Glass and the pearl band

two prior:

FOR AN ARCHAEOLOGIST, or anyone specialising in a some specific field of technology or art, one’s first instinct when presented with a problematic artefact is to seek that point, within the axes of time and of geography, that it rightly belongs. In the present case, though, another preliminary step must intervene, because since 1912 Beineke MS 408 has been seen through an old and narrowly-defined Eurocentric lens.

That narrative is still substantially that which Wilfrid Voynich created, which was early adopted and maintained by William Romaine Newbold, and later fixed in the public imagination by its repetition in prestigious sources such as d’Imperio’s Elegant Enigma and the holding library’s catalogue entry.

Pressures of repetition, and earnest efforts to justify one or more aspects of Wilfrid’s narrative after the fact (while still altering it the better to support some variant) have fixed an impression among most people that among the few items we can say ‘we know’ is that the whole content of the manuscript should exhibit an exclusively western Latin Christian character.

Given the consistency with which those assumptions have been maintained despite (or perhaps because of) never being investigated with a critical eye, it is perfectly understandable that any suggestion about the content’s perhaps including unmediated foreign matter would cause disquiet.

So in this post, rather than risk being thought to have dispensed arbitrarily with a Eurocentric focus, I’ll do what I can to re-define what might be called the medieval ‘European horizon’.

In the map below, the darker coloured area had been, over the centuries, part of the Persian empire, then of Alexander’s empire, and next of the Median-Persian and Sasanian empire. It then became part of the Islamic empire until, during the thirteenth century AD, much of it fell to the Mongols, whose policy during the first wave of conquests was to wipe from the map any city offering active resistance.

Some sites named in that map (above) were household names in medieval Europe because they find mention in the Bible. Nineveh is mentioned repeatedly and not only in the Jewish religious books incorporated into the Christian bible but in the Christian testament itself (e.g. Luke 11:32).

Babylon was another proverbial name, so well known that when the western pope took his court to Avignon and it remained there almost seventy years (1309 to 1376), the period was commonly called its  ‘Babylonian captivity’.

Tabriz I’ve had reason to mention* as the city where Claudius’ Ptolemy’s astronomical co-ordinates were updated and that new data acquired  by the Byzantine scholar Gregory Chioniades between 1295-96. He called it the ‘Persian syntaxis’.

*see post of July 11th., 2021

Across the whole width of that territory and to as far as China, western Christian missionaries, diplomats and traders were already passing before the end of the thirteenth century.

By 1350 – about half a century before the Voynich manuscript was made – a census of Franciscan houses lists twenty-two on the route from Constantinople through the Black Sea and overland to as far as China, with four houses established by then in China itself – two in Peking at the terminus of the overland routes, and two in the southern, foreigners’ port known as ‘Zayton’ (Guangzhou) where the Genoese or Venetian Katarina Vilioni had died in 1342.

For a time, early in the seventh century, the Sasanian Empire had included the whole of present-day Iran and Iraq and also much of the eastern Mediterranean (including Anatolia and Egypt.

The Byzantines had reason to remember the Sassanians, whose army had alone succeeded in resisting Rome, and it was never forgotten that in c.260AD King Shapur had captured the Roman Emperor Valerian and him kept in captivity for the rest of his life.

(Those familiar with the Voynich manuscript may recognise in Shapur’s stepped-turreted crown a form similar to that given a female figure appearing twice in the Voynich calendar. In both cases (see diagrams for July and August); the figure holds a large 9-pointed ‘aster’ and is set on the innermost tier at 90 degrees right from the vertical. The inset in the picture (below) shows the example from July, where the crown and certain other details are evidently late additions to the original.

In 532 AD and following several major losses to the Persians, the Byzantine emperor Justinian I agreed to pay 440,000 gold pieces in return for an ‘eternal peace’.

Justinian evidently treated this final defeat as a triumph of diplomacy, and it is memorialised in a mosaic made for the basilica S.Vitali in Ravenna, the work begun in 526 and completed in 547.

Sassanian seal-ring set with a carnelian ‘sardion’.

The mosaic shows Justinian wearing as his ‘badge of honour’ a gem then called a ‘Sardion’ after the city of Sardis, stones of this type often used as a seal-stone by the Sasanians (see example at right).

Worn as Justinian’s badge of honour, the stone is shown surrounded by ‘ring of dots’ as pearls – another typically Sasanian-Persian motif in textiles, ceramics and glass but one equally characteristic of Byzantine art.

