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