A Visual Map of Voynich Evidence, Theories & People…

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Unless you just happen to have been an expert in Voynichese for a decade or more, making sense of all the evidence and the theories (and even the people) surrounding it can be quite daunting. So I thought I’d help by drawing a map!

theory-evidence-map

From my perspective, the general problem is that once you really latch onto a piece of evidence or a particular angle, you can easily become trapped inside it: and even though the solution you then reach may be entirely logical, it is almost always inconsistent with the other kinds of evidence and types of angle, and hence is almost always nonsensical.

I’d say this is precisely what happened with Gordon Rugg’s hoax theory, Jorge Stolfi’s East Asian language theory, and William Friedman’s artificial language theory – they all relied too heavily on one particular kind of evidence, and so arrived at untenable conclusions. But you will doubtless have your own thoughts on each of these. 🙂

It should also be clear that, like a kind of hummingbird theoretician, I’ve dotted around this diagram over the years, adding different ideas to the mix that try to explain different aspects of the evidence. I still believe that each of these suggestions will turn out to be largely correct, but the big trick will be finding a way – Intellectual History style – of making them all right at the same time!

The unfortunate life of the Army’s Cysquare cipher…

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When I was trawling through WW2 pigeon / cipher-related documents at the National Archives, I found a brief mention of a medium grade Army cipher called “Cysquare”. I half-remembered the name and that it was (unsurprisingly) a cy[pher] based around a square, but couldn’t remember the context at all.

However, when I later searched for it on the Internet, it all started to come back to me… because Cysquare had been devised by my cryptological hero, master codebreaker Brigadier John Tiltman (‘The Brig’). Very much as the NSA PDF paean to him would have it, few would disagree that Tiltman was indeed “A Giant Among Cryptanalysts“.

Tiltman himself wrote a short introduction to his Cysquare (recently declassified, though brutally redacted) called “A Cryptologic Fairy Tale“, on the basis (a) that he’d lost the original material and had had to make up some examples, and (b) that it had a happy ending (which I guess was that the Allied Forces won the war). Here’s how The Brig described it (though with a few linefeeds added to make it acceptable to our modern short attention spans):-

Sometime later in 1941 I produced the “Cysquare” which was accepted by the War Office as a low-echelon cipher to replace the “Stencil” cipher and issued to the Eighth Army in North Africa, Figures 8 and 9 [both redacted, *sigh*] give photographs of two pages of the printed instructions.

The grille has 676 (26 x 26) squares. Each column and each line contains 10 white (permitted) squares, with the exception of 3 “plus” lines containing 20 white squares each and 3 “minus” lines which contain no white squares at all. The key for the day consists of 26 letters of the alphabet in random order with the numbers from 1 to 26 written under them also in random order. For each message the operator selects a 4-letter indicator from a random list of such groups provided him for use in turn. The indicator in the case of the example given [but redacted] is GMBX. The numbers corresponding to this indicator are 11 19 20 7, i.e., position 11, line 19, column 20, taking out number 7. The grille could be used with any of its sides at the top. Position II indicates that the grille is used as shown with numbers 8 to 13 at the top.

The numerical key for the day is written from left to right at the top of the grille and from the bottom upwards on the left hand side. The plain text is written into the grille starting at the next white square after the square described by the line coordinate 19 and the column coordinate 20, using the elements of the key to define the corresponding lines and columns. If and when the operator reaches the last white square in the grille he proceeds from the top left-hand corner. He then takes out the columns of letters starting at the top of the grille and in the column designated by the taking out number, i.e., in this case 7.

The message is written out in 4-letter groups preceded by the 4 letter indicator and followed by the number of letters, the indicator repeated, and the time and date. No message of more than 220 letters was permitted. If a message handed in for transmission exceeded this length it had to be divided into parts, none of them exceeding 200 letters in length.

However, somewhat contrary to Tiltman’s story’s name, Cysquare itself didn’t really have a happy ending. For a start, a number of people thought that cryptanalysts such as Tiltman shouldn’t be messing about with making their own cipher systems, and so there was a certain amount of resistance to it from within, right from the beginning.

