Consider this – ‘4’ as numeral (concluded).

I’ve spent the past three weeks looking into occurrences of the ‘4’ shape as an alphabetic (and alphanumeric), attested before 1440. The research wasn’t difficult, though it was tedious and necessarily included scripts for which I found no sure identification, but overall it was not so difficult that it needs a whole blogpost here. The most time-consuming part is not collecting formal versions of scripts, but testing the homogenised ‘official’ version against historical examples. Omniglot is a convenient place to begin, if you are interested to follow that question.

Here are two illustrations showing unidentifed script, and both – if they are different scripts – have been mentioned by Voynich writers.

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I wouldn’t say that my investigation of the ‘4’-shape as numeral is complete. There are examples from Armenian, Syrian and Byzantine mss which I haven’t addressed but it was gratifying to find, after back-checking and cross-checking what I had done that my findings accord with the best-qualified commentators’ opinions on the manuscript before imagination and speculation came finally to supplant informed opinion as preferred basis for ‘Voynich’ narratives.

Specifically: the results accord with the views of Georg Baresch who had the longest certain familiarity with the manuscript and who said its contents had not originated in the culture of western Europe. In his time, of course, and even to as late as the twentieth century – as witness works catalogued by British and French libraries – Jewish works were classed as ‘oriental’.

Again, the findings accord with the view of Erwin Panofsky, as it was given in 1932, that the manuscript was from ‘Spain or somewhere southern’ and displayed characteristics both Arabic and Jewish with (perhaps) something of Kabbalah in it.

And finally, they accord with the opinion relayed by H.P. Kraus’ assistant in the early 1960s, and which said that specialists had agreed on a date of manufacture “about 1400” and focused on Italy as most likely place of manufacture.

The early occurrence for that ‘4’ shape as numeral; the pattern of its subsequent dissemination, and the lines of diaspora from the south-western Mediterranean during the last decades of the fourteenth century, allow us to see how those those separate evaluations need not be supposed incompatible with the manuscript’s internal evidence, given the historical events, lines of regular travel and population movement over the period from c.1350-c.1430 AD. I have supposed, and may be proven mistaken in supposing, that whoever wrote the Voynich glyph had a hand accustomed to writing the numeral so.

The same events promise to shed light on the manuscript’s codicology, but I won’t elaborate on that point.

In the next post, I’ll resume the series ‘How to Voynich’ which was broken off to look more closely at the ‘4o’ after noting* Rainer Hanig’s passing comment that “it “seemed obvious” the Voynichese ‘4’ was meant for the letter ‘q’.

*passage was reproduced in earlier post.

I had intended to pursue the question of the ‘gallows’ glyphs, but as you’ll see from those two ‘unknown’ scripts illustrated above, the solution to that question may be better left to specialists in palaeography.

Since my survey considered only some of the areas in which we see Italian-and-Jewish interaction, and omitted other important centres where use of the ‘Arabic’ numerals occurs during the century from 1350-1450 AD, I can only offer a conditional conclusion about the ‘4’-shape as numeral and as Voynich glyph: I’d suggest those who are chiefly interested in Voynichese should be wary of assuming that the ‘4’ shape denotes the letter ‘q’ in any instance let alone in all; and also be very careful about supposing that the usual transcription into Roman letters is ‘as good as’ reproducing the original. As one example of why I reached that conclusion – the illustration below shows forms for ‘8’ and ‘9’ as they are found on a single folio of a manuscript cited by Hill. Just one example, I know, but enough to make the point. In EVA transcription, its use of ‘q’ might obscure distinction in the original between (say) the letter ‘q’, the numeral ‘4’ and even the numeral ‘8’ – just for a start. Some alphabets include two or more letters whose forms, to an untrained eye, appear similar to each other, to this ‘8’ and to the Voynich ‘4’ shape(s).

Afterthought.

Just by the way – here’s a cipher alphabet from the eastern Mediterranean. Early 14thC.

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.

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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.

Consider this.. (cont.). Numerals, networks, Spain and something of Kabbalah.

This post is almost 2800 words.

The earliest close examples of an upright ‘4’ numeral noted so far come from Florence at the beginning of the fourteenth century and then in Cresques’ great pictorial compendium of 1375, which includes various diagrams and a great worldmap, gridded by the ‘rose’ and containing what is still the first known inset ‘compass rose’ (see further below).

