Consider this.. for James (brief note).

about 1230 words

My thanks to James Barlett, the first of my correspondents to protest that I’d been “a bit quick” in the previous post, and (as James put it) “tossing out meaningless phrases like ‘star measures.’ “.

Re-reading the post from James’ point of view, I see his point, so  for James and other who like details, I add this short post.

Charts of the ‘rose-gridded’ type are not ‘mappamundi’ but navigational charts –  as Datini’s agent understood, and the person who described Cresques’ Atlas for the Bibliotheque nationale.

Such charts are a product of the surveyor’s arts, but when it comes to navigation, the ‘surveyor’ must survey not only his horizon, but what is above it.

 Sidereal navigation was not an art widely known in the medieval Mediterranean – at least not to the level it was practiced by Polynesians and, thanks not least to them, to some among the Arab mariners  in the eastern seas – or, as Majid sometimes calls them collectively, the ‘great sea’. 

‘Surveying the sky’ was an art which Majid and his fellows did know and he counted among those ‘fellows’ certain of the piratical mariners of the north African coast, the original ‘Barbary men’. This part of north Africa is of considerable interest to us since, as we’ve seen, it was there that Leonardo of Pisa first gained his basic knowledge of calculation using Hindu-Arabic numerals; one of our earliest of the rose-gridded cartes marine was also made in Tunis and pre-dates the earliest extant examples from Genoa or from Majorca, and in the same region Kabbalism was widespread.  

At one point, Majid compares himself (and the north African navigators) to the ordinary Mediterranean seamen,  whom he groups together as ‘Egyptians’, and says:

“they [the ‘Egyptians’] are not able to do these things nor can they understand what we can do, although we can understand what they do ..they have no qiyās measurements,* no science and no [navigation] books only the ‘compass’ and a number of “miles”, neither do they use “star fetterings”. We can easily travel in their ships and upon their sea …

They acknowledge that we have the better knowledge of the sea and its sciences and the wisdom of the stars in the high roads of the sea.” (p.121).

*qiyās. Pole altitude measurements. In the story of Marco Polo, we are told that the Arab mariners of the eastern seas had good charts and in the account of his sailing up the eastern coast of India, the height of the Pole Star above well-known ports is given.  As Tibbetts says, in recounting these things (p.6) “we can be quite certain that qiyās measurement was practiced by the navigators of the Arabian sea in his day”.  Determining the position of a port or other landmark by reference to the star which ‘stood’ over it is, of course another instance of corresponding star-and-place positions.  On land, a similar practice was well known to the desert Arabs and also informs the story of Jesus’ birth in the Christian gospels. This was a practice more ancient than astrology, and quite independent of it, though chiefly known to those who crossed the trackless wastes of sea and sand.

  • G.R. Tibbetts, Arab Navigation in the Indian Ocean before the Coming of the Portuguese: Being a Translation of “Kitab al-Farawa’id fi usul al-bahr wa’l-qawa’id of Ahmad b. Majid al-Najdi”.  Originally published with maps and charts in 1971, in London, by the Royal Asiatic Society. My copy included four charts: The Red Sea and Gulf of Aden; the Arabian Sea, including part of Somalia and of the Persian Gulf; India and the Bay of Bengal; a sheet containing two charts – the East African coat and the seas of South-east Asia. Compiled from the Arabs’ navigational texts.  

 

Qiyās is one of those ‘star measures’ I was thinking of. 

It’s not entirely true that Mediterranean mariners knew nothing of the navigational stars.  They used two other stars in Ursa Minor to determine the position of the Pole star if sight of it was obscured,  and to tell the hours of the night. And of course they knew Orion, whose setting nominally ended the Mediterranean sailing year, and the Pleiades and Bootes, by the aid of which Odysseus says he sailed home, eventually, from Troy.  But in medieval times they did indeed, as Majid says, have to rely on their wind-compass and measure the distance from one place to another in terms of the following wind which would – in theory – take a ship directly from the one place to the other.

Majid’s navigation was more like the surveyor’s art, and his tools were cousin to those used by the surveyor – a rod or ‘wood’ and a length of knotted cord.  These had been the land-surveyors’ tools from memory out of mind, and certainly from the time of dynastic Egypt.   The ‘rod or pole’ measure of the navigators was much shorter, of course, but it was also a standard measure. The same was true for the knotted cord.  

kamal Ifland

The measuring rod is depicted in a Mozarabic manuscript, where a correlation is made between the earthly and the heavenly vault, and the ‘angelic measures’ are tacitly equated with those who worship the deity on earth as in heaven.   While I don’t suppose the monk who made this image knew very much of navigation, but it should be recalled that Spain was not part of the Latin domains in earlier centuries. Before and even after the Muslim conquest, parts of Spain and north Africa remained part of the Byzantine empire, just as Muslim Spain remained initially closely connected with the Caliphate in Baghdad. Notice the form of these ‘star flowers and dots’ which are meant to represent the fields of stars. (cf. ‘Compostella’).

celestial measure rod Silos Apocalypse

Correlating celestial and terrestrial ‘rule’ by the measures of the pole,  or rod can be expressed in diverse ways.  