The second problem was to do with implementation: even though it relied on disposable pads containing pre-printed grilles, somewhere along the line someone had the bright stupid idea that they could economize by getting the Army cipher clerks in North Africa to reuse the pads, by writing messages in pencil and then erasing them with a rubber. However, before very long it became impossible to tell a blank square from a dark square – everything in the grille ended up fifty shades or grey (so to speak). Hence the cipher clerks refused to use the system, and it was quietly abandoned.

However, when Germans captured Cysquare pads and implementation notes, their cryptographers rather liked it. And so in 1944, a new system started to appear in German messages: the Rasterschlüssel (also known as RS44), a system derived directly from Tiltman’s Cysquare cipher. Of course, Tiltman quickly recognized it: and had the Germans not made some mistakes when designing their pads’ grille designs, they might have been extremely hard to decipher.

So… was Cysquare a success, or a disaster? It was certainly quite secure (if somewhat awkward to use): but in the end, it nearly gave Germany a cryptographic edge late in the war.

For fans of the pigeon cipher story, it seems unlikely that its message used Cysquare… and so the search for that goes on.

PS: there’s an 2004 article in Cryptologia by Michael J. Cowan called “Rasterschluessel 44 — The Epitome of Hand Field Ciphers“.

John Tiltman’s 1968 Voynich paper…

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Here’s a particularly interesting Voynich Manuscript paper declassified by the NSA in 2002 (but only recently released as a PDF scan) – so many thanks to the ever-vigilant Moshe Rubin (of Chaocipher Clearing House fame) for pinging me with a link to it, much appreciated! 🙂

Of course, Brigadier John Tiltman’s The Voynich Manuscript – “The Most Mysterious Manuscript in the World” is in many ways no more than an introduction to the VMs (and we have far better scans nowadays, so its pages 15..46 need not really concern us): yet all the same, it does contain plenty of incidental meaty morcels for modern Voynichologists to lightly dine upon. For instance:-

  • “Newbold’s solution left a legacy of ill-feeling which persisted for many years and which I found reflected in a letter which Charles Singer wrote to me in 1957.“
  • Plate 5 [f56r] – “has been identified as some sort of Bindweed (Convulvulus)“
  • Plate 6 [f4r] – “seems to me a fairly natural representation of cross-leaved Heath (Erica)“
  • “All the zodiacal drawings carry the name of the month in the centre in a later hand and in readable script though the language has been disputed.“
  • Tiltman was introduced to the VMs in 1950 by William Friedman (which to me reads a bit like a cryptologic version of Cluedo), and started by looking at some of Quire 20’s starred paragraphs.
  • “Charles Singer, in a letter to me, put the date at late 16th Century. Professor Panoffsky [sic] and the keeper of the manuscripts at the Cambridge Library both independently insisted on a date within 20 years of 1500 A.D., and the manuscript as we have it may be a copy of a much earlier document.”
  • Tiltman discusses Cave Beck’s 1657 universal language at reasonable length (pp.9-10, Plates 21-23), given that Friedman had told him that this was the kind of thing he believed the VMs to be. However, Tiltman was plainly far from convinced.
  • In 1957, Tiltman showed photostats of the VMs to various medieval herbal specialists. One of these was Dr. T. A. Sprague in Cheltenham, who – having spent many years on beautiful, well-annotated herbals – found that its “awful pictures” made him “more and more agitated“.

Yet the real substance of the paper arguably lies in the summary of Voynichese’s properties which Tiltman passed back to Friedman in 1951 (remember that Tiltman was arguably the 2oth Century’s greatest non-machine cipher cracker). Tiltman’s own transcription reads Voynichese as being comprised of 17-odd symbols, several of which have second variant forms. The reproduction of Plate 17 is far from crystal clear, but I’m reasonably sure the following is what Tiltman means (converted to EVA), though I’m not 100% sure about “2” because it seems to overlap with “R” and/or “S”:-

Tiltman:     D H E G 8 4 O A L S 2 R I C  T  DZ  HZ
EVA:         k t l y d q o a n s ? r i e ch ckh cth
2nd variant: f p m                       sh cfh cph