Contrary to what you might find said elsewhere, Cresques’ map is not a ‘mappamundi’ and its connection to the rutters or ‘portolans’ is certainly debateable, given that the same notion was rejected on technical grounds as early as the mid-twentieth century.

The recent, astounding assertion by one writer, on a nicely presented and official looking website was that Cresques had all his information from a couple of northern European Christian missionaries and that is surely pure invention. The sources of Cresques’ inscriptions for that map are already known, and include sources such as Ibn Jubayr’s journeys and the Alf Layla wa Laya. Allusions are also made to Jewish legends, such as that Noah settled north Africa after the flood and began viticulture again from there.

One cannot now discover how that modern author came to entertain the ‘Christian missionaries’ notion, for he died during the pandemic and I know only that he claimed some connection to the Central European university of Prague. With both authors of that project now lost, the translation of all the labels into English may be stopped or at least halted for the foreseeable future, but we do not have to rely on that material to consider the problem of the ‘4’.

IN the same way that Genoa was under Milanese control by the time the Voynich manuscript was made, so it was with two more of the four once-independent Italian maritime states.

Amalfi had earlier been taken by Pisa (August 6th., 1136) and in 1406 Pisa itself was taken, by stealth, by the Florentines. Amalfi had been absorbed into the Kingdom of Naples during the late fourteenth century.

Oddly enough, Florence did not develop Pisa as its maritime arm, but on the contrary suppressed the naval activity of both Amalfi and Pisa.

The significance of Florentine control of Pisa, Neapolitan control of Amalfi and Milanese rule in Genoa, is that direct political power meant access to all technical secrets, skills and any system of ciphers earlier held exclusively by the neighbour. Trade secrets were treasure then, just as now.

When we find the ‘4’ form appear briefly in Florence, early in the fourteenth century, within a copy of the Pisan ‘Liber abaci’ we know the exemplar might have been a local copy, or an earlier one acquired directly from Pisa or indeed from Amalfi, noted for its schools of mathematics. The best copies were known to be ones closest to the date of composition.

It should be noted here too that (to quote an online tourist site) “by about the 1230s Amalfi became one of the first locations in Europe to produce paper…. [which] was soon sold all over the Mediterranean. Paper making continued as an important local trade throughout the Middle Ages and Renaissance.”

My own view of the ‘4’ numeral’s history, at present, is that we shall probably never know absolutely who first wrote the numeral as ‘4’ in Europe and that if there were a single key to the problem it may well have been lost in 1343, when a tidal wave obliterated Amalfi’s harbour and lower town, ushering in a period of decline from which the town never recovered. It s relevant, in my opinion, that all four – Genoa, Amalfi, Pisa and Venice had allotted quarters in medieval Constantinople. (see interactive map by Saffran and Nicolescu)

However, we may still regard Amalfi or Genoa as likely to have brought that ‘4’ form to Italy, because of a demonstrable connection between those maritime states and Cresques’ great work.

The semi-legendary Amalfitan surnamed ‘Gioia’ is popularly credited with having first placed a magnetised needle over a diagram of the western wind-rose and enclosed all in a glass-covered box. Properly, that was not the ‘compass’ but the bussola (buxula), and the true navigational compass (as qumbas) the eastern navigator’s ‘rose’ whose points were named for stars. In my opinion it was in that sense Cresques describes himself as ‘master of bussola and compass’. The islands of Majorca and Minorca were remarkably cosmopolitan at that time and Arabic had been the island’s official language until just 70 years before. What is more, the original ‘Barbary’ pirates of the north African coast around Sicily, who were Berber and Arabs, are said by Ibn Majid to share the same skills and know-how as he – an Arabs master of the eastern seas.

Seen in daylight, Cresques’ great worldmap shows the world below, but at night with no illumination save a few candles what one sees is as if a veil scattered with golden dots were laid over the darkened world. Makers of terrestrial maps and marine charts also made maps of the heavens. Bussola and qumbas.