If I were to explain in detail why the term ‘kav’ relates so well to this mesh of ideas, I’d probably have to begin by explaining that many words in the shared vocabulary of medieval Mediterranean mariners did not originate with Latin or even with Greek but have been maintained from remote antiquity and some terms are clearly from ancient Egyptian, including terms as basic as ‘cabin’ and ‘governor’. 

Majid had his reasons for  saying that the majority of Mediterranean mariners were ‘Egyptian’.

But if you simply imagine that ‘rod or pole’ as a long, hollow reed, then you may better appreciate the underlying idea which those varied associations for the ‘kav’ carry in ordinary usage, and in kabbalah.

Here is evidence of the surveyor’s rod and knotted cord in antiquity: ‘measuring the fields’. 

surveying earth and heavens Pharaonic Egypt

 

Any reader wanting to go deeper into any of the points I’ve mentioned is welcome to email for the references. I won’t add them here; they’re not part of a Voynich research bibliography.

_________________

Postscript,

for Voynicheros still unconvinced by the detailed explanation offered earlier* about the ‘Voynich archer’ and his hat alluding to Spain, here’s another illustration from the 10thC Mozarabic manuscript, the Silos Beatus. (* through voynichimagery).

Michael Beatus Hell headwear hair scales

The curious position of Michael’s legs is not (as it would be if in a later, Latin, manuscript) a sign of heterodoxy but rather of an obduracy in the face of temptation.  The fallen angels were, after all, his natural brothers.  Here, as in the vocabulary of Byzantine art, wild hair signifies a wicked and untamed character.  

I’m not sure if this is enough to satisfy James that there was more to my mentioning star-measures than just tossing words about, but I hope it will do.

Consider this… Halts and stops.

about 3200 words. Farewell to 2021.

As any experienced researcher knows, there will be times when a promising line of investigation comes to an apparently impassable barrier. In some cases, this can be a permanent stop, but in others only a temporary halt and some insight will be offered months, years or sometimes even decades later.

As an example of ‘dead stop’, see my ‘Colorni’ note in the sidebar.*

*In an effort to see whether any of Colorni’s encryption methods might apply to the Voynich text, I first approached Cryptologia to find someone both able and willing to test the possibility and two cryptologists were kind enough to offer to work with me, and if things went well to produce together a paper for publication. However, then Nick Pelling also offered, and it seemed only fair to give him first shot at it. My reason for wanting to test this possibility is that Colorni’s book, Scotographia, was published in 1593 after he’d spent a decade in Rudolf’s Prague, so it seemed to me that had anyone still known at that time any key (if there is a key) to the written text, they might have approached Colorni, and he then included that method among the others gathered to make his book.

It was possibility, and  a new possibility (though Rene Zandbergen immediately tried to claim priority on the grounds that he thought he recalled having once mentioned Colorni’s name). Nick Pelling, for some inexplicable reason, imagined I’d “fallen over” Colorni, but in fact it was an endpoint to research into levels of adherence among Jews to the religious prohibition against creating false characters, including enciphered texts. An academic paper on the subject led to my wanting to test the ‘Colorni’ possibility.  However…

In the end, our ‘Colorni’ experiment went no-where.

It happens.

But on the other hand, it can take as little as one article to indicate one’s way forward, or even solve problems whose investigation earlier met a blank wall.

A single article referenced in an online journal recently allowed me to pick up again not one but two problems earlier laid aside as ‘halted, perhaps stopped’.

The first question had been – Why ‘Kabbalah’?

I felt it important to understand just what it had been about the manuscript that prompted Erwin Panofsky’s allusion to Kabbalah in 1932. Was it format, page layout, vellum finish, the images, or script or something else?

It has become usual to suppose the manuscript written by someone trained in the Italian Humanist hand (another of the many objections to the ‘central European’ theory), but I’ve often had doubts. Within the frame of a traditional Eurocentic ‘all-Latin’ theory-creation, the only other option seemed to be the Carolingian – for which Barbara Barrett is said to have argued in one or more articles published by The Fortean Times.

Yet while I accept a fifteenth century date for our present manuscript, I thought the script might as easily be compared with the general style of thirteenth-century Sephardic cursive. (Note the “might”; it was a palaeographic question – not a ‘theory’).

The examples which I cited, in my posts, were in a Bodleian exhibition entitled ‘Crossing Borders’ and for copyright reasons could only be linked, not shown, in my blogposts of that time. Today, the Bodleian appears to have replaced that page so I can only repeat some of my comments from those posts.

