The Voynich manuscript consists of 240 pages of text and fanciful illustrations written in an unknown script. It is first mentioned in the 16th century, then largely disappears from the record for several centuries, only to resurface in for sale in 1903. An independent carbon dating assigns a early 15th century date to the vellum, but some scholars speculate it may have been inked or re-inked at a later date. Other scholars believe it to be an elaborate hoax or forgery. A recent paper in Transactions of the Association for Computational Linguistics (TACL) by Bradley Hauer & Grzegorz Kondrak (henceforth H&K) entitled Decoding Anagrammed Texts Written in an Unknown Language was touted to have enabled a decipherment of the Voynich. Have H&K succeeded where others have failed? Unfortunately, having reviewed the paper carefully, I can say with some certainty that they they have not.

H&K propose two techniques towards decipherment. First, they describe methods to determine the underlying language of a plaintext using only the ciphertext, assuming a simple bijective substitution cipher. Their preferred method does not depend on the linear order of strings within the ciphertext, and thus works equally well when the ciphertext characters have been permuted within words (assuming that word boundaries are somehow clearly delimited in the ciphertext), a point which will be become important shortly. Then, they describe methods for cryptanalysis when the encipherment consists of a bijective substitution cipher under certain degenerate conditions, such as where the ciphertext lacks vowels, or where the ciphertext characters have been randomly permuted within words.

That much is fine (though I have some quibbles with the details, as you’ll see). My major issue with H&K is that they don’t provide any evidence that the Voynich is so encoded, they simply assume it. And, despite the press hype, their preferred method fails to produce anything remotely readable.

I don’t have much to say about their method for identifying source language; it is a relatively novel task—they only cite one prior work—and their method and evaluation both appear to be sound. I appreciate that their evaluation includes a brute force-like method of simply attempting to decipher the text as a given language, and as a topline, an “oracle” scenario in which the decipherment is known and the problem reduces to standard language ID. But I was struck by the following claim about their decipherment method (p. 79):

“We conclude that our greedy-swap algorithm strikes the right balance between accuracy and speed required for the task of cipher language identification.”

It’s hard for me to imagine in what sense “cipher language identification” might be considered something which needs to be fast (rather than merely feasible). I think, in contrast, we would be just fine with using supercomputers for this task if it worked.[1]

So what does their preferred method say about the plaintext language of the Voynich? It assigns, by far, the highest probability to Hebrew.[2,3] Naturally, the oracle scenario is inapplicable here; whereas most archaeological decipherments have worked from a small set of candidate languages for the plaintext, there is nothing like a consensus regarding the language of the Voynich.

H&K then consider methods for decipherment itself. This problem is essentially a type of unsupervised machine learning in which the objective is to identify a mapping from ciphertext to plaintext (a key) such that for the ciphertext, we maximize the probability of the plaintext with respect to some language model. Kevin Knight and colleagues have, in the last two decades, proposed three distinct applications for this scenario:

• Unsupervised translation: Knight & Graehl (1998) use this scenario to learn low-resource transliteration models, and some subsequent work has applied this to other low-resource, small-vocabulary tasks, but as of yet such methods don’t scale well to machine translation in general.
• Steampunk cryptanalysis: Knight et al. (2006) use this scenario for unknown-plaintext cryptanalysis of bijective substitution ciphers, and subsequent work has also applied this to homophonic and running key ciphers. But the aforementioned ciphers have been known to be vulnerable to pencil-and-paper attacks for a century or more, and it’s not clear that these methods are effective attacks against any cryptosystem in widespread use today.
• Archaelogical decipherment: Snyder et al. (2010) attempt to simulate the automatic decipherment of Ugaritic, a Semitic language written in a cuneiform script in the 14th through the 12th century BCE; these were manually deciphered in 1929-1931 by exploiting the language’s strong similarity to biblical Hebrew. Knight et al. (2012) show that an undeciphered 18th century manuscript is in fact a description of a Masonic ritual written in German and encoded using a homophonic cipher. However, others have argued that computational methods for archaelogical decipherment are still quite limited. For instance, Sproat (2010a,b, 2014) draws attention to the unsolved problem of determining whether a symbol system represents language in the first place, and to the long history of pseudo-decipherment.

Regardless of the application, it should be obvious that decipherment is a computationally challenging problem. Formally, given a bijective cipher over an alphabet K, the keyspace has size |K|!, since each candidate key is a permutation of K. Three classes of methods are found in the literature:

• Integer linear programming (ILP; e.g., Ravi & Knight 2010)
• A linear relaxation of the ILP to expectation maximization or related methods (e.g., Knight et al. 2006)
• Search-based techniques using a beam or tree (e.g., Hauer et al. 2014)

H&K’s preferred method is a case of the latter; they refer to this prior work as “state-of-the-art”, but skimming Hauer et al. suggests they are state-of-the-art on decrypting snippets of text randomly sampled from the English Wikipedia article “History“. This doesn’t strike me as an acceptable benchmark, even if there’s some precedent in the literature, and what’s worse is that they use snippets as short as two characters, which are well below the well-known theoretical bound.

