Consider… Maths & memory Pt 1.

Four posts in one. Take your time. Hope to see you in a month’s time.

Afterword (Feb 7th., 2022) – Yes I *know* that Maur misunderstood the nature of that ‘squaring the circle’ problem. That’s rather the point and why I said ‘in a way’.. but that passage nicely illustrates three points (a) early medieval learning went from the accepted canon to consideration of the ‘pagan’ information, not vice versa; (b) the Psalter served as the primer in early medieval education and was the constant foundation and point of reference for building higher studies and finally (c) the mere existence, or possession, of a book doesn’t mean the book was fully understood by those who owned or had access to it – something as true for medieval as for modern times.

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One thing to emerge so far, while tracking use of the simple ‘4’ shape as a numeral – and we haven’t yet begun to track its use as an alphabetic form – is that, before the Voynich manuscript’s date-range of 1404-1438, it has been found only among the commercial and working classes of the south-western Mediterranean, and chiefly in the Majorcan kingdom with its Jewish cartographers and residents of certain maritime and trading cities of Italy – Venice not being among the earliest to show it.

Since that particular short-stemmed and angular ‘4’ shape, as a numeral, appears earliest in that region and it was also in the south-western Mediterranean that Kabbalism flourished among sectors of the Jewish population, in the thirteenth and fourteenth centuries, it is not surprising that there might be in matter now in the Voynich manuscript, as Erwin Panofsky thought, ‘something of Kabbalah’.

NOTE – throughout these posts I mean by ‘the Mediterranean’ the greater Mediterranean, containing all the waters from the Black Sea to Gibraltar. The ‘south-western’ region is defined as west of Sicily, between the coasts of Italy and of north-west Africa.

Nevertheless, aspects of the manuscript’s drawings and codicology make clear that wherever and by whomever the current content was put together to make Beinecke MS 408, much of the copied material originated outside the Latin domains.

I would hope that, in the third decade of the twentieth century, Voynich researchers will have no difficulty accepting a possibility which earlier Voynich writers found inconceivable – that is, that the manuscript may have no direct connection to those texts which for Wilfrid, Newbold, the Friedmans, d’Imperio and others moulded by nineteenth-century attitudes, defined the scheme of Euope’s intellectual history.

Fixation on ‘high culture’ as on ‘high society’ was for many decades a mental barrier to the manuscript’s proper study – and its effects linger. This is why (for example) no other form of art save manuscript art, nor any type of manuscript save in the official herbals was ever considered when attempting to read the Voynich plant-pictures, despite the fact that even within Latin Europe vegetable images appear in a variety of forms, from attempted naturalism to the fantastic and in media as diverse as stone, wood, embroidery, gem-engraving, and frescos.

Nor should we now, in the third decade of the twenty-first century, maintain another idea long outdated in historical studies – namely the idea that nothing foreign could enter Europe’s mental horizon unless some Latin went elsewhere, selected and ‘fetched’ it, or at least acted as a sort of customs agent at the gate of a non-existent ‘white-walled Europe’.

It is now well-known, if not widely admitted in works for the general public of Europe and America, that medieval Europeans were not rarely passive beneficiaries of information, ideas and goods conferred upon the west by ‘foreigners’.

Nominating some single Latin figure in the role of sole agent and gate-monitor has a long history in Europe. Nestorian Christian works, for example, were often attributed to one John of Damascus; Gerard of Cremona was (and still is) credited as if author of translations from Arabic, Hebrew and other languages though the translations are known to have been made by multilingual Jews and Muslims, and the same works to have been translated previously or subsequently without any such ‘monitoring eye’.

In this way, too, the English nominated Roger Bacon, and the Germans a semi-mythical ‘Meister von Kriechenland Niger Berchtoldus’ to substitute for the Chinese as responsible for Europe’s acquiring knowledge of how to make gunpowder.

The habit has been as consistent as it has proved persistent. It is solely to serve as such a ‘gatekeeper’ between Jewish Kabbalism in north Africa and the Iberian peninsula on the one hand, and the Latins of mainland Europe on the other, that Ramon Llull has been imagined as knowing anything of Kabbalah, and why – despite the testimony of Leonardo of Pisa that knowledge of Arabic numerals and their calculation-methods was already known in ports of North Africa from Bejaïa to Egypt, and “Syria, Greece, Sicily and Provence” in all of which (as he says) he studied it in connection with his family’s trade in eastern goods, Leonardo of Pisa (Fibonacci) is nominated sole ‘gatekeeper’ for the introduction of Hindu-Arabic numerals. The difference was that by producing a book about it in Latin, rather than in the vernaculars in which most ‘second-tier’ writings were produced, Leonardo’s ‘Liber abaci’ facilitated the establishment in Italy of specifically ‘commercial maths’ classes of the sort in which he had been trained elsewhere.

As one reviewer emphasised when reviewing an English translation of the Liber Abaci:

“Use of the advanced Hindu-Arabic system of numerals, [was] gained through Fibonacci’s commercial connections in North Africa and the Levant… It must be remembered that Fibonacci’s home city-state of Pisa had an extensive mercantile fleet operating in, and beyond, the Mediterranean to Byzantium.

A. F. Horadam [review of] “Fibonacci’s Liber Abaci”: a Translation into Modern English of Leonardo Pisano’s Book of Calculation by L.E. Sigler (Springer 2002).

If the hand which wrote that ‘4’ form in the Voynich manuscript was accustomed, already, to write the numeral in that way, the probability is strong that he (and ‘he’ is statistically more likely) is more likely than not to have belonged to a social and intellectual class beneath that of Latin Europe’s political and learned elites and to have had a direct link to the interests of those who were either engaged in the type of maritime trade that brought exotic goods (termed ‘spices’) from the Black Sea, Byzantium or ports of Egypt and North Africa, into Italy or, on the other hand, in naval service as was Michael of Rhodes.

In this context of multilingualism, sea-journeys, trade, exotics, favoured nation status and scripts, I think I should here again quote from a late fifteenth-century account that I quoted first some time ago when considering the possible implications of Baresch’s phrase “‘artis thesauros medicae Aegyptiacos”. In the present case it is especially relevant to note which maritime cities had favoured status in the ports of Egypt, and related issues of multilingualism and translation in such exchange. And, of course, resources for any possible alphabetic substitution cipher.

We have already seen how casually the author of one zibaldone refers to the trade in exotics from Alexandria as example for a problem using the ‘new math’ and Michael of Rhodes’ use of that simple ‘4’ shape for the numeral before 1440.

In Alexandria I saw four large fondaks [warehouses, Lat: thesauri], one for the Franks and another for the Genoese .. and two for the Venetians..

re: Misr [Cairo].I swear that if it were possible to place all the cities of Rome, Milan, Padua and Florence together with four other cities they would not, the whole lot of them, contain the wealth and population of Misr, and this is true…

In Misr there are many fondaks … a thousand and more warehouses in each fondak.. There is nothing in the world that you do not find in the fondaks of Misr…

If you ask how I could converse with the interpreter [when in Misr].. the interpreter is of Jewish descent and came to Misr to return to Judaism, because he is a Spaniard.. He knows seven languages – Hebrew, Italian, Turkish, Greek, Arabic, German and French.   ..