At the linked site, I’d like especially to point out among the Jewish manuscripts of the thirteenth and fourteenth centuries that of NAHMANIDES’, Torat ha-Adam, in the ‘oriental’ Sephardic cursive script (Catalonia, Spain, 1330) . And again on that site, a Manuscript of MOSES MAIMONIDES, also in Sephardic cursive, though with additional notes and emendation.

I was most struck by how reminiscent of the Voynich script was that in the copy of Nahmanides’ Torat ha-Adam. I’d make here, again, the point I made back then viz, “I’m speaking of the letters not made ‘sharp’ and the text giving equal visual weight to each of the letter’s elements. .”

The ‘Crossing Borders’ exhibition went to America, receiving there a review by Moshe Sokolow (Wednesday, December 19, 2012) of which I also quoted part in relation to the sort of informal manuscript described as ‘viliores’ – a  term I’d introduced in an earlier post:

… lacking the influence of centralized authorities and catering to more widespread literacy, [Jewish codices]  were produced by private copyists, many for their own personal use, and tended toward greater individualism.  …

  • M. Sokolow, review of ‘Crossing Borders..” exhibition. (Dec. 19th., 2012)

  • The term ‘viliores’ :  adopted after Francis Newton, ‘One Scriptorium, Two Scripts: Beneventan, Caroline, and the Problem of Marston MS 112′, The Yale University Library Gazette, Vol. 66, Supplement to Volume 66: BEINECKE STUDIES IN EARLY MANUSCRIPTS (1991), pp. 118-133. (JSTOR).

The point, as I’d said when introducing that term,* was that manuscripts of such a kind are very often free of diacritics and have the simplest type of ligatures.

* ‘Seeking the Voynich hand- continued’, voynichimagery, (May 27th., 2015)

The relevance of these various details, in connection to understanding why Panofsky mentioned Kabbalah and ‘Spain or somewhere southern’, was then (and is still) that ‘Spain and somewhere southern’ was where Kabbalism flourished during the thirteenth and fourteenth centuries. It was part of the region where, at the same time, the scripts known as Sephardic cursive and Sephardic semi-cursive were being employed. And of course the environment in which Abraham Cresques’ ‘Catalan Atlas’ was created.

In that same post introducing the term ‘viliores’ I’d quoted from a paper by Maria Segol, ( voynichimagery, May 27th., 2015) and that quoted paragraph deserves repeating here:

Unlike other kinds of Jewish books… or other sorts of illuminated manuscripts, kabbalistic books were not sent out to workshops for illustration….. In almost every case the diagram is drawn in the same ink and in the same hand as the text it accompanies. They are rarely colored and rarely graphically elaborate or impressive. And medieval and early modern kabbalistic manuscripts are seldom deliberately aesthetically pleasing. They are in some ways the ugly ducklings of medieval manuscripts. This shows that they were reproduced as home operation, for use by those who copied them or by their colleagues and students.

  • Marla Segol, Word and Image in Medieval Kabbalah, (p.7)

The idea of Kabbalah has been tossed about from time to time in Voynich studies, and in a purely theoretical vein has been incorporated into a couple of theories, most prominently in Tucker and Janick’s ‘New World/Nahuatl’ theory, but no evidence for it has been adduced from the manuscript’s palaeography, codicology, materials or from any formal analysis of its images.

Yet Panofsky’s opinions were always opinions offered by consideration of just those things, not created to serve a speculation as ‘theory’ – so something about the physical evidence and present in the primary document must have provoked that comment.

What was it?

He was clearly thinking of the work as Jewish, and thus of the original – not any Christianised – Kabbalah. He said plainly enough, ‘Jewish and Arabic influence’. Nor was it he who inserted the figure of Ramon Llull or redefined Kabbalah to mean only forms of Christianised ‘Cabala’.

It was a question that wouldn’t go away – what had he noticed?

When it came to the Voynich drawings, I could see some points of comparison with a couple of late fourteenth-century Jewish texts, and again with a few details in later Kabbalistic texts, but it proved very difficult indeed to find that critical key to imagery – the maker’s informing language, vocabulary and cultural context.

There were seemingly inexplicable gaps in the literature – no translations into English of the medieval Kabbalistic commentaries, for example, though some among the core-texts were translated. It had to be in English because that’s the only language in which I can assume all my readers are fairly comfortable.

And that was the point of impasse. Without identifying the informing word, I could not in conscience offer any analytical commentary. So that question had to be laid aside. Until I had that notice of an article in the Seriform blog.

There was another question illuminated by the same article, and again a question that no amount of digging had seemed able to resolve before I laid it aside almost ten years ago.