H&K propose two adaptations of the Hauer et al. model. First, they consider a variant which can handle ciphertext in which characters have been permuted (“anagrammed”) within words (assuming that word boundaries are clearly delimited in the ciphertext and are the same as word boundaries in the plaintext). H&K they mention that this has been suggested in prior Voynichology—though this might well be pure speculation, since we can’t read the manuscript—but do not themselves argue that the Voynich is anagrammed. Random permutation of letters within words strikes me as a poor cryptographic strategy due to the non-determinism it introduces. Rof nnastcie anc uyo adre shti eetnencs? That’s hard to read, in my opinion, though not complete impossible with enough context.[4] While I can’t really put myself into the mind of the creators of the Voynich manuscript, it seems that a wide degree of hermeneutic freedom is undesirable in most written genres, even texts of, say, an occult nature: you don’t want to accidentally turn yourself into a newt! Secondly, H&K adapt their model so that it can restore vowels omitted in the plaintext.[5] They refer to the resulting ciphertext with vowels omitted as an “abjad”, using a rare term of art for consonantal writing systems, i.e., those in which vowels are omitted. Phoenician, the ancestor of the Greek & Latin alphabets, did not originally write vowels at all, but they are inconsistently present in later texts and both Hebrew & Arabic write certain vowels. In Standard Arabic, for example, all long vowels are written explicitly, and Hebrew during the Renaissance era was normally written with the Tiberian diacriticization (or niqqud) developed several centuries earlier. H&K seem to be assuming a total omission of vowels which would be both anachronistic and typologically rare, and had H&K mentioned either of those facts in a brief disclaimer admitting to their slight abuse of terminology, I’d wouldn’t think they weren’t mislead, or misleading the reader, about what an abjad (normally) is.

It seems to me that H&K have, at this point, taken a method-free leap of faith towards the hypothesis that the Voynich is vowel-less Hebrew, anagrammed and encoded with a bijective substitution cipher. Perhaps I’d be willing to forgive it if these assumptions allowed them to produce some readable plaintext. Here’s what they have to say about that (p. 84):

“None of the decipherments appear to be syntactically correct or semantically consistent. […] The first line of the VMS [Voynich manuscript]…is deciphered into Hebrew as ועשה לה הכה איש אליו לביחו ו עלי אנשי המצות. According to a native speaker of the language, this is not quite a coherent sentence. However, after making a couple of spelling corrections, Google Translate is able to convert it into passable English: ‘She made recommendations to the priest, man of the house and me and people.'”

So the authors, neither of whom apparently are native speakers of Hebrew, post-edited the output of their system until the MT decoder produced this sentence. As others have noted, this is not an acceptable method—modern MT systems are extremely good at producing locally coherent text from degenerate input.

H&K suggest two possible interpretations of their results: “the results presented in this section could be interpreted either as tantalizing clues for Hebrew as the source language of the VMS, or simply as artifacts of the combinatoric power of anagramming and language models.” (p. 84f.) So they are not really claiming, at least in this article, a decipherment—that’s an addition of the subsequent, irresponsible press coverage, for which I can’t really blame H&K—but I can’t imagine calling this “tantalizing”. I don’t see any reason to think H&K have any confidence in their decipherment, either: they don’t provide more than a single plaintext sentence, and don’t provide a key. Had I been asked to review this paper, I would have requested that the portion of the paper dealing with language identification employ corpora of non-linguistic symbol systems (such as those in Sproat 2014), and I would have insisted that the portion of the paper dealing with the decipherment of the Voynich be essentially scrapped. The Voynich angle is a red herring: there is nothing here. Had they just removed it, this would have been a perfectly good TACL paper!

In 2010, my colleague Richard Sproat wrote a brief article for the journal Computational Linguistics (Sproat 2010b) which reviewed a recent paper by Rao et al. (2009), published in the journal Science. Rao et al. claim to provide statistical evidence that the the Indus Valley seals are a writing system. Now there are quite a few reasons to suspect the seals are not writing under any common-sense definition thereof. More importantly, though, Rao et al.’s method fails to discriminate between linguistic and non-linguistic symbol systems (see, e.g., Sproat 2014). Sproat implies that had the Science editors simply retained computational linguists as referees, they would have been made aware of the manifest flaws of Rao et al.’s paper and would thus have rejected it. With respect to my colleague, he has been shown wrong on both counts. First, when these journals retain computational linguist referees, they simply ignore negative reviews of technically-flawed, linguistically-oriented work when it has sufficient “woo factor”. Secondly, woo factor trumps lack of method even in the one of the top journals for computational linguistics and natural language processing, one which I review for and publish in. Some recent research suggests that fanciful university press releases are a key contributor to scientific hype. As far as I can tell, that is what happened here: the “tantalizing clues” in a flawed journal article were wildly exaggerated by the University of Alberta press office, and major publications took the press release at its hyperbolic word.

PS: If you’re interested in more wild speculation about the Voynich manuscript, may I suggest you check out @voynich_bot on Twitter?

Acknowledgements

Thanks to Brian Roark & Richard Sproat for feedback on this.

Endnotes

[1] The hacks at the Daily Mail are rather confused here; Carmel isn’t a supercomputer—it’s a free software package for doing expectation maximization over finite-state transducers—and at worst you might want to run these kinds of experiments using a top-of-the-line microcomputer, possibly with a powerful graphics card (e.g., Berg-Kirkpatrick & Klein 2013).

[2] An alternative method prefers Mazatec, a which H&K correctly reject as chronologically implausible; a couple other top possibilities are Mozarabic, Italian, and Ladino, which H&K consider “plausible”. Mozarabic is an extinct Romance language that was spoken (but only rarely written) by Christians living in Moorish Spain; it is unclear whether H&K are using the Arabic or the Roman orthography (neither were really standard). Ladino was spoken in the same region and time period but by the Sephardic population; it was written using Hebrew characters. As far as I know, both languages would have declined rapidly after the conclusion of the Reconquista, which imposes a terminus ante quem of roughly 1492, if either is the plaintext language of the Voynich.

[3] For reasons unclear to me they only use 43 pages of the manuscript in their Voynich experiments. This seems like a major flaw to me. