Conundrum – can readers help?

Two previous


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

Here’s the diagram again.

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

to which JKPetersen (alone) replied, saying::

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

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


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

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

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

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

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



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

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

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

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

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

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

Numerals in Medieval texts vs Voynich manuscript.

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

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

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

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

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

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

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

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

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

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

Note – Recommending Voynich writers..

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

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

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

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

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