That second question had arisen while researching the ‘ladies’ folios, and initially asking why the stars in the month-folios should be formed as spiky-looking ‘flowers’. Why diverge from the simple drawing of a star? Why not employ a more typical flower-form, with rounded petals? Equivalence between a star and this flower-like form had to be a result of cultural – and most likely linguistic – habit, and so if that question could be resolved, it should offer a little more insight into the Voynich images’ antecedents.

It could have no connection to modern botanical designations, of course. The genus ‘Aster’ (Gk. ‘star’) wasn’t defined until 1706. There had to be some earlier link between the two ideas, and Greek was the most obvious possibility.

I found in one translation of the Georgics of Nicander of Colopon a phrase which spoke of the ‘aster’ and that passage I’ve included in an earlier post. The Gow and Scholfield edition, however, translates the same phrase as ‘shining blue daisy”. Once again, happily, an apparent contradiction was only ‘apparent’, and reference to the physical object shows these variants are in fact complementary and accord with the form(s) given the Voynich star-flowers, or flower-stars. The plant we now call the sea-aster, as you’ll see from the illustration below, can appear more, or less spiky-petalled; has varying number of points, and its colour shifts between white and blue. More, the centres change in colour between yellow and red as the flower ages. (cf. Quire 20).

So from this, together with various other details, I concluded that the month-diagrams (exclusive of their series of central emblems) had been first enunciated by a speaker of Greek.

In fact, I think the diagrams’ original form was probably Hellenistic, but their present form in Beinecke MS 408 displays in the anthropoform figures a cultural distaste for naturalistic representation which clearly opposes attitudes to the body in classical-, Hellenistic- and medieval western Christian (‘Latin’) tradition. On the other hand, the central emblems in the month-folios include some which don’t display similar avoidance, which that is part of the reason I ascribe their inclusion to a different environment, and a later period. The images in that fold-out show an evolution over time: from Hellenistic forms, through the phase of aniconic affect, to the Latin context which saw inclusion of those centres, addition of pigment and so on.

However, similar figures appear again in the bathy- section, and I see no reason to presume their purpose greatly different there, the problem was to understand how those in the bathy- section could relate to those in the month-folios, whose reference I’d found to be both astronomical and geographical loci.

Knowledge of Greek does not, of course, preclude knowledge of any other language, though an ‘either-or’ attitude is not an uncommon reflex among those forming Voynich narratives.

What created the impasse, in this case, was that I could find no linguistic key to explain why the ‘bathy-‘ section should include details showing what appear as pipes, channels, inlets or bays/basins. I could find no correspondence from Greek, nor Latin, nor any language – let alone in connection to ‘Spain and somewhere southern’ or Kabbalah.  I  admit that I did not consider Nahuatl, nor find any useful vocabulary from Jürchen.

I hunted out the few known drawings of plumbing systems in Europe before the fifteenth century, and also works counted as ‘anatomical’ but in neither case did such drawings display any points in common with those in the Voynich manuscript. Newbold’s ‘anatomical’ theory, like arguments about drawings in copies of the Balneis Puteolanis, I reject on iconological, historical and contextual grounds.*

Among these grounds are that illustrations for the Balneis are plainly meant to represent people, where the Voynich ‘ladies’ do not. The body-shapes, the type of head-dress, attitudes to the unclothed body, the representation of movement (so energetic in the Voynich ‘ladies’ and so leaden in the Latins’ Balneis imagery), like positioning of water in relation to the figures … and more… all set the Voynich ‘bathy’ images in quite a different category.

But – unable to get any linguistic clew for those ‘tubes’ – I could not in honesty publish an analytical study of the ‘bathy-‘ section.

It was yet another question which had to be laid aside – perhaps temporarily, perhaps permanently. In this case, it was only ‘temporarily’.

*…… ten years on …..*

A few weeks ago, regular notices from The Seriform Blog included:

And that article explained why I’d found such difficulty accessing English translations of the medieval Jewish commentaries on Kabbalah.

And that same article, in citing an example from such commentaries, directed me towards the solution of that other frustrating problem – the bathy- section’s ‘pipes’.

As one application for the term ‘KAV’, it gave the meaning ‘pipe’ … but then the author shows that in Kabbalah, the term ‘Kav’ has its philosophic and religious sense, which any person knowing it might apply, so as to express by that visual metaphor a wide range of ideas, including: line, ray, measure, bay or inlet.

Precisely!

Here’s the relevant paragraph:

map-carte-marine-detail-beccarius-1401-bar-scale

KAV – as ““Line” or “Ray”… The kav possesses two dimensions, an outer dimension and an inner one. The outer dimension of the kav, referred to as kav hamidah (“the line of measurement,” “the measuring rod” or “ruler”) corresponds to its power of “measurement,” the power to define boundaries…The two letters in Hebrew which spell kav are in fact the two inner letters of the word makom, “space”.