You may think such technicalities aren’t needed here but, as I first discussed some years ago in the course of providing a detailed analysis and commentary for the Voynich map, there is a precedent for Cresques’ inclusion of his ‘angel of the rose’ and for his map’s mirroring along its centre line. I won’t elaborate on the last point here, but refer again to the fourteenth century Genoese cartographer, Pietro Vesconte (sometimes found as ‘Vesconti’).

In one of his ‘rose-gridded’ charts, composed in 1311 1318 – that is, about or shortly after the time of that Florentine ‘4’ – there is another faint allusion to the same motif found in Cresques’ work and in the Voynich map and in all three cases – that is, the Vesconte carte marine, Cresques’, and the Voynich map, the motif of its ‘surveying angel’ is even placed within the same – north-west – quarter.

Note (added 5th. Dec. 2021] Pietro Vesconte’s date of birth is uncertain, but he is described as ‘flourishing’ c.1310-1330. Genoese by birth and education, his earlier charts and maps were produced there, but most of his extant work was produced in Venice.

This is less obvious in the Voynich map because it presents with its east and west reversed from the European norm. Western custom permits such east-west reversal with a constant North only in literal representations of the night sky.

I apologise to long term readers for again repeating points first made by me and in research published before 2020, but some of that research was treated as if its conclusions were just ‘an idea’ to be imitated, and its illustrations to be re-used without their context – so what was ‘lifted’ by the imitators was invariably – perhaps inevitably – badly mangled, and has never been well used by Voynich theorists and so must be repeated here. I regret having to deface the illustration for the same reason.

(left) detail from the Voyich map, its North-west roundel (upper right) detail from Abraham Cresques rose-gridded world-map, its north-western quadrant; (lower right) detail from a chart by Pietro Vesconte (sometimes found as ‘Vesctonti’, its upper-west corner). From the 1318 Vesconte atlas (Museo Correr, Venice)

and so, again..:

Since I have already said that the final recension of the Voynich map should be dated to c.1350, with our present copy dated to the early fifteenth, I think here again we may narrow the environment for the ‘4’ shape as numeral and, just possibly its use in the Voynich manuscript, to the specific environment of calculation and geometry gained in service to navigation and trade.

In other words to apprenticeships and the ‘abaco’ school rather than in schools offering a more literary, theoretical or philosophical education. More evidence may demand that opinion be altered, but that’s where I stand so far.

It might even be that the Voynich ‘4’ shape is meant in the manuscript as a numeral, even if also used, or originating, as an alphabetic sign, though I should be wary of assuming that the Voynich script’s other glyph of similar form – that with a more curved ‘eye’ – is necessarily to be read as it is.*

*a question I’ve not ever looked into, but which arises from time to time, is a possible origin for the ‘Cistercian’ numerals in a version of Syriac script. See later note on a mixed alphanumeric system.

For those who enjoy the slog of using pictorial archives of kind typified by the Index of Christian Art (as was), it might be fun to see what else turns up for ‘4’ in European sources around 1300.

In any case, the story which puts Leonardo of Pisa and his ‘Liber abaci’ centre stage is an over-simplified one. That story’s short version runs something like ‘Arabs brought the Hindu numerals westwards. Leonardo (‘Fibonacci) saw them, and brought them to Europe’.

But Leonardo didn’t use that ‘4’ shape. His relevance to our present problem is rather the pattern of his travels, which illustrate nicely contemporary networks of trade and travel.

The Pisan Leonardo first learned Arabic numerals in a major Berber-speaking city of North Africa, during the last decade of the twelfth century. His sobriquet ‘the traveller’ was well earned.

Fibonacci states that his father wanted him to stay and be taught “for some days” in a “calculation school” in Bejaïa, where he was introduced to the “art [of calculation] by the nine figures of the Indians”. The knowledge of this art pleased him so much that he learned all he could about how it was studied in Egypt, Syria, Greece, Sicily and Provence when going there for the sake of trade.

So there it is. Those ‘Indian’ numerals were already known in Greece, in Sicily and in Provence before the end of the twelfth century. I’ve used the quote only so I can reference:

  • Charles Burnett, Numerals and Arithmetic in the Middle Ages (Variorum Collected Studies Series CS967) 2010.

There were especially close ties between Pisa and Béjaïa during the twelfth century. In c.1350, it was rather with Tunis and Cairo that the Venetian traded who wrote the zibaldone now Beinecke MS 327.

