The Index of Coincidence

Voynich, Part III

To read the first two installments in the Voynich Cycle, go here, and here.

There can be no audio VoiceOver today, as the piece is necessarily image-dependent, and images cannot, ordinarily, be sounded out (though I tried).

“The text you write must prove to me that it desires me.” —Roland Barthes

1. Say It with Flowers

We have, recall, previously established the high probability that a 1920 article in The Florists’ Review, entitled “‘Saying It’ in Cipher” and attributed to one Cora J. Jensen of the Department of Ciphers at Riverbank Laboratories in Geneva, Illinois, was in fact written by none other than William F. Friedman. Regular readers will already have marveled at the several achievements in diverse fields of this polymathic yet elusive character, who did as much to consolidate American global power in the twentieth century through his work in military cryptography as he did to advance the humanistic study of Thomas Chaucer and Guillaume Chéquespierre. We know, also, that our man was no stranger to the art of the jest, or of what a century earlier would have been easily identifiable as the genre of mystification, working to win our confidence, but soon enough tipping his hand to reveal, at least to those who are paying sufficiently close attention, the ambiguous nature of his source material.

Yet even for Friedman it is a bit much —is it not?— to go and make up an alter ego only to publish an article ostensibly about cryptographic flower-arranging in a Chicago-based industry monthly dedicated to the global trade in flowers and seeds. Surely, we must suppose, he would only bother to do this if he were in fact trying to do something more. What else might be happening, then, beneath the topsoil of this bright yet evidently substanceless mental florescence?

2. 💍🌞🌹⬆️❤️🌞🌹🤺🌹

It will be recalled that “Jensen’s” article draws its principal inspiration from the Leipzig author Johannes Balthasar Friderici’s 1685 work, Cryptographia, oder Geheime schrifft- münd- und würckliche Korrespondentz welche lehrmässig vorstellet eine hoch-schätzbare Kunst verborgene Schriften zu machen [Cryptographia, or, The Secret Textual, Oral, and Actual Correspondence Didactically Presenting a Most Valuable Art of Hidden Writing].

This book, on the face it, appears nearly as mystifying as anything Friedman himself ever conjured. “The art of remaining silent,” Friderici begins his preface, “is a noble thing; yet more noble in my view is the art of remaining silent while speaking.” Friderici notes that this is the very same art by which the “wise Egyptians” and the “sensual Chinese” first concealed their thoughts within the manifold forms of animals and plants rendered by the stylus as characters upon papyrus or leaf. But over time the connection between the signs and the signified (to speak in terms that would become available only in the twentieth century) would be lost, so that writing now mostly appears arbitrary to us.

We no longer recall for example that the capital “A”, when turned upside-down, looks something like an ox’s horned head, as indeed it long was for the Phoenicians. Yet once we remind ourselves that writing is drawn from the world, Friderici thinks, we are thereby enabled to use that same world as the limitless fount of elements for our secret compositions. Whether communicating with sounds, flowers, or winks, Friderici conceives it all as “writing”, since what is represented by actual objects, or by knocks or tones or gestures, can be made to have exactly the same effect as words on a page.

The book is divided into several “classes”, in the first of which one learns “how to send something secret, in a concealed fashion, to a good friend, by changing or replacing the letters”. The second class teaches you how to encode a text by replacing individual letters with “mellifluous syllables”, with entire words, or even with sentences, so that, to take the simplest example Friderici offers, the imperative Bleib! [“Stay!”], becomes “Babalabebolobabolobebalababalabu”. The third class introduces the student of cryptography to a method of transmitting messages to correspondents by means of such unconventional units as musical notes:

Or points:

Or lines:

Or yet other elegant mathematical figures:

These figures may of course be rendered with ink on paper, Friderici notes, but they may also be “painted, sewn, woven, or embroidered”.

Finally, in the fourth principal class (there is a short fifth class that teaches the art of concocting various “juices” [Säffte] with which to write invisible characters) the initiate learns “many and various unusual inventions, by which one may correspond in secret, not only by means of actual signs, but also plants and flowers, playing cards, flags, fire, bells and other instruments, strings or laces, tapping on the wall, blinking the eyes, and the like, but also by oral speech”. Much of the discussion in this class is focused on the construction of “emoji”-like systems, which seem to offer Friderici an opportunity to test out the limits of early modern typography. Thus:

Yet it is the example of flowers and other plants that is of most interest to Jensen/Friedman among the methods taught in the fourth class, so let us dwell on that one.