Which is why, when I’d introduced to Voynich studies another image, preserved as the frontispiece to a Christianised ‘Introduction to Cabbala’, it had been in the context of that link to Majorcan Jewish cartography and gridding ‘by the Rose’.   Both items in the following illustration are Christian European works, but (as I argued in the original ‘Ring o’roses’ series in Voynich imagery), from Jewish precedents.

The rays emanating from a circuit of points, and by which both astronomical and geographic locus is determined.. that’s the prosaic, secular sense of such maps.

But as you see, there can be a correspondence with higher ways of seeing.

kabbalah-intro-map.

By identifying that ring of points with stars and/or angelic souls..  you have another sort of drawing altogether… the power to define boundaries.

“Line, ray, measure, bay or inlet… and ‘pipe

To speak of the Voynich manuscript in terms of the then-new cartes marine was a new idea, or insight, when I introduced it to Voynich studies, and still more when I was at last able to connect them both with the ideas, vocabulary and that southern Jewish environment where Sephardic cursive script was being employed by Jews of that region.

As each stage of the research was published, overt response from the ‘Voynich community’ was quite odd; overt expressions of disdain paralleled by covert methods of adoption and re-assignment of authorship, including the habit of immediately trying to invent ‘alternatives’ more compatible with a Voynich theory of all-Latin ‘possession’ of the manuscript and its origins. 

  For the charts, an alternative Latin story; for Kabbalah, a revival of the old ‘Ramon Lull’ suggestion – and again of Christianised ‘Cabala’.

Superficially, the ‘Voynich Theory War’ presents as a dispute about nationality: which section of western Christian Europe shall ‘own’ the text. 

In fact the true opposition is between that traditionalist medieval-European-Christian narrative, and any opposition to it. This includes not only an overt suppression of unsupportive information (by subverting and re-directing the original evidence) but an active hostility to those who bring such dissenting evidence to light. Picking ‘bits’ from others’ research and re-using them to suggest support for what that evidence was shown to oppose has become habitual for a certain section of the online ‘community’. Apparently from the ‘think-tank’ principle that when confronted with unwelcome information, the thing to do is to invent and disseminate another theory-patch.

  So today you may well find, incorporated into some other Voynich site,  later-invented and often appallingly bad efforts to create an ‘alternative’ context for the medieval charts, for images used to illustrate and prove some point (such as the plant identification for folio 13r) made against the usual Eurocentric narrative, and this sort of thing isn’t done only with matter published by the present author but has become endemic among a certain prominent sector of the ‘online community’.  The most aggressive of these plagiarists are not beyond pretending to themselves and others that such theft is a form of moral obligation – rather as schoolyard bullies  ‘properly punish’  some classmate for daring to have more lunch-money than they do. 

The property is ‘re-distributed’ in this way to persons they deem more worthy to have it, and  whom they feel it will not be beneath them to name in footnotes and citations.  That the invented ‘alternative’ uses may not serve the manuscript’s study seems not to occur to those in whom ambition and intellectual poverty have formed their always toxic mixture.

But to return to our subject:

One can see now how persons  acquainted with the language(s) of Hebrew and Greek in addition to any others, might quite naturally give such form to ideas of the ‘Aster’ as flower and as star, to the  ‘chord/chora/hora’ and to the Kav.

Star-measures, distances, spaces and …. places.  This complex of ideas is such that, when the astronomical aspect is considered alone, it can be compared to  what the Latins called the radii stellarum or to Majid’s bashi, yet which in terms of topography is just easily explained using terms still current in English.  

The varied facets of meaning for the term ‘KAV’ allow us a rational reconciliation of the ‘ladies’ presence in those two sections of the Voynich manuscript, namely the month-folios and the ‘bathy-‘ folios so called, and of those the ‘pipes’ and bays seen in in the latter section’s margins.

In the same way, the term provides a way to reconcile the fourteenth-century rose-gridded map made in Majorca or Genoa, with concepts of Kabbalah.  These are also an expression of perceived correlation of astronomical- with geographic loci. It does not imply that the written text will be all about Kabbalah, but does help explain Panofsky’s recognition that there might be ‘something of Kabbalah’ in it. That is to say – the combination of informal format, the script with its absence of vertical emphasis, aniconic affect evident in the marring of anthropoform figures and informing construction of the vegetable images etc.

Speaking of places –  Gerona lies across the strait from Majorca. With North Africa, and southern France, Gerona was the major centre of Jewish Kabbalism during the thirteenth and fourteenth centuries.  After the fourteenth-century expulsions, the places to which Sephardi Jews went from this region went included, among other places, northern Italy and Dalmatia.

Postscript – etymology for ‘aster’.

Proto-Indo-European root meaning “star.” Buck and others doubt the old suggestion that it is a borrowing from Akkadian istar “venus.” 

It forms all or part of: aster; asterisk; asterism; ..; …constellation; disaster; [etc.]