Though most of the paper is dryly factual (though written in an accessible style), Tiltman managed to sneak his own summary into page 9 – “My analysis revealed to me a cumbersome mixture of different types of substitution.” Of course, this is exactly my conclusion too… but regular Cipher Mysteries readers knew that anyway, so I won’t press the point. 🙂

So, the rest of this post contains Tiltman’s notes (but with the notation converted to EVA), with a few light annotations from me. Note that Peter Long mentioned was a senior figure at GCHQ who corresponded extensively about the VMs (he died in 1999): he’s also mentioned on p.216 of Kennedy and Churchill’s book, though mostly in regard to the “K:D:P” (Kelley/Dee/Pucci) theory of Long’s nephew Tim Mervyn, who has continued his uncle’s Voynichological interest. Enjoy!

* * * * * * * *

(a) Following are some notes on the common behaviour of some of the commonly occurring symbols. I would like to say that there is no statement of opinion below to which I cannot myself find plenty of contradiction. I am convinced that it is useless (as it is certainly discouraging) to take account at this stage of rare combinations of symbols. It is not even in every case possible say what is a single symbol and what is not. For example, I am not completely satisfied that the commonly occurring <a> has not to be resolved into <ci> or possibly <oi>. I have found no punctuation at all.

(b) <ckh/cfh> and <cth/cph>appear to be infixes of <k/f> and <t/p> within <ch>. The variant symbol represented by <m> appears most commonly at the end of a line, rarely elsewhere.

(c) Paragraphs nearly always begin with <k/f> or <t/p>, most commonly in the second variant forms [i.e. <f>/<p>], which also occur frequently in words in the top lines of paragraphs where there is some extra space. [Also known as “Neal Keys”.]

(d) <y> occurs quite frequently as the initial symbol of a line followed immediately by a combination of symbols which seem to be happy without it in any part of a line away from the beginning. Otherwise it occurs chiefly before spaces very frequently preceded immediately by <d>. Hence my belief that these two have some separative or conjunctive function. (I have to admit, however, the <y> also seems sometimes to take the place of <o> before <k/f> or <t/p> (though rarely, if ever, after <q>); this is particularly noticeable in some of the captions to illustrations in the astronomical section of the manuscript – these most commonly begin <ok>/<of> or <ot>/<op> and it is here that we occasionally see <yk>/<yf> or <yt>/<yp>.)

(e) I have tried, for convenience of handling, to divide words into what I call “roots” and “suffixes.” This arrangement is show in the bottom of Plate 17. [Which is, as best as I can tell, the following table:-]

Roots: <ok>/<of>, <ot>/<op>, <qok>/<qof>, <ch>/<sh>, <s>, <d>, 2 [??] <lk>/<lf>
Suffixes: either (i)  <e>, <ee>, <eee> followed by <y> or <dy>
            or   (ii) one or more of the following -
                <an> <ain> <aiin> <aiiin>
                <ar> <air> <aiir> <aiiir>
                <al> <ail> <aiil> <aiiil>
                <or> <ol>

Regarding the second type of suffix, some of the combinations are so rare that I have been uncertain whether to take any account of them at all. Some are very common indeed. It seems to me that each of these combinations beginning <a> has its own characteristic frequency which it maintains in general throughout the manuscript and independent of context except in cases where two or more <a> groups are together in series, as referred to later). These <a> groups e.g. <ar> or <aiin>, frequently occur attached directly to “roots,” particularly <od>, <ot>, <d> and <s>.  <okaiin>, <qokaiin> and <daiin> rank high among the commonest words in the manuscript.

(f) There are however many examples of 2, 3, 4 or even 5 <a> groups strung together on end with or without spaces between them. When this occurs, there appears to be some selective preference. For example, <ar> is very frequently doubled, i.e. <ar ar>, whereas <aiin> which is generally significantly commoner, is rarely found doubled. Perhaps the commonest succession of three of these groups is <ar ar al>. <al> very frequently follows <ar>, but <ar> hardly ever follows <al>.

(g) <o>, which has a very common and very definite function in “roots,” seems to occur frequently in “suffixes” in rather similar usage to <a>, but nearly always as <or> and <ol>. <or aiin> is very common.

