Category: Voynichese & voynich glyphs

‘Weaving the Voynich’ -reprint by request.

The author’s rights are asserted.

c.2300 words

Introduction: (2022)

In 2012 Julian Bunn did something entirely new; he colour coded pages from the Voynich manuscript to show the position of the ‘gallows’-glyphs.

I had expected that Julian’s blog would appear among those listed in the Voynich ninja ‘Blogosphere’* but today I see that while a number of non-existent blogs are in their list, Julian’s is not. [update – 20th Dec. 2022 – Julian’s blog is now back in the list. 🙂 ]

*The ‘Ninja’ forum’s claim to “track the Voynich blogosphere so you don’t have to!” is a nice example of theorists’ putting higher value on assertion than on fact. 🙂

When Julian’s new approach was first published, his posts met near-complete silence. No buzz, few comments. Recently, though, it has re-surfaced and one would hope that credit is being accurately assigned by the more recent revivalists to the author of that ground-breaking study.

By June of 2021 2012, Julian had presented every page of the manuscript with the gallows glyphs colour-coded, and presently those images remain visible online.(HERE).

He would later publish a full-colour version, giving every glyph its own colour, but the post I’ve been asked to re-print (the request didn’t come from Julian) was written before he found time to make the full-colour version.

I might add that Julian is no crony of mine. He is (or was) an arch-conservative of deepest dye – and as you will see from the list of researchers whose existence he chose to advertise on his personal blog.

When he first published that work in 2012, I was still mulling over something he had written a few months earlier:

I am convinced that it is not as simple as it appears (i.e. that the words are not words at all)

Julian Bunn, ‘How was the Voynich Manuscript text written?‘, computistical attacks (blog), August 23, 2012.

The post from which I’m republishing what you see below contained more than I republish now, and was one of perhaps only four or five I’ve ever published that wasn’t a summary of my own research and its conclusions.

As a rule I consider it a complete waste of time to publish mere “ideas” and as a rule I try not to offer opinions about the written part of the text.

In this post, published almost a decade ago, I set aside both self-imposed rules, one of only four or five times I’ve ever done so.

—————-

taken from:

D.N.O’Donovan ‘Weaving the Voynich – seriously’, Voynichimagery (first published December 28th., 2012).


Here is a new set of images, for each of the folios in the VMs, that shows the positions of the various gallows glyphs.

To clarify – these “positions” are not the positions as seen on the image scans of the manuscript itself, they are the positions in terms of glyph position along each line.

The difference between these and the ones in the previous post is that these have Gallows “f” coloured blue, “g” coloured green, and the other gallows coloured red (as before).

Julian Bunn, ‘Page positional gallows Mark II’, computistical attacks (blog) 28th December 2012.

Shortly before publishing this recent post, Julian said in another that “I am convinced that .. the words are not words at all).

to which the natural response is – “well, if not words, what are they?”

I have received Julian’s permission to include some pictures from  Julian’s blogpost.

As he says, the distributions of gallows on those pictures aren’t exact matches with positions on the folios, but I don’t think it matters very much.

You will see that in Julian’ s picture for  f.58v  the left-hand margin shows a vertical series separated from the rest –  separated in Julian’s picture by grey, though the interval is filled with non-gallows glyphs in the manuscript.

One section in that margin resembles one of the simplest  arrangements for thread in a woven fabric. and in this same image you will see (to the right of the margin), a staggered vertical line of blocks echoing another which is typical of some patterns generated in weaving from that first.

How are the two related?

The two most basic forms of weave are linen weave (‘tabby’) and twill.

Tabby is the usual 1×1 over-and-under pattern used for linen. Twill creates a diagonal line, achieved partly by the way the loom is threaded up, and partly by the order in which certain elements are brought up while others are lowered. The first is called the ‘threading pattern’ and the second the ‘treading pattern’. More technical details are included further below.

Distinction between a separate representation a fabric’s threading pattern, and (with a more sophisticated loom) the treading pattern. Today, a weaving pattern will use the margin (left or right) to record the treading pattern, with the basic threading pattern shown across the top of the diagram, as shown in the illustration below.

Patterns represented on graph paper, and modern gridded instructions will present an artificial, theoretically-even thickness and distance for warp and weft.

Julian’s illustrations have an artificial regularity of a different kind. If any were weaving patterns, what you see on a diagram would come closer to a pattern’s intended form but in practice hand-woven fabrics rarely emerge so regular.

As you see from the following example, the illustration (below, right) is  a copy of Julian’s data for  f.103v, but I’ve stretched it to reflect a typical difference between a formal diagram and what one sees in practice.

The second illustration (below, centre) comes from a different inner Asian [Turkmen] rug from that illustrated on the far left, but shows more clearly the ‘gol’ pattern whose equivalent is seen in a number of Julian’s diagrams – that is, facing diagonals which form just two sides of a potential lozenge motif. In other words, I’m suggesting the glyphs could be used to represent (by alpha-numeric?) as many different hues or tones.

To colour opposite sides of a medallion (gul/gol) differently is characteristic of the Turkmen style, sometimes called the Kurdish. The regions native to Kurdish people include southeastern Turkey, northwestern Iran, northern Iraq, and northern Syria.

Glyphs, Number, colour.

This brings up the question of the glyphs’ number and how they might relate to a colour-range. I hadn’t any notion, when I wrote a first brief version of this post some days ago [in 2012] that the ‘weaving’ technique can be equated more-or-less roughly to a ‘bilateral cipher’.

Here is an old post (ciphermysteries of course) referring and crediting Tony Gaffney with making the [bilateral cipher] suggestion. 

Nick himself raised the theme of bilateral ciphers again very recently [26th December 2012] and  shortly after my original short preview- for this ‘weaving’ post went up.

I suggested that if there were seventeen distinct gallows glyphs (an idea I’d picked up at some time), they would offer a natural system for someone to describe a type of colour-wheel, if they were being employed by persons accustomed to describing a circuit of 32 in terms of a basic 17, as occurs among the eastern mariners, who named each Pole by a separate word, but the other thirty by naming 15 around the eastern curve with the epithet ‘rising’, with the same fifteen on the opposite curve as ‘setting’.

Thirty-two is a number well-suited to recording languages. A quick check of Omniglot gives 32 components for:

Islandic; Estonian; modern Persian; Coptic; Tigrinya; Russian; Lithuanian; Perso-Arabic; Belarus; Bulgarian and Kurdish (Kurmanji-).

To use the ’17’ system, you’d need a  couple of  glyphs that were unique, and fifteen having their ‘pairs’ – one supposes, in the present case, as a gallows-and-glyph with each gallows having a different following glyph.

I’m not suggesting that the Voynich text refers to nothing but weaving and colours; I’d assume colour would be one of many sets of associations that could be built on an alpha-numeric series, just as Latins built upon the Roman alphabet and from a foundation in the Psalter or – to take another example, as Ibn Arabi built his set of associations upon the series of  27 lunar mansions.

If there were a correspondence here between the set of colours and the set of  glyphs ( or simply of gallows glyphs), and they were disposed as pairs (and or as darker and lighter tones), that correspondence, if it could be established,  might be a way into identifying the language natural to the maker of the manuscript. A slender hope but a possibility.

Relationship between a ‘letter’ and sound might be direct, but between a letter, its position, and/or a colour the relationship need not be so simple.

I mean that – to give an example – the word for green might start with  ‘g’ but by custom that colour imagined the primary element in a people’s cosmology and so, by that people, accorded the number one or letter ‘A’ position.

A wheel of numbered hues which could be described in terms of the ‘bright’/rising and the ‘dark’/setting curve

OMNIGLOT has a table for colours in many languages. I think it was extremely brave of them to post it!

This isn’t the only suggestion of textiles and textile arts in the manuscript.  In discussing the botanical section last year [i.e. in 2011] I illustrated fairly copiously the way the drawing style in many folios from that  section echoes those of inner Asia ( especially patterns of Suzani work in Uzbekistan) and also types of textiles created near ports of medieval India and south-east Asia.  I wont’ repeat it all, but here are a small number of the illustrations from traditional Suzani work. (However, the picture in the bottom row, a Javanese batik,  was allegedly made in the 10thC AD, and though I haven’t been able to check its provenance, I do wonder if the caption didn’t confuse the Islamic for the Christian system of dating years.

Note (2022) – a few months after I’d shown those examples of Suzani embroidery in the course of discussing stylistics in various folios of the plant-section – the first time textile art had been referenced in Voynich studies, so far as I could find – a woman promoting her theory of the entire manuscript as an expression of a European Baltic and female ritual culture posted images of Baltic embroidery. I’m afraid I’ve since forgotten her name.

TECHNICAL NOTES:

[note – some repetition here, but it keeps this section self-contained]

I have never seen any type of weavers’ instructions or recipes from the fifteenth century nor earlier – not from Europe; not from anywhere.

It is often easier to produce a complex pattern by having someone call out the order of operations. I know this was done until recently in workshops producing Persian carpets but as with so many skills, I expect that in the case of traditional weavers most had simply learned their craft at the elbow of their parent or trade master.

Not even Agnes Geijer, whose masterful study of textiles is now sadly out of print, has much to say about how detailed instructions were preserved and transmitted for such complex designs as those on damasks and cut- velvets. From the accuracy with which some western medieval centres such as Venice were able to re-create eastern patterns, we know some sort of textile-analysis must have been possible and this also implies some system for recording and transmitting the information. I’ve never encountered any study which addressed that question for a period earlier than 1450.

The basics of a modern pattern consist of the pattern’s depiction in a grid, with the pattern of threading-up in the margin of one axis, and of treading in the other. Like this. (The section in the upper right corner describes how the heddles, through which the warp threads are strung, are to be linked to one another and the treadles)

The basic threading-up pattern (here the upper margin) has variations created by the treading pattern (in the image above, the right margin). The threading pattern thus provides you, more-or-less, with a profile view of the design, and this will also appear in the selvage.

A modern hand-weaver will find fully graphed patterns in any reference book,  but an experienced weaver wouldn’t trouble to draw up a whole design unless it were extremely complex.

Most modern hand-weavers use numbers for threading and treading order, but if the warp is multicoloured, it’s possible to use colours instead and I have seen it done in some American graphs.

To show how many variations on a basic threading can be produced, here are twelve from a single threading-up.

[2022].  The link to that diagram is broken, though if you care to chase it through ‘Wayback’ etc., just undo the caps below.

http://www.weavingtoday..com/cfs-filesystemfile.ashx/__key/CommunityServer.Discussions.Components.Files/50/4606.4Shaft4BlockSamplerProfileA1.jpg

Postscript “not words at all”

A most important question which any reader is bound to ask of a Voynich writer is “What first suggested this idea to you?”

If the answer is ‘It just came to me’ or ‘It is a theory’ or they refuse to reply but adopt a pose of hauteur, then you’re entitled to wonder if their argument is actually unjustifiable, whether because it is literally a baseless notion or because it is not a result of the speaker’s own work but merely what they could grasp from work done by someone else.

You can see clearly enough how Julian came to conclude (temporarily or permanently) that Voynich words were ‘not words at all” by following the series of posts he published leading up to that one published on August 23, 2012..

You might also enjoy some posts that bear a more recent date:

Julian Bunn, ‘Nine Cipher Wheels‘, Computational attacks… (August 9th/update August 12th., 2021).

___________, ‘Word-length Distributions‘, Computational attacks (August 12th., 2021)

___________, ‘Fun with Grove Words and Cipher Wheels‘, Computational Attacks.. (August 18th., 2021)

_____________, ‘Grove Word lengths’, Computational attacks… (August 19th., 2021)

Consider this.. Lull, Kabbalah and ciphers.

or:

“Still speculation after all these years.”

.

Question-set 1:

Is it true that Ramon Llull was acquainted with Kabbalah? How long has the idea been around? Who first suggested it? Was there, then – or is there now – any evidence to justify the idea/assertion?