The bowl which Justinian carries is also patterned in Sasanian style, though the glass appears richly gilded.

(detail) Justinian I. 6thC mosaic, Ravenna. Basilica San Vitale.

Chan mentions that within each of the hexagons that form that bowl’s basic honeycomb pattern is set another and smaller one. In the upper left of the photograph (above) one of them can be seen fairly clearly – it appears as a ‘dot’.

However, the Sasanian emperor almost immediately broke that first ‘eternal peace’ and another mosaic portrait of Justinian, made for Sant’ Apollinare Nuovo in Ravenna, shows Justinian now without his ‘sard’ and wearing a different expression.

This mosaic is believed made in 561 AD or shortly before, when work on Sant’Apollinare Nuovo was completed. A second ‘eternal peace’ would finally be achieved in 562, after six hundred years’ war between the Romans and Sasanian Persia.

The point I want to make is that even if we ignore the probable significance for the Sasanians of that ‘circle of pearls/dots’ it was an established motif in Byzantine art, and for those who made glass, and fabric, and mosaics.

Tesserae of both stone and glass were employed for mosaics, and such motifs as the ‘pearl band’ remained as a constantly present model for the ‘finishing’ or ‘crowning’ touch, even when the subject was not a member of the Byzantine court.

Ravenna is a little more than a hundred miles down the Adriatic coast from Venice, and its magnificent basilicas remained a model of what could be achieved, if only one had the technical means and skilled artisans. Thus, we know (although not every Venetian site will say so) that when Venice decided to remodel the Basilica of S.Marco during the thirteenth century, it imported both eastern materials, and workers. A nicely condensed account of this basilica’s complicated history is offered by the author of a wiki article, who writes:

The earliest surviving [mosaic] work, in the main porch, perhaps dates to as early as 1070, and was probably by a workshop that had left Constantinople in the mid-11th century and worked at Torcello Cathedral.* They are in “a fairly pure Byzantine style” but in succeeding phases of work Byzantine influence … was reduced by stages, disappearing altogether by about the 1130s, after which the style was Italian in essentials, reflecting “a change from a colonial to a local art”. The main period of decoration was the 12th century, a period of deteriorating relations between Venice and Byzantium, but very little is known about the process .. The main work on the interior mosaics was apparently complete by the 1270s, with work on the atrium continuing into the 1290s.

*we have already noted, in the post previous to this, that at Torcello  the glass objects were made ” using cullet (glass refuse) or glass cakes imported from the eastern Mediterranean’.

The basic drawings may have been ‘local art’ but the artisans were apparently not from any local tradition of mosaic-making, for..

After [the 1279s-90s]the St Marks workshop seems to have been disbanded, so that when a fire in 1419 caused serious damage, the only Venetian capable of the work had just died and the Signoria of Florence had to be asked for help; they sent Paolo Uccello.

San Marco never made the transition to fresco wall paintings … probably partly due to Venetian conservatism and also to a wish to support the local Murano glass industry, which supplied the tesserae. The point is that from 1290 – 1419 (at least) no mosaics were added.

Who then is the ‘old master’ among the 13thC images of Venetian trades? His ‘Sasanian’ cap is enough to point us in the right direction, even without the visual pun of his ‘Mosaic’ beard.

It cannot be Master Aldrevandin, but is perhaps his teacher.

Work on S. Marco’s mosaics finished officially in the 1290s – during which time glassmakers were first confined to Muran and then prohibited from leaving the city. Master Aldrevandin, as we know, then made beakers which introduced the the long-traditional ‘pearl band’ of Sasanian and Byzantine work into the traditions of Muran. They served initially in western Europe as his own hallmark and then became a standard motif on Murano glass. Sasanian ‘crystal’ glass had been known to as far as China by the 3rdC AD.

Sasanian clear glass beaker
coins Sasanian headwear
photos: (above) two versions of Sasanian headwear.

Ge Hong (283-343), a well-known .. Daoist philosopher with an expertise in alchemy left an important information in his work ‘Baopuzi’ that ‘the crystal bowls made in foreign countries, are in fact prepared by compounding five sorts of (mineral) ashes. Today this method is being commonly practiced in Jiao and Guang (that is, Annan and Guangdong). Now if one tells this to ordinary people, they will certainly not believe it, saying that crystal is a natural product belonging to the class of rock crystal.’