(h) The behaviour of the <a> (and <o>) groups has suggested to me that they may in fact constitute some form of spelling. It might be, for instance, that the manuscript is intended to demonstrate some very primitive universal language and that the author was driven to spell out the ends of words in order to express the accidence [i.e. the inflectional morphology] of an inflected language. If all the possible <a> and <o> combinations can occur, then there are 24 possibilities. They may, however, be modified or qualified in some way by the prefixed symbols <k>/<f>, <p>/<t>, <ok>/<of>, <op>/<ot>, <ch>/<sh>, <s>, <d>, 2 [??], etc., and I have not so far found it possible to draw a line anywhere. This, coupled with ignorance of the basic language, if any, makes it difficult to make any sort of attempt at solution, even assuming that there is spelling.

(i) <l>, usually preceded by <a> or <o>, is very commonly followed by <k>/<f>, much less commonly by <t>/<p>, with or without a space between. In this connection, I have become more and more inclined to believe that a space, though not intended to deceive, must not necessarily be regarded as a mark of division between two words or concepts.

(j) Speaking generally, each symbol behaves as if it had its own place in an “order of precedence” within words; some symbols such as <o> and <y> seem to be able to occupy two functionally different places.

(k) Some of the commoner words, e.g. <okeed>, <okeedy>, <qokeedy>, <odaiin>, <okar>, <okal>, <daiin>, <chedy> occur twice running, occasionally three times.

(l) I am unable to avoid the conclusion that the occurrence of the symbol <e> up to 3 times in one form of “suffix” and the symbol <i> up to 3 times in the other must have some systematic significance.

(m) Peter Long has suggested to me that the <a> groups might represent Roman numerals. Thus <aiin> might be IIJ, and <ar ar al> XXV, but this, if true, would only present one with a set of numbered categories which doesn’t solve the problem. In any case, though it accounts for the properties of the commoner combinations, it produces many impossible ones.

(n) The next three plates show pages where the symbols occur singly, apparently in series, and not in their normal functions. The column of symbols at the left in Plate 18 [i.e. the vertical column at the left edge of f49v] appears to show a repeating cycle of 6 or 7 symbols <t> <o> <r> <y> <e> <o> <k> <s>. In Plate 19 [i.e. f57v] the succession of symbols in the circles must surely have some significance. One circle has the same series of 17 symbols repeated 4 times, an interesting column of symbols. Plate 20 [i.e. f66r] also has an interesting column of symbols. In all three there are symbols which rarely, if ever, occur elsewhere.

(o) My analysis, I believe shows that the text cannot be the result of substituting single symbols for letters in the natural order. Languages simply do not behave in this way. If the single words attached to stars in the astronomical drawings, for instance, are really, as they appear to be, captions expressing the names or qualities of those stars, there can hardly be any form of transposition system involved. And yet I am not aware of any long repetition of more than 2 or 3 words in succession, as might be expected for instance in the text under the botanical drawings.

D’Imperio’s “Elegant Enigma”, now a downloadable PDF!

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A highly surprising message just arrived here at Cipher Mysteries from our Chaocipher Clearing House chum Moshe Rubin:-

Is your readership aware that NSA has placed the entire text [of Mary D’Imperio’s “An Elegant Enigma”] on its site?

I couldn’t find the link on your site so here it is!

This is a great find, highly recommended for all Voynich researchers – if you haven’t read it already, download it straight away! Having said that, even though it took me six attempts to download it completely (doubtless they were tracert’ing me to see if I just happened to be a terrorist, bless ’em), I did get it all in the end. But please let me know if this happens to get removed (which is always possible).

Incidentally, this is just one of a number of cryptological history publications the NSA has kindly made available on its website. The 2007 article by John Clabby on Brigadier John Tiltman (“A Giant Among Cryptanalysts“) is also well worth looking at (though not nearly so essential as D’Imperio, naturally).

Arthur Wallis Exell…

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Sometimes a passing comment can open up a brief window onto an otherwise lost world. A 2002 email I made to the VMs mailing list I stumbled upon earlier today brought to mind one such instance, and six years on I found myself wondering just what had been said, what had been going on in a very particular context. Let’s start with the email, which quoted Mary D’Imperio’s book “An Elegant Enigma” (as copied by Luis Velez):-

A.W. Exell, in his letter to Tiltman, August 1957, refers to a theory (not further specified) that early Arabic numerals were built on from one, two, three, four or more
strokes in a similar Oriental manner; he suggests a sketchy and incomplete correspondence between Voynich symbols and conventional numerals along these lines. No one has, to my knowledge, worked out a “stroke” theory of this kind in sufficient detail to test it out as a hypothesis (p.24)

Of course, D’Imperio’s work was built squarely on Tiltman’s foundations, so it’s entirely unsurprising that a letter to Tiltman should end up in it. Yet Exell was a botanist working at the Natural History Museum: so what was he doing talking about possible Arabic numerals in the VMs?

I followed up the post with a short post about ladybirds (the subject of Exell’s final book in 1991), somewhat amused by the fact they are known to Italians as “The Devil’s Chicken”, concluding that Exell died some time after 1991. But far more information is quickly available now than was the case in 2002 (though no English-language Wikipedia page): for example, the Natural History Museum archives have this to say about him:-

  • Exell; Arthur Wallis (1901-1993); Botanist in the Department of Botany;
    2nd class assistant 11 Aug 1924
    1st class assistant keeper 1934
    Deputy keeper 1950
    Retired 1962

So at the time of the 1957 letter, Exell was the NHM’s Deputy Keeper in the Department of Botany, having worked there for 33 years (more than half his life).

What fascinates me about all this is the notion that a whole group of people probably linked to the Natural History Museum (of which Exell was merely one) must surely have been looking at the VMs circa 1955-1957. Perhaps if someone looked at Exell’s correspondence from around that date (at least some of which is held in the NHM’s archives), a whole “invisible college” of Voynicheros might well present itself.

This isn’t just an academic exercise on my part: I genuinely believe that the kind of broad (yet classical) education you would need to understand the VMs has become a rare thing in modern education, to the point that there may be plenty we can learn from what Exell and his friends thought about the VMs. In fact, I would argue that probably the most useful writer on the subject is Lynn Thorndike (and he died in 1965). Is it coz we are too modern to unnerstand it?

Pseudo-science and The Curse of the Voynich…

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A German Voynich article by Klaus Schmeh just pinged on the Cipher Mysteries radar screen: the ten-second summary is that in an interesting mix of observations and opinions, Schmeh clearly enjoys playing the skeptic trump card whenever he can (though he still fails to win the hand).

In some ways, Schmeh’s bias is no bad thing at all: authors like Rugg & Schinner (who both took one transcription of the Voynich out of the manuscript’s codicological context) deserve a far more skeptical reception than they received from the mainstream press. Yet Schmeh is also critical of my Filarete hypothesis, seeing it as merely the most recent pseudo-scientific approach in a long line of (let’s face it) Voynich cranks. That’s OK by me: I see his piece as merely the most recent shallow summary from a long line of journalists who failed to engage with the Voynich Manuscript, and I hope that’s similarly OK by him. 🙂

With The Curse of the Voynich, I took what business writers sometimes call an “open kimono” approach (though if you know where “transparency” ends and “Japanese flasher” begins, please say), insofar as I tried to make plain all the evidence and observations relevant to my thesis, and not to hide any murky stuff beneath layers of rhetoric. Many Voynichologists, particularly those with an axe to grind, responded by drawing their swords (if that isn’t mixing too many bladed metaphors) and charging: yet most of the attacks have been ad hominems rather than ad argumentums, which is a shame.

I suspect Schmeh sees my book as pseudoscience because of a category error. Rather than being a scientific proof, “The Curse” is actually a detailed historical hypothesis (who made it, when they made it, how they made it, what need it satisfied, how its cipher system began and evolved, what subsequently happened to it, etc) announcing an ongoing art historical research programme (developing and testing those ideas through archival and analytical study). The kind of deductive scientific proof (A.K.A. a “smoking gun”) which people like Schmeh demand would most likely come as a final stage, not as a first stage.