Question-set 2:

Is it true that Llull’s ‘combinatorial’ system was devised, or used by Lull, as a method for encryption? Who first suggested that use for it? Was there then, or is there now, any evidence to justify the idea?

Question-set #3.

Who first associated Ramon Llull with the Voynich manuscript? What reason did they give? Was there then, or is there now, any evidence dating from between c. 1260 (Lull’s maturity) and 1348 1438 which might lend support to that notion?

The short answer to all three ‘Is there any evidence..?’ questions is a simple “No”.

There is no evidence to support, and much to deny even the possibility that Ramon Lull was familiar with Kabbalah, or that his combinatorial system was ever devised from an idea that it might be used to encipher or encrypt text. There is no evidence that anything in Lull’s work influenced Alberti, his wheel, or the Voynich manuscript.

So before any revived “Llull-Voynich” notion transmutes into another faith-dependent ‘doctrine’, here’s the lineage for the three-link, circular, ‘Llull-Alberti-Voynichese’ storyline.

.

To break it down:

  1. Lull and … Kabbalism.

This speculation arose first in connection with a specific and unusual Kabbalist, the messianic Abraham ben Samuel Abulafia. But after almost five hundred years’ intermittent scholarly investigation, that imagined link has been found an idea without merit and rejected by a consensus very neatly summarised by Jan R. Veenstra’s note within his review of a book published in 2004 and whose author was attempting to justify the old idea. Veensta’s footnote reads:

The issue has been touched upon by a few scholars and was first raised in the fifteenth century by Giovanni Pico della Mirandola who, in one of his Conclusiones , suggested that Llull’s combinatory art resembles Abulafia’s ecstatic Kabbalah.

The systems, however, are too distinct to argue for any kind of substantial influence and any research focusing on a text-immanent reading of Llull and his possible sources will be bound to conclude that Kabbalah plays no significant role in his works ….. Explicit references to Kabbalah seem to be absent; parallels between Lullian and Kabbalistic concepts are often too vague or incomplete to warrant an undeniable influence.”

  • Jan R. Veenstra, [Review of] Harvey J. Hames, ‘The Art of Conversion: Christianity and Kabbalah in the Thirteenth Century’. Vivarum,  Vol. 42, No. 2 (2004), pp. 262-266.

  •  David Abulafia’s review of Hames’ Like Angels on Jacob’s Ladder: Abraham Abulafia, the Franciscans, and Joachimism (2007), review published in Speculum, Vol. 87, No. 2 (April, 2012), pp. 561-562.

So the judgement of half a millennium’s investigation of Lull’s works and of Kabbalism rejects Pico della Mirandola’s impression of common character between Abulafia’s Kabbalism and Llull’s approach to preaching Christianity to Muslims.

To the first set of questions, therefore, the answers are:

The first person to ever suggest connection between Lull and Kabbalah was Pico della Mirandola, in a non-specific simile proffered without evidence and for which no support has been found to this day.

.

2. Lull … and cipher. (specifically, polyalphabetic substitution ciphers).

In 1980, David Kahn claimed responsibility for this one. Wanting to provide a different explanation for how Alberti came to invent his cipher-wheel, and while disputing an earlier posited explanation, Kahn wrote:

Alberti himself never said where he got the idea for his epoch-making invention. … the significant feature of [Alberti’s] cipher disk [is] the juxtaposition of two [alphabetic] sequences…. I propose [as its source]  the mechanism devised by the medieval Catalan mystic Ramon Lull (c. 1232-1315) to combine letters, which stand for philosophical concepts, in groups of three. Although it cannot be proved that Lull’s device inspired Alberti, there are grounds for suspecting that it did.

  • David Kahn, ‘On the Origin of Polyalphabetic Substitution’, Isis , Mar., 1980, Vol. 71, No. 1 (Mar., 1980), pp. 122-127.

  • Note – 9th Jan. 2022 – I apologise for not having earlier noticed that Kahn’s name had been ‘autocorrected’ to Khan.  

I’m not sure how grounds for supposing so can be judged if they don’t admit of proof, but here I want to make the point that each of the three links in that Lull-Kabbalah-cipher chain has been introduced by persons interested in cryptography, and not by persons adducing such a connection from their close study of Lull’s life and works nor (on the other side of the coin) of medieval Kabbalism. It’s a cipher-guy (or gal) thing.

If Kahn ever suggested that the Voynich text is the product of an Alberti-style polyalphabetic cipher, I’ve not seen the article, so if you know of his ever making such an argument, please leave a comment and reference below and I’ll add a note of correction here.

Readers uninterested in cryptography and unlikely to buy Kahn’s books, will find a Voynich-context discussion of polyalphabetic substitution ciphers in a post by Nick Pelling (2016) and if the reader is disinclined to follow the following link and read the post, with or without its 891 comments (yes, that is eight hundred and ninety-one), I’ll quote you just a couple of paragraphs from it.

Since the Voynich Manuscript surfaced in about 1912, many of the best-known codebreaking experts have studied its writing (‘Voynichese’) in depth. Of them, many have concluded that it was written using a cipher system that was (a) stronger than a simple (monoalphabetic) substitution cipher, yet (b) mathematically weaker than a polyalphabetic cipher.

If the University of Arizona’s 2009 radiocarbon dating of the Voynich Manuscript’s vellum (which points to the first half of the fifteenth century) is correct, the most likely reason for (b) becomes blindingly obvious: polyalphabetic ciphers (such as those of Leon Battista Alberti, Abbot Trithemius, and Vigenère) hadn’t yet been invented.

To which I’d add “… in Latin Europe, so far as we know.”

The history of cryptography is still a little old-fashioned; a bit ‘Europe-and-its-important-men’. On the other hand, statistical analyses are indifferent to nationality and vested interest in any theory, so it looks as if the chief contrary argument isn’t whether Alberti was old enough to have made Voynichese as a polyalphabetic cipher, but that the statistics don’t support the idea of the text – if it is enciphered – as either or both a product of Latin Europe and of Alberti’s system.

Simple alphabetic substitution ciphers had been known for not less than five centuries by the thirteenth century when Roger Bacon described that system. For Roger Bacon’s text and (again) John Block Friedman’s important article, it’s easiest to just start from this post:

With regard to documentation in Voynich studies, and the ludicrous obedience of Voynicheros to ‘rule by meme’ asserting that to refer to precedents and sources is ‘unnecessary’, here is a perfect example of why documentation defines ideas as legitimate or otherwise. Pesic’s perfectly enunciated lineage for the “Lull and ciphers” storyline is how I came to know of David Kahn’s paper, too.

In the remoter background also lies Ramon Llull’s ‘Ars inventiva veritatis’, his “art of finding truth” through the symbolic use of letters to stand for philosophical concepts. Leibniz was interested in Llull, whom David Kahn has proposed as the source for the idea of polyalphabetic substitution, especially in the form of Alberti’s cipher disks. See David Kahn, “On the Origin of Polyalphabetic Substitution,” Isis, 1980, 71:122-127; rpt. in Kahn on Codes (New York: Macmillan, 1983), pp. 56-61. For Leibniz’s reading of Llull see Frances Yates, The Art of Memory (Chicago: Univ. Chicago Press, 1966), pp. 379-389; and Allison P. Coudert, Leibniz and the Kabbalah (Dordrecht: Kluwer, 1995), pp. 148-149, 153-154. Beyond Llull lies the kabbalistic Sefer Yezirah, the Book of Creation, which for Vigenère gave an account of the divine cipher immanent in the creation and which he thought also was the source of polyalphabetics. On the Sefer Yezirah (ca. third-sixth centuries) see Gershom G. Scholem, On the Kabbalah and Its Symbolism, trans. Ralph Manheim (New York: Scholem, 1969),pp. 166-169.

  • Peter Pesic, ‘Secrets, Symbols, and Systems. Parallels between Cryptanalysis and Algebra, 1580-1700’, Isis, Vol. 88, No. 4 (December, 1997), pp. 674-692. **highly recommended.

You see the point?  Vigenère thought that a Kabbalistic text, Sefer Yezirah,  was the source of polyalphabetics.  David Kahn thought, on the contrary, that Alberti had the idea for his  polyalphabetic cipher wheel from Ramon Llull.

But cryptologists often show an excessive preoccupation with the requirements of their craft – that a text be composed as ‘plaintext’ and transmitted encrypted in a form to which the intended recipient has not only the key but the same standards with regard to spelling, grammar, and a single target language. 

Yet in the real world, as anyone may know who has lived in an international student house abroad, or in a multicultural and multilingual community at home – mixed terms and even mixed forms of writing are the norm, not the exception.  We learn new terms from the mouth of someone who uses his/her own language to express them and, more or less often, others simply adopt that term rather than hunting to find their own.  As the joke has it, the English speaker asks ‘What is the French for je ne sais quoi?’ Or: ‘… the Italian for chiaroscuro?’ Where does Yiddish fit, or any other among the dozens of ‘combinatorial’ languages.. Among them one might include English if it hadn’t been elevated to the status of a true language rather than a heterogeneous patois, part Latin, part Greek, part Gaelic, part.. well, you get the idea. The classic etymologies tell only half the story.

And so now, at last, we consider the addition of the Voynich manuscript to that lineage of passing impressions, false assumptions, tenuous and even plainly disproven connections, the basic compounding of speculation, ignorance and error.

After Voynichese was stirred into the mix, the result just sat simmering for half a century. Not even tested. Just left to sit there.  

.

Llull … and Voynichese 

It is likely that to re-present d’Imperio’s mentions of Lull other than entire will lead some to suspect it may be over- or under-emphasised so here they are, in full. I apologise for the horrible quality of the print.  Perhaps one day we’ll see the text re-typed and put it up as a digital text. 

d’Imperio’s Index in Elegant Enigma spells Llull’s name ‘Lull’. (If you don’t have a touch-screen, you can open the image below in a new tab).

d'Imperio Llull

Note: Llull was never a Franciscan nor, according to the latest update of the Stanford Encyclopaedia of Philosophy, a Dominican.

For the other side of the coin – to show just how badly mangled information can become when ideas are presented without any lineage in the form of precedents and cited sources, here’s a writer who plainly never read Pesic’s paper, or many of the sources Pesic included in his note.

Sieburth is here discussing a poem written by Quirinus Kuhlmann, born in 1651 in  Breslau (Silesia) and  executed for heresy in 1689, in Moscow. 

 Kuhlmann’s sonnet is accordingly entirely made up of monosyllabic Stammwdrter (stem-words) ? nouns, adjectives, interjections all treated here like those primal Chinese ideograms that Leibniz thought could be manipulated into the perfect conceptual components of the combinatory machinery of symbolic logic ? an idea that reached back toward the ecstatic thirteenth-century Christian Kabbalah of the Catalan Ramon Llull.

Quirinus Kuhlmann and Richard Sieburth, ‘Love-Kiss XLI’, Poetry, Vol. 194, No. 1, (April 2009) pp. 13-16.

Oh dear..

Another paper I’d recommend to anyone interested in how this curious idea arose that Ramon Llull had anything to do with Beinecke MS 408, is: 

  • Janet Zweig, ‘Ars Combinatoria: Mystical Systems, Procedural Art, and the Computer’, Art Journal, Vol. 56 (1977): Digital Reflections: The Dialogue of Art and Technology, No. 3,  pp. 20-29. Recommended.

My recommending Zweig’s paper comes with a caution.  Readers should take as it’s pivotal sentence,” Contemporary with Abulafia, and not far away, Ramon Llull was born ...” and so be able to appreciate the way Zweig separates a discussion of Abulafia’s Kabbalism from discussion of  Ramon Lull’s Christian thought.

