Squaring the circle (with Dante)…

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Flicking through a fairly recent copy of the New Yorker in the dentist’s waiting room just now, I read a review of Jean Hollander’s translation of (and Robert Hollander’s extensive notes on) Dante’s Paradiso, the third part of the Divine Comedy. To be honest, I never had much patience with the Paradiso, all the fun in Dante was in the Inferno, a point of view this Slate article basically seems to agree with: so I never got to read about the pilgrim’s meeting with God right at the end…

Which is a shame, because there’s something interesting there which deserves a closer look. While it’s not strictly speaking cryptographic, it is linked in with the whole sacred geometry thing which people insist on projecting onto late medieval / early modern paintings and architecture, and which is essentially a form of hidden messaging (“Neoplatonic steganography“, if you will).

In the final canticle (Canticle 33) of Paradiso, Dante struggles to find words to describe the experience of meeting God: and in the end settles on an intense light (but one which the eye is attracted to rather than repelled away from), inside of which can be seen “three orbs of triple hue” (though I think the Hollanders translate these as “circles”). Dante finishes by comparing his attempts at describing the experience as no less futile than attempts to square the circle: where Man (extending the geometric metaphor just that little bit further than other poets would) is the square and God is the circle.

Anyone with even a passing familiarity with Leonardo should be aware of his representation of “squaring the circle” in his ‘Vitruvian man’. But there are a number of other early modern artworks which supposedly use a square to represent Man or Earth and a circle to represent God or Heaven. Jerusalem was supposedly round because it was a representation of Heaven, which (as any fule kno) was perfectly circular (Ptolemaic epicycles notwithstanding): which forms a (forgive me) circular argument within whose causal chains it is hard to disentangle the Platonic from the Ideal from the proto-religious.

Having said all that, Charles Hope’s argument as to the non-existence of most claimed examples of Neoplatonist allegories in Renaissance art would seem to cut a big Wile E. Coyote hole beneath most supposed examples of Renaissance sacred geometry. Even a big modern book in this general vein such as Richard Stemp’s “The Secret Language of the Renaissance” contains hardly any persuasive examples of sacred geometry: Stemp’s discussion of Massaccio’s Trinity (pp.210-213) seems a little forced in the way he ‘finds’ a circle in the background to enclose the square he has constructed around Christ.

But there is at least one artwork of the period with an inherently geometrical construction, and where Man is represented as a square and God as a great big dove at the centre of a circle, with Christ in the overlap between the two (though I can’t for the life of me think of the name of it). I had thought of this as a possible counterexample to Charles Hope’s skepticism about Neoplatonism, in that it does seem to bear the hallmarks of what is generally known as sacred geometry. However, a careful visual reading of it (when I can remember what it is!) may instead simply show it to be no more than an allegory literally derived from the last canticle of Dante’s Paradiso: in which case it may well be that we can basically consign Renaissance sacred geometry to the historical scrapheap.

Something to think about, anyway. 🙂

Hidden writing on f1v…?

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I’ve spent a long time (though “far too long” probably covers it better) hunting down obscured fragments of text in the Voynich Manuscript: so my Spidey-sense tingled almost uncontrollably when I saw a claim for hidden text on f1v in the “Marginal Writing” picture gallery on Glen Claston’s Voynich Central.

I’d never heard of this before: just to be sure, I checked Reuben Ogburn’s 2004 page on “Writing in and around plant illustrations” in case it had slipped in there, but no sign. If you run this through Jon Grove’s colour separator filter, you can see that the brown ink used for the drawing and the brown paint used to fill it in are very slightly different: in the image below, the white area is where the filter thinks the overpainting happened.

But is there writing beneath? If you squint at the topmost image here long enough, you can start to make out something that might almost be writing. But if you filter it slightly differently, I think the answer emerges: the “signal” (below) appears to be not writing, but only compression artefacts from the MrSID wavelet encoding. Sorry, guys: false alarm! (Though next time I’m at the Beinecke, I’ll have another quick look, just to be completely sure…)

"Is this feeling an eternal flame?"