Friderici begins his introduction to horticultural cryptography with a fairly elementary case, in which different quantities of stalks of common garden herbs are used to represent the Latin alphabet:

Once this key is established, the author illustrates it with a simple message composed from rosemary, sage, marjoram, and spearmint, rendered backwards for a bit of added security, or perhaps of simple mischief:

That is: YDAER LLA SI TI EMOC; or, straightened out and written as convention dictates: “Come, it is all ready.”

Next Friderici moves on to flowers. He notes that strictly speaking one would need only two kinds, or even just two colors of the same kind, in order to represent the alphabet in binary form. But for simplicity’s sake his initial example proposes various combinations, for each letter, of up to four each of white narcissus, red tulips, yellow tulips, red-and-white tulips, red-and-yellow tulips, and, finally, white tulips:

In this way we are quickly able to generate a wreath —assuming we know how to recognize the individual flowers, which indeed requires some additional “hatching” conventions in view of the monochrome limitations of common print in Friderici’s era— such as this one:

Which, the reader is invited to convince himself, by consultation also of the original work as needed, bears the poignant message: Ich bleibe dir getreu bis in den Tod. “I will remain faithful to you unto death.”

Surprisingly little is known about Friderici’s life. He is believed to have been born in 1635, and to have died sometime around 1704. No entry for him can be found on German-language Wikipedia, nor even in the usually very exhaustive Deutsche biographische Enzyklopädie. One might be tempted to imagine that his only known work, the Cryptographia, was a fabrication conjured from scratch by Friedman himself. But I have examined an actual copy of the book (it is held at the Bibliothèque Nationale de France), and, though I have not subjected it to radiocarbon dating, all of its physical properties suggest a seventeenth-century origin. So at least on this point we may not accuse Friedman of mystification. Friderici’s book exists, and it says what it says.

3. The Index of Coincidence

Yet we may be forgiven for feeling haunted by coincidences. This feeling, however, must not be permitted to loom like a specter, but rather, if we have our wits about us, must be channeled productively through the methods and apparatus of modern science.

And fortunately, another of Friedman’s publications, appearing just two years after his pseudonymous contribution to The Florists’ Review, permits us to do precisely this. In The Index of Coincidence and Its Applications in Cryptography (Paris: L. Fournier, 1922), the American cryptanalyst introduces a revolutionary method for measuring the likelihood of two randomly selected letters being equal. His technique involves placing two texts side by side and counting the number of identical letters that appear in the same position in both texts. In this way his “index” furnishes a measure of the probability of obtaining two correspondingly letters upon randomly selecting two letters within a given text. Since the letters of any natural language are never distributed evenly, the measure is higher for such texts than for strings of letters that are uniformly randomized.

With this work, Friedman effectively established himself as the Copernicus, the Newton, the Darwin of the cryptographic science. It is highly technical, and I fear there is much of value in it that remains quite over my head. Nonetheless, circumstances have compelled me to master it as well as I am able, and to apply its insights for determination of the authorship of a certain well-known and highly enigmatic Renaissance manuscript, to which I shall turn soon enough.

4. The Tatur Attachments

Because I am a researcher in a field that often attracts marginals and crackpots, I receive a great deal of unsolicited e-mail, often including large attachments with unbelievably long-winded explanations of arcana that the established research community considers, in the absence of further documentary revelations, simply inexplicable. Many of these, for reasons that would require a separate investigation, seem to come from retired engineers in provincial Russia. A good portion of the time, these explanations appeal to dark forces operating derrière les coulisses —the Jesuits, the Freemasons, the Jews—, and so I do what any reasonable and enlightened researcher would do: I send the paranoid lucubrations of these lonely conspiracy theorists straight to the trash.

Yet something, I do not know exactly what, captured my attention when, this past March, I received a message from a yandex.ru address, and sure enough, upon opening it, found that it was sent from a certain Vitaly Ibragimovich Tatur, a retired professor of computer science at Ryazan State University. Tatur seems to have made a name for himself in the 1980s with his work on “rank degeneracy”, which, however it may sound, has to do not with the uncouth criminal underclass, but rather with the mathematical modeling of informational relevance in what would only later come to be known as “search-engine” queries.