The Karaites’ script is different from all others, and they have not the letters ayin, he, aleph, or het, bet, tsade. .. {The Hebrew alphabet uses 22 letters; the Karaite thus only 16.]

from a Florentine ms. translated in  Elkan Nathan Adler, Jewish Travellers (801-1755), London: Routledge (1930) pp. 156- 208. cited passages p.162; 166-7; 171. First cited in connection with Voynich studies in D.N.O’Donovan, ‘ ” …thesauros Artis medicae Aegyptiacos” Pt1’, voynichimagery (blog), July 6th., 2013. The account is by Meshullam Ben R. Menahem of Volterra, in 1481 AD.

That account was given by a Jew of Volterra in 1481. The map below shows it in relation to Genoa, and to Florence, the cities with which the rest of this post will be concerned.

  • What is known from the records about the Jews of Volterra is reported in the Encyclopaedia Judaica under ‘Tuscany‘.

If indeed there is anything of Kabbalism in the Voynich manuscript, it is most likely to have come from the south-western Mediterranean and there is no necessity to explain its entering the Latins’ mental horizons by attributing any knowledge of Kabbalah to Ramon Llull. The reasonable explanation is that since Kabbalism was Jewish, knowledge of it was conveyed across the religious divide by Jews and was by them directly explained to a few Latins – willingly or otherwise – by refugees, corresponding scholars, Morescos and/or as newly-created converts serving as translators. The great wave of assaults against the southern, Sephardi Jews in 1391 finds a parallel increase in Jewish presence in Italy, Dalmatia and elsewhere.

An example may be in order before moving to consider the ‘commercial math’ classes in fourteenth- and early fifteenth century Italy and two Italians named Paolo, one of whom lived in the fourteenth and the other in the fifteenth century.

Example – Ha-Kohen and Lippomani, and a fifteenth-century hand.

We know, certainly, that one Italian ‘renaissance’ scholar living in Venice before 1430 wished to learn both classical Hebrew and the dialect of the Moriscos or Arabic-speaking Spanish Jews, the dialect known as Judeo-Arabic. We still have letters explaining the ‘grammar’ of Judeo-Arabic, the teacher being one Isaac ha-Kohen, a resident of Syracuse in Sicily and the student Marco Lippomani. A typically snide remark by Filelfo allows Kokin to date this exchange to a period before the 1430s; that is to the years in which the Voynich manuscript was made.

  • Daniel Stein Kokin, ‘Isaac ha-Kohen’s Letter to Marco Lippomano: Jewish-Christian Exchange and Arabic Learning in Renaissance Italy’, The Jewish Quarterly Review, Vol. 104, No. 2 (SPRING 2014), pp. 192-233.

Here again, I might mention that the form of the Voynich month-folios’ month-names was argued Judeo-Catalan by Artur Sixto. I quoted that comment which Sixto originally left at Nick Pelling’s ciphermysteries in an earlier post to this blog (here).

Script in a different fifteenth century Hebrew manuscript referenced by Kokin is shown below (n.114).

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Fibonacci and Commercial maths.

To illustrate how the influence of commercial maths schools would expand in parallel with the rising importance of the merchant classes between the time when Leonardo of Pisa produced his ‘Liber abaci’ and when the Voynich manuscript was made, I take the works od two men named ‘Paolo’. Born a century apart. both were mathematicians whose careers flourished in Florence.

The first was born in Datini’s city of Prato about forty years after Leonardo (Fibonacci)’s death. The other was Florentine by birth. He, being born in 1397 and living through the period when the Voynich manuscript’s vellum was made (1404-1438) is of especial interest for us.

This second Paolo died a year after that description was written of the situation for traders in Alexandria and Cairo.

Two men named Paolo.

The first would be known best by his nicknames: “Paolo dell’Abbaco” and “Paolo the Surveyor” but his name was properly Paolo Dagomari.

In early adulthood he moved from Prato to Florence where for many years he taught ‘business math’ classes from the Trinity church in Florence.

In this case, as in many others where the term ‘school’ or even ‘academy’ is used, it is wrong to imagine a dedicated building like a modern school or college. We should think rather in terms of adult education classes where all that is needed is a person willing to teach and a group of voluntary students – or more-or-less voluntary depending on their age and the degree to which parental wishes were law.

Dagomari’s students were merchants and their sons. His basic text, as his nick-name suggests, was probably the Liber abaci, and by 1374-5, when Cresques’ world map was being created in Mallorca, Dagomari died in Florence having become by then a close friend of Boccacio and having seen 65,000 students pass through the course he offered in his Trinity Church ‘school’. We know that Francesco di Marco Datini, by then resident in Papal Avignon more than fifteen years, had also gained his education in commercial math in Florence, but there is no doubt at all that Dagomari taught the son of Dante Alighieri.

That connection to Dante is significant, for Dante also addressed himself to that ‘second tier’ in society, writing in the vernacular and not in Latin.

Nonetheless, Dante’s imagined journey though Hell, Purgatory and heaven in the Divine Comedy is a navigator’s sky-path along those “high roads of the sea” (to use Majid’s beautiful phase, which saw seas above and below the horizon).

As Gunter reports, Dante included in an early copy a parallel list of of Latin and of the increasingly-used ‘Arab’ star names in order that – in Dante’s words – those without Arab instruments might still follow the paths.

It is in an early copy of the Divine comedy, one probably made in Genoa, that we find certain characteristics unusual for formal art in medieval Latin Europe, but which come close to how the ‘ladies’ are represented in the Voynich calendar and ‘bathy-‘ sections.

(detail) from Bodleian Library, MS Holkham 48 p.4. Place of manufacture given as Genoa or Milan. Dated 1350–1375 AD. The text is described as written in a ’rounded Italian gothic hand’.

Points of similarity seen in this particular detail and figures in the ‘ladies’ folios of the Voynich ms include over-large heads, and relatively slender lower limbs. The ‘renaissance’ view of the human body was still unknown to that draftsman but occasionally, in the Voynich manuscript, its later date and probable Italian provenance is evidenced by a copyist’s slip which sees an occasional figure drawn little more shapely than the rest, and more shapely that the figure ought to be.

The differences between images in that copy of Dante’s Divine Comedy and the Voynich manuscript would make long and tedious list – too long to be included here – but with regard to these bodies, an obvious difference is that in the illustrations for the Divine Comedy, the figures are to be read as ‘people’ albeit souls, and while some effort is made to avoid emphasising male genitalia, they are drawn – whereas they are not in the Voynich manuscript’s images. And while in one sense the Voynich ms’ anthropoform figures might be regarded as ‘star-souls’ and/or as the soul of a given place, there is no evidence of intention to have them represent specific people. Of course, in this, if the labels are ever read, it may be that someone at some stage did associate each with some historical character. We shall have to wait and see.

Overall, too, we have very different vocabulary of gesture in these two work, and a very different approach to use of the ‘speaking gesture’.

As you’d expect, images in western Christian manuscripts are saturated with western Christian Europe’s two great pre-occupations (one might say obsessions) – organising everything in the universe into hierarchical rankings and then defining any person, thing, or quality according to whether its assigned ‘place’ is higher or lower than that accorded another. Ask a learned medieval scholar whether composing music was a ‘higher’ or ‘lower’ activity than designing a building and he’d surely have an answer. The disease of ‘class consciousness’ in Europe was not limited to the usual social classes, but it would allow a musician to look either up or down on any architect to whom he might be introduced.