Béjaïa, formerly Bougie and Bugia was by Roman times known as  Saldae.    Béjaïa is still among the centres where the Berber language Kabyle is in daily use.  

Poor Ramon Lull would arrive in Béjaïa during the early fourteenth century (in 1314) as an 81 year old Dominican friar hoping to make converts to the Latin Christian church. He was dead within a twelvemonth, though accounts of his death differ, some saying he was executed for trying to persuade Muslims to become apostates to their faith – something prohibited in every region under Muslim governance as indeed it would have been in regions under Latin Christian governance had the reciprocal occurred.

Other accounts have Llull dying on the ship returning him to Majorca.

——-

Correction. (December 15th., 2021).

I see that my sources are out of date, superseded by an updated (Feb.2021) entry in Stamford University’s Encyclopaedia of Philosophy, where it says that Llull did not enter the Dominican order, nor the Franciscans’ and gives the following account of his fruitless trip to Béjaïa.

‘De vita’ narrates this trip in detail. Llull spent most of the time in prison. Instead of seeking to meet intellectuals, as he did on his first trip to Tunisia, right after disembarkation, he went to the main square and harangued passersby and anyone present at the time. The crowd was infuriated, and Llull was placed under arrest. The authorities questioned and imprisoned him. He would stay there for six months, receiving visits from sages who sought to convert him to Islam. He was later expelled from the city, but his hardships would not end there. His ship sank on the trip back to Genoa, but Llull and another passenger managed to survive by reaching the coast. He would then remain in Pisa, where he would finish texts he had previously began writing, such as ‘Ars generalis ultima’.

——-

Llull has his place in western Europe’s history, but unless one of his works contains examples of Majorcan-Florentine ‘4’ he is less relevant to our present question than the more congenial, secular, interactions between Berbers, Jews, Arabs and Italians before 1300, including within the naval, commercial and cartographic schools.

Voynich writers interested in the possibility that the Voynich ‘alphabet’ may be composed of elements taken from a number of other systems may be interested in an account of the invention, during second quarter of the twelfth century, of a new mixed system of mathematical notation.

Burnett writes:

*Charles Burnett, ‘The Semantic of Indian Numerals in Arabic, Greek and Latin’, Journal of Indian Philosophy, Vol. 34, No. 1/2 (April 2006) pp.15-30. [JSTOR]

 For those who’d like to see what Greek script of the fourteenth century looked like, here’s a detail from a Greek fourteenth-century map in Codex Vatopedinus 655.

“Europe gained its numerals from the Jews”

“The Jewish community… reconstituted in 1306” from ‘Amalfi’ in the Encyclopaedia Judaica JVL online. 2005.

As early as 1891, when European scholars were just beginning to enquire into the history of the forms for their numerals, it was already being accepted as fact that they had come from Spain. (See for example the off-hand “or rather, from Spain” in a review published in the Scottish Antiquary (Vol. 6, No. 22, (1891) p.54).

But even more unexpectedly, an association was made with Kabbalah as early as 1839!

I’ve just learned the last fact thanks to Phineas Mordell’s meticulous documentation of his sources and precedents in a very brief note of 1925. For its historical value, I’ve reproduced this note in full.

  • Phineas Mordell, ‘Note on the Theory of the Kabbalistic Origin of “Arabic” Numerals’, The Jewish Quarterly Review, Vol. 16, No. 2 (Oct., 1925), p. 207.

Of course it is possible that by 1932, Erwin Panofsky had read one or more of those sources listed above, or even an article published late in 1931; in addressing Friedman’s list of Questions more than twenty years later, Panofsky mis-remembered the year in which he’d seen the manuscript – writing ‘1931’ when it can only have been in 1932, as explained in an earlier post.

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

Panofsky was never so vapid as to mistake for an ‘idea’ the conclusions of genuine research, nor was he obliged to parrot others’ assertions for want of ability to form balanced and well-informed opinions of his own – but he may well have read one or more of those articles for the same reason that G.F. Hill wrote his monograph (see previous post) that is – to assist in accurately provenancing artefacts and quickly identifying fakes.