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit star-; Hittite shittar, Greek aster “star,” with derivative astron; Latin stella, Breton sterenn, Welsh seren “star.”

The source of the common Balto-Slavic word for “star” (Lithuanian žvaigždė, Old Church Slavonic zvezda, Polish gwiazda, Russian zvezda) is not explained.

For its intrinsic interest – if you’re into scripts – here’s a webinar where palaeographers are chatting about their research into scripts of the Aegean Bronze age, including Linear A and B.

Minor typos and a couple of dropped phrases corrected – 24/12/2021

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.

__________________________________

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.

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.

‘Swallowtails’

Header image – detail from Pietro Vesconti’s chart of 1321 with (inset) ‘swallowtail’ crenellations on a castle in Almeria.

In treating the large, square, foldout drawing d’Imperio mentions this ‘swallowtail’ motif, initially describing one detail so adorned as being ‘like a castle’. The passage occurs on p.21 of Elegant Enigma. I’ll quote what isn’t speculation.

… a structure like a castle .. [with] a high crenelated wall and a tall central tower.”

Even in that passage, there is an implicit assumption that the detail will be a ‘portrait’ having a physical counterpart somewhere – but let that go for the moment.

We may date the beginning of modern conversations to about 1996, when Guy Thibault was wrestling with the whole drawing and working from an idea that it represented a map and a presumption that everything in the drawing, and in the manuscript altogether, would be a product of, and would refer to, nothing but western Europe’s ‘Latin’ (i.e. western Christian) culture.

He had reached a point where he was homing in on some such region as Venice, or Avignon, when Rene Zandbergen mailed a note to the list. It was not addressed to Thibault and did not engage with anything Thibault had shared from his own work, but was addressed instead to the ‘audience’ at large. Since the drawing was Thibault’s current project, others on the list (quite properly) did not reply and left responses to Guy.

Rene Zandbergen had written:

Tue Jun 18 11:02

Dear all,

I think that it is reasonable to assume that the little castle on f85/86, near the upper right rosette on the mega-foldout is a ‘fantasy’ castle, not intended to represent an existing one…. What I have been trying to find out (so far unsuccessfully) is whether the style of the crenellations of the square and circular buildings give any indication of age and origin of the VMs. These crenellations are .. of the ‘swallow’s tail’ type. ..

So far I have only seen this on medieval buildings in Northern Italy. If this style was already ‘en vogue’ in the earlier middle ages (up to, say, 1200), then, even if it is confined to N.Italy, it does not help us much. Anybody could have seen these or known about them; even Roger B[acon]. If the style is from a later period, it might tell us something, especially if it is regionally confined.

Anybody have any ideas?

Note – what I find surprising is that Zandbergen’s problem was easily resolved. Any good history of medieval architecture in general, or military architecture in particular could have provided the information that such crenellations are not used in Latin Europe before c.1100 AD. Since some examples are extant today, it is clearly impossible to date or place all the matter in the manuscript by reference to that one detail. It might be argued to offer a provisional terminus a quo of 1100AD with the radiocarbon dating providing the terminus ad quem of c.1438 AD. But if the rest of the drawing pre-dates the inclusion of the ‘swallowtails’ by any greater period of time, only the terminus ad quem might stand.

There is nothing about the way the crenellations are drawn in the manuscript which can tell us, of themselves, where, when or by whom the ‘swallowtail’ details were included. Considered in isolation, the ‘castle-like’ form cannot be asserted to have been a ‘portrait-style’ image. I’m not sure what genre of medieval imagery might be described as ‘fantasy’. The map has nothing in common with the drolleries, nor with the religious-visionary imaginings of persons such as Opicinus or Hildegard of Bingen.

In response to Rene Zandbergen’s introducing this note of fantasy, Thibault had replied, evidently a little disconcerted:

18 Jun 1996 11:19:03

I don’t recall if I have even commented on this castle, so please excuse me if I re-state these ideas… Suppose the connection between circles are indeed bridges, is there any way to find out [i.e. identify] ALL the medieval towns with nine (or more) bridges? I guess Venice and Avignon would fit, are there more ? If we find a point linked with those bridges in the same way as depicted in the “map” maybe we could progress a bit…

Did you notice the writings on the right side of the fold out seems to be upside down as if the scribe did not notice/know the full pattern of the circles when he was writing…