That the Voynich manuscript is so glaringly devoid of such signals in its imagery is one among the many indications that the origin of its content is owed to persons and regions outside the Latin Christian domains.

There are no royal thrones, no horses, no military uniforms (save perhaps one Roman or Genoese ‘kilt’ on folio 80v). There are no figures of clerics, nor of kings. There is not a single chair to denote the teacher, nor any throne to denote royalty. Such costumes as are painted over the figures belong to a late stage of their evolution, as is also true for the cross-topped Byzantine style crown given one of the ‘ladies’. But the most resounding absences are the halo and the horse.

It is those details which are not there which have, for a century, reduced persons attempting to read the Voynich manuscript’s imagery to speculation, imagination and theory-driven narratives, attempting to assert the opposite of what any external and dispassionate scholar would say, and that many have said, viz: that they’ve seen nothing like it in the corpus of western Christian works, including the medical and alchemical texts.

In the detail shown above, the figures’ gestures are more limited in range than those in the Voynich manuscript but do (of course) speak directly to the conventions of medieval Latin Christian art, signalling such sentiments as pleading, despair, grief, remorse for sin and so on.

Gestures in the Voynich manuscript are more energetic, and the figures differently adorned with veils and classical headdress, their gestures so far outside the set of those employed in medieval western Europe’s Christian art that their meaning is still, most often, expounded only from a writer’s imagination, rather than from results of any wider horizon in their research.

One among the very few exceptions to the ‘theory-first’ approach was Koen Gheuens’ investigation of where and when we find other examples of the ‘deformed lobster’ in Europe after about the thirteenth century. He did not attempt to discover any earlier instances or define its time and place of first origin.

Despite such things, that detail from the early copy of Dante’s poem deserves our consideration, because it appears in manuscript made during the period of interest to us (1350–1375 AD); is attributed to northern Italy and probably to Genoa, one of the major maritime centres of Italy at that time.

I am NOT suggesting any direct or indirect connection between content in the Voynich manuscript and Dante’s poetry. Such a scenario was espoused, as I recall, in about 2008 or so, since when Dante’s name as been often invoked, and then dropped, and picked up anew, and dropped again in that peculiar parentless style of Voynich theories. If you’d like to re-create the lineage for that idea, you might begin from references in d’Imperio, then search ‘ciphermysteries’ and from there go through the archives of Jim Reeds’ mailing list. Unfortunately, though Rich Santacoloma promised a couple of years ago to do the same for that mailing list since the early 2000s, he has not yet found occasion to do so.

Paolo dal Pozzo Toscanelli

Generally believed indebted to Dagomari’s mathematics, the Florentine Paolo Toscanelli belonged to a family whose members were ( I’ll quote the wiki biography) “traders in eastern luxury goods (‘spices’) and who thus traded regularly with north Africa, Egypt and the eastern Mediterranean”.

He offers one of the clearest examples of a bridge between commercial maths, surveying, astronomy, cryptography and theology and, in terms of Italian society, between the ‘commercial class’ and the rulers’. For a time he collaborated with the Genoese Gian Battista Alberti, a figure of particular interest for cryptographers so I hope readers will forgive another digression, this time to consider Alberti.

Born in Genoa in 1404, Alberti moved to Florence but his career developed late being suppressed until 1446 by the fame of Brunelleschi. Alberti, like his elder, worked chiefly for what one writer has called the “high bourgeoisie” and brought to bear the same practical and commercial mathematics on which the ‘abacco’ schools focused.

That the range included problems of mapping is evident from the nickname given Dagomari as ‘Paul the Surveyor’ and though our later example, Paolo dal Pozzo Toscanelli is usually described as a ‘cosmographer’, his wiki biography quite rightly says that “astronomy was a close science to geography at that time”.

We know that Toscanelli was also a competent cartographer, because in 1474 he produced a map which argued for a fairly easy run westwards by sea from Spain or Portugal to ‘Cathay’. What is fascinating about that map and the accompanying letter (the map itself is now lost) is not so much their influence on the rulers of Spain and thus on Christopher Columbus, but that Toscanelli speaks of having had access not only to Ptolemy’s works but to those of the Phoenician ‘Marinus of Tyre’ – the original source which, as Ptolemy himself says plainly that he had simply edited and updated a little. Could Toscanelli have meant it? Was there still to be had a copy of the original work in Greek or in translation?

Practicalities.

Ever since Wilfrid Voynich presented the public with the manuscript and his own imaginative description and ‘history’ for it, the attitudes and assumptions of cryptographers have greatly influenced both how the manuscript was imagined and what approaches have been taken in attempting rightly to read both its written- and its pictorial text.

It is perfectly normal and understandable – part of standard method – ift a cryptographer should consider any text as a source from which to extract a body of quantifiable data, and then to engage in a process of creating a theory and considering nothing but that theory and how well it suits his or her data-base. It is natural for the cryptograper to presume a written text deliberately made opaque, and to presume that ‘underneath it all’ there should be a nice, clear literary ‘plaintext’.

Unfortunately, once the Friedmans had effectively co-opted the manuscript’s study and assumed all other sorts of research inferior and thus necessarily at the service of their own, they created a model which not only proved fruitless in their own case, and despite 30 years efforts, but has proven equally fruitless when adopted at large by Voynich theorists who were not concerned with the written text or issues around cryptography.

The lack of balance in Friedman’s attitudes – towards the manuscript and to the work of specialists in manuscript studies, as in the history of western art – continues to affect approaches to the Voynich manuscript to this day and is particularly noticeable within that ‘bible’ of the Voynich traditionalists, Mary d’Imperio’s Elegant Enigma.

It became the norm, from the early 2000s, to behave as if not only the written part of the Voynich text were ‘encrypted’ but as if everything in it were.

The cryptologists’ method was then generally adopted, that is, of first hitting on a ‘theory’ – a speculation as desired solution – and then hunting for ways in which to present that speculation as being sufficiently supported by evidence (evidence sought only within the parameters of that speculation) to deserve description as ‘plausible’ by persons who had no greater knowledge of medieval manuscripts, art, cryptography or scripts than did the person attempting to be voted ‘right’ as if by simple-headcount, social-media style.

It has not been so much as case of the blind leading the blind as of researchers first selecting a set of blinkers and then congregating according to the colour of those blinkers.

Much baseless ‘doctrine’ has resulted on the basis that it’s “widely accepted”, to the point where I was present when the edict went out (as the usual authorative-sounding but anonymous ‘meme’) that it was ‘unnecessary’ to consider any sources save fifteenth century German manuscripts.

On another occasion, the ‘meme’ asserted, in effect, that a scholar’s whole body of research might be ignored because they hadn’t made enough wisecracks.

In a very small way, I can see what that last meme was about.

Whatever their flaws and historically-inappropriate assumptions and limits, the cryptologists never treat the text casually, or produce theories to suit a popularity contest – tossing off nonsense with a gay grin and self-deprecating wisecrack.

On the other hand, I wish they would lighten up a little and give more thought to the ordinary experiences of people in the medieval world. You don’t need to find clues to Alberti’s creation of his cipher-wheel by turning to high society and theology, to Ramon Llull or Kabbalah, to understand how such an idea might have occurred to him. Why should he have had it from anyone else, or anyone in particular?