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A quick pop-cultural aside: the song “Eternal Flame” was written by hugely successful American songwriter Billy Steinberg with Tom Kelly and Susanna Hoffs (of The Bangles). The inspiration for the song came from an eternal flame seen by Bangles’ bass-player Michael Steele burning at Gracelands in Elvis Presley’s memory, as well as from one at a Palm Springs synagague Steinberg had seen when very young. Though “Eternal Flame” was produced by Simon Cowell, I won’t hold that against it. 🙂

But historically, claims of actual eternal flames go back a very long way: in my book, I mentioned briefly that many in the Renaissance believed a “perpetual light” burned in the Temple of Vesta in Ancient Rome. Leon Battista Alberti’s 1450 book “Momus” mentions (though admittedly in a fictional context) a “perpetual flame, tending itself even though no material is laid under it and no liquid poured over it“, Giovanni Battista Della Porta documented many attempts at reproducing eternal flames in his Natural Magic in XX Books, while in his libro architettonico Antonio Averlino described a continuously-burning candle he saw in Sant Maria in Bagno. Another related story concerns Abbot Trithemius, who allegedly sold two “unquenchable eternall lights” to Emperor Maximilian I for 6000 crowns.

I thought this was one of those things for which there was unlikely to be any significant literature: I’d collected all the pieces together from scattered footnotes. However, recently I was inspired by Archer Quinn’s, ummm, perpetual ranting to properly read through Kevin Kilty’s well-known page on perpetual motion. All good stuff: and he even mentions eternal flames!

Kilty, who seems to have derived his information on this subject from Arthur Ord-Hume’s 1977 book “Perpetual Motion: history of an obsession“, mentions that:-

“Fortunio Liceti (1577-1657) made a lifelong study of these lamps, so many of which were supposedly found in old tombs, vaults and temples. Ord-Hume spends several pages examining ways to explain the observation of perpetual lamps. This is giving too much serious attention to a fantasy. It is likely that no one ever observed any such lamp.”

(Though I should of course point out that Averlino claimed to have observed an eternal flame). Fascinating! I was not aware of Fortunio Liceti‘s connection with eternal flames, and so rushed to buy Ord-Hume’s book as quickly as I could. I shall continue this thread when it arrives…

The Florentine Renaissance & evolution…

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OK, I’ll admit it: people who talk about the Renaissance as a coherent historical phenomenon get on my nerves. There were numerous strands of thought at the time, all vying for the oxygen of attention, all trying to supplant medieval scholasticism: but arguably the two biggest new kids on the block circa 1400 were Renaissance humanism (think of Petrarch, etc) and Renaissance inventorship (think of Brunelleschi). While the former grew out of philology and a theoretical reverence for Classical texts, the latter emerged from the empirical world of clock-making.

Lynn Thorndike was happy enough (in his “Science & Thought in the XVth Century”) to point out that these two major strands were very often at odds with each other: but it should also be noted that the intersection between the two was far from empty. In fact, you might well look at the architects Leon Battista Alberti and Antonio Averlino – both born near Florence near to 1400 – as examples of “Renaissance Men” in the purest sense, in that they exemplified both strands at the same time.

The mystery of the Italian Renaissance (as described by Burckhardt and the generation of gung-ho pro-humanistic historians that followed him) is this: why did it emerge at such a narrow time (circa 1400) and place (Florence)?

For a long time, the dominant view has basically been that this was a random event, just one of those things that happen from time to time. However, some modern writers have begun to speculate whether a particular freak event or a subtle change in diet or eating habits might perhaps been the real “cause” of the Italian Renaissance.

For me, I would be unsurprised if insomnia turned out to be a key: Alberti writes, in his 1441 “On the Tranquillity of the Soul”, of “the agitation of his soul”at night, and how he can relieve this by trying to devise amazing machines for lifting and carrying weights. I wonder if an entire generation of Florentines suffered from a kind of intellectual insomnia, perhaps as a result of effectively becoming hyperthyroid from ingesting a particularly iodine-rich salt being brought into the city?

Or might the Florentines have simply become addicted to the sugar confections that had not long before suddenly filled the city’s apothecaries and markets? Might the Renaissance have simply been a metabolic balancing act as people tried to compensate for a giant communal sugar rush?

But there’s another possibility. If you were looking for a statistical explanation why a particular population produced more geniuses (while the overall bell-curve distribution probably remained intact), there would be two obvious candidates to consider – either (a) the mean IQ got shifted up (i.e. everyone somehow got smarter) , or (b) the variance increased dramatically (i.e. more extreme cases appeared at both ends of the scale).

This set me wondering: as I understand it, one of the problems often put forward with Darwinian evolution is that the natural rate of mutations is too low to support the amount of random change needed. So could it be that stable contexts inhibit mutations (i.e. encourage low adaptation rates), while troubled contexts somehow encourage mutations (i.e. encourage high adaptation rates)?