Note – I’ve corrected a few typos in the original. I do not think that English was Guy’s first language. 
As full disclosure, I should say that my own analysis of the larger drawing –  engaged after reading Nick Pelling’s post of May 29th., 2010 –  led finally to a conclusion that the whole of the large drawing is a map, one in which western Europe does not feature, save for Sicily, and that altogether it is no product of the western or the Arabic cartographic traditions, though some elements occur in common with the earliest Genoese and Venetian cartes marine
The ‘castle’ is no literal portrait, but it is certainly no fantasy. In much the way images of Egyptian deities or Christian saints’ images were constructed, the so-called ‘castle’ detail combines a reasonable idea of its subject, before adding the ‘swallowtail’ motif for the cultural significance it bore.
The ‘swallowtails’ thus serve to add practical and informative detail for anyone able to read the whole map. The spiral of ‘stars’ is a version of the motif (also seen in slightly different form, later, in the charts of Piri Reis), indicating a body of water mostly enclosed and relatively shallow. Almost all of the map’s research which I decided share online was published between 2011- 2013.
For people who have difficulty understanding why someone might use star-motifs to signify  seawater, may I recommend  … this.  It may also help explain why Hammond felt comfortable translating Homer’s οἶνοψ πόντος not, as was customary, by “wine-dark sea” but by “sparkling sea”. On which see D.M. Goldstein’s review, for the Bryn Mawr Classical Gazette,  of Mark Hammond, The Odyssey (2000).

2001.

During the five years from 1996-2001, Zandbergen’s invitation does not seem to have moved his own efforts much further forward. By the end of that time, it was no longer Guy Thibault but John Grove who was actively working on the large drawing which, in honesty, I can only describe as the Voynich map.

Much of what Grove says in the following passage is anachronistic. His understanding of the Guelf-Ghibelline split is inaccurate if, as it sounds, he perceived it in terms of national identities, but so far as I can discover it was he who first informed the ‘Voynich community’ of the swallowtails’ political connotations in medieval Italy. He presumes the ‘stars’ must refer to the heavens and also imagines that images cannot be read without written text to explain them..

Still:

Grove wrote:

I’ve been having fun reading about the two types of battlements that seem to have evolved directly from the dispute between the two opposing factions in Italian/German history. The Guelph used the square battlements, while the Ghibelline supporters flaunted their support in their architecture with the ‘fishtail’ battlements. I believe from what I’ve been able to locate on the web that these Ghibelline designs on castle battlements are indeed limited to castles in Northern Italy and Germany that were built in the period 1100-1300. Since the factions were not so big a deal in the 15th and 16th century, the castle design in the VMS only leads to (once again) presenting us with a rough geographical region – the same as has been discussed for quite some time (!).

Why a Ghibelline Castle is present in the large foldout and not a Guelph style may be meaningless to the author except that he lived near one and drew what he knew. The wall extending from the castle around the spiral of stars may be indicative that the castle and wall are only a symbolic representation of a formidable enclosure protecting the ‘heavens’. I don’t know if this sort of speculation has any place in discussions because one could never really prove any number of suppositions until we can actually read the text.

-John

Again to be fair to my readers, I should say that my own survey of the ‘swallowtail’ motif’s occurrence in Europe to1438 (including in manuscript illustrations, charts and other artefacts,chess-rook-ivory-persian-style-12th-c.-constantinople-bargello-mus such as mosaics and early chess-pieces) led me to conclude that, during that period, the ‘swallowtail’ motif as such signified the limit of an area whose people were subject to an emperor, and examples show that in drawing it could refer not only to areas connected to the western emperor but, also, to the eastern Christian emperor, or the Mongol-Chinese emperor. It signified an ‘imperial boundary’.
Image (right)’ Castle’ – rook – chess piece in Persian style. 12thC. from Constantinople. now in the Bargello Museum. First published though voynichimagery, 31st. October 2012. A Persian embassy came to Charlemagne’s court, and a mosaic in Bobbio (c.10thC) shows chessplayers adjacent to Persian-Parthian motifs. 
A comparable – not identical – form has the same significance as early as the Roman Tabula Peutingeriana. Because instances of the ‘swallowtails’ still survive on buildings in and beyond Europe, it is evident that their significance in architecture, generally expressed, is also as marking the boundary of territory regarded – in something of the way a modern embassy is – as one whose residents declare in this way a level of independence from other duties and laws, owing allegiance to their own emperor and being entitled (at least nominally) to imperial protection.
A prime example of expatriate/colonial use is found in what was once a Genoese enclave at Caffa, in the Black Sea.

Back in 2001, John Grove had begun another mailing list topic entitled ‘Dovetail battlements in Rome?’ where he mentioned a drawing he had noticed. 

In response, Jorge Stolfi commented (14th Jan. 2001), nipping in the bud any suggestion that ‘swallowtails’  adorned the walls of ancient Rome, and incidentally proving a model for how such research should be organised.  He first shows that he has considered, and checked, Grove’s reference (the precedent), then provides full details of his own sources, and adds his own comments.  

> [John Grove:] While scanning the online Vatican Library images I found this 1498 sketch of Rome…
> http://www.ibiblio.org/expo/vatican.exhibit/exhibit/b-archeology/images/arch25.jpg

Jorge Stolfi:

The caption to that figure is
http://www.ibiblio.org/expo/vatican.exhibit/exhibit/b-archeology/Extra_objects2.html

J. Annius, Antiquitates
Rome, 1498

[Image]

This image of the earliest stage in the development of Rome is much cruder than Pietro del Massaio’s. Though the unknown artist tried to represent the small compass and exact contours of the early city, and labeled the Forum and other places of note, the crenelated walls and towers reveal the limits of his imagination. Unfortunately the text he illustrated was even less accurate; it was a forgery by the papal theologian Giovanni Nanni of Viterbo.

Inc. II 274 fol. M verso arch25 TG.15

… Jorge Stolfi.

Rene Zandbergen  had replied by posting link to his website where two images of a castle in Friuli could be seen.

Dana Scott had replied to Grove:

6th. January 2001

Then again, just maybe the author of the VMS (whom I think may have been Andrea Cesalpino) supported the Ghibellines of Arezzo (Andrea was born in Arezzo) and Pisa (where he was educated and taught) and the fact that Dante ended up switching his support from the Guelphs to the Ghibellines. Perhaps.

Regards,
Dana Scott

Which – for all that I admire Scott’s work on the plant-pictures – is another example of chaining speculation to speculation, on premises insubstantial.

But Dana’s response shows that even so early as 2001 the study was moving away from efforts to discover the sense of the manuscript’s drawings, to using bits and pieces from the drawings to serve as springboard for a preferred theory.

Dana’s ‘givens’ – as untested assumptions – are clear enough: that the ‘castle’ is a literal representation of some Italian building, that the significance to be attached to the ‘swallowtail’ or ‘fishtail’ crenellations is limited to Italian politics; that the whole content of the Voynich manuscript is the work of a single author, and that this imagined ‘author’ was a person of such importance in Europe’s intellectual history that his name was recorded in contemporary documents – and so on, and so forth.

Unrecognised by most members in 2001, what Nick Pelling would later describe as the ‘theory-wars’ had already begun.

A majority still held to the opinion, expressed by Kraus and reported by d’Imperio, that the manuscript had been made in Italy.

A couple accepted the opinion offered by Panofsky in 1932 that it was ‘from Spain or somewhere southern’. In fact, the entanglements between regions in the south-western Mediterranean make the ‘Italian/southern’ positions less oppositional than complementary.

The Prinke-Zandbergen ‘Germanic central Europe’ theory was still that of a small minority in 2001, for the simple reason that it found no support in the primary document (exclusive of some marginalia) and no competent specialist had ever suggested that the vellum or binding indicated origins in a German-speaking region.

So long as research remained focused on the manuscript itself, this would remain the case. As attention shifted to ‘theory-wars’, and standards dropped, so too did the process of interaction and the tactics employed by adherents of that novel theory.

It is a curious thing, but true, that neither of that theory’s chief proponents has ever, in twenty years, presented it formally with evidence, argument and the usual documentation. Attempting to find out just what the believers believe has proven very difficult indeed. The two key words appear to be ‘Germanic’ and ‘Rudolf’ but there’s surely more to it.

In 2006, Pelling would publish his Curse of the Voynich, which remained in print for about a decade. Pelling’s research, and opinions having evidently moved on by the end of that period, he withdrew Curse from publication. To me it seemed a pity, because the book contained more than its theoretical history for the manuscript; it included numerous original contributions to other aspects of the study, including codicology, palaeography and ‘Voynichese’ which – whether Pelling’s opinions were the ‘right’ answers or not – were a stimulus to further enquiry and discussion.

Who drew the ‘swallowtails’?

The simple fact is that by 1438, even if the so-called ‘castle’ had been a portrait of some structure then existing, the drawing could have been made by an Englishman, an Ethiopian, an Armenian or a Syrian, a Persian or a Nestorian Chinese, a Jew from Majorca or from Venice.. The greater Mediterranean was a very busy international thoroughfare and to the papal court of Avignon or Rome, as to the Sicilian court, came ambassadors and pilgrims, traders and travellers. Within Rome itself, hospices were built to house foreign pilgrims, so numerous were they, and one ws was built solely for the Ethiopians’ use. Anyone who saw any instance of the Latins’ usage would know what the ‘swallowtail’ signified. Anyone might have used it to signify ‘imperial boundary’.

Of itself, as one small detail in a large and complex drawing, the ‘swallowtail crenellations’ motif tells us only that this particular detail’s first enunciation is most likely to have occurred at some time between 1100AD and 1438.

One might then ask, a more ordinary research environment, what aim Koen’s group has in mind as they try to ‘map’ such physical examples as survive in 2021. We must just wait and see.

I chose a Spanish example of ‘swallowtail crenelations’ for the header. I might as easily have shown one from Caffa in the Black Sea, or another and important example from Sicily, but since most Voynich theorists are focused on Italy or on Germany, I thought to widen the lens a little.