The underlying principle of such ‘revolutionary’ things as gridding maps ‘by the Rose’, diagrams associated with Kabbalism, developments in Italian architecture which brought fame first to Brunelleschi and then to Alberti, or indeed Alberti’s wheels are fairly simple and embodied in activities as old as human settlement. In this case, the construction of things formed as domes, or as globes.

Alberti didn’t have to know Llull, nor Llull to know anything of Kabbalah, though architects might well need to do, as Alberti did, and see how the dome-makers of Hagia Sophia work out problems of load-bearing and materials.

Dome, and domes composed of lattice work are still made today, just as they were in ancient and even in prehistoric times, but especially where it was important to keep watch over ripening crops.

This is how it’s done. In an area where some plant grows that produces long, flexible stems or branches, you cut and make a pile of them.

Then you trace a circle on the ground and, at regular intervals around one side, press a withy or ‘wand’ firmly into the ground. That’s the wand’s rising point.

Now, directly opposite each, around the other curve, you insert the free ends.

The lattice-pattern will appear as shadows on the ground so encompassed. At night, within the shelter, you will see the heavens ‘gridded’.

Of course, you can the cover the basic lattice, if you like, with whatever you like – fabric adorned with stars and stretched out as a tent, or something more substantial such a pise or plaster. It is not co-incidental, I think, that domes from China to the far west were customarily painted with images of the night sky.

The example shown below was made of willow wands in modern-day America.

If you need something placed at a given point around the ‘horizon’, you can nominate each space or each point with a letter, or a number, or the name of a real place on earth or (by the example of Majid’s compass-rose) by the names of stars.

But if such a dome is meant to evoke, or to represent the heavens as a dome, the question then naturally arises about how the points of that circuit actually connect with the initially matching points about the earthly horizon, when earth is imagined always stationary yet the sky perceived as wheeling over it, year by year.

As a mathematical and surveyor’s problem, that one is among the meanings embodied in this famous image of Roger Bacon.

Bust of Roger Bacon in the Oxford University Museum of Natural History. Photograph taken by Michael Reeve 2004.

Any such problem, expressed algebraically, must begin by having one specific unknown position defined as ‘x’. What Alberti’s wheel does, in effect, is have a series of circular points of correspondence defined not as a series of ‘x’s, but as a pair of alphabetic series.

I’m not saying that this was the original purpose of Alberti’s ‘wheels’ – I’d be more inclined to think that as a mathematician his interest in ‘unknowns’ had allowed his attention to shift from purely mathematical ‘unknowns’ to issues of encrypted documents.

My point is that there may be immediate and very practical observations, rather than reliance on important figures of European history, to explain his development of those cipher-wheels and much else impacting on ideas about the Voynich manuscript – such as that the imagery must be illegible in terms of western European conventions because deliberate made obscure rather than – as I hold to be the case – because it didn’t spring from those traditions in the first place.

By the middle of the fifteenth century, the construction of domes and the idea of ‘significant number’ were both hot topics in Florence but as you see, the basics of Brunelleschi’s famous dome in Florence are pretty much the same as the rural domed shelter which country-people everywhere have been making – and I’m speaking literally – from before the first cities were built. What made their monumental versions different was an ability to do the math.

The death of Brunelleschi in 1446 brought to the fore Leon Battista Alberti (1404-1472). Like Brunelleschi’s, Alberti’s career had long been delayed…

*Franklin, N.J., Borough schools, ‘Architecture of Brunelleschi and Alberti ..’ (pdf). I reecommend this as a very good first guide to works of Brunellleschi and Alberti online as a pdf, but one worth reading even if you’re well acquainted with their work.

And so, back to Toscanelli..

He appears in a Florentine fresco placed beside the ‘Greek-Syrian’ neo-Platonist Marsilio Ficino – one must always place close attention to the headwear given figures in Latin Christian art.

Here, Toscanelli wears the head-dress of a ‘Moresco’ and his facial features appear to have been painted so as to suggest to emphasise foreign and/or Jewish antecedents. ‘Moresco’ was a termed used, as said above, to describe those Spanish Jews who still spoke and read Arabic, and/or such dialects as Judeo-Catalan or Judeo-Occitan.

I can’t compress Toscanelli’s story better than did the author of one wiki article:

Thanks to his long life, his intelligence and his wide interests, Toscanelli was one of the central figures in the intellectual and cultural history of Renaissance Florence in its early years. His circle of friends included Filippo Brunelleschi, the architect of the Florence Cathedral, and the philosopher Marsilio Ficino. He knew the mathematician, writer and architect Leon Battista Alberti, and his closest friend was Cardinal Nicholas of Cusa—himself a wide-ranging intellect and early humanist, who dedicated two short mathematical works in 1445 to Toscanelli, and made himself and Toscanelli the interlocutors in a 1458 dialogue titled On Squaring the Circle (De quadratura circuli).

wiki article, ‘Paolo dal Pozzo Toscanelli’

In one sense, ‘squaring the circle’ was not a ‘modern-ancient’ problem but one long addressed and resolved in terms of Christian theology in the west.

It was precisely how Rhaban Maur had managed to introduce ‘pagan’ Euclid into an extremely conservative monastic environment during the ninth century. His copy of Euclid had probably arrived with a recent Nestorian embassy from Baghdad, the same eastern Christians having only recently translated it into Arabic.

In what follows, I’m not only quoting matter I’ve quoted in treating the Voynich manuscript, but which I’d quoted even longer ago in connection with other medieval European images, but since I can’t just collapse the text and make it optional, here it is.

—–

Maur began by formulating the quaestio, or problem by setting it as a problem about interpreting the Psalter correctly. Thus he begins,

“It is well that we should enquire what the Psalmist means by the circle of the earth and why, in several other places, he says that the earth is comprised of the same figure. On the other hand, in the 106th Psalm [Vulgate numbering: Ps cvii.3] he comprises the earth under four cardinal points… A very similar statement appear[ing] in the Gospel where it says: He shall send his angels with a great sound of a trumpet and they shall gather together from the four corners of the earth”

and so, having made Euclid an aid to theology, Maur continues:

Whence it is fitting to enquire how far the quadrate and circular shapes of the earth can agree, when the figures themselves, as geometricians maintain, are different. The Scriptures call the shape of the earth a circle for this reason: because to those who look at its extremity [i.e around the horizon] it always appears as a circle. This circle the Greeks call a horizon [a word meaning ‘belt’ or cord], signifying that it is formed by the four cardinal points; these four points signify the four corners of a square contained within the aforesaid circle of the earth.

Maur understands the horizon line as a knotted cord, resembling a monk’s waist-cord with its knots, and akin to the surveyor’s measuring-cord, also knotted at intervals and worn in the same way about the waist when not in use. But the geometric figure Maur has just begun to describe is the ancient figure for the world in microcosm. He suggests as much, speaking of the ‘Eye’ as simultaneously urbis (city) and orbis (orb/circle).

So then, taking East as his primary point, just as medieval Europe’s mappamundi did, but as Cresques’ map and the Voynich map do not, Maur locates the heart of the world as the microcosmic ‘city’ saying:

  • For if you draw two straight lines from the East, one to the south and one to the North, and in the same way also draw two straight lines from the Western point, one to each of the two aforesaid points, namely the south and north, you make a square of earth within the aforesaid circle. How this aforesaid square (demonstrativus quadrus) ought to be inscribed within the circle, Euclid clearly shows in the Fourth Book of the Elements.”