To end, a pictorial cipher from an image  included in Pesic’s paper, This cipher is said to be in a volume held by the Beinecke Library, but I found no mention of it today, and as you’ll see, no shelf-number was provided.  I hope that, under the circumstances, the library will forgive my reproducing it.

stars celestial cipher from Persic Beinecke quarter

Postscript –

Could any reader who visits the ninja.forum be kind enough to refer them to Ellie Velinska for her study and data about how many figures in the ‘ladies’ folios are made to resemble men, and how many, women.  She did that work several years ago; I don’t think it needs to be re-done as if for the first time.

Similarly, the whole discussion, a present, of the ‘ladies’ having been given one breast each, and then at some unknown time a second breast, is another instance of the ‘groundhog day’ fog which results from denying ideas their proper lineage by refusing to cite precedents and contemporary studies, even ones  whose conclusions a given Voynich theorist may not like.  

There are a few old-timers at the forum and they will know this perfectly well the true origin of those ideas and who should be credited with having contributed them to Voynich studies. It matters not at all whether the matter is still ‘in print’ – if you know, you know. If you pretend not to know, you are lying by omission,

Pelling’s observation about the originally one-breasted figures (he calls them nymphs) was part of his interview in 2009 and was referenced again – for example  – in a ciphermysteries post dated June 29th., 2015. 

I won’t pretend that Pelling  and I have often agreed when it comes to iconological analysis of the images in Beinecke MS 408,  but his confidence in his own powers of observation is not wholly unjustified and in this case certainly his observation is an original and valuable contribution to the study.

I do, absolutely, accept his observation that the ‘ladies’ had originally a single breast.  Where Pelling and I differ is in the inference drawn from that fact. About others of his comments in the same blogpost I’ll not comment here. 

But see:

Consider this… (cont). Kircher, scripts, languages & Aramaic.

Header image: ‘Alphabet iliricum sclavor’ included in a model book of 1561 . Libellus valde doctus elegans, & vtilis, multa et varia scribendarum literarum genera complectens. –  archive.org

approx. 3300 words.

Taking the ‘4’-shaped glyph as the constant, the last few posts have sketched out roughly the patterns of connection, movement and exchange – affecting peoples, ideas, and skills – throughout the south-western Mediterranean and most particularly during that half-century from c.1350-1410 when (pace Hill), we first find the numeral ‘4’ written with that same simple, open-eyed shape as is used for one of the Voynichese glyphs.

The situations in which that exact form occurs, before the Voynich manuscript’s date-range, were found to be practical rather than intellectual – the world of traders and artisans, and particularly of Jews and Italians involved in maritime matters, and notably cartography.

Then, at just the same time when Beinecke MS 408 was being put together, we find a first use of that ‘4’-shape in a cipher-key, that cipher using the Jewish ‘atbash’ method to encipher a secular document in Italy.

The date-range for da Crema’s cipher-key coincides with our manuscript’s, and with a period when Italy saw an influx of Jews from territories owned by the kings of France and of Aragon, who between them now owned what had been the territories composing the kingdom of Majorca.

However, da Crema’s script does not resemble that in the Voynich manuscript, and so this post is about the problem of scripts and languages.

It should be kept in mind that the same Genoese, or Pisan, who had access to a Majorcan-Jewish carte marine might also take ship for Egypt, Tunis, or Trebizond, and at this same time, if a Genoese, might have relatives living in Baghdad, in India, or in Constantinople or Caffa on the Black Sea.

It is not a small matter that, as late as the seventeenth century and over a period of no less than thirty years, Athanasius Kircher should have failed even to identify what script or scripts have provided the Voynich glyphs.

So now, before turning to Girona (Gerona) and the matter of Kabbalah in medieval and later Europe, I’d like readers to consider this problem, and while keeping in mind that for just as long a period, NSA cryptographers failed in the same way – either to identify the source of the Voynichese glyphs, or to extract any ‘plain text’.

It seems to me, altogether, that those working on the written text would do well in future to avoid simply presuming that the Voynich text must prove ‘underneath it all’ a literary* plaintext in a western European language – including Latin.

*By a ‘literary’ text, I mean one composed of sentences more grammatical than ungrammatical –  including subject, verb and object –  employing a fairly standardised orthography, and forming altogether a narrative whose parts can be classed as prose and/or poetry. A shopping list, for example, is normally not a literary text.

From 1633 onwards, Kircher’s position and high-level patrons meant he had access to an extraordinary range of information relative to scripts and languages. Baresch was not wrong to choose Kircher when, trying to find someone who might recognise the origin of the Voynich script, he commissioned and sent careful copies of sections from the manuscript to Kircher, asking only that the script be identified.

To most people of his time, it would have seemed that if anyone could do that, Kircher could. .

Kircher was already, by 1633, interested in other matters of current (and recurrent) interest to Voynich researchers, including cryptography, Kabbalah and Ramon Llull.*

*I don’t propose to say much here about Llull, having now seen the excellent, updated. entry in Stanford University’s Encylopaedia of Philosophy website. (here),.  though see also ‘Postscript #2’ at the end of this post.

A letter which Kircher sent to Pieresc tells how a first interview with the immensely influential Cardinal Francesco Barberini – who would remain Kircher’s sponsor for the next five years -turned into a conversation about “the interpretation of hieroglyphs, Kabbalah and Arabic literature”. 

*Letter from Kircher to Peiresc, Rome, 1 December 1633, BNP FF 9538, fol. 234r. I have this reference from Stolzenberg. 

And to about this same time (1633-4), Daniel Stolzenberg dates a plan for a ‘universal history’, written in Kircher’s own hand, among the Barberini collection and which Stolzenberg found, then transcribed, translated and commented on. That plan has a section for cryptography (mainly Trithemius’ method) and another for Kabbalah and Lull, whose ‘combinatorial method’ we may suppose Kircher had at least heard of by then.

  • Daniel Stolzenberg, ‘ “Universal History of the Characters of Letters and Languages”: An Unknown manuscript by Athanasius Kircher’, Memoirs of the American Academy in Rome , Vol. 56/57 (2011/2012), pp. 305-321.

  • Alexander Boxer is producing a parallel Latin-English translation of Trithemius’ text for those interested in the history of cryptology. See trithemius.com.

Of interest to us now, though, is the section laying out the languages and scripts which were known to Kircher four years before Baresch’s request reached him.

The plan looks like nothing so much as the sort of ‘map’ or key you might find on a printer’s wall. The comparison is not arbitrary.

Here is Stolzenberg’s translation, from his transcription of the original (folios 33-4 in Vatican Library, Barb. Lat. 2617).

The range, and the organisation of these scripts/languages and the table’s otherwise surprising omissions, shows it organised according to the ideas of western European Christianity (i.e. Latin Christianity) and doctrinally Catholic. Consider for example how ‘Greek’ is classed as the language and script of an ‘oriental doctrine’ and imagined descended from Hebrew.

Kircher’s allusion to ‘missals and holy books’, quoted further below, serves to re-inforce the suggestion that Kircher gained this information because, thanks to Barberini and others, he had the entrée to the Vatican printeries in whose work scholars, native speakers and missionaries were all involved in different ways, composing, producing, proof-reading and disseminating those products throughout the world – which by the seventeenth century meant from as far as China to the most distant parts of the Americas.

We needn’t suppose Kircher knew more than the names for most of these scripts and languages but when, in about 1637, he received via Theodore Moretus’ posts, the copied sections of the unreadable manuscript and a request to identify the script, you’d expect that Kircher had access to persons and sources that could provide him with the answer more or less immediately.

For a full eighteen months, however, Kircher was silent – apparently. Not a civil note thanking Baresch for the gift and his enquiry; not so much as a brief note sent on receipt, unprompted, to reassure Moretus that the package hadn’t gone astray.

When, finally, Kircher did respond in 1639, it is clear that his silence was due simply to his continuing failure and consequent chagrin, for he seems only to have written then to Moretus, refusing in that letter to so much as acknowledge Baresch’s existence. And after eighteen months, Kircher could say nothing about the script except what he had plainly gained from some other person and, trying to pretend it an utterance from his own authority, he clearly failed properly to understand.

At first, certainly, Kircher’s letter sounds authoritative, but if one fact-checks, it is shown a faintly pathetic attempt to present what had been beyond him as merely ‘beneath’ him. He even uses the childish excuse ‘I could have if I wanted to, but…’

His letter includes no apology for delay but begins with the “you-and-I-are-superior-types” ploy (a form of ‘cosying up’ not unknown today) then after a few paragraphs about magnets, Kircher pretends he has only just looked at ‘the book’, writing:

As for the book … which you enclosed with your letter, I have looked at it and have concluded that it requires application rather than insight in its solver. I can recall solving many writings of this kind when the occasion presented itself, and the itch of my mind working would have tried out some ideas on it if only many very urgent tasks did not call me away from unsuitable [sic!] work of this kind. However, when I have more free time and can take advantage of a more suitable moment, I expect I shall try to solve it when the mood and inspiration take me.

Finally, I can let you know that the other sheet which appeared to be written in the same unknown script is printed in the Illyrian language in the script commonly called St Jerome’s, and they use the same script here in Rome to print missals and other holy books in the Illyrian language.

Kircher never did solve it, in thirty years, though he still wanted the manuscript when he finally gained the original in 1666 or so. That he was determined to have it may be inferred by Marci’s oddly-apologetic tone in his letter of gift.

But in his earlier letter to Moretus, Kircher revealed his source for the ‘Jerome/Illyrian’ idea as the Vatican printery and those associated with producing foreign-language ‘missals and holy books’. All the same, it sounds good, doesn’t it? The script – ‘Jerome’s Illyrian’. The language ‘Illyrian.’

But nothing followed – not during Kircher’s lifetime, nor apparently up until 2011 when I was somewhat surprised to learn there had still been no follow-up on that ‘Jerome’s Illyrian’ identification.

You may find the following illustration, today, on some other Voynich site/s, but in 2011, there was nothing of the kind. The Voynich script and language are not my area, but I felt it had to be asked – What exactly was ‘Jerome’s Illyrian’ script? For what languages was that script being used in ‘missals and holy books’ during the 17thC?.

The following comes from my post of 2011. Since the image is the important item, I’ve included just a couple of sentences from the post and, in square brackets, clarifications for what is omitted.

———–

from 

  • D.N. O’Donovan, ‘A few curiosities: “Illyrian” said Kircher’,  published first in ‘Findings‘ (blogger blog) Sunday, Nov. 11th., 2011; reprinted ‘Voynich imagery‘ (wordpress blog), Nov. 2nd., 2012.

… not too long before Kircher’s time, late in the sixteenth century, the Vatican issued a book in which was a copy from a manuscript showing this “Illyrican” script credited to Jerome – who lived fully four centuries before Cyril, but while ‘Illyricum’ remained the name of that province [on the Adriatic coast, about Dalmatia].

So when Kircher thought ‘Illyrian’ script, he could have been thinking of [and confusing] this ‘Illyrican’ script for the Cyrillic, or Glagolitic.

script-illyrican-glagolitic-att-jerome

  • text and image first published in ‘Findings‘ (blogger blog), Sunday, Nov. 11th., 2011; reprinted in ‘Voynich imagery‘ (wordpress blog), Nov. 2nd., 2012. Click to enlarge.

———–

The signs used in Jerome’s Illyrican (not ‘Illyrian’) script have little in common with those of Voynichese, as you see. Taken at face value, Kircher’s airy and seemingly off-the-cuff statement sounds wonderfully authoritative – unless you fact-check – and the same is true for much else that is asserted with an air of certainty about this manuscript today.

It is certainly possible that Jerome’s script was used to print some language called ‘Illyrican’ in the sixteenth century (I’ve included another ‘Illyrican’ script as header for this post), Kircher’s saying it was used to print the ‘Illyrian’ language raises certain other difficulties. Here, the wiki article is nicely succinct:

The Illyrian language was a language or group of languages spoken in the western Balkans in Southeast Europe during antiquity. The language is unattested with the exception of personal names and placenames… In the early modern era and up to the 19th century, the term “Illyrian” was also applied to the modern South Slavic language of Dalmatia, today identified as Serbo-Croatian. This language is only distantly related to ancient Illyrian and is not descended from it.

Could Voynichese be Serbo-Croatian? If so, why did Kircher not ever claim to have ‘broken’ the text. Has anyone ever suggested such a thing in more recent times, or claimed to have produced a translation of the Voynich text as Serbo-Croatian? More to the point – has any non-Voynich-related person, competent in Serbo-Croatian, offered a balanced assessment of some such translation? Anyone wanting to can just search Voynich+Serbo-Croatian to find an example to examine.

I will say that the same formerly Illyrian region  – around Dalmatia – cropped up a few times during the course of my own research: in connection with a map found in a Franciscan monastery and whose place-names, as discussed by Goldschmidt and Crone, were a mixture of several different local dialects from the Black Sea region; second in connection with the figure of the Voynich archer, his clothing and other matters maritime, and thirdly in connection with other letters in the Kircher archive –  but I published summaries of these things at the time, and they are beside the point at present. 

The problem is, of course, that whoever identified the Voynich script as supposedly ‘Jerome’s Illyrian'(sic) presumably also knew the languages for which it was then being used, and could have directed Kircher to one of the native speakers, or scholars, who oversaw works produced in that language. But that seems never to have happened, or to have drawn a blank. Kircher was not a modest man. His silence must be taken, in the absence of other evidence, as signalling failure, and for thirty years.

What seemed another obvious approach again, I found had never been tried, at least not as far as I could learn by about 2010: that is, to run a statistical survey to discover when, and where, glyphs closely similar to the set of Voynich glyphs are attested in alphabets or abjads.

I would suppose there’d be little point in collecting data about such ubiquitous signs such as ‘o’ but it seemed to me that a pattern of distribution for some of the more unusual forms should be enlightening.

Again – not my field, but I did attempt one amateurish test-run, my target being the glyph I describe as an ‘ornate ‘P’. I found that scripts in which such a form occurs – or occurred- mark a path from the eastern shore of the Black Sea, inward for a distance, and then turning south towards the Persian Gulf, extending as far as southern Arabia.

I found, further, that the form occurs with a fairly consistent phonetic (or should I say phonemic?) value within an ‘s-to-t’ shift.

But what tied those gleanings together was learning that all those scripts had evolved from, or were consciously developed after the model of, imperial Aramaic.

That made sense of the distribution pattern and here again, because it will be easiest for readers to check, I’ll quote a wiki article rather than the more academic sources I used in those posts published in 2012.

Aramaic

Since I have explained that the earliest stratum informing the Voynich manuscript’s imagery is one whose origins I date to the Hellenistic period, I’ll start from the period immediately before Alexander’s arrival on the scene.

The Achaemenid Empire (539–323 BC) continued this tradition [of using Imperial Aramaic], and the extensive influence of these empires led to Aramaic gradually becoming the lingua franca of most of western Asia, the Arabian Peninsula, Anatolia, the Caucasus, and Egypt.

And so that explained the otherwise odd-looking distribution for scripts containing an ‘ornate P’.   Here’s another of the examples I found as part of that research. It comes from southern Arabia and is popularly known as zabur or ‘psalm’ script. It’s not the best of my examples, but I still have the digitised image.

On this script again, I’ll quote a wiki article:.

“Zabur writings were used for religious scripts or to record daily transactions among ancient Yemenis. Zabur writings could be found in palimpsest form written on papyri or palm-leaf stalks.”

In that same article,* there’s another and better illustration of the script. The writer of that wiki article associates zabur script with monumental Sabaean script – itself derived from Aramaic.

*’Ancient South Arabian script‘ – wikipedia

I’m not offering any theory that the Voynich script originated in the Yemen, or is Sabaean or anything else – zabur is just one example of the numerous informal scripts which, developed from imperial Aramaic, include a form of “ornate P” as one of their letters. As does the Voynich script.

—————

This Image (below) added 20th December 2021. I’d not intended to include it because the accompanying files were among wildfire losses in 2013 and I cannot provide the usual bibliographic information.  I’m adding it after three correspondents’ kindly let me know that discussion of ‘ornate P’ forms makes no sense without an illustration.   

————————

A wiki article, ‘Aramaic’, was evidently written by someone for whom the whole point was that it was the ‘language Jesus spoke’ and it omits a number of important matters, including the continuing use of Aramaic by Jewish scholars, including ones in medieval western Europe and, also, that the Kabbalistic Zohar is written in a form of Aramaic, though not, I understand, in old Aramaic script.

For those linguists who’d like to tackle Aramaic and/or the Zohar…

  • According to this website – “If you’re looking for The Book of Zohar PDF or the wisdom of The Zohar PDF, then here it is in its original Aramaic language, with Hebrew commentary by Kabbalist Yehuda Ashlag.”  The PDF (which I haven’t downloaded) sounds as if it may be an interlinear Aramaic-English main text, with Hebrew commentary. Caveat downloader.

  • Other resources listed here.

  • N.B. For Aramaic’s history, script(s), evolution, grammar, morphology, pronunciation and orthographies – not to mention a full text of grammar – there is a very comprehensive entry at JVL (here).

  • Interestingly enough, that comprehensive article about Aramaic, from the Encyclopaedia Judaica, doesn’t refer at all to Kabbalah or to the Zohar. For that, there’s another article – here.

Kircher’s table, written up in 1633-4, did not include Aramaic, but by 1652, in his Oedipus Aegyptiacus he includes it in the list of languages he claims to have.

Still, even by 1667, he could not answer Aloysius Kinner’s question about whether he had yet ‘proven an Oedipus’ in regard to the Voynich manuscript which, by that time, Kircher had had in his possession in copies for thirty years and in the original manuscript for about six months. It seems that in that case, too, Kircher had made no acknowledgement of the gift. He was not a man to be modest about his accomplishments or honest about his sources. Failure he met by stubborn refusal to engage, as he refused to engage during that three decades with any question about his progress in understanding the Voynich text.

Wanting to set himself up as an ultimate authority, before whom none mattered and after whom none should utter, Kircher succeeded in persuading some people of his own time that he was a marvel. Things that he claimed falsely as his own invention, or more slyly allowed others to attribute to his genius by neglecting to credit his source, were more accurately credited after his death, and today the judgement of scholarship may be represented by one sentence from the Encyclopaedia Britannica (2007):

Kircher is not now considered to have made any significant original contributions, although a number of discoveries and inventions (e.g., the magic lantern) have sometimes been mistakenly attributed to him.

And so now, at last, back to North Africa, Kabbalah and Gerona.

—————————–

Postscript

1.- Illyrian and Illyrican.

Kircher would appear to have confused ‘Illyrian’ for ‘Illyrican’ and further confused the script attributed to St. Jerome (4thC AD) with what we now call Glagolitic, at that time sometimes also termed ‘Illyrican’ – as was Cyrillic, whose creation (9thC AD) is traditionally credited to Cyril and Methodius who lived half a millennium later than Jerome, and who based their work on “the local dialect of the Slavic tribes from the Byzantine theme of Thessalonica.” Thessalonika is not near ancient Illyria or Dalmatia but  in Macedonia, where it faces not the Adriatic sea but the Aegean. (corrected 21.12.2021.  See note 3, below on the cult of St.Jerome in Dalmatia where Glagolitic script seems to have remained in liturgical use to the fifteenth century, though little is extant as physical evidence.)

2. Llull’s Ars brevis in Hebrew

It may interest readers to know, that, just as Llull showed an interest in Kabbala and studied it to the best of his ability, so we have evidence of the reciprocal – Llull’s Ars brevis was translated into Hebrew in 1474, in Senigallia on the Adriatic coast of Italy.

What we don’t know is whether the translation was made by persons wanting to debate with Jews in Hebrew, or by Jews wanting to understand Lull’s thought. James assumes the latter.

  • Harvey J. Hames, ‘Jewish Magic with a Christian Text: A Hebrew Translation of Ramon Lull’s ‘Ars Brevis’, Traditio, 1999, Vol. 54 (1999), pp. 283-300.[JSTOR]

3. (added Dec. 20th., 2012).  

” After the papal blessing of 1248, the story of St. Jerome’s Slavic heritage also received recognition outside of Croatia. The liturgy in a sacred Slavonic tongue according to the Roman rite drew the attention of the Czech king and Holy Roman Emperor Charles IV. In 1347 he invited a group of eighty Benedictine Glagolite monks from the island of Pašman to establish a Slavonic Glagolitic monastery in Prague’s New Town, which became known first as the Slavonic Monastery (Monasterium Slavorum in Latin documents) and from the seventeenth century as the Emmaus Monastery.”

  • from:  Julia Verkholantsev, ‘St. Jerome, Apostle to the Slavs, and the Roman Slavonic Rite’, Speculum, Vol. 87, No. 1 (JANUARY 2012), pp. 37-61. 

Verkholantsev’s historical perspective is a little simplistic – she appears to accept as if valid the forgery known as the  ‘Donation of Constantine’ for example – but these small flaws (and some of mine in the post above) are easily repaired, by reference to Ilievski’s excellent analytical history of the Cyrillic and the Glaglolitic scripts. Both papers can be accessed through JSTOR.

  • Petar Hr. Ilievski, ‘GLAGOLICA: An Iconic Script for Visual Evangelic Preaching’, Illinois Classical Studies , Vol. 27/28 (2002-2003), pp. 153-164

——-

from: Libellus valde doctus elegans, & vtilis, multa et varia scribendarum literarum genera complectens (1561)

Consider this… (cont) Moving about, bringing gifts.

a little over 2600 words.

Having now seen a few pages from the Liber abaci manuscript in Florence* which seems such an outlier within Hill’s Tables, it looks as if Hill was misled by a similar-looking form, and that there is not a plain, open-eyed ‘4’ shape in it, but one more like that seen in the Venetian zibaldone (Beinecke MS 327). This leaves us at present with the earliest usage noted within the Latin domains being Cresques’ ‘Atlas’, made for Charles V of France and completed in 1375.

It also leaves us with a clear context for emergence of this specific ‘4’ form in the south-western Mediterranean before 1400: maritime trade, related commerce, and cartes marine gridded ‘by the rose’.

*current description being Ms. Biblioteca Nazionale di Firenze, Codice magliabechiano Conv. Soppr. C 1, 2616. One folio (Fol. 124r) is used as an illustration to  the wiki article ‘Fibonacci‘, and that alone shows two chief forms for the numeral: one in the page number as heading, another in a side-bar showing the Fibonacci numbers as summary for the text’s ‘rabbits’ problem. There are at least three varieties in the symbols used there for ‘four’  but none with the large eye and simple form seen in  Cresques’ work  – and in the Voynich glyph.

Cipher.

The earliest example of this ‘4’ form in any European cipher I’ve seen, so far, occurs in a cipher- key recorded by Simeone da Crema in Mantua, and dated variously between 1401-1438. The method used for the encipherment is described by Pelling as a form of ‘at bash‘.

Although da Crema’s cipher key was discussed by David Kahn (1967) and has often been reproduced (including in the context of ‘Bacon-was-Shakespeare’ theories), with a more recent technical paper published in draft by Pelling (2017) – little attention has been paid to the question of how a fifteenth-century Christian in Mantua could have come to learn of that element in Jewish, and chiefly Rabbinical, religious exegesis, or in Kabbalistic writings.

However, Mantua lies within Lombardy throughout which, as we’ve seen, Duke Gian Galeazzo Visconti had granted privileges to the Jews in 1387 – coincidentally the year in which Abraham Cresques died. But events had meanwhile occurred in Spain, in France and in Mallorca which offer a possible explanation for this early use of the atbash technique by a Latin in Lombardy.

  • David Kahn, The Codebreakers: the Story of Secret Writing. (1967).

  • Pelling, N., ‘Fifteenth Century Cryptography Revisited’ – academia.edu.

  • On dating da Crema’s cipher-key see also comment by M.R. Knowles (March 19, 2021 at 12:49 am) below a post at ciphermysteries.com. 

1391-1401

An event or more exactly a wave of events had occurred during the decade 1391-1401, following loss (by sale) of the Majorcan possessions of Montpellier and Roussillon, and loss of immediate Papal oversight and protection for the Jews of France and Spain when the papal court returned to Rome in 1376.

Since Jews were treated as personal servants or chattels of a monarch or a pope, and were transferred along with title to a city or territory, so the Jewish community’s quality of life and level of protection depended on the personal disposition and effectiveness of a given pope or noble.

As expulsions began increasing in number through Europe, once the English king had demonstrated its usefulness as a way to avoid repaying debt, so the flood of refugees necessarily considered not only where they might go, but to whom.

For England and the first of the European expulsions see:

  • Robin R. Mundell, The King’s Jews (2010)

———-

image courtesy Encyclopaedia Britannica.

Montpellier was among the lands which had been sold by Majorca to France. Though permitted in 1387 to build a new synagogue, the Jews of Montpellier were faced immediately by a suit for its demolition, issued by the bishop of Maguelonne.

Increasingly violent and vile accusations followed, culminating in an order of expulsion issued in 1394, and which applied to all territories then held by the king of France.

Three years before, in Mallorca, and thus only four years after Abraham Cresques’ death, his own community and family suffered dislocation, forced conversion and/or obligatory re-location, Majorca now being part of Aragon.

Inevitably, under such conditions, as families and communities were broken apart and newly-converted Jews became officially ‘Latins’, earlier traditions and scholarship within a family, trade or community were lost, diluted or simply became more widely accessible.

An example from the commercial records of the Datini company offers a glimpse of the situation by 1399, perhaps no more than a couple of years before da Crema employs that ‘4’ in a cipher described as an ‘atbash’.

In the summer of 1399 Baldassare degli Ubriachi, an ivory- and jewel-merchant of Florence, set out on a journey to Aragon, Bordeaux, England and Ireland carrying pearls and jewels for sale. From the Kings of Aragon and Navarre he obtained, and from the King of England he hoped for, rights of free passage through their territories. On his outward journey he formed the intention of presenting maps as gifts to one or more of these monarchs, and while in Barcelona he commissioned four ‘world maps’ (which he described, generically, as ‘mappamondi’) from cartographers then resident in the city, Master Jacme Riba (or Ribes) of Mallorca and Master Francesco Becaria of Genoa. Contracts were agreed and payments made, on Ubriachi’s behalf, by Simone d’Andrea Bellandi, a partner in the Florentine merchant banking house of Francesco Datini of Prato and manager of its fondaco [combined office, residence and warehouse] in Barcelona. (p. 107)

  • from R. A. Skelton, ‘A Contract for World Maps at Barcelona, 1399-1400, Imago Mundi, Vol. 22 (1968), pp. 107-113.

The person named as ‘Maestro Giame (Jacme) Riba or Ribes’ was in fact the son of Jafuda Cresques and grandson of Abraham Cresques. The attacks of 1391 had seen Jafuda – who had earlier worked under his father in making the Atlas for Charles V – baptised, re-named and removed to Barcelona ‘temporarily’. As late as 1399, the Datini documents make a point of distinguishing his son Giame, as Jewish master of charts, from the other person commissioned – the Christian illuminator. To Giame’s name is added not only ‘maestro di charte da navichare‘, but also (and no doubt reassuring to some),’cristiano novello’, while the illuminator, Maestro Francesco Beccha, is just ‘di Genova, dipintore di charte da navichare‘. The Jewish master received far greater payment than the pictor, but (as we’ll see), Becca or Beccarius received other treasure.

  • Skelton, op.cit.

Degli Ubriachi was relatively free to cross from territories claimed for one king as against another, had enough knowledge and clearly enough means, to identify and then commission the sort of gift that a king coveted in those days – not the old half-fabulous sort of ‘mappamundi’ but the new, detailed ‘charte da navichare’ of which the Jews of Mallorca and Majorca were the recognised masters, and of which a magnificent example – still breathtaking today – then adorned the French court, doubtless displayed with the specific aim of creating envy in the heart of any visitor, but especially a foreign one.

Datini’s agent in Barcelona brokered the commission; Datini himself, born in Prato, had re-located to papal Avignon in 1358 at the age of about 24 or 25, remaining almost thirty years, before returning to the town of his birth in 1382.

His company records show that he had had regular and easy business dealings with Jews, often working together with one or another as his representatives or as free agents in Arabic-speaking regions – particularly on commissions involving North Africa.

Datini – and thus his agents – certainly knew the difference between a person making ‘mappamundi’ of the half-fabulous, half scriptural sort, and one with the knowledge of mathematics, geometry, astronomy and geography needed to produce cartes marine or (as the term appears in the Datini documents),’charte[s] da navichare‘.

The ‘master’ laid down the line work, including the place names and points for divisions ‘by the rose’; the painter worked on the ornament and perhaps (the issue is uncertain) the criss-crossing lines of the ‘rose’ divisions..

But with Gaime now a ‘new Christian’ and obliged to work with a painter from Genoa, he must have known that the work he produced would be not just illuminated, but copied.

A chart of relatively poor quality, dated to c.1401 appeared under Beccarius’ name. Today it is in Yale University’s Beinecke library.

It is inscribed with a long, boastful passage by Beccarius, in which all the numerals are still letters of the Latin alphabet. The only ‘Arab’ or ‘Spanish’ numerals are those drawn on a bar-scale, part of which is shown (right). They are surely the ‘right sort’ of numerals. The question is whether Beccarius simply tried to copy the Mallorcan style or whether in fact the line work is that from Gaime, or simply the depiction, in the map, of a sliding rule used by the masters of charts. In a different sense ‘denominators of the degrees’.*

Beccarius’ chart. Beinecke art storage 1980 158. Image ID: 1027149.

*the standard history of the modern slide rule, associated specifically with logarithmic calculations, is as follows: 

“The slide rule was invented around 1620–1630, shortly after John Napier’s publication of the concept of the logarithm. Edmund Gunter of Oxford developed a calculating device with a single logarithmic scale, which, with additional measuring tools, could be used to multiply and divide. The first description of this scale was published in Paris in 1624 by Edmund Wingate (c.1593–1656), an English mathematician.”

I’d suggest that  it is precisely because Latins of Europe still had a lingering perception of the Arabic numerals as specialised calculation-symbols – much as we’d now regard the curly brackets and elongated ‘∫‘ of calculus –  that their use as symbols in cipher suggested itself to a few Italians, early in the fifteenth century and, further, that this is the reason da Crema’s cipher uses not only numerals in the style of the older Mallorcan Jews, but employs what was the specifically Jewish  custom  of  atbash – now adopted by da Crema not as a tool of exegesis but to encipher secular Christian text. Da Crema’s is the very simplest version of atbash. I suggest that its method is most likely to have come to his notice through Jewish refugees, and at first- or at second-hand from the conversos.

In the Datini records, quite apart from the ‘iv’, there are several variants for the form given the numeral ‘four’.

Considering the number of clerks, agents, accountants and notaries whose writings are part of that archive, and compiled over so many years, it is not surprising to find such variety. Indeed, in a ‘summary of summaries’ that was drawn up in Barcelona and dated July 14th., 1395 there is even a very modern-looking, open-topped ‘4’ – but I’ve seen no usage so consistent, nor just the same form for the numeral as we see in the fourteenth-century Mallorcan work, and the early fifteenth-century manuscript by Michael of Rhodes. And of course in the Voynich glyph.

To date, studies of the Datini archive have been focused on the history of accounting or on social-domestic history with much of the latter less interested in Datini’s networks and activities than on his personal life, and specifically Datini’s wife. If any palaeographic studies of the documents have been published, I’d welcome directions to them.

*Mikhail Kuter, Marina Gurskaya, Angelina Andreenkova and RipsimeBagdasaryan, ‘The Early Practices of Financial Statements Formation in Medieval Italy’, The Accounting Historians Journal, Vol. 44, No. 2 (December 2017), pp. 17-25. [JSTOR] Includes some rather poor reproductions of the original documents for that ‘summary of summaries’.

At this point I must turn again to the links with north Africa and Gerona, in connection with Kabbalist writings and contemporary Jewish communities’ responses to the emergence of Kabbalah in mainland Europe. It is matter required here because of Panofsky’s allusion to Kabbalah, in 1932, and da Crema’s use of atbash method so close to when the Voynich manuscript was being put together. However, rather than make this post impossibly long, I’ll break here.

References:

For readers’ convenience, once again:

  • Solomon Gandz, ‘The Origin of the Ghubār Numerals, or the Arabian Abacus and the Articuli’, Isis. 16, No. 2 (Nov., 1931), pp. 393-424

  • Yakir Paz and Tzahi Weiss, ‘From Encoding to Decoding: The AṬBḤ of R. Hiyya in Light of a Syriac, Greek and Coptic Cipher’, Journal of Near Eastern Studies , Vol. 74, No. 1 (April 2015), pp. 45-65. A recent study of medieval Jewish atbash [JSTOR]

  • Tony Lévy and Charles Burnett, ‘”Sefer ha-Middot”: A Mid-Twelfth-Century Text on Arithmetic and Geometry Attributed to Abraham Ibn Ezra’, Aleph, 2006, No. 6 (2006), pp. 57-238. with regard to the practical mathematics involved in cartography. [JSTOR]

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Postscript (editorial) – I notice in an otherwise interesting amateur site about the history of western cartography, that its author holds a peculiar idea that some unnamed Latin Christian from mainland Europe (and yes, imagined male) must surely have ‘kickstarted’ the Mallorcan cartographic tradition.

It is a peculiar idea of a kind found very often employed, and in all sorts of contexts, in European works of the nineteenth and earlier twentieth century, its basis (often unconscious) being a presumption that others perceived as inferior are inherently passive, incapable of discovery, of invention or of scientific observation and so must have been ‘kickstarted’ by some whiteman.

One sees this tacit ‘feminisation’ imposed on peoples of India, of Asia, of Africa, on Jews and on any non Anglo-Germans even within Europe, as on one sect of Christianity but not another, and indeed generally on notions about women everywhere in various works of the nineteenth-century Anglo-German school. One does wish such notions were less persistent and less prevalent today in western popular culture.

Speaking of which phenomenon..

I’m sure that many of those Voynicheros presently enthused by a theory that the Voynich drawings were done by women imagine themselves forward-thinking and generous, but from a longer perspective it’s just another depressing example of presuming, first, that the customs of the Latin west, or the Mediterranean cultures, constitute ‘the normal’ and inability to read the drawings by those conventions must imply the drawings ‘inferior’ in some way, and their maker/s equally so. Over time, this unfounded presumption has seen an ‘author’ imagined for the whole, and that ‘author’ then declared infantile, mentally deficient, deranged, physically impaired, sexually obsessed and so on. Anything except that the first enunciators of the images were simply not habituated to, nor interested in, medieval Latin Europe and its conventions – social, religious or graphic.

One wonders just what matter will be produced and asserted support for the notion that Christian, Jewish, or Arab women invented images of naked females by the hundreds and still drew them “badly”.

Women in Armenia, Persia and in Jewish communities of Europe certainly did copy manuscripts, as I pointed out with examples and references years ago, but they did it neither better nor worse than men of similar condition.

Perhaps the people enthused by the ‘women did it’ idea will try citing manuscripts produced by nuns, or the tired old ‘Trotula’ theory, or the still older and more tired ‘Hildegarde’ theory, and will again speak of the law passed in Norman Sicily in 1244 obliging medical students to take an oath “never to consult with a Jew or with illiterate women.” The argument, one supposes, will be that the reason the great majority of the Voynich images don’t reflect western Christian attitudes, priorities, social hierarchies or graphic conventions is because (mere) women would be ignorant of them.

Oh joy.

(I know… lowest form of wit … wait to see the evidence offered. But really – must they? ).

Consider this.. (cont.) Doing the math.

This post/essay is more than 3,600 words.

THIS SERIES of essay-length posts is prompted by questions about the form of one sharp, angular glyph resembling the modern short-stemmed ‘4’. Our paradigmatic example being:

This post outlines the communities and inter-connections between them over time which would finally see emerge the same ‘4’ shape numeral and other matter whose reflection is found in our present, fifteenth-century manuscript with its many unusual features.

In the instance seen above, the long bar above it makes it easy to interpret the glyph as alphabetic, and so take this pair as abbreviating some such word as q[u]o – yet the glyph’s form is not written as a Latin ‘q’ of the early fifteenth-century and allows us to suggest that even if, here, the ‘4’ glyph wasn’t intended for the numeral ‘4’, it has been written by a hand accustomed to writing the numeral in that way.

Before 1440 ‘four’ represented by this shape was still uncommon – unattested (to date) in Germany before the Voynich manuscript was made (1400-c.1440), and rare;y in England. Thus, so far, we must attribute it to the south-western Mediterranean and to the communities having attested ties to Majorca at the time our earliest clear example of the ‘4’ numeral occurs there (1375 AD).

The following passage, appended as a comment to the previous post, deserves greater prominence.

“James I appears to have chosen Majorca as his first target because of the island’s geographical importance and its closeness to the Spanish coast. Almost equidistant from Catalonia, the north of Africa, and Sardinia, the island’s ports dominated the trade routes of the western Mediterranean. James’s army included … large numbers of townspeople from the main trading cities of Catalonia and southern France, especially Barcelona, Marseilles, and Montpellier. Unlike the barons …many townspeople actually settled in Majorca and contributed to its prosperity. Some of the settlers came from further afield. While Catalans were the most numerous, there were also Aragonese, Navarrese, men from southern France, Italians (from Naples, Sicily, Genoa, and Pisa), Castilians, and Portuguese. In addition to the conquered Muslims, there was also an important Jewish community in Majorca from very shortly after the Christian conquest of 1229. This community had ties not only to Catalonia and southern France, from which many of its members had come, but also to north Africa, and Italy.” (p.335)

  • passage from J.N. Hilgarth, ‘Sources for the History of the Jews of Majorca’, Traditio, Vol. 50 (1995) pp.334-341, though other recent sources will include the same information.

To do a reality-check here – to ensure we’re not straying too far from evidence and veering from historical research into merely hunting support for a theory – we now test our present emphasis on the south-western Mediterranean against earlier informed opinion about Beinecke MS 408.

The set of connections exemplified by the Majorcan population accords with Erwin Panofsky’s attributing the manuscript -or perhaps something about its vellum and style of drawing – to ‘Spain or somewhere southern, with Arab and Jewish influence’ and shows there need be no opposition supposed with the consensus opinion of specialists in manuscript studies who were known to H.P. Kraus and his assistant Hellmut Lehmann-Haupt in the 1960s – their focus having been clearly on Italians.* Again, the month-names’ orthography has been variously described as Occitan (also spoken in Genoa), and as Judeo-Catalan, and so forth. (These things have been treated as separate issues in earlier posts. For a list, with links, see Table of Contents page in the top bar.)

*The views relayed to John Tiltman by Lehmann-Haupt, research assistant to the bookseller H.P. Kraus, are recorded by Mary d’Imperio, Elegant Enigma p.7 and 8).

Checking, again, if the class of text early using ‘4’ numerals is appropriately described as practical, navigational and/or commercial, those parameters easily present us with another instance prior to 1440.

That detail comes from manuscript known as the ‘Handbook of Michael of Rhodes’. It is in private hands but has been studied and summaries of the study are online.

  • Michael of Rhodes’ book website (here).

Michael’s education was gained as a mariner, his education by apprenticeship and in keeping with ‘tradesmans’ mathematics taught by schools of the kind known to the Italians as ‘abaco’ or ‘calculation’ schools. He began writing an account of his life and nautical-commercial calculations in 1434, his year of death being 1445. (see pages at the Galileo Institute site). As one might predict, he served one of the Italian maritime city-states – Venice.

Appropriately enough, his example for that calculation (partly illustrated above), is about the purchase of pepper – obtained by Venetians of his time from Alexandria or Tunis, but which had been traded since Roman times (at least) into the Mediterranean via Egypt from commercial pepper plantations in southern India. Alexandria remained a principal centre of that trade in Michael’s time, with Tunis, though in the earlier medieval period, the carriage of eastern products to Christian Europe had been principally in the hands of Jews and others classed and taxed as Jews in areas under Muslim governance.

Such links with Egypt and exotic goods naturally again reminds us that Georg Baresch believed the manuscript’s content had been gained ‘in the east’ and contained matter that was – in some sense unspecified – both Egyptian and ‘ancient’. He also said that the plant-pictures referred to ‘exotics’ whose forms were still unknown to German botanists in his time, when Germans led all Europe in that field.

My study of Beinecke MS 408 also found much to support Baresch’s opinion about the plant-pictures.. but presently we are not concerned with meaning so much as with forms – the form of the written text, of the pictorial text and the manuscript’s presentation.

On that basis, we may lay aside (pending possibly better information) such Voynich theories as the ‘Norwegian’ or the ‘central European’ or the ‘New World’ theories, which offer no comparison for the ‘4’ shaped glyph, or for the apparently anomalous ‘gallows glyphs’ with their elongated ascenders (if that’s what they are), nor comparable styles of script, drawing, page-layout or -disposition, nor the presence in any such manuscript noted so far of quires both quinion and septenion as we do see in the Voynich manuscript and have also found in Italy and in Hebrew manuscripts from the south-western Mediterranean – on paper, on membrane and in a combination of both (see earlier posts).

Even within Italy, it seems at present that perhaps we should discount the higher levels of education and of society, since the only instance of a ‘4’ shape which might be associated with nobility or bureaucracy known so far, is in one cipher-ledger from Urbino dated to 1440, brought to notice by Nick Pelling in 2006. But 1440 is sixty-five years (nearly three generations) after our earliest clear instance of that ‘4’ in Abraham Cresques’ Majorcan ‘Atlas’ of 1375 and almost a century and a half after one brief appearance in Florence, in a copy of the Liber abaci.*

*The bankers of Florence were strongly opposed to use of the Hindu-Arabic numerals, attempting and succeeding for a time in blocking their use.  I don’t have an English-language source for this, but see  Anna Maria Busse Berger,Lada Hordynsky-Caillat and Odile Redon, ‘Notation Mensuraliste et Autres Systèmes de Mesure au XIVe Siècle, Médiévales, No. 32 (Spring, 1977), pp. 31-46 and particularly p. 34. [JSTOR]

On the other hand, while the written text’s inclusion of that ‘4’ glyph in Beinecke MS 408 directs our attention to the commercial and maritime interests of communities whose people are found settled in thirteenth- and fourteenth-century Majorca, including those maintaining ties with Italian cities, it is Panofsky’s “Spain or somewhere southern” which is given clearest support by content in our fifteenth-century document.

When I cited the Codex Vigilanus among examples explaining the Voynich pages’ page layout and dispositions, I found no previous allusion to it in any ‘Voynich’ writing though I should not be surprised to find it mentioned elsewhere today.

It crops up again now because the same manuscript is referenced in Hill’s Tables and in the review of Hill’s work by Louis C. Karpinski, who was at that time (1915) the foremost scholar interested in the history of European forms for the numerals.

As introduction and context for quoting from Karpinski’s review, I’ll reproduce a paragraph from one earlier post from voynichimagery. In it, I was making the point that the Voynich page design, especially but not only in the ‘bathy-‘ section, differs markedly from the consciously ‘Greek and antique’ simplicity of Italian ‘humanist’ manuscripts, yet it finds echoes in other times and places, including tenth-century Spain.

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excerpt from: D.N. O’Donovan, ‘Fold-outs in Europe – Afterword’, voynichimagery 20th June 2015.

(detail) Codex Vigilano [~Vigilanus] Albeldense fol.59. Spain. Mozarabic. Compilation 9th and 10thC

.. another example. This from Spain, in a volume containing material of the the 9th-10th centuries. Notice how these illuminations fill the sides of the page, and how the text seems to be fitted around the central figure, a little irregularly, as if the imagery had been set first, and the text written later – the very opposite method from that used in manuscripts from most of Latin Europe, but this was in Spain, under Muslim rule – though the degree of influence from Baghdad as against that of the Berbers from North Africa is debated along sectarian lines. However, that non-Latin character in contemporary Spain may explain the way these pages are planned, uncharacteristic of Latin texts per se, despite the language in which it is written. … these pages’ design offers points of comparison with MS Beinecke 408. Most particularly, in my opinion, with the ‘bathy-‘ section, which [because of anthropoform ‘ladies’] implies again connection with the [month diagram] foldouts … Note here, once again, that same convention [seen in Yale, Beinecke MS 408] of using roughly-parallel curved lines to denote curve and volume. … [and the makers’ familiarity with the ‘false-bearded’ face and the concept of a bicorporate form, all of which occur in Beinecke MS 408 –  D.]

Unitalicised text in the passage above  added  8th/9th December 2021.

excerpt from: D.N. O’Donovan, ‘Fold-outs in Europe – Afterword’, voynichimagery 20th June 2015.

__________________________________

Having previously cited that codex, it was pleasant to find it referenced by Hill and commented on by Karpinski, who said,

The earliest European forms are doubtless found in the Codex Vigilanus, written in 976 AD in the monastery of Albelda near Logrono in Spain. A second Spanish manuscript of about the same date, not described by Mr. Hill, also contains similar forms, and facsimiles. Both are to appear in the next issue of Professor John M. Burnam’s Palaeographia iberica.

from: ‘The Development of the Arabic Numerals in Europe Exhibited in Sixty-four Tables. by G. F. Hill. Reviewed by  Louis C. Karpinski’ for The American Mathematical Monthly,  Vol. 22, No. 10 (Dec., 1915), pp. 336-337.

Hill’s reference to the Codex Vigilanus was a note to his Table 1: 

1. 976. Escorial d I 2. Codex Vigilanus, written in the year 976 in the monastery of Albelda near Logrotio. See P. Ewald, Neues Arcbiv der Gesellsch. /. alt. deutsche Geschichtskunde, viii (1883), p. 357. Cp. Smith and Karpinski, p. 138. The forms are described as the Indian figures, quibus designant unumquemque gradum cuiuslibet gradus. Quarum hec sunt t”orm(e): 987654331. Ewald connects the form for 5 with the Roman V. Since he does not say that the year 976 is that of the Spanish era, we must assume that it is of the usual Christian era.

I have not sighted Burnam’s Palaeographica iberica.

Already, by the tenth century, mathematical studies were advancing within Spain as in North Africa. While few scholars consider any matter in terms of Christian, Jewish and Muslim scholarship altogether, the separate studies of western numerals and mathematics have, independently, commented on the situation in tenth-century Spain. It was from there that – for example – Gebert d’Aurillac was said to have learned his calculating ‘arts’* though I suspect that his original ‘abacus’ with its significant factors – 9 and 27**– is less related to that form later given his name than to something he first encountered during the period when Barbary pirates had him.

*D.E. Smith. A History of Mathematics (Vol.2, p.75) says ‘there is good reason for thinking Gebert’s knowledge of the numerals was gained in Ripol, at the convent of Santa Maria de Ripol.

**the ‘9 and 27’ are rarely mentioned in secondary accounts today. I have no English-language reference for it to hand, but see the review of O. Chasles, ‘Histoire de l’arithmétique. Explication des traités de l’Abacus, et particulièrement du traité de Gerbert; Extrait des comptes rendus des séances de l’Académie des sciences’, Reviewed by H.G. in Bibliothèque de l’École des chartes, Vol. 4 (1842-1843), pp. 382-386.

But that’s by the way.

With regard to the Maghrib, I quote from Ahmad Djebbar’s studies, which do show that we do better to focus on lines of connection over time and distance, than defining matters in terms of a static parochial ‘nationality’.

Abū ‘l-Qāsim al-Qurashī … was a native of Seville, in Spain, spent a period of his life in Bougie (Béjaïa) where he died in 1184. The biographers who evoked him consider him a specialist in Algebra … [in which subject] al-Qurashī is known for his commentary on the book of the great Egyptian mathematician Abū Kāmil (d. 930). This commentary has not yet been recovered but its importance is confirmed by the historian Ibn Khaldūn (d. 1406) who considered it one of the best treati[s]es written on the book of Abū Kāmil.

Djebbar does not consider the works of Christian or of Jewish scholars relevant to his study, yet traces the evolution of mathematical studies in the Maghrib to Kairouan, which had been a community of unusually ascetic Jews until mention of them and of Kairouan in a narrative known as the ‘Night Journey’ linked Kairouan directly to the Prophet of Islam, reverence for whom saw the town declared a holy place and the original inhabitants expelled.*

*In this connection, I’d mention that D.E. Smith (op.cit., loc.cit.) says the names given the Ghobar numerals in the earliest Latin texts are: igin, andras, ormis, arbas, quimas, calctis, zenis, temenias, celentis and sipos, which Smith says appear to be Semitic. 

By the tenth century there were remarkable Jewish scholars working from the region presently of interest to us, but before considering one Jewish mathematician of the fourteenth century – that is, one who lived at the time we see the early emergence of that ‘4’ shape, it will be as well to pause again to check our bearings.

So far, it appears that what we have as the content in Beinecke MS 408 may be – again to quote Panofsky – “considerably earlier” matter within the material which was copied to provide the quires of our present fifteenth-century manuscript, and if the copies were not inscribed within Italy itself (as is possible), I think that by considering other matter in the manuscript we may posit with some confidence that the material as we now have it was copied for an Italian sponsor – whether Christian or Jew – during the period 1400-c.1440.

It is also possible that the manuscript’s written part, being added to the page after the pictorial text in a custom contrary to that of mainstream Latins’ work, may have taken its form as ‘Voynichese’ not much earlier than our present copy and thus to require study within parameters different from most of the imagery in which so few details express the Latins’ worldview iand so much speaks to earlier and other customs.

A relatively late creation of the ‘Voynichese’ script offers us one reasonable explanation for the apparent discrepancy between (i) disposition of image and text, and primacy given image over text, against (ii) the scribes’ evident familiarity with a straight and short-stemmed ‘4’ form characteristic of western works from the fourteenth century and later, whether that form is used here as alphabetic or numeric. Of course, that is not the only possible explanation we could call reasonable. We have yet to consider scripts from other parts of the greater Mediterranean (let alone the world) in which a ‘4’ form occurs.

Yet Spain and the example of the Codex Vigilanus allows us at least to suggest that the earlier models might date from as early as the time when ‘elongated ascenders’ still appear in such documents as the Papal charter establishing the convent of Ripol.

The fact is that we can’t be certain, at this stage of investigation, that the Voynich ‘gallows glyphs’ do have their form such ‘elongated ascenders’.

They might – for example – imitate scribal conventions from some other language altogether. I expect that there were some readers who sat up on seeing one not-quite-match between the form of a Voynich ‘gallows glyph’ and a Greek form in that detail from Codex Vatopedinus 655 which is in the previous post.

Prague

A letter whose chief theme was the lamentable decline of mathematical studies among the Jesuit scholars of Prague was sent to Athanasius Kircher in 1667 from Aloysius Kinner, about six months after the Voynich manuscript had been sent from Prague to Kircher in Rome.

Kinner refers to the manuscript and to Marcus Marci, on whose behalf the manuscript had been sent.

Marci had included with it a covering letter whose final paragraph reported, but declined to endorse, a rumour that – as Marci recalled it – was told to him several decades before, and – as he remembered it – by Rafel Mnishovsky. Evidently sent in 1666 (though dated August 1665) that paragraph in Marci’s letter remains the sole basis for any alleged connection between the manuscript and Rudolf II.

In January of 1667, then, Kinner writes in connection with mathematics:

Our own Marcus, so widely known for his writings in mathematics and other studies has now fallen into the second infancy of old age. He barely understands everyday necessities, as I note with much sadness and distress whenever I happen to visit him…. Now these men are gone scarcely any are left who could be called mathematicians and those few are totally occupied with other studies and are obliged to sneak their glances at mathematics….There is a deep silence, not to say ban, on Euclid and Appollonius in this university so that we are now not even supposed to know the names let alone the thing….And now for other matters. Dominus Marcus has lost his memory of nearly everything but still remembers you. He very officially bids me salute you in his name and he wishes to know through me whether you have yet proved an Oedipus in solving that book which he sent via the Father Provincial last year and what mysteries you think it may contain. It will be a great solace to him if you are able to satisfy his curiosity on this point….I do not know whether you are interested in having your Organum Mathematicum which you once prepared for our Archduke Carolus…

It only remains, now, to compensate a little for the habit of historians of ‘parochializing’ specific studies. I’ll mention just one medieval Jewish mathematician – Immanuel ben Jacob Bonfils (c. 1300 – 1377).

In 1936 an optimistic George Sarton wrote,

It is extremely interesting that the streams of thought which led eventually to decimal calculations on the one hand and to exponential calculations and logarithms on the other, had apparently two main sources, a Christian one and a Jewish one – both being ultimately derived from the same Greco-Arabic fountain head.. Gandz and I have now placed him [Bonfils] – and forever- among the great mathematicians of the fourteenth century, in the company of Oresme and John of Meurs. Henceforth the city of Tarascon should not remind us only of the famous Tartarin but also of one of the great mathematicians of the Middle Ages, the Provencal Jew, Immanuel ben Jacob Bonfils.

The remarks speak of Sarton’s acquiring a photostat copy of BNF Hebrew Ms IO54.6 and Gandz’ translation of the text (‘Derek (i) hilluq’). Gandz’ prefatory remarks, outlining earlier errors of the text’s description and interpretation incidentally offer another good example of that complex mix of forward and backward movement by which an historical study so often proceeds.

On the mathematical text, Gandz writes:

The invention of Bonfils introduces two new elements: the decimal fractions and the exponential calculus. In the latter case he substitutes the addition and subtraction of the exponents, or of the denominators of the degrees, as Bonfils calls them, for the multiplication and the division of the decimal powers. Our impression is that Bonfils is primarily interested in the demonstration of this method of the exponential calculus.

As you’ll see by consulting wiki articles about Algebra or Calculus, Sarton’s confidence was misplaced. We are yet to see Bonfil’s role properly acknowledged in mainstream narratives.

Quotations from Sarton and from Gandz from

  • George Sarton and Solomon Gandz, ‘The Invention of the Decimal Fractions and the Application of the Exponential Calculus by Immanuel Bonfils of Tarascon (c. 1350)’, Isis , Vol. 25, No. 1 (May, 1936), pp. 16-45.

I haven’t yet spoken about that illuminating recent article (mentioned in last week’s post) but it will have to wait.

More recommended readings.

  • Yakir Paz and Tzahi Weiss, ‘From Encoding to Decoding: The AṬBḤ of R. Hiyya in Light of a Syriac, Greek and Coptic Cipher’, Journal of Near Eastern Studies , Vol. 74, No. 1 (April 2015), pp. 45-65. A recent study of medieval Jewish atbash [JSTOR]
  • Tony Lévy and Charles Burnett, ‘”Sefer ha-Middot”: A Mid-Twelfth-Century Text on Arithmetic and Geometry Attributed to Abraham Ibn Ezra’, Aleph, 2006, No. 6 (2006), pp. 57-238. with regard to the practical mathematics involved in cartography. [JSTOR]
  • ‘Ptolemy’s Table of Chords‘ – wiki article.
  • Pamela O. Long, David McGee and Alan M. Stahl (eds.) of The Book of Michael of Rhodes: A Fifteenth-Century Maritime Manuscript. (2009).
  • Frederick M. Hocker & John M. McManamon, ‘Mediaeval Shipbuilding in the Mediterranean and Written Culture at Venice’, Mediterranean Historical Review, Volume 21, 2006 – published online in Issue 1, 24 Jan 2007.

O’Donovan notes #2b: the ‘4o’ Revised and updated edition.

math numerals 40 in 1375 Majorca
Header image. Numeral ’40’ –  c.1375 AD.    Majorca.   Jewish work. Made for the court of France, attributed to Abraham Cresques. The present writer has already, in work previously published, explained in detail the points of connection between the Voynich map and Cresques’ masterly work. This was an original contribution to the study, and its source in the present author’s work, should be credited in the normal way.

Original post published November 19th., 2021. Updated and revised version – November 25th., 2021.

READERS PLEASE NOTE – this post contains original work and references to an ongoing research ‘conversation’ between three researchers. Be good enough not to pretend the findings are just an ‘idea’ but if you wish to repeat the information, attribute it correctly and give the source accurately. To do otherwise is dishonest.

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Unresolved problem – the ‘4o’ glyph.

Some very recent comments made in a conversation between Mark Knowles and Nick Pelling, together with a little cross-checking of my own on other points, together leads me now to issue a revised and corrected version of this post’s second part.  

This post considers comments made about the still-unresolved question of the ‘4o’ glyph or string.

A paper up at academia.edu dismisses the question in a single short paragraph.

Hannig is saying that it ‘seemed obvious’ that the sign ‘4o’ was Latin and represented the sound ‘qu’ [sic] but that if you regard it as deriving from Hebrew ….

A reader would not gain from this any sense that the ‘4o’ had ever been studied in depth. Though Rainer Hannig is described as a Faculty member at Philipps University, Marburg, he has provided nothing by way of footnotes or references to help his readers get a clear idea of what has been said before. The impression given is that this posited ‘Latin’ rendering is owed to no-one and is not supported by any research. ‘It seemed commonsense’ is not a reasonable argument but another of those annoying ‘believe it or else’ statements.

In fact, the ‘4o’ is mentioned in d’Imperio’s book (1978), in conversations at Reeds’ mailing list etc. (for these, see ‘Constant References’ in the Table of Contents page).

The most informative comments I’ve seen about it, in Voynich writings from the first hundred years of this manuscript’s study were those in Pelling’s book of 2006. If any reader thinks I should mention another researcher’s discussion please leave a comment.

Written before the radiocarbon dating, Pelling’s work identifies an early example of non-numerical use for a ‘4o’ glyph or string in Urbino, in a ledger dated 1440. In that example, the reading is given: “quo”.

So the Latin reading wasn’t a product of ‘commonsense’ but of historical investigation, with a specific historical document explaining why the reading ‘quo’ was offered in Italy in 1440. Pelling wrote:

“Though you might think it fortuitous to find it [the ‘4o’] even once, it actually turns up in two [cipher-] ledgers, and in at least four separate [northern Italian] ciphers. The earliest mention is in the Urbino cipher ledger (in a cipher dated 1440), as well as in the main Milanese cipher ledger in ciphers dated 1450, 1455 … and 1456.   Later on, the same shape crops up in numerous other number-based ciphers, but by then it was used simply as a number. By contrast, the four earlier ciphers are all linked, because although they contain both ‘4’ and ‘4o’ symbols, relatively few other numbers appear. (p.177).

