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

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

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

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

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Unresolved problem – the ‘4o’ glyph.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

As for MILAN, (this comes from JVL)

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

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

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

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

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

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

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

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

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

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

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

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

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

Only research can clarify the still-unresolved problem.

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

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

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

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

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

‘Commercial …’.

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

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

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

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

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

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

Byzantine accounting.

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

Location of later diplomatic documents:

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

Sound’ and Linguistics.

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

Associations for the number ’40’.

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

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

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

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

Remember..

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

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

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

Expert opinion vs materials science 4

Header illustration: (left) A swiss pocket-watch, the most complicated in the world; (inset) ‘no hammers’ sign; (right) bench of Swiss watchmakers’ tools. And for the smart-guys who immediately look for a hammer among the watchmaker’s equipment: that’s not a hammer but a very small mallet.
two previous:

This post is about the equipment, chiefly intellectual equipment, needed to treat with a manuscript as problematic as Beinecke MS 408 – so it’s  more about expertise than about materials science; I’ll get back to codicology in the next post.

I expect that my broaching this subject may cause hackles to rise on some readers, while others will think it self-evident that any person who knows too little can only misinform those who know still less.

But from the range of matter on the internet, in papers issued as pdfs and even books in print, it is evident that the idea is general that with this medieval manuscript anyone can ‘have a go’ .

The bar for newcomers is certainly set highest for cryptological theories, of which few survive unless the proponent has taken time to study the history of cryptology and of methods already tried.

 

Next are studies that involve linguistics and statistical analyses. New readers should consider the work done by Julian Bunn, E.M. Smith and Koen Gheuens‘ latest post (and comments made to it) to get a clear idea of the present level of discussion in that subject.  Nick Pelling‘s recent post on ‘Currier A’ and ‘Currier B’ should also prove illuminating.

The bar against novices is less high when translations are claimed – hence the regular claims that the text has been translated.  Part of the problem in this case is the lack of persons with the time, languages and inclination (Voynicheros or not) to test and review such claims.  One wonders what sort of ‘peer reviewer’ is being invited by the publishers today; the book by Tucker and Janick was published by Springer (no less) but it is only thanks to the kindness of Magnus Pharao Hansen  that we know their claimed “Nahuatl” is not.

A neat illustration of the fact that it is inherent value, nor format, which makes information valuable.   Tucker and Janick’s book appeared in print;  Hansen’s refutation of their ‘Nahuatl’ translation in a blogpost.  The benefit of information published as book or blogpost is that it comes with a date-stamp – very helpful when trying to clarify questions of precedence, originality and attribution. 

Poorest of all are standards for accepting or rejecting assertions made about the manuscript’s iconography or quasi-historical narratives.  Some adopt the form of scholarly papers while lacking such quality. Others don’t bother. Some few are by scholars who (like Newbold) made the basic error of accepting, untested, other persons’  unfounded or ill-founded assertions as their ‘givens’.

I am not suggesting everyone must leave the field who hasn’t formal qualifications in manuscript studies, materials sciences, comparative cultural history, or cryptography… or anything else.

A doctorate is no promise of  a balanced attitude and the history of Voynich studies shows its course regularly de-railed or misdirected by individuals who, being qualified in one field, imagine themselves omni-competent.

William Friedman is one of the earliest examples; his skill in cryptography is a matter of record but he was mistaken in supposing that all other matters – codicology palaeography, and the pictorial text – were inherently inferior studies which might be treated as ancillary to his own.

Where he might have set reasonable  limits for his search for ‘the cipher method’ by accepting the opinions of those better qualified to date and provenance manuscripts, his narrow focus meant that on the one hand he accepted many of Wilfrid’s assertions uncritically and, on the other, pursued his imagined ‘author’ as far as the seventeenth century.   He treated persons such as Fr. Petersen and Erwin Panofsky less as valuable guides than as sources from which to extract computable ‘yes-no’ data and overall showed that lack of balance and over-confidence that ensures failure, barring a miracle.

Again, Hugh O’Neill was a qualified  botanist, but his area of competence was the native flora of  Canada – and to a lesser extent, of Alaska.  Nothing in his writings, or in what others said of him during his lifetime  indicates any particular knowledge of, or interest in, medieval history, art, or manuscripts.  Nor does he seem to have paid due attention to Fr. Petersen, who had told him plainly and repeatedly that no palaeographer could support O’Neill’s bright idea.  O’Neill himself had so little interest in the question of historical context that he cannot have even tested the  ‘Columbus brought sunflowers’ theory against primary documents relating to Columbus’ voyages.  As for his ability to read the manuscript’s imagery  …  well, let’s call it naive.