Interestingly, one medieval obsession presents itself here: that of whether “monsters” (freaks of nature) were signs (de-monstr-ations) of something greater happening in the world. Perhaps “monsters” in the human population were (and possibly still are?) literally a sign that the variance of the population is high.

Thinking about all this, it suddenly then became clear to me why low sperm counts make evolutionary sense: if a body is in significant physical difficulties, it makes no sense for it to try to reproduce offspring that are the same as it, as they would likely experience the same difficulties in the next generation. Instead, perhaps the body deliberately produces crippled, damaged sperm to try to encourage mutations that might be better adapted to the changing physical context. Otherwise, why would the body ever want to deliberately produce poor sperm or eggs? Perhaps the current medical view of “healthy” sperm is somehow clouded by an anti-mutation bias of some sort.

My prediction here is that that there will turn out to be reproductive mechanisms by which (a) healthy eggs repel damaged sperm and (b) damaged eggs discourage healthy sperm: leaving the two pivotal cases of (healthy eggs + healthy sperm) => low mutation rate (low variance, well-adapted to environment), and (damaged eggs + damaged sperm) => high mutation rate (high variance, poorly-adapted to environment).

But there’s a timing issue. Whereas sperm production is essentially a “just-in-time” process, women’s eggs are produced all in one go, and so form a lagging indicator to environmental adaptation (i.e. egg health in reproduction gives an indication of environmental fit 15-25 years earlier). So, could it be that, when looking for the source of the Renaissance circa 1400, we should instead look for a traumatic event in Florence circa 1380 that significantly affected women’s reproductive health, causing a change in the population’s IQ variance?

I really don’t know (this is a blog, not an article in Nature): but it is tempting to speculate whether it was simply coincidence that the Florentine Renaissance began two generations after the plague had ravaged Florence in 1348 (Boccaccio famously wrote about it). Might children born after the plague have stirred the Florentine gene-pool up in just the right way to set the Renaissance in motion a generation later?

Review of "Shopping in the Renaissance"…

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Once upon a time, history was a really hard subject to enjoy: a dreary rollcall of [macho/loser] kings and [powerful/scheming] queens, endlessly (a) conspiring against other, (b) fighting expensive wars where both sides tended to lose, and/or (c) endlessly frittering extorted tax money on self-glorifying monuments masquerading as high culture.

Then along came a new generation of “social historians”, who despised the superficial cheesiness of relying on historical records left by the victors, and wanted instead to read “history from below“. To do this, they sought out “authentic” (i.e. non-propagandized) documents to try to give a voice to ordinary people through the centuries and so reconstruct histories of the mundane, the plebeian – the salt rather than the spice.

Of course, each of these two kinds of history is no more or less a lie than the other. For all the self-aggrandizement and posturing implicit in ‘Big Man’ history, the truth of any matter will normally find a way of squeezing through the cracks in the text, particularly with the big-brain close readings of the modern linguistic turn to help it on its way. And even supposedly non-propagandistic items such as wills, inventories and account books are subject to understatement in the age-old “sport” of tax evasion. And so attempts to reduce history to a totalising big picture (whether from above or from below) simply don’t work: historians cannot avoid having to “sweat the small stuff“, because the answer all too often lies in simply getting the details right.

It is in the tension between these two extrema that I look at Evelyn Welch’s “Shopping in the Renaissance: Consumer Cultures in Italy 1400-1600” (2005, Yale University Press). When I was researching my own book on Filarete, her “Art and Authority in Renaissance Milan” (1995, also Yale University Press) was permanently by my elbow, always at the ready to prevent me becoming entrapped by the sticky bubble of historical propaganda inflated around the Sforza court by Cicco Simonetta (and all too readily accepted as fact by older historians): so I had high hopes for her “Shopping”.

On the one hand, Welch’s book is a slab of social history par excellence, teasing out numerous otherwise marginal strands of ordinary life in the early Renaissance – street-sellers, auctions, lotteries, indulgences, fairs, shoes, shopping hours, pawnshops, feast days, credit, charlatans, and so forth. Yet on the other, Chapter Nine (“Shopping with Isabella d’Este”) is from the diametric opposite end of the social scale, an account of the elitist shopping habits of someone who would have been aghast to find out she had been born 350 years too soon for haute couture. After 240 textured pages of closely observed text riffing on various social historical shopping themes (richly illustrated with wonderful images of the ordinary), I felt somehow betrayed by the abrupt switch: a (quite literally) materialist snob like Isabella d’Este had no right to be there.

As is typical with horizontal historical studies, if you stick with them long enough you’ll find a prize to return home with: in my (Voynichological) case, pp.151-158 contained splendid descriptions and images of apothecaries’ shops, many including the kind of albarelli I put so much time into researching six years ago. A very pleasant surprise!

The one thing I found irritating about the text itself was the jarring style used for the incipits and desinits in each chapter. Rather than using the elegant yet spare historical prose of the chapter bodies themselves, these chatter with the abstracted, vacuous tokens of contemporary sociology-speak: space, surveillance, visibility, environment, transience, consumption, embedded, relations, networks, production. It is as if these were written by another hand, perhaps one attempting to weave together the threads of a decade’s-worth of individual papers into a tangibly coherent theoretical tapestry. If so, I think it was a failed experiment: social history is an activity based not around synthesizing the kind of vaguely structural frameworks beloved by sociologists, but around reconstructing the texture of ordinary lives. Essentially, the rich tapestry was already fully present, so there was no need to embellish the edges as well. Oh well!

The 1860 Road Hill Murder…

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The Saturday Guardian “Review” section contained a fascinating summary of “The Suspicions of Mr Whicher; or, the Murder at Road Hill House” (2008, Bloomsbury) by its author Kate Summerscale. In it, she argues that the gruesome events at a country house in Road Hill in Wiltshire (and the police response to them) formed the template for English detective novels, such as in Wilkie Collins’ well-known novel “The Moonstone” (1868).

The London detective sent to Road Hill, Inspector Jonathan Whicher, quickly “developed an ingenious solution to the mystery”: however, when his theory became publicly known, he was “reviled in the press and the House of Commons”, causing him to have a nervous breakdown and to retire from the force. Yet when, five years later, the murderer confessed, the grisly details were essentially as the detective had thought. All too late for poor Whicher, though.

What particularly caught my (Voynichological) eye in Summerscale’s article was the Road Hill case’s echo in Mary Elizabeth Braddon’s (1862) novel “Lady Audley’s Secret“. Braddon’s “tormented amateur detective Robert Audley” fearfully wonders who is the real madman – the woman he suspects of murder, or Audley himself caught in some kind of “obsessive delusion”:-

“What if I am wrong after all? What if this chain of evidence which I have constructed link by link is constructed out of my own folly? What if this edifice of horror and suspicion is a mere collection of crotchets – the nervous fancies of a hypochondriacal bachelor? Oh, my God, if it should be in myself all this time that the misery lies.”

All of which I think near-perfectly expresses the self-reflective terror that is (or at least should be) ever-present in the Voynichologist: reconstructive imagination perched on a precipice.

Before “The Moonstone”, the American history of the detective story goes back to Edgar Allan Poe’s (1841) “The Murders in the rue Morgue“, a locked room mystery with a surprising twist: but there is something about the English country house – its self-enclosed world of servants, class, envy, superficiality, insularity, etc – that lends itself to novel-length fiction.

Yet this is a false kind of knowledge, as the real Road Hill case demonstrates (Kate Summerscale reveals that Whicher believed two people were complicit in the murder, though only one confessed). In the context of constructing a 250-page book with neat closure, it is attractive: but the real world rarely fits into neatly filed boxes, carefully abstracted case-studies like the ones Harvard Business School professors famously used to construct in the 1960s and 1970s.

To me, this whole Victorian quest for smoking guns – for Holmesian certainty – is a kind of adolescent fantasy thinking, a pipedream of pure causality. In the real world, all we can actually do is sign up for the chase and give it our best shot: perhaps we will reach a satisfactory resolution in our attempts, perhaps we will not. But we must continue to try, all the same.

Beale Papers: solved (or not)?

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Here’s a claimed solution to the Beale Papers (but press Cancel on the login popup, and if browsing there under Windows, I wouldn’t advise installing the ActiveX control that pops up) which I didn’t know about until very recently. I thought I’d mention it here because, as any fule kno, the Beale Papers are one of the few encrypted historical mysteries to parallel the Voynich Manuscript to any significant degree.

To be precise, the Beale Papers comprise not one long ciphertext (putting the VMs’ thorny Currier A-B language continuum issue to one side) but three short codetexts, all allegedly dating from 1819-1821: part 2 was publicly announced in 1885 already solved (for its codebook, the encoder used a slightly mangled/miscopied version of the Declaration of Independence)… but the directions to the buried treasure were in the undecoded part 1, while the shorter (and also undecoded) part 3 listed the people involved. Of course, only someone who has broken the two remaining codes would know if all of this is true or not. 🙂

So, it’s basically a kind of Wild West bandit take on a pirate treasure map (which to me sounds like an Alias Smith and Jones script, oh well) but made obscure with some kind of dictionary code: all of which is reassuringly familiar if you’ve just read PopCo. Confusingly, some people argue that the Beale Papers are a fake (possibly by the promoter of the 1885 pamphlet, or even by Edgar Allen Poe, etc), claiming justification from statistical aspects of the cryptography and/or on claimed anachronisms in the language, etc: but a definitive answer either way has yet to be found.

For what it’s worth… my opinion is that, as with the VMs, cries of hoax are more Chicken Licken than anything approaching an ironic postmodernist reading. Really, it does look and feel basically how a home-cooked Victorian code-text ought to, with an emphasis towards lowish numbers (up to 350) plus a sprinkling of higher numbers (possibly for rare or awkward letters): Jim Gillogly’s observation (in October 1980 Cryptologia) of an alphabet-like pattern in part 1 (if you apply part 2’s codebook) seems to me more like a clue than a reason to reject the whole object as a hoax. As an aside, a few years ago I heard (off-Net) whispers of one particular cryptographic solution that had yet to be made public: but Louis Kruh in Cryptologia reported several such plausible-looking solutions as far back as 1982, so what can you say?

However, all of this is an entirely different claim to the “Beale Solved” code solution linked above, which was (re)constructed by Beale treasure hunter Daniel Cole (who died in 2001). Even though the dig that was carried out as a result of Cole’s decryption revealed an empty chamber (the website claims), the cryptographic details (ie, of how the codetext links with the plaintext) have yet to be released… which is a tad fishy.

A quick check of the first page of Cole’s version of part 3 reveals that he didn’t read it as a simple cipher or codebook, because repeated code-numbers only rarely get decoded as the same letter (for example, the five instances of ’96’ get decoded as “s / e / r / h / n”). Yet this seems somewhat odd: if there was some kind of strange offsetting going on, the distribution of code-numbers would not need to so closely resemble the kind of distribution you see in code book ciphers.

But once you confess to having taken a single step down the whole “it’s actually a strange cipher pretending to be a codebook code” route, nobody will believe a word you say, right?

Updated reading list…

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“Shopping in the Renaissance“, Evelyn Welch [finished, still need to write review]

“Astrology: a history“, Peter Whitfield [about half-way through, lots of good stuff]

“Elizabeth’s Spy Master“, Robert Hutchinson [80 pages in, but a bit of a dour character to read much about]

“The Renaissance in Europe: A Reader”, Keith Whitlock [Still not yet started this, beginning to wonder if I ever will]

“Decipher” Stel Pavlou [33 pages in, a nice bit of superficial fun, shame I don’t have a beach holiday to take it on]

“History of Magic & Experimental Science” Vol. IV (Fourteenth and Fifteenth Centuries), Lynn Thorndike [20 pages in, but everything else has to go on hold while I read it]

New Byzantium book…

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Over the years I’ve spent looking at the Voynich Manuscript, I’ve become progressively more accustomed to its ways, to the point that it is no longer an enciphered grimoire to me, but simply a book we cannot as yet read. When learning to juggle, the primary force which keeps the ball in the hand is not gravity but fear: all the while people see the VMs as a dark, Necronomicon-like repository of ancient evil (basically, confusing unreadable with unspeakable), their fears prevent them from grasping what it actually is.

Yet there’s still something odd about how the Voynich Manuscript is rooted, upon what it stands: specifically, it seems to my eyes to have one foot in early modern European (specifically Northern Italian, I would say) culture and the other in late medieval Byzantine culture. Though I’m still unable to satisfactorily express how this works, what I can say is that many of its herbal drawings have a structural quality that is neither medieval European (slavishly copied, overstylised, unrealistic) nor Renaissance European (emblematic rather than symbolic, abstract). The closest match I’ve found is in Byzantine herbals, many of which are drawn from life, but which have a kind of secret inner numericality: not Kabbalah, but topology / geometry.

I’m therefore always on the lookout for good stuff relating to Byzantium, but its 1000-year history is fascinating for many other reasons: the rich seam of inspiration the Romantic poets found in the marvellous decay of Venice was perhaps but a shadow of the irony and wonder to be discovered in Byzantium’s own history.

And so a book I’m looking forward to is “Byzantium: The Surprising Life of a Medieval Empire” by Judith Herrin (Princeton, 2007), which seems to have exactly the kind of overall historical narrative all the fragments of Byzantine history I’ve ever read lacked. There’s a helpful review here: the hardback’s £25 RRP is a little hard to swallow, for sure, but what can you do? (Errrm, wait for the paperback?)

Voynich magic circles (Part 1)…

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I’m just collecting my thoughts after an exhilarating lecture by William Kiesel (the publisher and editor of Ouroboros Press) on magic circles at Treadwell’s in Covent Garden (Christina’s post-lecture blog entry is here). William presented a long series of images of magic circles (manuscripts diagrams, woodcuts, paintings, etc) from the Middle Ages right through to the 19th century, including many of John Dee’s strange diagrams.

Voynich Manuscript, page f57v (the ‘magic circle’ page)

The reason I’ve been trying to find out about magic circles for years is because, as you can see above, page f57v in the Voynich Manuscript apparently contains one. Or (more precisely), whatever f57v actually contains, it seems on the surface to follow the constructional rules and layout of genuine magic circles. However, this is hard to research because the topic of magic circles has attracted relatively little academic interest over the years, Richard Kieckhefer’s (1997) Forbidden Rites (an in-depth study of a 15th century necromancer’s manual) being one of the few honourable exceptions. Which is why I was so excited about the lecture.

Having said that, there are many things about f57v that cast doubts on its ‘magic circle-itude’. For example, I could find no other magic circle with the directional spirits given faces rather than simply named: depictions in every other magic circle I had seen were instead abstract diagrammatic renderings (swords, pentacles, rings, sigils, etc), and names of the directions (to help orient the circle, the first thing any proper necromancer would want to do). But even more brutally: when magic circles are all about the power of names, why ever would someone want to replace them with images?

And so… after the lecture, I asked William for his thoughts on f57v (which, delightfully, he had looked at before). As far as the directional faces go, he agreed that this was pretty much a unique feature: though a tiny number of magic circles he had seen do have sigils shaped to broadly resemble faces, that would seem to be a completely different strand of development to that which we see in the VMs. Overall, even though he did note that it was intriguing that the postures of the four “people” on f57v were all different, the main impression the page left him with was that each of the four faces faced in a different direction (though he didn’t know what that meant).

On the train home, I sat there wondering what this might have caused this, letting all the various aspects swirl around me (though, no, I didn’t have any of Treadwell’s wine that night). And then all the bits clunked into place, with that sound very familiar to any Simpsons fan: “d’oh!”

I should explain. Perhaps the biggest trap Voynichologists fall into is that of overthinking issues: when many complex explanations for a given phenomenon exist, sometimes simple ones gets overlooked, or (worse) rejected for appearing too simple. And the simplest explanation here is that, because almost every magic circle has the directions of the compass written on it, that would be both the first thing you would want to keep and the first thing you would want to hide. And so it seems highly likely to me that the four faces on f57v code for N/E/S/W. In short, I think that (like the VMs’ “Naked Lady Code” I described in my book) the four faces employ a misleadingly elaborate way of enciphering something very simple – the compass directions. But which is which – and how – and why?

  • The left figure is facing forward-left
  • The top figure is facing backward-right
  • The right figure is facing forward-right (and holding a ring / egg)
  • The bottom figure is facing backward-left

But how do these four map onto N/S/E/W? The first thing to notice is that magic circles are very often written in Latin, with the four points written Oriens [E], Meridies [S], Occidens [W], Septentrio [N]: and so an encipherer would only need to hide one in order to hide them all.

While I don’t know for sure… I do predict that the nose and eyebrow of the left figure’s face was elaborated around an “S” to denote “Septentrio” [i.e. North]: and that the only useful information is that a ring (as rings are far more common than eggs in magic circles, The Black Pullet notwithstanding) should be placed opposite it [i.e. South]. The flower-like shape at the centre is probably an elaborated shape around the central o-shapes, which probably denote locus magistri, the place where the exorcist / conjuror / master of the magic circle should stand. Finally: might the heavily-drawn straight line on the shoulder of the ring-carrying person denote a sword? Very possibly.

 

Voynich Manuscript, page f57v – four central figures

This doesn’t answer every question about f57v (how could it?): but it does give a good snapshot of my current thoughts on how (beneath all the deception) it is actually a magic circle (though perhaps not as complex a magic circle as you might initially think).

Part 2 will move on to the VMs’ other magic circles…