And since I’ve been once more obliged to quote from my own work I’ll add here two images which I included in a post published at voynichimagery in 2017. Details of my source, which was not speaking about the Voynich manuscript, were given at the time as seen in the images below. Today, however, that address is no longer current, though the second image (still dated October 25th., 2012) can be seen, with commentary, at luwanarch .wordpress com. This is how Alberti mapped Rome.

Again, about methodologies and Voynich research –

Between 1912 until 2012 or thereabouts, the most commonly seen approach, among those hoping to ‘solve’ the manuscript was to ignore the codicological evidence, the palaeographic evidence, the materials’ evidence, all earlier independent specialists’ opinions, and interpret the images only if and in a way compatible with their initial theory, often a theory naming some prominent European as ‘author’, effectively re-defining the manuscript as a slab of written text, which despite being lavishly illustrated, was all designed by one mind to deceive.

The common practice of ignoring the manuscript’s own testimony in favour of promoting a Voynichero’s pet theory reached its peak of absurdity about three or four years ago, when another of those borne-on-air sort of memes asserted that, since the written part of the text was also now to supposed a mere nonsense – a joke of some kind – that thus might also be treated as being quite as ‘irrelevant’ as the manuscript’s images, codicology and palaeography, so everyone should just adopt one of the most promoted theories as if it were of more substance than the manuscript itself.

It’s no wonder that Beinecke MS 408 needs its few friends. Who in the world would put up with such treatment being accorded the Vienna Dioscorides, or the Book of Kells, or any other important and apparently unique manuscript?

After which grumpy remark, I propose we adjourn for now.

Gd and the weather willing, I’ll be back in 3-4 weeks’ time.

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.

Elevated souls Pt 2a. ‘Astro —-‘

  • Header image: (left) stars of northern latitudes; (right) declination and right ascension  -image courtesy ‘Sky and Telescope’.

Previous two:

 

David Pingree

In 1982, the Journal of the Warburg and Courtauld Institutes (Vol. 45) published the paper:

David Pingree,  ‘An Illustrated Greek Astronomical Manuscript. Commentary of Theon of Alexandria on the Handy Tables and Scholia and Other Writings of Ptolemy Concerning Them’.  ( pp. 185-192).

I begin by mentioning it for several reasons.

The late Prof. Pingree is one of the “two Davids” whose works are among those indispensable for study of what some pre-modern peoples knew about stars and – most pertinent to our chief study – how they thought about and imagined the heavens.

The ‘other David’ of the two is David A. King, whose works include the Ciphers of the Monks, in which King drew attention to the same Picard instrument whose orthography for month-names is – as I think Pelling first observed – closely similar to that of the Voynich month-names’.

Since the matter of  ‘Occitan month-names’ is among those affected by metaphorical ‘palimpsest-ing’,  I add more detail.

Writing in 2004, Shaun Palmer credits Stolfi with the proposal and (quite properly) notes that Pelling had come earlier than himself and independently to hold a similar view.  Pelling’s book (2006) then treated and illustrated the issue in  detail (pp. 21-23).  Those three  references should give you a clear idea of the evidence and substance behind this now-widely-accepted view.Searching for ‘Occitan’ today at voynich.nu I found the references given on this point to be an anonymous blogpost of 2012  and a note of thanks to Don Hoffman for providing Zandbergen with bibliographic details of King’s book. Following the principle that  “no acknowledgement asserts no debt”, readers might assume all  unprovenanced matter on that page (which is copyrighted  to  the owner as is every blogpost)  must be a result of the owner’s own research, crediting Zandbergen accordingly.

That paper by Pingree is chiefly concerned with the manuscript Ambrosianus H. 57. sup. (= 437). The ‘tables’ in question are known as  ‘Ptolemy’s Handy Tables’ but were compiled from Ptolemy’s data a century later, by Theon of Alexandria.  Researchers working on the Voynich manuscript might like to consider, in addition, matters associated with Ptolemy’s Geography, as balance for a tendency to associate Ptolemy solely with astrology, or even solely with astronomy. See e.g.

  • Dmitry Shcheglov, ‘Hipparchus’ Table of Climata and Ptolemy’s Geography’, (available through academia.edu)

 

Question 1: Is there Astrological matter in the month folios?

Caution Newcomers should be aware  that nothing in the manuscript has yet been proven related to any branch of occult or pseudo-scientific practice including that of astrology, though  speculation has been so common –  thanks initially to Wilfrid Voynich and his inflation of the ‘Rudolf rumour’ – that many imagine it has been proven beyond doubt.  Yet the stars are part of the natural world and natural, too, may be their observation and depiction.  To represent the theological position of the earlier medieval west, we may refer again to  Augustine:

Amiens Cathedral exterior: Virgo = Threshing               see   labours of the months.

Who can fail to perceive how great is the difference between useful observations of the heavenly bodies in connection with the weather, such as farmers or sailors make … and the vain hallucinations of men who observe the heavens not to know the weather. or their course … but merely to pry into the future ….

from Augustine’s Letters  55 15

  • Anne Lawrence-Mathers, Medieval Meteorology: Forecasting the Weather from Aristotle to the Almanac (2019)
why is the astrological  idea a problem?

Objection 1.  The idea’s introduction depended entirely on ideas about John Dee’s connection to the manuscript, in combination with consideration (only) of the month-names and central emblems from the month-folios.  The latter were taken to depict the ‘signs’ forming a tropical zodiac, rather than taken literally as a depiction of the physically-visible constellations which appear in sequence through the seasons of the year.  The conflation of constellation with astrological ‘sign’ is endemic in Voynich discussions, even today.  

Even if the emblems did constitute a representation of the zodiac ’12’ there is no necessary connection between their depiction and that aspect of mathematics which defined astrology in the medieval world.  In other words, there is no necessary connection between a depiction of the ecliptic constellations and tropical- or sidereal astrology.  

That the opposite idea should be so prevalent in Voynich writings today is due to the fact that most modern readers, living in an industrialised society and urban environment, don’t need to know the stars as people did in earlier times.   Today, we use clocks, watches and phones to know the time; we learn from the weather man what sort of weather we’ll have today; we rely on automatic or printed calendars to tell us where we are in the cycle of months and seasons.   Reflection from city lights, and nights spent indoors (or outdoors) under artificial lights means  many see none but a few of the brightest stars in the night sky.   And all this, together, means that the word ‘zodiac’ instantly evokes the motifs of ‘birth-signs’ and daily horoscopes for us today, and thus seems the ‘most obvious’ interpretation for any comparable series, especially if stars are depicted. 

 Thus, the constant error has been an imposition on a manuscript  six hundred years old, the hierarchy of ideas proper to twentieth- century urbanites.

Things were different six centuries ago.

Objection 2.  No  zodiac sequence contains (as the month-emblems do) two goats, or two sheep,  or a sheep and goat adjacent to one another.

This issue and others raised by the month-emblems are rarely even noticed today by Voynich writers. and of the few who do notice, fewer speak, and of the very few who do mention a problem, the majority do not address that problem so much as seek a way to turn back into the fold any who show signs of doubting that “its-a-zodiac-and-zodiac-means-astrology” proposition chain.    In private conversation a Voynichero once said that he didn’t include both pros and cons in his own writings  because “if your mind is too open, your brains fall out” – which sounds to me like some conservative slogan gone wrong. 🙂

Objection 3. Even if we grant that,  in adding the month-names later, the person who did that truly  believed  the emblems represented constellations from the zodiac, more cannot be deduced from it than  he had  regarded the series as a series of months and their stars.  It is no support for an idea that  “months+stars means astrology”.  