So, Klaus: while I welcome your skepticism in the VMs arena, I can only suggest that – as far as The Curse goes – your train perhaps arrived a little before the station was built. 😮

As far as the details in Schmeh’s article go, many are outdated (and wrong): for example, the notion of a 20th century forgery has been very strongly refuted by letters found in Athanasius Kircher’s archive. The dates Schmeh gives for Anthony Ascham are for the (more famous) 17th century Anthony Ascham, not the (less famous) 16th century one proposed by Leonell Strong. The idea that there are zero corrections in the VMs has also been proved wrong. John Tiltman was a non-machine cipher specialist (one of the finest ever, in fact), and only indirectly connected with Colossus.

If my German was better, I could doubtless produce more, but none of that (nor even his dismissal of my hypothesis!) is really the main point here. What I most object to about Schmeh’s piece is his repeated assertion that we still know almost nothing about the VMs, which he uses to support his skeptical position. Actually, we’ve come a very long way in the last few years – but the online hullabaloo tends to hide this.

Introduction to the Voynich Manuscript…

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Every few days, I get asked to recommend a good introduction to the Voynich Manuscript (the ‘VMs’ for short). But each time this happens, my heart sinks a little: given the size and scope of historical research you’d need to have to properly grasp the subject, it’s a bit like being asked to recommend a good 5-page encyclopaedia. Or rather, as none such exists, like being asked to write one.

However, you can describe it in a paragraph: it’s a handwritten book that’s 230+ pages long, very probably about 500 years old, and filled with strange words and obscure pictures no-one can understand. I call it “a Scooby Doo mystery for grownups“, but one where everyone is trying to pin the blame on a different janitor: and so the story loops endlessly, as if on a lost satellite cartoon channel.

For once, the Wikipedia Voynich Manuscript page falls well short of being genuinely useful: the VMs is so contested, so politicized, so intensely rubbish that the whole neutral tone Wiki-thing fails to please (I gently satirized this in my VQ questionnaire). Bucketfuls of worthless opinions, and endless pussyfooting around: throw all that junk away, I say, and start from scratch. *sigh*

But if Wikipedia’s faux-scientific neutrality can’t get you started, what can? If (like me) you are a fan of Ambrose Bierce’s “The Devil’s Dictionary” (1911), your ideal introduction to the Voynich Manuscript might well be succinct, partial, and cynical (in fact, almost toxically so). In this vein, I heartily recommend “Folly Follows the Script“, an article by Jacques Guy (AKA “Frogguy“) in the Times Higher Education supplement from 2004. While ostensibly reviewing Kennedy and Churchill’s recent book on the VMs, Guy rips apart a lot of the pretension and falsity that now surrounds the manuscript, in particular Gordon Rugg’s much–vaunted (but actually resoundingly hollow) hoax papers. Which is, errrm, nice.

If you prefer lots and lots (and did I say lots?) of data, the best introductory site by miles is Rene Zandbergen’s excellent voynich.nu, in particular his “short tour“, and the even shorter tour. But frankly, it’s hard for most people to care about Newbold, Petersen, Friedman, Strong, Brumbaugh, O’Neill, Feely, Manly, and even John “The Brig” Tiltman unless you’ve already lurched over the line into Voynich-obsessive mania: none of them could read a word of the VMs, and they’re all long dead.

Alternatively, if you prefer a kind of gentle postmodern defeatism, I could happily recommend a very readable article by Lev Grossman called “When Words Fail“, which first appeared in Lingua Franca magazine way back in April 1999: sadly, nothing much of substance has changed in the intervening decade (or, indeed, over several preceding decades too).

This might seem a horrible thing to say, given that so much ink has been spilled (and, more recently, so many HTML tags wasted) on the VMs over the last century in the honest pursuit of this wonderful (yet devastatingly cruel) enigma. But we still know next to nothing of any real use: the kind of intensely Warburgian art-historical research I’ve been slaving over for the last six years seems totally alien to most ‘Voynichologists’, a title that perpetually hovers too close to David Kahn’s Baconian “enigmatologists” (see “The Codebreakers” (1967), pp.878-9), with their “deliriums, the hallucinations of a sick cryptology“.

All of which is to say that both cynicism and nihilism are probably good starting points for reading up on the VMs: a century of careless credulity has got us all nowhere. But this is not to say that I am pessimistic about any advances being made. In fact, I would say that “the Devil’s in the details” or the alternative “God is in the details” (both of which are sometimes attributed to Aby Warburg!) to flag that, beyond the superficial flurry of foolish and wishful opinions out there, I think there are things we can (and eventually will!) know about the Voynich Manuscript; but that for the moment these remain hidden in its vellum margins.

All of which is another story entirely…

365 starred paragraphs (revisited)…?

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Just thought I’d post a quick comment about Vladimir Sazonov’s suggestion that the “starred” recipe pages in the Voynich Manuscript form some kind of calendar, ie that they originally contained 365 / 366 stars arranged in some kind of date order. Here’s his page (from Sept 2005) describing this idea:-

The basic idea of a calendar here is not new: D’Imperio noted (“An Elegant Enigma”, p.21, 3.3.7) that Tiltman pointed out in 1975 that the original star-count would very probably have been 365, “thereby providing one ‘star recipe’ for each day of the year, possibly a set of astrological predictions or prescriptions.” The essence of Vladimir’s new idea is to count the days forward from the start and from the end, and to then note that many of them start at the 1st of the month (particularly in the second half). Feb 29th/Mar 1st would then align with a particularly ornate star, and there is a tiny star apparently added at the Spring Equinox.

If true, then to make the remaining 324 starred paragraphs fit the magical 365/366 number, the two folios (f109 and f110) in the missing central bifolio of the last quire would need to contain 41 or 42 starred paragraphs, ie roughly 10-11 per page. This is possible… but seems somehow out of sequence to me, as the only two folios with 10 on a page are f105 and f116. Also, Vladimir’s March/April/May/June seem just out of step, as though a few extra days have been inserted before them.

One important thing to consider here would be whether the pages as numbered are in the correct order (as per my book). If the rest of the ms is anything to go by, the answer would probably that it is not, but that there is still a high chance that any two adjacent folios were originally adjacent.

Here are some alternative ideas for a calendrical solution. If you group the months of the year together into sets of 3 at a time, you get the following four possible quarterly cycles:-

  • Jan – 90+1 / 91 / 92 / 92
  • Feb – 89+1 / 92 / 92 / 92
  • Mar – 92 / 92 / 91 / 90+1

Interestingly, f106-f108 contain 91 stars and f111-113 contain 92 stars in total. If these correspond to the Apr-Jun and Jul-Sep quarters, this might suggest that the f109/f110 bifolio was originally placed somewhere between the outermost bifolio 103/116 and the bifolio 106/113. If so, f109 might have contained only 10 or 11 stars (to bring 79 up to 90+1), while f110 might have contained 31 (to bring 61 up to 92).

At first sight, this seems counterintuitive: why have a folio with only 10 stars on? I would point out that the author has already done this on f116 (which would mark the end of the calendar year), while the 10-star f109 would also contain the end of the astrological year (at the Spring Equinox).

I also suspect that the 106/113 bifolio is out of order: and so my proposed sequence of pages would then be something along the lines of:-

  1. f103 – 19+14 – Jan 1st
  2. f104 – 13+13 – Feb 3rd
  3. f105 – 10+10 – Mar 1st
  4. f109 – 10+0 – Mar 21st – Spring Equinox to end of month, followed by blank page
  5. f107 – 15+15 – Apr 1st
  6. f108 – 16+16 – May 1st
  7. f106 – 15+14 – Jun 2nd
  8. f113 – 16+15 – Jul 1st
  9. f111 – 17+19 – Aug 1st
  10. f112 – 12+13 – Sep 6th
  11. f110 – 16+15 – Oct 1st
  12. f114 – 13+12 – Nov 1st
  13. f115 – 13+13 – Nov 26th
  14. f116 – 10+0 – Dec 22nd – Winter Solstice to end of month, followed by blank page

I don’t claim to know why this should be so: but it seems to me a slightly better calendrical match than Vladimir’s proposal. Perhaps one day when I get the chance to re-examine these pages, I might notice something that might confirm or refute one or both of these ideas… something to think about, all the same. 🙂