I will have more to say about Tatur and his work in subsequent notes. For now my purpose is only to inventory the contents of his peculiar e-mail to me. The entire message of it was contained in the subject line — Уважаемый коллега, посмотрите пожалуйста приложенные файлы / “Dear colleague, please see attached files”. There were seven attachments in total, three pairs of two files each, and one stand-alone Word file (to which we will turn in the final section). Each pair features one photographic image in .jpg format, and one corresponding Word file. These latter share the same name as the photographs, while differing in their extensions, and include, first, a reference to a source work that Tatur calls the “clavis”, followed by a short text. In none of the first two cases have I been able to find any trace in any library catalog of the work cited, nor, in the final case, have I been able to find any trace of the alleged “Appendix”.

Yet this minor mystery aside, Tatur’s meaning is clear enough: the photograph, for him, is an enciphered “text”, the key for the decipherment of which would in principle be found in the work referenced, while the text that follows the clavis is what he takes to be the decipherment, or as it were the “translation”, of the image in the corresponding photo.

Let us now look, with minimal commentary —for in any case these juxtapositions remain nearly as mysterious to me as they surely will be to you—, at the three pairs in turn.

I. корни.jpg / корни.docx [roots.jpg / roots.docx]

I.1. Exemplum

I.2. Clavis
Pierre-Marie Hyacinthe Brouillet, Dictionnaire héraldique ; ou, la science de la blason, Paris : Imprimerie Militaire, 1838, pp. 274-79.

I.3. Decipherment
“We see what appears to be a succession of more or less vertical roots on a tree growing in an urban environment (Hong Kong). They are differentiated by their thickness, and by their shade. But look harder, and you will see, in the fimbriations of light and shadow, some crapaudy, ged, or sea-dragon naiant; some pascuant herbivore, chewing; a pelican in her piety, silently vulning; or two salmons crossed and hauriant, soon to be discorporated by some patiently sejant ursus.”

II. лошади.jpg / лошади.docx [horses.jpg / horses.docx]

II.1. Exemplum

II.2. Clavis
Anonymous, La guerre franco-prussienne de 1870-71. Souvenirs d’une pâtissière parisienne, Quimper : La Résistance, 2004, p. 81.

II.3. Decipherment
“Thou art my battle axe and weapon of war: for with thee will I break in pieces the nations, and with thee will I destroy kingdoms.”

III. рыбы.jpg / рыбы.docx [fish.jpg / fish.docx]

III.1. Exemplum¹

III.2. Clavis
Izaak Walton, The Compleat Angler; or, The Contemplative Man’s Recreation, Being a Discourse of Fish and Fishing, Not Unworthy the Perusal of Most Anglers, London: Richard Marriot, 1653, Appendix 1: “Fishes, Encipher’d”.

III.3. Decipherment
“Please stop reading. Turn back now. You don’t know how dangerous this blurring of the line between fact and fiction really is. It’s not your fault. No one knew. I myself had no idea. But neither is it too late for you to set the future on another course. All you have to do is to stop reading, and ████ ████████ ████████████████ now.”

5. Coda

There is, as I have indicated, still one more attachment to Tatur’s e-mail, bringing the total to seven. It is paired with no sample text, but consists only of a single .jpg exemplum that might, in its almost jarring graphic simplicity, seem at first sight rather unpromising:

This exemplum might have seemed unpromising to me, that is, if I had not been intensively studying Friderici’s Cryptographia at the very moment I received Tatur’s strange missive. In the circumstances, however, I immediately recognized it as among the figures found in chapter XII of the Third Class of the Cryptographia, where we are taught several techniques for enciphering messages by means of points. The decipherment of these particular points, however, is not the one indicated by the point-based clavis furnished in the same chapter (which is also featured as the second image in the present essay).

At first, when I thought this was the only possibility, I was frustrated upon applying the equivalencies given in the clavis and obtaining only a garbled alphabetic string, which I knew at once was far too ugly to be code for something else in turn. So I continued to stare at the points, and little by little I came to understand that Tatur was, in effect, inviting me to fill in the clavis myself, with nothing other to rely on than my own intuition… along with whatever knowledge I might have of the statistical frequency in German of the various letters of the alphabet.