  • Mei-Ling Chen, ‘The Importation of Byzantine and Sasanian Glass into China during the fourth to sixth centuries,” in Harris, Incipient Globalization?, 47-52 [pdf].

One of the curious details relayed to Nick Pelling by the curators of the Murano glass museum was the secret by which Angelo Barovier produced his hard, clear glass in 1450, was allegedly  “a special flux, made of a sort of alum obtained from eastern plants.” (Curse p.). 

Plant-ash sodas are not a form of alum, but that type of plant-ash alkali was regularly preferred in Muran, even when other Italian glassmakers used natron, and was known popularly as alluma catana, literally ‘basin alum’.  Of itself, however, it couldn’t harden or clarify glass and in theory the ashes from sola kali would not produce a different result, whether burned in Spain, in ‘the east’ or in Italy. The important question, of course, is “how could Barovier know?” If the seller told him the virtues of a new type of plant-ash, it was not Barovier’s invention. If not, where and how would a man restricted to his island and prohibited from discussing his craft, even think to look for and then to find and import the right sort of ‘plant-ash’? Is it more likely that some Venetian trader brought back both the material and an understanding of those ‘five mineral ashes’?

I suspect the ‘eastern plant ash’ was another of those memories passed down in Murano from the time of Master Aldrevandin, but Barovier’s method for clarifying and hardening glass is still not easy to discover.  The answer may lie in one of the following references. I’ve been unable to sight either during the past few months.

  • Cesare Moretti and Tullio Toninato (eds.) and David C. Watts and Cesare Moretti (ed. and trans.),Glass Recipes of the Renaissance: Transcription of an Anonymous Venetian Manuscript. (2011).
  • Antonio Neri, L’Arte vetraria = The Art of Glass, translated and annotated by Paul Engle, 3 vols., (2003–2007).

for those references, I am indebted to the author of

Ravenna mosaic three wise men and artefacts. Basilica of Sant'Apollinare Nuovo

(above) The three wise men from the east. Artefacts display characteristically Sasanian techniques in metalwork (and glass?). detail of a mosaic in Sant’Apollinare Nuovo, Ravenna.


POSTSCRIPT – regarding the figure who holds a nine-point ‘aster’ in the Voynich calendar’s months of July and August:

Persia’s star was ever Perseus ‘the destroyer’ envisaged as a horse mounted by a skeleton or phantom rider. The equation was known to Herodotus in the 5thC BC and still in the fifteenth century AD – at least to some. Herodotus therefore has Perseus as the progenitor of the Persian people. Ibn Majid, writing in the fifteenth century, names this horse (as the constellation was earlier envisaged) ‘Al Kumait’ – the unbridled. The image on the card below, showing the rider ‘backward-turned’ is the older and more authentic form.  See also Alamy image (WP338D) which I cannot include here.

The pictures in this set of 17 cards show a markedly different origin and intellectual level from all others known in Europe. Unlike most who comment on such game-cards, I’m of the opinion that these represent an original type and I’m quite prepared to believe such cards as these might have served as tutorial aids in fourteenth century France.

Perseus and Perseids





Sasanian head band

Sasanian hunt backward turning

If that ‘aster’-holding figure is meant for the Persians’ star, it is most likely to refer to Algol, properly named Al-ghul in the Arabic, though I don’t know the old Persian term for it.  The star was envisaged as a blaze, or trophy (see above, and below) on the horse’s hip, though at other times represented as a trophy-head -or even as a wine or water-skin.  (see further below).

Sasanian hunt with trophy.

…as a wine-skin or water-skin. 

Sasanian hunt as stellar triumph oveer zodiac

Due to precession, Perseus’ ‘rain of arrows’ (the Perseid meteor showers) now  peaks in August.  For more on this see: here. The floating scarves parallel the wisps of the Milky Way.

On retention of pre-Islamic elements in later Iranian art, including the ‘flying gallop’ and the scarves, see ‘ART IN IRAN xii. Iranian pre-Islamic Elements in Islamic Art’, Encyclopaedia Iranica. (online).

image courtesy Encyclopaedia Iranica.

In the Greek astronomy, Perseus is a human figure and the ‘ghul’ the trophy as Medusa’s head.

PPS – apologies to readers for the numerous ‘updates’ – mainly typos, grammatical errors and other small annoyances. Just had my second inoculation and the brain isn’t working properly.

Skies above: certain measures Pt 2: presence and absence

Two previous:

Header  (left) detail from Brit.Lib. Add. MS 22413; (right) detail from Paris, Bibliotheque Nationale de France, manuscripts Sp.30.  (inset) portrait of William Romaine Newbold.


recap of Pt 1.

As explained in the previous post (here),  when presented with something never encountered before, our brain hunts for ‘nearest match’ from what we already know, but in doing that will ignore some or even many points of difference. The narrower the person’s range of knowledge/experience (or limits which they impose on the search) the greater the risk of mis-reading the image.

This isn’t such a problem in everyday life – a person may say that people from some region of the world ‘all look alike’ and so on, but if the task is to  understand the origin and intention of difficult images, the hardwired habit has to be consciously balanced out.  The  cues needed to understand a difficult image may lie in those very details.


Postscript – The only way I can thank readers for putting up with long posts is to include something original, so there’s a bit more unpublished research  in this post.  Enjoy.


Voynich studies was established in 1921 with the first research paper attempting both to describe and to explain the manuscript’s content.

Many ideas and habits still found in Voynich writings have their origin in that paper – as when those  ‘tags’ are re-used by which its author described his impression of images as    ‘pharmaceutical’ or ‘herbal’ or ‘zodiac’.

Indeed, so many items from that paper have been taken up as if so many facts that by far the greater proportion of what has been written about the Voynich manuscript since 1921 has been predicated on belief that the author’s perceptions and opinions were right about this point and others –  whether or not those later writers had been told the original source.  That paper is well worth reading. Not only as a landmark study but because it solves many of those  “where-did-that-idea-come-from” problems,  including the problem of why the idea took hold that the month folios were meant to serve an astrological purpose and why no-one seems later to have asked whether that was true.


That paper was presented by Professor  William Romaine Newbold, and its contents  –  or more exactly what is found in pages 461-474 of the printed version- entitles Newbold to be honoured as the founder of Voynich studies.

Unlike many who followed him, Newbold did realise that no picture can be defined by only one or two elements in it.  In speaking of the month-diagrams, he offered his explanation for more than just the central emblems; he considered the tiered figures, and why the tiers ( “bands”) should appear as they do. He describes them as:

“representing a lune of the celestial sphere formed by circles drawn through the extreme points of the sign and the poles of the zodiac”.

citing Bacon’s Opus Maius (see Bridges’ transcription  here).

He had apparently realised that geometry matters – and ‘geometries’ are the chief subject of this present post.  I begin with mention of his essay for that reason and – if one dare dream – in the hope of slightly reducing the number of persons who, being unaware of predecents, continue reduplicating ideas already proposed and even tested.

Again, his is the credit due for first mention of the lunar mansions (‘lunar stations’) in Voynich studies, as for positing Aldebaran as the subject of another detail.  This isn’t about whether he was right or wrong – just about making clear the line between an original contribution to the study and any later support for it (independent or otherwise) so to assist, rather than obstruct, others’ study of how ideas have developed about this manuscript.

Here is part of his commentary to slides shown the audience – including his brief description of the month-folios.

  • Professor Romaine Newbold, ‘The Roger Bacon Manuscript’Transactions of the College of Physicians of Philadelphia, Series 3: Vol.43, (1921)  pp. 431- 474. But see especially pp.461-474.

Like everyone else, then and now, Newbold had limits and biases which distorted his vision. There is no-one without any..

His focus on Roger Bacon shows that he, like everyone else of his time, believed the rumours allegedly repeated by Mnishovsky. That is no reason to think less of Newbold.  For all we know, the content does derive from some work known to, or even composed by Bacon, but to date there is no more real evidence for that piece of hearsay than for the other two attributed to Mnishovsky – not excluding his ‘Rudolf’ rumour to which some Voynich writers have been just as devoted, creating post-hoc circumstantial narratives in justification just as Newbold and Wilfrid did for the ‘Roger Bacon’ idea. It should not be forgotten that the ‘Roger Bacon’ theory remained current, ignoring dissent, until the vellum was radio-carbon dated, less than 20 years ago.

Also affecting Newbold’s perception was his specialised study of western philosophy and his sharing that typically nineteenth-century habit of reducing the history of the medieval Mediterranean world to what occurred in some parts of western Europe – chiefly in France, northern Italy, England and Germany.  Wilfrid’s saying he could ‘think of only two people’ who might have put the manuscript together, with his one being English and the other German, was another example of that narrow vision which, though embarrassing by comparison with what is known of the period today, was typical of his time.