I think Panofsky could have known those precedents- not that he would say anything of the sort unless it were suggested to him by aspects of the materials, pigments, imagery and vellum which he observed during the two hours he spent studying the manuscript itself. But now to that list of things observed we may add (with a query) the form of one or more of the Voynich glyphs – perhaps even the ‘4’. We don’t know. All we do know is what some long-term readers of my blogs probably know by heart now, but for newcomers..

Panofsky’ freely-given opinion was given to Mrs. Voynich and Anne Nill, the latter soon reporting it in a letter to her friend, Herbert Garland. She wrote*

“he is convinced that the MS. is Spanish (or something southern near Spain) and shows strong Arabic and Jewish influences. He thinks there is some influence of the Kabbala in it.!!!!!

**for details of Nill’s letter, see the transcription made by Rich Santacoloma which I believe was the first published transcription. See his post. ‘Anne Nill speaks‘.  For my earlier comments, in this blog, about the letter and about Rich’s thoughts see here. 

To the question,  ‘What exactly had Panofsky seen in the manuscript which led him to mention Kabbalah’? I never did find a clear answer, and ran into unexpected difficulties, such as the lack of modern scholarly articles about the medieval commentaries or even modern translations of those commentaries that I could quote in an English-language blog.

As with many other research questions, one sometimes has to leave a problem aside for a time, until new information or pure serendipity offers a way forward.  Very recently, a single article in n online journal has explained the apparent barriers and, quite incidentally, offered a line to another and quite different question that I’d laid aside pending better information. I’ll try to get to that journal article in the next post.

For a short comment and an initial bibliography for the question of any influence from Kabbalah in Beinecke MS 408 see  (Post #15). 

With this question, as with the history of European forms for its numerals and most other fields of historical research, the public’s idea of a positivistic ‘forward march’ is deceptive.

Very often a study moves over time more like a pretty complicated sort of quickstep, involving  not a few trodden toes, losses of direction and ‘excuse-me’ interruptions, backwards moving which takes one forwards and some few straight-forward passages.  In the history of European numerals, for example, there was a period in the 1950s and in America, where the story was badly misdirected by an ideological fixation on the Babylonians and a transmission-theory gone berzerk.  As example, here’s one such paper, though if you don’t feel like reading it all, here’s a taste of that author’s ‘commonsense amateur theory’ approach.

… a casual inspection of the Arabic numerals suggested that these symbols might have evolved from forms such as are shown in Fig. 10, hereafter termed Ancestral Arabic numerals. It is evident that they are a variation of the Prototype numerals which the writer later derived from hand-signs, and still later discovered had been widely employed..

from: W. Clyde Richey, ‘On the Origin and Development of the Arabic Numerals’,  Proceedings of the Pennsylvania Academy of Science , Vol. 26 (1952), pp. 134-146. [quote shortened .. 5th Dec. 2021]

Not ‘handsigns’ but methods of finger-calculation may, in fact, prove relevant to our efforts to read Voynichese.

But I digress.

When quite early insights are overlooked or shrugged away in favour of worse ones, as happens more often than laymen suppose, it is also true that they may be recovered or re- discovered again later thanks to properly documented work in the meantime, or because the sum of historical evidence requires it.  

As example, here’s Charles Burnett, writing in 2006, and after years of close study of the question…  and evidently arriving at a view held by at least one person in 1891, in Scotland. 

One can observe, too, that, during the course of the twelfth century, alternative forms of the Indian numerals dropped out of use, especially the ‘eastern forms’ which were briefly shared by Arabic scholars in the Eastern Mediterranean, Greek scholars, and Latin scholars in Italy. The forms which drove out their competitors (in my view) were developed by scholars in Toledo, and quickly spread to northern Italy, where they were used by Fibonacci. (p.21)

  • Charles Burnett, ‘The Semantic …’ op.cit

except for that form of ‘4’, which Fibonacci did not use….

(detail and enlargement) Brit.Lib. Burney MS 275 f. 334

MS Burney 275 is described as

Scholastic miscellany, Central France (Paris), 1309-1316. Priscian, Cicero, and Pseudo-Cicero, Boethius, Aristotle, Euclid, Adelard of Bath, Ptolemy, translated [nominally – D.] by Gerard of Cremona.

