Home > cipher, gallows, Rene Zandbergen, Stolfi > Nine Cipher Wheels

Nine Cipher Wheels

UPDATE (12 Aug 2021): the plots and results discussed in this post used a version of EVA that replaces some common glyph sequences by a single glyph, namely ch, sh, ain, aiin, and qo. Clearly, this tends to reduce the average word length. A later post will discuss the distributions obtained with words without this simplification.

The lengths of VMS words follow the binomial distribution for 9, as observed by Stolfi, and as discussed in Rene’s recent paper. This binomial distribution can be obtained from a set of 9 cipher wheels, where each wheel has a 50% chance of contributing one of its glyphs to the word being assembled, and the lengths of the resulting words plotted:

Words lengths obtained from a set of 9 cipher wheels where a glyph is picked from each wheel with probability 0.5.

In the above plot, the orange line shows the distribution of word lengths from EVA, and the blue line shows the distribution of word lengths obtained by using the following set of 9 cipher wheels to generate a large number of random words:

Example cipher wheels used to generate words.

With the cipher wheels shown, about 50% of the generated words will contain a gallows glyph, and this is, perhaps not coincidentally, the case in the VMS text, too.

Using the same technique as applied in my earlier blog post, where I looked at the counts between gallows glyphs in the VMS text, we can look at the same distributions for words generated with the above wheels, assembled into lines of text, and ignoring spaces between words. The results are very similar, and shown below.

Comparing the counts from f to the next gallows in the VMS (left plot) and synthetic text generated with 9 wheels, one wheel having gallows glyphs (right plot).

Here are the others:

  1. August 12, 2021 at 6:40 am

    Hi, I think that you are missing one character from the word length distribution. The minimum is one, not zero, which I solved by having one (hypothetical) wheel generating not 0 or 1, but 1 or 2 characters.This will bring the graphs closer together.

    A crucial issue is the uncertainty of word spaces in the MS. Some long words may be concatenations of shorter words…

    In any case, I am not really that convinced that this ‘wheels’ approach can work, but it is an interesting avenue of attack that may lead to new insights.

    • JB
      August 12, 2021 at 11:04 am

      I had to revisit what I did to make the plots in this post! I was reducing some common glyph sequences like ch to a single glyph. Without that, the word length distributions are binomial but not of 9. I guess Stolfi must have made the same or similar reductions.

  2. November 26, 2021 at 5:02 pm

    Julian, I no longer have Flint’s book, but I know that when I was researching the preacher’s wheels (years ago, as part of a commissioned study), it was among those I considered.

    Couldn’t for the life of me recall her name, but thanks to Nick Pelling’s open-discussion style blog, I found the details below a post he put there in 2011, ‘A Brief History of Generated Texts’ ciphermysteries, (November 4th., 2011). He speaks in detail about wheels of different types. I’d also spoken of other-than-preachers-wheels in several studies published through voynichimagery. Let’s hope you manage to crack the problem.

    In 2011, Pelling asked about the term ‘preachers wheels’ and even a decade ago it was old stuff.. I wrote:

    [open quote]
    I read about this in depth about 18 years ago, so it’s just something I know now.

    OK – there was if I recall a brief discussion in a so-so book on the history of magic, in relation to a paper astrolabe attached to a manuscript. (Looked it up – Flint is the author’s name ‘The rise of Magic… should be around p.200s where she talks about the Sortes Sangalensis). I now have only one of Carruther’s books.

    Very nice short discussion in her ‘Book of Memory’ pp251ff. She speaks of John Garland and the Rota Virgili. Also that ms above may be sameas ms.bodley177 fol.62r.
    Carruthers’ ppp foll. go straight on to talk of Lull. (I expect there’s more relevant matter too in her later books. Can’t recall offhand).

    .. I can’t quote you the manuscript/s for the Scala Paradisi, but the edition I had is still available, and the intro might have the details for you.
    John Climacus, The Ladder of Divine Ascent, (1984) Classics of Western Spirituality Series.

    [end quote]

    For Nick’s post and the ensuing discussion and exchange see:


    It wasn’t a new thought even in 2011, but I think Pelling dealt fairly topic, and – just as importantly if a study is to progress – to the others before him.


  1. April 27, 2022 at 8:47 pm

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: