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.

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only way I can thank readers for putting up with long posts is to include something original, so there’s a bit more unpublished research  in this post.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

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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.

Details

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.

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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).

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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.

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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?

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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.

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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