Note – after some thought, I’ve altered the spelling of the Genoese cartographer’s name from ‘Vesconti’ to ‘Vesconte‘ as less likely to create confusion with the Milanese Visconti family, though researchers hunting secondary sources should search both versions of Pietro’s name.

Conundrum – can readers help?

Two previous

 

THIS is another aside, but research into medieval calendars, computus, astronomy and astrology involves palaeography and the history of notation, so it isn’t too far off topic.    A detail mentioned in ‘Chronological Strata Pt 1’ (Feb. 5th., 2020) raised a few questions, for two of which a Voynich writer has offered his opinion. What is needed now is some source as verification, and means to have light shed on the usual ancillary questions.

Here’s the diagram again.

The two questions I asked help with at Nick Pelling’s blog were the simplest: 1. Why is the ‘3’written in this form? and 2. How should we understand that ‘gate’ under the diagram?

to which JKPetersen (alone) replied, saying::

The symbol above the 3 indicates that it is an ordinal. It is the third diagram. Ordinals were written in many different ways (with a, with o, with m, with 9, the “us” abbreviation). You can see examples of ordinals in the VMS quire numbers.

If you go to folio 9r a couple of pages later, you will see the number 4 with the same symbol above it, to represent the 4th drawing. The same with the one following, which is the 5th drawing.

and

The “gate” emblem is a Nota symbol. The double-cee shape with a line over it is an early-medieval way of writing the letter “a” (omega is sometimes written that way too, but in this case it is “a”).

So to break it down, to make it easier to interpret it… you have N (the fence-like shape), T (the upright shape on its right-hand side), the “o” (obvious), and the “a” above it.

He’s putting emphasis on either the diagram above or the paragraph to the right, but since the text underneath the Nota symbol is erased, it’s hard to tell which.

-for which interpretation I am very grateful; it seems entirely credible to me.

Various Voynich writers (including the present one) had earlier written or posted about the history of number and numerals.  Petersen’s contributions can be found on his blog.  See e.g.  ‘Latin’s “Om-age” to Indic Numerals’, voynichportal, Nov.5th., 2017.

 

Sources.

Apart from one slight problem – the Harley manuscript is not an early medieval manuscript, but thirteenth-century – Petersen’s interpretation does, as I say, seem reasonable to me.

Unfortunately, though, he could provide no secondary source or reference work in support, so I’m now asking if readers can think of any.

I’d already asked about, and consulted the usual standard references before asking those initial questions at Pelling’s blog.  What I’d been looking for was some perspective on the range and period over which these forms occur – whether  Scot invented the ‘gate’ form, or  whether it is attested only in England or Paris or Toledo (or common in all of them), and whether the -3- with that ‘omega’ is found only in Latins works and so on. This I’d expected to learn from the secondary studies. It is surprising how little attention is paid in histories of mathematics, notation, and palaeography to forms for writing ordinals.   Bischoff, for example, offered just this (p.176):

In early medieval manuscripts the numerals are set between points in order to stand out. In rare cases suprascript strokes are added (without change of meaning). 

In evidence for which, he cites Mallon and, later Bruckner on the point that this practice lasts only until the 12thC.   The suggestion occurs that if the Harley text is a close copy of Scot’s then Scot was inclined to use near-archaisms.  One would need to consider the evidence, in either case.  Bischoff also refers to Hill’s tables (1915)-  which are still used today as a convenient if less-than-representative survey.

  • Bernhard Bischoff, Latin Palaeography: Antiquity and the Middle Ages (CUP  1990)
  • G.F Hill, The development of Arabic numerals in Europe: exhibited in sixty-four tables.  (Oxford, Clarendon  1915).  A copy from the microform is now at the internet archive).
  • A contemporary review of Hill’s work, by L. Longworth Dames in Man, Vol. 15 (1915), pp. 143-144  comments that “the representation is very unequally distributed among the nations of Europe, German examples being in excess of all others, followed by those of Italy and the Netherlands. France, it is surprising to find, is hardly represented at all…[and].. it would be of great interest if more evidence could be obtained from Spain… for the close association with Arabs in the peninsula would (prima facie) lead us to expect a closer resemblance [there] to the Eastern forms for the cyphers than that found elsewhere in western Europe”.
  • Louis Karpinski, among others, has written more on the practices in medieval Spain (where Scot obtained the text of al-Bitruji’s text) and done something to address earlier failures to include Jewish astronomical sources.    An interested reader will find Karpinski’s papers easily enough.