Form and purpose

Ninty-nine years later,  it is impossible to know just what details were perceived as ‘first-level/essential’ for that nearest-match by every later writer, but if  we suppose they did rely on

edited from April II diagram (f.70v-ii)

(i) the ‘star-flowers’; (ii) the centre emblems and (iii) the inscribed month-names, then the amount of visual information omitted or disregarded would be  … most of each drawing. (see right)

In almost a century, the ‘astrological’ theory has failed to explain the organisation of these diagrams, the number of figures in each, their disposition in, and around tiers.

Which brings us to another important issue –  evident absence of  astrological  measures in the month-folios.   This  distinction didn’t escape Clark  or Campion, though the former expresses it more plainly (see post of Feb. 9th., 2020).

I’d rather approach the problem in a wider framework than astrology, and in terms of iconological analysis, where it can be  expressed in terms of a general rule that:

When a given practice,  involving calculations, produces ‘calculation diagrams’  the measures employed will be consistent and the diagrams will consistently imply and almost always display those standard measures and/or intervals.

When it comes to the heavens, a ‘calculation diagram’ is normally marked by arrangements of radial lines and ‘boxes’ (not necessarily rectangular).

At the same time, the presence of such forms is not necessarily evidence of astrological purpose, in illustration of which (see illustration below) we have a picture of the modern replica of an old tide-calculator.   It contains month-names, hours and degrees. It shows images of sun and moon. It includes schematic images of the 12 constellations of the Roman zodiac and even that notation which astrologers use for those 12 as ‘signs’.  But this object’s purpose was not to serve astrology; it was meant for a practical, workaday purpose.  It could, I suppose, be put to use to indicate the phases of the moon in their application to medieval-style medicine, but that isn’t the purpose for which it was made.    … source).


Even the clear presence of the Roman zodiac’s twelve constellations is not evidence of astrological purpose. 

For the moment, I’ll leave aside the problem of whether the month-folios’ central emblems are or are not a  Roman zodiac series, or truncated version of it,  keeping instead to this other problem of measures and ‘star-related’ pictures.

For convenience, here, we can use just four classes:

  1. Pictorial: the sky as ‘landscape’ with little (if any) effort to identify specific stars or groups of stars.
  2. Moralised/allegorised: the real disposition of stars is known but the image depicts them in such a way that emphasis is on another narrative and the astronomical subjects may be obscure to an untutored eye.
  3. Mensural* – stars’ disposition expressed in terms of measures.
  4. Mixed.

*mensural’ in the general sense of measurements – not specifically those of music.  I have omitted another type – the ‘narrative’ –  which relates to epic, allegory and moralised astronomy).

For the first two classes, indications of measure and calculation are optional.

Three of the four are present in the ‘mixed’ example shown below.   We have a section in starry ‘landscape’ style, and others displaying those radial divisions and ‘boxes’ denoting calculation and especially in connection with the heavens.

I’ll have reason to return to its Gemini and the female’s body-type, but for now note that even with the swelling belly which was then becoming a fad disseminated from France, the woman’s body still relates to that tradition of the elongated, even emaciated body which is so marked a feature of earlier medieval Latin art.

detail from the Tres Riches Heures de Duc de Berry – a work as widely known in medieval studies as the Mona Lisa (La Gioconda) in Renaissance studies.


Absent measures – an exercise with folio 70v-ii

At this point, for readers interested in analytical method, I’ll add an exercise.

It’s another exercise in ‘musing’ – this time of the sort that art historians and critics are often doing when they just move back and gaze at a picture. The mood is not too far from day-dreaming – rather than ‘thinking’ –  but ‘musing’ seems to be the best way to describe it. And – as I hope you’ll see – it needn’t be waste of time.

It includes a LARGE (non-phone-friendly!!) jpeg.

Measures exercise

See what happens if you  print this picture and pin it on your wall,  in a place where you come and go – and can return to it for a couple of minutes at a time, over a few days.  And yes, the smallest room is ok. but a hallway or the other side of the room from where you work is probably better.  🙂

If you’re like most people, then you’ll find that as you look at it without any particular focus or theory-making, your mind will start to play with what you see.  It will envisage virtual ines of connection across and between the items.  And this sort of relaxed, nothing-invested-in-it approach lets the more flexible part of your brain come up with things that may be worth looking at in ‘thinking’ mode – that is, research mode.  

To show I’m not pulling your leg, here are a couple of illustrations showing a few of the results from my doing this a good while ago.  I won’t say more because commentary might contaminate your own experiment.

The first illustration below, centre) is of the March diagram (folio 70v-i). I haven’t erased the stars etc.  The radial lines were formed by taking the inner boundary’s ‘terminus-marks’*  as if they had been meant to show where a line would pass, between centre and perimeter.  The red lines indicate the folio’s true horizontal and vertical axes according to the Beinecke website’s presentation.

*The ‘terminus’ mark – (illustrated left) is is not present in every case where one type of marking meets another – which I think is significant.


The second experiment –  shown here in its first and purely schematic form – could be described as ‘sort-of-geodesic’ I suppose.  Not aesthetically pleasing, but engaging in other ways.

So now – what happens when you muse on the other folio?


Geo-metry and  astro-metry.  (With much of Euclid).

The illustration at left is not a sign I support Newbold’s theory about the telescope’s invention. It illustrates how angles were described in a Latin manuscript believed to date from the 12thC or early 13thC.

Thony Christie published a fine history of trigonometry while I was selecting material for this series, saving me the trouble of treating that, but co-incidentally using the title I’d intended for this post. 🙂

  • Thony Christie, ‘It’s All A Question of Angles‘, renaissance mathematicus (Feb. 12th., 2020).
  • With apologies to Thony and other mathematici, I’m going to group trigonometry within geometry in these posts.
Geometry in medieval Europe – references

If you start from the traditional view that everything in the Voynich manuscript originated in, or was accepted into medieval Europe by the authority of some Latin ‘author’ or other individual person, then you will have a comfortably narrow range of ‘geometry’ to consider up until AD 1438.

  • The reading list will consist of Euclid –   treatises by Euclid, or attributed to Euclid;  translations and excerpts from Euclid;   works derived from, or developed from Euclid and from pseudo-Euclidean texts –  by Latins or translated for Latin use from works written in Arabic and Hebrew.

Because I think it quite important for amateurs to learn something of how medieval Europe saw geometry’s role, I’m recommending a number of manuscripts of the type often called a ‘miscellany’ although these are better considered  theme-based anthologies. The sort of thing a modern publisher calls, ‘A Reader…’

These should also provide illustrations for the way technical diagrams’ notation changed  between the late thirteenth century and the early fifteenth century.

  • Euclid, The Thirteen Books – original Greek text online by  Dimitrios E. Mourmouras. N.B. Don’t forget to credit Mourmouras!
  • Brit.Lib. Add 20746.   Moses ben ibn Tibbon, ספר היסודות. (Sefer ha-yesodot), ibn Tibbon’s translation of the thirteen Books of Elements of Euclid, with the addition of two Books at the end which are ascribed to Hypsikles.
  • Brit.Lib. Harley MS 13. includes  [pseud.] Euclid, Catoprica, known as ‘Catoptrics‘ to distinguish it from Hieron of Alexandria’s ‘Mechanica and Catoptrica’.
  • MS Burney 275 iincludes Adelard of Bath’s translation of Euclid, and shows how conventions for notation had changed within a century.

The next I’ve chosen to show that the idea of connection between astronomy and music went beyond the purely philosophical.  Music and astronomy both required standard intervals.

and in connection with music, I must also mention:

  • Joscelyn Godwin, Harmony of the Spheres. A Sourcebook of the Pythagorean Tradition in Music. Rochester, VT: Inner Traditions International, 1993; also published in Spanish (Girona: Atalanta, 2009).

An English translation of Euclid’s Thirteen Books at the Internet Archive

  • Thomas Little Heath (ed. and trans.), The thirteen books of Euclid’s Elements from the text of Heiberg (Cambridge Press 1908). Vol.1, Vol. 2, Vol 3.

A good historical overview of mathematical studies in medieval western Europe is described in a series of posts designed to help secondary-level teachers.


Finding stars using co-ordinates.

It is a curious fact that the ‘astrological purpose’ theory, by itself, led to a certain routine angle of approach towards the month-folios.

The diagrams were first assumed ‘astrological’ and of Latin European origin, and then the ‘star-names’ were assumed to be the Latins’ ‘Arab’ star-names, and finally the month-folios’ labels were assumed an enciphered version of some ‘star-name’ from those theoretical limits. And following exactly that pattern, step by step, efforts to read the ‘labels’ proceeded.