And so I stared at the points, and after another day I had nothing at all. After another day, I still had nothing, so I went back and studied Friedman’s revolutionary formula, which first set code-breaking on a steady footing when he published it in 1922:

I tried out countless German phrases and sentences, in the aim of determining the Friedmanian measure of their coincidence with the sequence of points. After the fifth day, I believed I had all the vowels settled, but the sentence I had come up with seemed to concern the flora and fauna of a place called Inaccessible Island, an uninhabited volcano within the Tristan da Cunha archipelago in the South Atlantic Ocean — uninhabited by people, that is, but not, I was to learn, by the intriguingly named “Inaccessible rail”, a mysteriously flightless bird of the Rallidae family.

Yet I felt in my gut that something so obscure could not possibly be the true subject of Tatur’s message, so I continued staring, and analyzing, and staring some more, and as I studied from time to time new flashes of hope would flutter through my mind as visions of a plantain tree, or of the Edict of Nantes or its Revocation some years later, or of a sign outside a cosmetologist’s shop in a strip mall in Phoenix offering eyebrow threading on the installment plan. I thought I saw all these things in the text, as brief irruptions of sense, but they all invariably disappeared just as suddenly as they had come.

So I studied the math some more, and I stared some more, and on the evening of the seventh day it came to me in a flash a thousand times more vivid than all those dull flightless shadows that had come before it:

DER AUCTOR DES HEYMLICHEN KRÄUTER-BUCHS VON RUDOLFF IST NIEMAND ANDERES ALS KAÏKOS VON SIZILIEN.

Which, being Englished, is:

THE AUTHOR OF RUDOLF’S SECRET BOTANICAL MANUSCRIPT IS NONE OTHER THAN CAECUS SICULUS.²

I have stared at the points for countless more hours since this epiphany hit me, and the longer I stare, the more certain I become. This, quite simply, is what it says.

Now, if my interpretation is correct (after all I am not a crackpot, and notwithstanding my feeling of certainty I am mature enough to conserve a sense of epistemic humility about me), then we may be certain that Jensen/Friedman did not simply decide to write an article for The Florists’ Review in order to share his love for horticultural cryptography with industry insiders. Rather, he seized this opportunity, as I believe he also did on several similar occasions, to plant, as it were, a key piece of information for the eventual decipherment of the mysterious manuscript to which he devoted a considerable portion of his life’s work.

In subsequent notes I will reveal more of what I have been able to learn of the life and fate of Caecus Siculus. And I will do so in infinite debt and gratitude towards William F. Friedman, without whom our shared field of research would never have got off the ground, nor come forward —like all honest longing for truth hopes to do— as a science.³

1. It is not at all clear how Tatur came into possession of a photograph from my own childhood, and indeed I have allowed myself at least a quick shudder of unease at the discovery of this vaguely familiar image. But any consideration of our Russian colleague’s motives and tactics will have to be saved for a subsequent note.

2. That is, the botanical manuscript recently in the possession of the Holy Roman Emperor Rudolf II (1552-1612) — i.e., the “Voynich Manuscript”.

3. The entirety of the text presented here under the title, “The Index of Coincidence”, constitutes a single footnote (fn. 102) to Justin Smith-Ruiu, The Voynich Manuscript: A Complete Translation (forthcoming).

—

To help fund the publication of The Voynich Manuscript: A Complete Translation, slated for 2024, please consider becoming a paid subscriber (those who opt for a “founding member” subscription will receive a free copy when it appears):

Or give a gift subscription to someone you love:

—

There’s an interview with me in The Sun Magazine, in which for some reason I am permitted to hold forth at great length about language and languages. European friends and acquaintances will roll their eyes at the interviewer’s claim in the preface that I am “fluent” in French, German, and Russian, though I do make a considerable effort in what comes after that to account for my limitations, and to explain that interest —in languages, for example— is not necessarily the same thing as talent or ability. I’ve often said that only a monoglot would ever think to ask, “How many languages do you speak?” and that any true polyglot could only ever answer: “I have no idea! One? None? All of them (potentially)?” I suppose in this sense I do count as a polyglot, though my sincere view is that I am “fluent” in precisely zero languages, and competent in at most one of them (even in that one, I have still never found a way to say the things I’d really like to say).