6 and 7–12, or rather 0–5 and 6–11?)