Objection 4. is that the the Voynich series names only  ten months, and the months omitted (January and February) are – perhaps coincidentally or perhaps not –  the months when the fields were dormant, and when  ships of the Mediterranean stayed in harbour. The ‘sailing year’ ran from March until (nominally) November but the historical records show that in fact ships of the harbours where the most competent seamen were based might continue  sailing coast wise even as late as December.

Other points:

  • An argument that the remnants of two cut pages following  the month-diagrams  had once contained two more diagrams of that sort is – like theorised astrological purpose – only speculation at present. 
  • As I’ve explained elsewhere, correlations of month-name, month-marking constellation, and associated ‘labour’ were not uniform  even within Latin Europe., and the correlations made in the month-diagrams between emblem and month-name are not those of the northern latitudes (England, Germany and northern France).
  •   When responding to a Voyichero’s query,  Prof. Ewa Sniezynska-Stolot of the Jagiellonian University in Cracow – whose area is given as the history of European art, especially its traditions of astrological imagery-  also mentioned calendars in connection with the month-diagrams’ central emblems.  Here the difficulty is that her opinion was a short note written in response to a Voynichero’s query and it appears she was given no indication there was any reason to doubt that the content in this manuscript might have any but a medieval Latin European origin.  The answer of an expert is typically provided within the framework of the question posed.  Not knowing that explains why William Friedman got so little from Panofsky, where Anne Nill had received so much more  – and we’re not talking word-count here.
  • Nor do we know what Sniezynska-Stolot was shown of the manuscript at the time (2000), or whether in colour or copy-flo.   As translated by  Rafel Prinke and  reported in Reeds’ mailing list, her note has a distinctly off-hand tone.

By  13 Jan 2001 her note’s content was already reported to Reeds’ mailing list and members were discussing it in  connection with specific problems of the kind no longer acknowledged as existing by the most conservative faction and whose discussion is thereby discouraged, with ‘blanking’ from the record of any non-conservative who might do so. 

Still – let’s move on to one possible hint of the astrological… and trust our brains won’t fall out. 🙂

Astrological versus (purely) Astronomical

Exaltation and Depression?

Consider the following pair  from the first of the ‘April’ diagrams (folio 70v-ii), keeping in mind that the fifteenth-century draughtsman could draw ‘nicely’  but for reasons as yet unclear, didn’t wish to.  What message are we to take from their presentation? What aspects are we supposed to  read as meaningful? What about their postures, for example?

 

Did the original maker  intend the male  figure is to be read as ‘elevated’/’exalted’ and the female as ‘dejected’ or dismayed?   Or are our  subjective reactions focusing on details he would have dismissed as irrelevant?

If he meant attention paid to their posture, we must realise that such terms as ‘elevation’, ‘exaltation {Gk. ὕψωμα]  and ‘dejection/depression’ [Gk. ταπείνωμα] were used technically of the planets in Byzantine astrology, while  “seldom, if ever, found in the West” -as Pingree observes, though he finds that their illustration  in  Ambrosianus H. 57. sup is drawn ‘in western style’.

Indeed, the draughtsman’s style may be western, but it has  little in common with that of the person who drew the unclothed figures in the Voynich month-folios, except perhaps a common implication (also found in certain Islamic texts) that when figures from polytheistic religions are presented, the images should express moral censure. (see further, below) I say ‘perhaps’ because we have no proof thus far that the Voynich figures were intended as deities or anything of the sort. Neither have I seen any argument which proves that  the Voynich manuscript depicts any of the five planets, let alone all of them.

*The planets proper, the ‘wandering stars’, included only Mercury, Venus, Mars, Jupiter, and Saturn in medieval times.

re planets…2001

In 2001, a member of the first (Reeds’) mailing list responded to Robert Firth’s comment on the fact that the ‘celestial’ folios hadn’t served as key to the written text as many hoped they might,  by saying  that “we” ‘ ..have quite a number of good (even if not dead certain) [identifications]:- the Pleiades and Aldebaran; – the seven planets; – two sets of twelve labels in 12-segmented circles; – one (or two?) set of 28 segments, “obviously” indicating the mansions of the moon. (12 Jan 2001).  All members of that list, at the time, would have known which of them had contributed each item, with what evidence and what argument (if any) but as yet I don’t know. If you can enlighten me on the point, please do. I’ve seen nothing one could call a cogent argument for it between 2008 and today.

detail) Milan, Ambrosianus H.57.sup. f.112v. Venus – on which see Pingree (1982) p.32

The unclothed pagan deities for each planet are depicted with a certain censure in the Ambrosianus manuscript  –  e.g. Venus (right) is depicted as as a debauchee – given the face of a young and pretty woman but a body heavy, old and exhausted from bearing children by various fathers. I see little obvious similarity between the draughtman’s style and that in the Voynich month-folios.  Expressions of moral censure in depiction of figures from polytheistic religions are  also seen in some Islamic works, notably in the  ‘Book of Marvels’ ‘Kitab al Bulhan’ (MS. Bodl. Or. 133) a seventeenth-century work (or copy) where Voynich-like “glyphs” were also inscribed.

That-last point was initially brought to notice by – I believe  – by Nick Pelling in his review (2008) of Okasha El Daly’s book. A detail (‘Crab’) from the same Bodley ms was later considered by one Voynich blogger whose blog I cannot find online today. In two posts of 2013 the present writer commented on several of  images from that manuscript, together with  other examples of ‘Voynich-like’ glyphs.

An image posted to pininterest by Marco Ponzi associates a detail from the Bodleian ms with one on folio 67v 2. His commentary may appear elsewhere but I’m not willing to join that site to find out.  (Again, if anyone already has more detail, I’d be happy to include it in the comments section below this post.)

On the Greek astrological terms and their significance see e.g.

  • Roger Beck, (2008) A Brief History of Ancient Astrology, pp. 57-8
  • Roger Beck, (2017) A Brief History of Ancient Astrology  pp. 242ff.
  • Chris Brennan, Hellenistic Astrology: The Study of Fate and Fortune.
  • James Evans. Time and Cosmos in Greco-Roman Antiquity (p.135). Evans’ equating ‘Chaldean’ with ‘Babylonian’ is over-confident.
  • Tamysn Barton,  Ancient Astrology (2002).

Neither  Aratus/Cicero’s Aratea, nor Manilius’ Astronomica  (written  c.30–40 AD) makes use of the planets, a point to be kept in mind given the date for Vat.gr. 1291 and possible  pre-Christian (but anti-Greek? anti-polytheist?) origin for its ‘women of an hour’ (see previous post).