I haven’t been able to discover mention of any other approach being employed in a century, and over time it seems that the effort to explain these diagrams as they actually appear on these folios, was all but abandoned.  What we see today are efforts to persuade readers of some variation on the ‘astrological’ theory, often by producing appallingly bad ‘nearest-fit’ images.  There might be out there, somewhere, a large amount of alternative work but if so I’ve found no mention of it.

There are other ways to go about understanding these folios and geometrical relations are one way.

It means discarding the usual, and often unfruitful ‘What is it?’ sort of research question and re-framing it as:  ‘What are the measures?’ 

It’s not an easy way to approach the month-folios, but not impossible. It means identifying the stars’ position first and then finding which system of co-ordinates, if any, accords with what is depicted in each month-diagram. Co-ordinate systems differ, and not least by the measures employed, but the easiest to begin is to start with the sort of system a researcher’s environment has made them most used to.  If those are eliminated, it’s time enough to move on to researching others.

The idea of finding the locus, and from that identifying the reference of a given figure in the tiers may seem far-fetched or over-hopeful, and I’m not underestimating the amount of work needed, or suggesting it could be quickly done.  But I think it possible and considering the past century’s complete failure to explain these images by the now-usual methods, two or three years would not seem an unreasonable time to spend.

Before 1438, even in western Europe, there were various star-lists described by co-ordinates.   They might differ from one another, and manuscripts differ between versions, but they did exist and not all uses were abstract, astrological or hypothetical. The stars’ relative positions have not greatly changed and that’s good to know.

One can’t expect absolute precision in the Voynich drawings, either, but given the limited number of stars for each month-diagram, and the fact that they are arranged month-by-month, leads me to think that error might be within reasonable limits.

I suggest this method because though I’m fortunate in being able to approach them otherwise, I cannot pass on in these posts enough to allow others to have the same background – not if this series is to finish in a reasonable time and I can hardly expect readers to cope with too much reading that isn’t Voynich-specific.  So another way may appeal to some readers.

Suppose for argument’s sake that you accepted my identification of the ‘Amazon’ star as Bellatrix or even as Betelgeuse (see post of Dec. 19th., 2019).

And suppose further that for  the figure above it (in folio 70v-ii) you posit a star in Virgo – for reasons I’ll explain in the next post – then you might ask what the actual relationship is between the two, in terms of the maker’s intention and in terms of  astronomical geometry.

I can only outline the method I’d try. Each researcher must be free to work out their own.  But in fact I’d start with the March diagram rather than folio 70v-ii, which is a halved, or a doubled month.

My first reaction to any theory raising its head, including my own, is to test it immediately against the real world and the historical evidence – not to seek justification but to get rid of it as soon as possible if it’s anachronistic or plainly impossible. As readers know, I’m not keen on theoretical explanations for historical images.

I’d ask whether anyone could really have seen both Bellatrix and Virgo in the sky at the same month, and whether that month is the one named in the diagram, and ask this for each band of latitude beginning (say) with Lat.30 degrees north- and for a specific period (say AD 1330-1430 to begin with).  For this, historically accurate star-maps must be generated which  take account of precession and ideally also of proper motion.

(Since this is only a hypothetical example, I won’t generate the historical chart, but here’s the idea: (and note the east-west reversal  typical for earth-view of the heavens, but also found in the Voynich map).


So yes, both are visible and their relative positions in the sky in fact suggests two things: that one or more of my identifications is wrong, or that the relationship between the inner and outer rings in the diagram is not immediate but complementary.  When Virgo and Orion may be seen in the sky together,  Virgo has emerged in the east, but Orion is moving towards the west.

Once again, at this stage, I’d ask whether there is any historical evidence of a ‘complementary’ approach to astronomical or to astrological diagrams, or any other attested system of this kind, whether or not recorded in calculation diagrams.

As it happens, I know of two – though still bearing in mind that the identifications of Bellatix and [a star in] Virgo might be wrong.  It’s an easy trap, and one into which many have fallen, to mistake an hypothesis for the manuscript as the subject of one’s research.

However, the two systems I mean are the eastern seas’ sidereal compass where the assignment of star and point of direction is nominal, though the names appear in ‘opposites’ and the pre-Islamic Arabs’ anwa’ [ today often described as rain stars and associated with divination but they also marked periods in the calendar and assisted wayfinding]

The conceptual star-compass marked a point on the eastern horizon by  a star’s name (-‘rising’)and the opposite point on the western horizon by the same star (-‘setting’). Since the northern and southern points were unique, the compass could name 32 points with only seventeen stars: the Poles, and fifteen stars with a rising and setting for each. Of the two possibilities I know – without more research – the anwa’ seems the more reasonable of those two.

However, whether or not those posited identifications prove right, the first stage towards establishing a number of historically appropriate set of co-ordinates according to different systems then known, would be  to generate grids from contemporary documents, covering that initial test-period (say) AD 1330-1430, and preferably using Byzantine, Latin, Coptic, Arabic and as many other sources you can work with.

The next stage would be to produce a list of stars in order of apparent magnitude (i.e. how big and bright they look to people on earth). By being able to say which stars were known at a given time and place, and how the grids used in that time and place described stars relative to one another, in a given month, so you need only one or two identifications to ‘pin’ the grid and – hopefully- identify the actual identifications for the remaining stars in a diagram, without pre-empting ideas about purpose or what the ‘labels’ might mean. As a first test, the bightest stars (greatest apparent magnitude) are a sensible place to start because the brightest-looking stars are normally the first to be noticed and used.

‘Apparent Magnitude’ can be confusing at first because the brighter a star or planet appears to be, the lower its number.   So I’d have  Sirius (-1.49) and Aldebaran (0.75–0.95) top of the list and then move down the list of stars visible in a given month (through the target period) until the number in the list agreed with the number of stars (or barrels, or figures) in a given month-diagram.  (Bellatix in Orion is listed with apparent magnitude of (1.59 – 1.64), and Spica in Virgo as (0.97 – 1.04).

So none of these is so dim that it couldn’t be seen with the naked eye – and they are likely to have been included in most star-lists, you’d think, by the fourteenth century.

But here again, it isn’t theory but demonstrable evidence which matters.  What may seem ‘common sense’ or ‘logical’ to a modern urban person may simply not be true of the historical events.  Telling history it ought to be more logical is a waste of time. The evidence is either there, or it’s not in this sort of study.

‘Star-names’ and co-ordinates.

Even in Latin Europe, a co-ordinate system of ‘Latitude’and ‘Altitude’, based on the astrolabe’s design, was certainly known by the middle of the eleventh century, and in connection with the ‘Arab’ star-names (see below).  Despite this manuscript’s early (11thC) date, the star-names’ orthography is pretty close to what would become the norm for non-Arabic works and though there are indications that the scribe was transcribing phonetically, the number of times his star-names refer to stars in the next constellation to that named suggests either an effort to correlate a classical source with a contemporary one, or that he was defining regions of the sky in terms of a vertical slice like the section of an orange – as wide as the limit of the zodiac  constellation and bounded by meridians extending between the northern and southern celestial Poles. (which is one definition of the ‘hour’).  Thus, the name ‘Algorab’  listed for sign Virgo is – at least today – used for the delta star in Corvus, below (south) of Virgo, while ‘Rigel’ applies to a star in Orion, not in Gemini.   The term ‘sign’ can often have an astrological sense but can be used to mean an emblem, as we speak  of an inn’s “sign” and medieval people spoke of meeting “at the sign of the Boar’s Head”and so forth .so the ‘signs’ here mean that part of the sky whose chief emblem is a figure from the zodiac.

I do understand, very well, what an enormous amount of work would be required to begin working on the diagrams from data of historical co-ordinate systems and attested star-names – a ‘co-ordinate geometry’ method – and that it’s not as easy as collecting set lists and making virtual grids; one would have to check the sense of the originals, decide where divergence was significant or due to error, and so on, testing each step against every other and waiting for it to click into place – not unlike the way meaning was extracted from ‘Enigma’-encoded messages.  But as I hope I’ve shown, one is aided by the diagrams’ being labeled by the months, and to ‘fix’ a starting point might be possible with just one or two identifications in each diagram.

As for the labels, I’d not discount, either, Newbold’s belief (later used, uncredited, by Brumbaugh) that the ‘labels’ are personal names.  Dante himself speaks of including the ‘Arab’ star-names in a volume of his Cantos so that people  using foreign instruments could follow his narrative more easily.  (The reference is found in  Guther’s Introduction to his study of the Ashmolean astrolabes, if I recall, but I read it almost a quarter of a century ago and it is impractical to try checking the reference just now.  Brumbaugh – again –  mentioned Dante and footnotes Gunther, but never admits his debt to the latter for his connecting Dante and the stars.  tut-tut.

  • 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