Hannig’s failing to direct readers to the sources he consulted was unfortunate, but worse is that he cites not a single source, medieval or later, to support his theory that the ‘4o’ is an abbreviation from Hebrew. A scholarly paper provides readers with the means to check whether the writer has done his ‘homework’ and explains how an opinion was first arrived at by giving details of the author’s background reading, and documents in proof.

As Pelling’s commentary did but Hannig’s. did not.

NOTE. (added 22 Nov. 2021). My point in the paragraph above was that scholars should not lower their standards when commenting on Beinecke MS 408.  I gather some individuals have created or adopted a theory that my paragraph was designed to cast doubt on Hannig’s position in Marburg.  It would have been better, from my point of view, to have that bit of fantasy put here as a comment, and I given the chance to set the memers straight.  That meme has merely produced a theoretical interpretation about a comment made about a theoretical comment,  in one paragraph of one paper, and concerning a single Voynich string/glyph.  *sigh*.

Now, this doesn’t necessarily mean that either Pelling or Hannig is right, and the other wrong, Their opinions are not necessarily exclusive of one another.

The example from Urbino (1440 AD) may be the earliest example of non-numerical use known so far for that closed ‘4’ like form, but there may be earlier examples to be found and – these may occur in diplomatic or commercial documents involving merchants or diplomats from anywhere within a very wide geographic range.

Interested in whether the non-numerical ‘4’ form came from the example of printing, a check against Smith’s History of Mathematics and pers.comm. with a master printer said the same – not before 1440.

However, I find reason to think that use of the closed ‘4’ occurs in a commercial context during the fourteenth century. More on that below.

As regards the Jewish population of Urbino during the time of interest to us, the entry at JVL says in part:

URBINO, town in central Italy, formerly capital of an independent duchy. The earliest record of Jews dates from the beginning of the 14th century, when Daniel of Viterbo was authorized to trade and open a loan bank. His family long continued to head the community. Other loan bankers, ultimately eight in number, received authorization to operate later. .. In the 15th century the dukes of the house of Montefeltro favored Jewish scholars and were interested in Jewish scholarship; Federico II [Montefeltro] collected Hebrew manuscripts.

Urbino had unusually strong and constant connection to the Iberian peninsula, and directly linked by an old road to Florence and the Mediterranean.

As for MILAN, (this comes from JVL)

In 1387, Duke Gian Galeazzo Visconti granted privileges to the Jews in the whole of Lombardy; these were confirmed by Francesco Sforza and his successors. An important court Jew was Elia di Sabato da Fermo, who, in 1435, became the personal physician of the duke Filippo Maria Visconti. When in 1452 Pope Nicholas V approved the Jewish right of residence in the duchy, he specifically authorized the construction of a synagogue in Milan.

Which shows that about the time the content was gathered that is now in Beinecke MS 408, conditions were especially favourable (and in the case of Milan, suddenly so) for commercial and diplomatic or political links across the religious barriers.

Pelling kindly clarified details of the Milanese cipher ledgers recently, because I was unclear whether they were only a record of ciphers used, or were enciphered commercial ledgers or ledgers recording items of diplomatic correspondence. He replied that “one is an ambassadorial ledger and the other is more of a local cipher ledger. So the story is a mix of both”.

So it is quite possible that there are, or were, earlier ledgers of some kind in which non-numerical ‘4o’ forms might be found, though not necessarily only the Italian ledgers. The practice might have been adopted by Urbino from some earlier, and other, example and from that example, later, by Milan.

It is no offence against history or logic to suggest, as a possibility to be investigated, that the instance in Urbino might have derived from commercial or diplomatic writings of Jews, but while that possibility might inspire some researcher to investigate in more depth, Hannig’s omitting to cite a single item of historical evidence means that for the meantime his idea can bear no weight, whatever its real merits might be.

We can be sure that within commercial and trade schools, in some Italian states at least, ‘4’ like numerals were in use by the fourteenth century. A merchant’s handbook now in the Beinecke Library (as MS 327) is one to which I’ve been referring Voynich researchers for a decade or more, for one reason after another – and here it is again helpful:

One thing of which we can also be sure, is that the ‘4’ does not derive from works produced by European printers. On this point, Smith’s History of Mathematics is clear and because that was first published almost a century ago, I’ve checked with a master printer who confirms it. The printed ‘4’ form comes much later.

On the political front, Milan’s relations with the two trading cities of Venice and Genoa are of particular interest. As a basic outline, and one that can be checked against any solid history of the period, I’ll quote briefly from a non-Voynich wiki article:

The tide of the war [between Genoa and Venice] reversed when in 1353 the Genoese navy suffered a defeat .. [loss of a fleet then] sparked civil unrest in Genoa, …. To combat this discord, the republic was temporarily dissolved and Genoa came under the rule of the Duke of Milan. …

A peace treaty was signed between Venice and Milan in 1355 [but hostilities between Genoa and Venice continued] ..Genoa broke free from Milanese control following the conclusion of the war, [specifically in December 1435] and the republic was reestablished. – from wiki article, ‘Genoese navy‘

Historians today refer often to ‘entanglements’ and place less emphasis on quasi-national boundaries than was the habit in nineteenth-century histories. The connections of Urbino and f Milan, of Milan and Venice, and those to Genoa, are as mutable as diplomatic chess between nations and more enlightening than focus on supposing ‘the Latin’ necessarily opposed to ‘the Jewish’ interpretations of ‘4o’.

In this case, we see that there is no reason to deny a possibility that the ‘4o’ form’s non-numerical use, might have originated among persons literate in Hebrew and so been adopted by patrons or commercial partners as a Latin ‘cipher’.

But that’s all it is – a possibility. Pelling’s opinion is derived from specific historical example and so must be granted greater weight than the self-referential and theoretical explanation by Henning. For all that, the two opinions are not necessarily opposed, but might prove complementary.

Only research can clarify the still-unresolved problem.

Should any reader feels attracted by the idea of investigating it, I’d suggest thinking about possible reasons why the ‘4o’ should have been employed as a non-numerical string or glyph. Among the possibilities are:

  • habit – the scribe was accustomed to writing the ‘4’ style numeral, and used it for the number and for ‘q’. This is a palaeographic question.
  • the Voynich ms ‘4o’ is unrelated to the numerical ’40’ but might have been deliberately adopted as form for ‘q’ for reasons unknown.
  • It may have been adopted – as a cipher – for the sound associated with that form, or pair. A correspondent suggests that it may have been used to remind readers that the ‘q’ was to be read as a glottal stop, not like the softer ‘q’ of quo, or quatre etc.
  • In the Vms, use of the ‘4’ shape might indicate a cipher in which forms from foreign or rare (or even imaginary) alphabets* were employed. Mixing alphabets was a well-known custom, both in aiding memorisation of texts and as a form of encipherment – the method is fourth among those described by Roger Bacon in the fourteenth century (See earlier post ‘here).
  • It may have been adopted by some for the number ’40’s significance. Personally, I don’t think it likely, in the Vms, but to illustrate what I mean by significance, I add an example below. I’ll give an example further below.
  • In the Voynich manuscript, it may not indicate cipher, but simply a ‘q’. Statistical analyses of the Voynich text, however, present objection to that idea.
  • I recommend those interested in recent discussion about the Milanese cipher ledgers see M.R. Knowles’ recent comment to Nick Pelling’s post ‘New Paper on Fifteenth century Cryptography‘ ciphermysteries, (July 8th., 2017). Knowles’ comment is date-stamped November 22, 2021 at 8:21 pm, the conversation between himself and Pelling continuing to the time of writing.

On rare and imaginary alphabets used in medieval Europe see ‘alphabets’ in Mary Carruthers’ The Book of Memory. 

One earlier alphabet (at least) contained a ‘4’ shape, the alphabet known as ‘Old Hungarian’ or as  Székely-Hungarian Rovás, derived from a Turkic script of inner Asia. Another ‘Rovas’ alphabet was the Khazarian, of which very little is known, though according to Omniglot it was ‘possibly used as late as the thirteenth century’.  Both links given above are to the Omniglot entries.  Personally, I like the idea of the numeral ‘4’ form having origins distinct from use in cipher, and the use in cipher deriving from a rare alphabet – seems to connect pretty well with other pointers to the Black Sea region and various Turkic languages… but questions about the Voynich manuscript’s written text are for others to explore. Not my field.  

This is the point at which it’s a good idea to check your skill-set against those possibilities – and others which may occur to you.

‘Commercial …’.

For someone unfazed by technicalities of commerce and accounting, a broader context for fifteenth-century Urbino and Milan can be found in e.g.

  • Raymond de Roover, Banking and Credit in Mediaeval Bruges (1948).
  • Quentin van Doosselaere, Commercial Agreements and Social Dynamics in Medieval Genoa. New York, New York: Cambridge University Press, 2011.

Don’t be offput by the publication date for the first reference. Herbert Heaton’s review, published in The Annals of the American Academy of Political and Social Science, Vol. 263, (May, 1949), p. 230, says,

[de Roover] found about 2,400 folios of ledgers or journals belonging to two Bruges money-changers, dated between 1367 and 1370. To decipher, interpret, and convert into living story this dry as dust collection, it was necessary not merely to scour the Belgian archives for further data but also to search in those Italian cities-Florence, Genoa, Lucca, and the rest-from which Italian traders came to trade in Bruges.

with regard to numerals in commercial bookkeeping of late medieval Europe, I notice that john Durham concludes than in account-books from medieval Europe, Arabic numerals are found ‘at least’ by the early fourteenth century, when he sees it as an innovation in European book-keeping and ‘probably a Pisan innovation’.  He’s not speaking specifically of the ‘4’ shape.  

  • John W. Durham, ‘The Introduction of “Arabic” numerals in European Accounting’, The Accounting Historians Journal, Vol. 19, No. 2 (December 1992), pp. 25-55.[JSTOR}.

Byzantine accounting.

  • Edward Peragallo, ‘The Ledger of Jachomo Badoer: Constantinople September 2, 1436 to February 26, 1440’, The Accounting Review, Oct., 1977, Vol. 52, No. 4 (Oct., 1977), pp. 881-892. [JSTOR]

Location of later diplomatic documents:

  • Vincent Ilardi, ‘Fifteenth-Century Diplomatic Documents in Western European Archives and Libraries (1450-1494)’, Studies in the Renaissance, Vol. 9 (1962), pp. 64-112 (49 pages) [JSTOR]

‘Sound’ and Linguistics.

What sound (apart from a Latin ‘quo’) might have been linked with the ‘4o’ by those who used it? If anyone has investigated this question, their findings haven’t yet hit the headlines, so if your skills and inclinations suit this angle of approach, you might find helpful E.M. Smith’s posts:

Associations for the number ’40’.

As I say, I don’t think the form likely to have been adopted for its significance but with cryptology you never know, so I’ll Hopper as illustration of cultural significance for number. He is not the first or last source that might be consulted.

“The forty days of Christ’s temptation harks back to the 40 days of Elijah’s solitude, or the forty days of trial by flood” (p.71) see also p.13, 15, 25, 26, 127.

  • Vincent Foster Hopper, Medieval Number Symbolism. (various editions)

If any researcher does find examples of non-numerical uses for the ‘4o’ before the example from Urbino, we may be very close to understanding the context from which we have matter now in the Voynich manuscript’s written text.

Remember..

Any Voynich writer who presumes that you will accept some proposition with no shred of historical evidence offered is a person who may have a transmissible case of ignorance. Treat with caution.

Item from the present author’s research. Fifteenth-century copy of a thirteenth-century text. England.

Postscript – ,my apologies to Rainer Hannig. The mis-spellings of his surname in the earlier version of this post was due entirely to my own dreadful handwriting, not the typist’s occasional errors in reading it.