Manilius in the west

Goold believed that before his election to Pope, Gerbert d’Aurillac had found in Bobbio a copy of Manilius’ Astronomica bound (as Gerbert said) with a copy of Boethius’ text on mathematics. Other scholars have doubted this, attributing the west’s knowledge of that text (as we have it) to Poggio Bracciolini’s practice of  commandeer manuscripts from monastic libraries by his position as papal secretary.  The ‘discoveries’ were then copied (at a price) for members of the Italian literati, who appreciated Poggio’s ‘little arm’. His own view is recorded in one colophon, which translated reads “This oration, formerly lost owing to the fault of the times, Poggio restored to the Latin-speaking world and brought it back to Italy, having found it hidden [sic] in Gaul, in the woods of Langres.” If he had acquired it from Bèze abbey, that copy is unlikely to have been older than the 11th-12thC.

Again with the older period in mind, and possible bridges between  pre-Christian astronomical works and the early fifteenth century when the Voynich manuscript was made, I’ll add here part of the description of Niceforous’ visit to Cyprus in the fourteenth century.  There was still a Lusignan ruler in the island, one who with his chief scholar George Lapithes asked the noble visitor from Constantinople to summarise for them as many astronomical texts as they could gather. They brought him copies of Ptolemy’s works, including the  Tetrabiblos, called Ἀποτελεσματικά ετράβιβλος in the Greek – but also,  according to  Niceforous (I quote from another paper by Pingree):

“all the books that still existed composed about such matters, by Ptolemy’s predecessors and by more recent authors as well as those that had been written in antiquity and by the  Chaldaeans and the Persians”. 

  • George Lapithes and David Pingree, The Byzantine Version of the “Toledan Tables”: The Work of George Lapithes?’, Dumbarton Oaks Papers, Vol. 30 (1976), pp. 85+87-132.

Pingree offers evidence and argument for a/the Greek translation of the Toledan Tables’  in Cyprus during the first half of the fourteenth century, to which same period, as it happens, I assign their ‘return to the Mediterranean’ phase for  the majority of parts in the Voynich manuscript.

Ambrosiana H.57. sup. – evolution 2ndC AD – c.1458..

Claudius Ptolemy lived in the 2ndC AD.  Theon of Alexandria in the 3rdC AD.   So then, discussing the content in the Amrbosiana manuscript, Pingree tells us:

We may conclude, then, that the original [i.e. the Ambrosiana] manuscript was copied in 1358, and that a series of owners for the next century added to it, rearranged it, and annotated it. It is likely that the manuscript was copied in Byzantium, and remained there while these changes and additions were being made to it. There is no absolute proof for this supposition in the manuscript itself, but it is known that the texts in Ambrosianus H. 57. sup. were copied in part from Laurentianus 28, 7;3 and that manuscript can be shown to be Constantinopolitan. (Pingree, op.cit. p.186)

and

There is no doubt, on the evidence of the script, that the codex could have been written in Constantinople in 1357-58. It is in the style associated with the Hodegoi scriptorium over a period of about half a century.  Western connexions of this scriptorium are not apparent. If they existed they would be more likely at this time to have been with Venice than with Southern Italy.   (ibid. p.192)

.. yet when it comes to those miniatures …(emphasis is mine)

The consensus of opinion is that the style of the miniatures is basically Western, though with an admixture of Byzantine elements. Islamic tradition lies behind the curious iconography, in which the planets are shown with their day- and night-houses, exaltations and dejections: this is seldom, if ever, found in the West. No immediate model has been located in an admittedly cursory search. An artist active in Southern Italy or Sicily may be indicated by the mixture of Italian and French styles. It is not impossible that an artist of, say, the Neapolitan school was working in Constantinople in the mid-fourteenth century – a time when others (Barlaam of Seminara, for example) travelled freely between that city and Italy. No artist answering to this description can, however, be securely documented in Constantinople at this time. Nor can it be assumed that the manuscript was decorated in the same place as it was written: the illustrations may be later additions. Indeed, they look very much as if they are.    (ibid. p.192)

 

For those who managed to come so far   –  here’s the sweet….

B. Astronomical?

Returning to the pair on folio 70v-ii, a closer look at the female figure…Short-ish hair, large head, figure’s right side drawn with a swelling line, indicating a breast. But where the figure’s left breast would be, there’s only what appears to be a piece of skin, marked with lines evoking sutures or something of that kind. Obviously not a skin-graft  (skin-grafting, history of)

We have a word for females who display just one breast. It’s from the Greek: a- (ἀ-) which means lacking and mazos (μαζός), which means breast   ..so, …”without breast”= Amazon.

Classical Greek and Roman imagery doesn’t depict Amazons  lacking a breast. They show a figure who is usually short-haired,  sometimes in armour which can include a breast-cover, or with only one breast covered by clothing and/or armour.

Interestingly, on fol. 70v-ii, the breastplate has been understood by the draughtsman to be of the high-collared type. The two images (at right) are shown simply to demonstrate that high-collared breastplates,  for females, are not entirely unattested.  An amazonian caryatid in Dresden wears armour very similar in deign to the Keralan type. That caryatid is described (by a seller of prints) as  ‘an ancient wall sculpture’. I can only say that their definition of ‘ancient’ is unusual.

The Keralan tradition marks by such means one of the eight chief patron- ‘mother’ goddesses, known to be warrior-women when necessary.

To this day women archers may don a breast cover in addition to the cover always provided for the forearm by the long, skin-tight sleeve and/or by a wrist-guard which might be better called a forearm-guard (but isn’t).  These were traditionally made of thick leather; The present day Olympian (below) wears ones of modern materials.

When you consider that women in pre-Renaissance Europe didn’t normally ever handle a bow, and that  the two drawings in the lower register were made  two thousand years apart from each other, the conceptual image informing the physical image per se has evidently survived remarkably well. The fifteenth-century draughtsman understood his exemplar.

 

So now – which star(s) if any might have been identified as  ‘Amazon’ by any tradition of star-lore, at any time between the 5thC BC and 15thC AD? Here are two possibilities from the Greco-Latin-Arab traditions with which I think readers will be most familiar.

 

  1. alpha [α] Virginis (Lat.Spica) ?

According to the 15thC Yemeni, Ibn Majid, the star α Virginis serves as the manzil (lunar station/mansion) and in that context is known as Simak al A’zal, ‘warrior without a spear’ (Tibbett’s translation p.100). And the figure from the first April diagram certainly has none.  However, women of the Arab tribes in Arabia, and more particularly of the Yemen, appear from the early accounts to have been treated more on par with men and in the pre-Islamic period to have been decidedly martial. By comparing with both older and early medieval works, it appears that until the seventh century AD, α Virginis may  have been often envisaged as a female warrior, one who roared or howled in the attack.   As Virgo, she is still armed in an image within the 9thC Byzantine manuscript Vat.gr.1291.

9thC Greek  (prob. from a late classical source)

A star-ceiling made in Egypt under the patronage of the Roman emperor Tiberius in 50BC, shows Virgo holding a ‘spike’ staff of some kind. The image shown here (below, right) is  as illustrated by Wallace Budge.

1stC BC. image in late-Hellenistic Dendera. If the spike is papyrus, the use of palm and scroll as alternative is understandable.

While Virgo’s spike-star  was generally envisaged as a stalk or sheaf of wheat for most of the Latin period, the alternative tradition was not forgotten, and the late image seen below shows how it was preserved – as a martyr-like palm branch held delicately by a more passive and ladylike virgin angel.

So if this is the intention behind the ‘Amazon’ on folio 70v-ii, her being without a weapon may be due to the same cultural attitudes (not necessarily Arab) which sees  the ‘ladies of an hour’ drawn with arms deprived of strength in Vat.gr.1291 folio 9r- as we also see   in the month-folios of the Vms.

Libra

In both instances, the informing ideas appear to me  indicative of deep-seated belief that the stars had effective power to harm and I doubt such fear derives from the classical Greeks or from the Orthodox Christians of ninth-century Constantinople. That Vat.gr.1291  has drawn on ideologically opposed traditions is evident if one compares the charming figure for Virgo in the ‘helios’ diagram (folio 9r) with the frankly unnerving and skeltal ‘ghost’ which is one of the few figures un-erased from the same manuscript’s planispheric ‘night sky’. (right)

So let’s return to the charming Virgo.  Unlike her counterpart on folio 23r of that manuscript, hers is not  the stocky body we associate with Europe’s late Roman art. She is envisaged as a slender and elegant messenger, whose ‘spike’  now appears more like rolled scroll. (angelos means ‘messenger’.)

This may be a good moment to remind readers that Alain Touwaide said the Voynich manuscript’s appearance suggested to him the sort of Byzantine hospital workers’ notebooks called iatrosophia, though it wasn’t one.

Touwaide has studied such manuals within his wider area of specialisation, and among his publications  is

  • Alain Touwaide, ‘Byzantine Hospital Manuals (Iatrosophia) as a Source for the Study of Therapeutics’, in Barbara S. Bowers (ed.), The Medieval Hospital and Medical Practice  pp.147-173 of Vol. 3 of AVISTA Studies in the History of Medieval Technology, Science and Art, (2007).

I agree that in the  Vms, we have a compilation of matter brought together for an entirely practical purpose, and find it possible the ‘bringing together’ may have occurred in comparable circumstances, and even within the Byzantine sphere, but having already treated in detail a large proportion of the Vms’ imagery,  I am glad that I am not in the unenviable position of having to differ from Professor Touwaide on the ‘practical handbook’ issue, or the ‘compilation’ issue, though I should have been obliged, unhappily, to do so had he said the whole was a work of medicine, or even of astrological medicine.

  • at the moment I can’t refer you to the printed version of Touwaide’s Voynich talk (or, rather first Voynich talk) at Mondragone.  The book is unobtainable, and Stephen Bax’ site where it had been shortly reviewed is presently infected by some virus.  Maybe later.

2. gamma [γ] Orionis.

Hinkley Allen informs us that in  “the Alfonsine tables” (no version or copy is specified) the star γ Orionis has a previously-unattested name, as  Bellatrix – a term from Latin and which means again, a female warrior.

Note – Ptolemy’s Tables, Alfonsine or Toledan Tables in Voynich studies

I was surprised to find no mention of any of these tables in Voynich writings or chats until speculations about occult topics had taken been current for about ninety years.

One would have thought an examination of standard sources for astronomical knowledge would be tested first before resort was had to speculation, but things went the other way.  Perhaps, yet again, we must attribute this oddness in the study first to Wilfrid Voynich’s tale, and a feeling among some that support for the ‘Rudolf’ idea had to marshalled.   However that may be, even today (Nov.2019), I find no mention of the Toledan tables at Nick Pelling’s site, or at voynich.nu.  I believe there was some talk of them in comments to Stephen Bax’ site, but at present it is under ‘virus interdiction’. I hope to check it and properly credit anyone who posted there if/when the site and its comments return.

Otherwise, I have found nothing about the Alfonsine or Tioledan tables (do let me know if you know better) until 2002 (ninety years after Voynich acquired the manuscript), when Luis Vélez’ says in  Reeds’ mailing list (Tue, 16 Jul 2002):

Thus, students of medicine at Bologna… learnt astrology [sic.] for four years, including grounding in Euclid’s geometry and Ptolemy’s Almagest. In addition, they learnt how to use instruments such as the astrolabe and the quadrant, and were taught how to use the Alfonsine Tables along with their canons. ..

 

Hinkley-Allen suggests ‘Bellatix’  was gained by mis-translation of an Arabic term, ‘roaring lion’.  I should have been inclined to dismiss this altogether, as mere transposition of some term for a star in Virgo – except that it survives experiment extremely well.  Experiment involves cultural and specific context, in addition to the image’s individual characteristics and drawing-style.

As you see, where the chap looks quite upbeat, the female looks decidedly “down”, doesn’t she?

Those interested in the written part of the Voynich manuscript might care to research uses for the opposition between elevation/exultation and subjection/ being downcast as applied by older works to matters other than planetary dispositions.

And with these two feasible identifications, mentioned  I’ll leave the astronomical and astrological possibilities for you to think about, except a last note that in another place, according to Tibbett’s note, al ibn Majid identifies Bellatrix with Orion’s hand [lit. Yad al Jauza’, usually Betelgeuse],  and it is in connection with this passage that Majid relates a condensed ‘cipher’ mnemonic for some fairly technical and mathematical matter.

Should it be of interest to any reader, description of that ‘cipher-mnemonic’ runs from the last paragraph on p.87 to the end of the first paragraph on f.88 in Tibbett’s English translation..

Postscript: From the research into historical and cultural context – I think one topic should have been mentioned, viz. the Indian tradition.  Thus, our Bellatrix (γ Orionis) is still recorded as ‘Yad al Jawzã’ al-Yusrã’ on astrolabes made in Lahore by a ‘dynasty’ of astrolabe makers in the sixteenth- and early seventeenth centuries.

  • see e.g. Mubashir ul-Haq Abbasi and Sreeramula Raeswars Sarma, ‘An Astrolabe by Muḥammad Muqīm of Lahore Dated 1047 AH (1637-38 CE)’, Islamic Studies, Vol. 53, No. 1/2 (Spring-Summer 2014), pp. 37-65

In the same context, the ‘serpentine’ extension behind Betelgeuse may allude to the ‘Ketu’ (headless body) of Rahu Ketu in Tamil and Hindu astronomy.  The sources differ considerably and I don’t want to give an impression that I place much importance on it.)

Also, we know that the Indian and Muslim traditions were both still present in Iberia during the fourteenth century, as Chabas and Goldstein (among others) have said:

quote stars Jews Spain astronomical tables 14thC Indian trad

Chorography..

I had meant to now talk about chorography, and identifications of stars with places – not by astrology but by an older system of observation and  a mythos of locality.. as well as by nominal superimposition of  celestial and terrestrial co-ordinates (made easier in medieval times if one had an astrolabe).

I would have begun from the classical sources’ identification of Amazon lands, by Herodotus and later authors, illustrated by a couple of maps, and then moved on to the technical correlations for star-and-place as well as the various astrological equations of peoples and regions …. coins, legends, Manilius, Dorothea of Sidon etc., remarks on Genoa’s colonies in the Black Sea (from c.1290s to the time the Plague came..) and so, eventually,  to Ptolemy’s co-ordinates.

But this post is already a trying length, almost 4,700 words, so I’ll leave all that material from my logs aside, except to say the Voynich ‘strings’ may bind place and star.

The star-place correspondence system has to be conceptual or temporary because the vernal equinox moves, as the first minute of right ascension doesn’t.  Then there are also the eastern navigator’s “fetterings” but …alas.. who’d ever read so much?

At least you have some sources for this last and  far from unimportant section.


edit (6th December 2019).

Can’t get the ‘comments’ to include this image, so here it is. Proof of relevance to c.1420.  See second of the comments following this post.