Numerals in Medieval texts vs Voynich manuscript.

As far as Beinecke MS 408 is concerned -an apparent absence of numerals from the main text has puzzled researchers for many years, though the quire numbers have been discussed of course.

On that subject, the seminal study (once again) is Nick Pelling’s, in his book of 2006 (pp. 15-21). Pelling’s approach became the model subsequently imitated and sometimes elaborated, but study of the manuscript’s quire numbers has not seen any qualitative improvement since then, so far as I can discover. (Do correct me if you know better).

The difficulty with all the instances which followed Pelling’s effort – again, so far as I’ve been able to find mention made of them – is that so many Voynich writers do not so much define the parameters of  research  as e.g. ‘Find the range over which  numerals occur in this form and see where the Voynich sort fit’  so much as ‘Assuming that my Voynich theory “x” is right, how can the quire numbers/images be argued to support that theory?”  When the parameters of investigation are pre-empted by the conclusions on which the researcher is already determined… well, you can finish that sentence for yourself.

This, of course, is the quintessential ‘Voynich flaw’ and has infected Voynich writings since 1912 – being naturally inherited thereafter by writers adhering to one of the traditionalist narratives.

Without being conscious of the shift, Voynich writers tend, for these reasons, to not so much explain the intention of the text itself, as to propound or elaborate upon their theory, using ‘clips’ from the manuscript as illustration.  This habit is far less noticeable in the linguists and cryptographers, but has been pervasive in approaches to, and assertions about the manuscript’s pictures and the many historical-fictional narratives.

That inherited flaw by which a theory is made the aim and focus of research is magnified by certain peculiar ‘dicta’ the effect of which is especially noticeable in what is said and written by core-conservatives and various traditionalists, viz. that alone among those claiming to treat of scientific, historical (or even art-historical) subjects,  a Voynich theorist need not refer to any precedent study, not provide any details of secondary sources they’ve drawn from … except in such such manner as they please.   In extreme cases, even details of what manuscripts  provided the theorist’s illustrations and ‘clips’ are absent and requests for such information – revisionist take note – are not rarely met with every sign of offence.

Some exceptions occur, of course, and Pelling’s custom is to provide documentation of the usual sort.

I’m sorry to say that my asking JKPetersen for details of his sources resulted in expressions of indignation, too.  The work of tracing just how the study of one or another ‘voynich idea’ has taken hold is made unusually difficult by such such things too.

As far as I can discover, the Voynich quire-numbers still await some solid, objective study.

Though Pelling’s book is out of print, his views can be read online.

Note – Recommending Voynich writers..

My practice is to recommend Voynich writers who are –  so far as one is able to see in the ‘Voynich fog’ –  the original contributor of some item or line of enquiry – or  because their writings show a consistently fair treatment of their readers and a sense of perspective: I mean, an understanding that a researcher is not necessarily so interested in a particular theory as in sources of evidence and the lineage for some particular element within the study – a contribution, assertion, canonised myth or popular ‘weed-seed’. An historian of voynich studies is constantly obliged to ask (sometimes soberly, sometimes incredulously) ‘Where did that idea come from?’

My referring to a given Voynich writer has nothing to do with whether or not I agree with their theory or opinion.  I not only differ from Pelling on many points, but on some disagree emphatically.  His definition of and discussion of “parallel hatching”, for example, is wrong, so that the inferences he takes on that basis are also wrong.  As what I suppose one might describe as a “small-t” traditionalist, Pelling’s basic assumption is that the manuscript’s content expresses European knowledge and material culture.  But he plays fair with his readers and answers requests for things like precedent studies and useful sources.

I do not refer my readers to Voynich writers (or indeed any writers) of the sort I think of as  ‘stone-soup men’.  To put it differently and if you’ll permit my quoting from something Einstein said :…

One should guard against inculcating … an idea that the aim of life is success, for a successful man normally receives from his peers an incomparably greater portion than is deserved by the services he has been able to render them. 

Every writer is perfectly entitled to prefer one source over another. I do not think it fair to any reader to present information derived from external sources or for which precedents exist, without honest account of them given.

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