And again,  Robert Brumbaugh.   A professor of philosophy with a chair at Yale, his area was the philosophers of classical Greece and, to a lesser extent, of Rome.  Presumably he knew something of classical history and languages as necessary adjunct to those studies, but his papers about the Voynich manuscript show no evidence that he was at pains to learn more about manuscripts, medieval history, botany, or the range and variety of star-lore and -science known in the medieval (or earlier) periods   What he read of cryptography seems only to have been in connection Voynich theories.  His acknowledgements reinforce the impression that he, too, imagined himself competent in all things because formally qualified in one.    His paper on ‘Voynich botany’ credits Hugh O’Neill’s paper, his own nephew Mr Eric Arnould and “a Mr Pero, of Syracuse, New York”.  Not a single colleague in botany or any other relevant discipline, not even from those at Yale.

  • Robert S. Brumbaugh, ‘Botany and the Voynich “Roger Bacon” Manuscript Once More’, Speculum, Vol. 49, No. 3 (Jul., 1974), pp. 546-548

Claiming to have ‘solved’ the text, Brumbaugh mentions Marjorie Wynne and Louis Martz, one being the Beinecke’s head librarian and the other its honorary director, a Professor of English.  But neither is mentioned as helping him learn more of codicology, medieval manuscripts or even medieval English texts –  but only for their ‘encouraging’ him.

  • Robert S. Brumbaugh, ‘The Solution of the Voynich “Roger Bacon” Cipher’, The Yale University Library Gazette, Vol. 49, No. 4 (April 1975), pp. 347-355.

However, give Brumbaugh some credit for keenness in observation.  As I write this, I see that I may cite him as precedent for noting as Dana Scott, and then I would later do, that the Voynich ‘aries’ are drawn as goats, not sheep, for he wrote in another paper the paper above that they are “[as] much like a goat as like a ram…”. See Robert S. Brumbaugh,’The Voynich ‘Roger Bacon’ Cipher Manuscript: Deciphered Maps of Stars’, Journal of the Warburg and Courtauld Institutes, Vol. 39 (1976), pp. 139-150.  (p.147)..  That the same observation had to be made independently in 1976, and (by Dana) about thirty years later, and again by me forty and more years afterwards can be attributed to two things: first, that a goat did not fit the usual theories and secondly the ‘groundhog day’ phenomenon which sees little accounting for precedence – an error which becomes exponential.  Today (in August 2019), the fact is being absorbed and repeated (if not explained) in a number of blog-posts and chat-rooms.  (Note corrected and expanded –  19thAugust 2019)

The issue, then, is not about qualified as against unqualified Voynicheros, but rather of an individual’s unreasonable self-confidence in their capacities, despite their limited range of intellectual tools, and their underestimating the complexity of problems and evidence presented by this manuscript.

To say that ‘anyone with two eyes’ can understand the imagery in the Voynich manuscript, or date its hands, or correctly attribute its manufacture to a time and place is as stupid as  a carpenter’s saying that because he has two hands and a hammer  he can put together a plane as good as any now flying.

To have one skill and a theory may be enough to make a useful contribution, but to suppose that instills the capacity for all other skills is to act like a child who claims they can fix a broken clock with just a  hammer.

The task of understanding this particularly difficult manuscript is better compared to the work of an old-fashioned watchmaker, who must put together a great many separate, interlocking elements, aware of how each relates to and contributes to the workings – and whether each has been accurately formed by the makers. In this case the parts are explanations for those cues embodied in manuscript’s materials, structure and iconography; in connecting the historical and cultural cues with the evidence of linguistics, palaeography .. and quite possibly cryptography…

It is not a simple process.  It requires solid evidence and input from a range of competencies.  It is not as simple as theory-creation, effective theory-promotion, relying on the age of ‘canonised myths’, nor simply of logical thinking.  As one of my students once said, “This is hard because you have to know so much stuff”,

Logic is the pride of many Voynicheros, but logic is a tool which produces results no better than its ‘givens’.  Nor should people with an ability in the critical sciences suppose those of the pragmatic sciences are less intellectually demanding or easier than their own – or vice versa.

As one scholar said, in speaking to a group of cryptologists in 2013:

“.. breaking ciphers is all about testing hypotheses and finding *the* consistent solution, of which there will be only one. Historical research doesn’t admit of one neat solution and works very differently.”

SirHubert” in a comment to Ciphermysteries, December 10, 2013)

We should be seeking less to ‘break’ the text, or ‘solve’ the manuscript than to understand it.  The manuscript isn’t the problem; the problem is that some basic flaws in the manuscript’s past study leave us still – after more than a century –  unable to rightly interpret the evidence  embodied in the manuscript’s form, materials, script and content.  I’d suggest a prospective revisionist always keep two questions to the fore when reading what has been, or is being said of the manuscript’s content: ‘Where’s the evidence for that idea?’ and ‘Is that inference valid?’.

Because, to repeat the revisionist’s theme-song:

It doesn’t make a difference how beautiful the guess is. It doesn’t make a difference how smart you are, who made the guess, or what his name is… If it disagrees with experiment, it’s wrong. That’s all there is to it.”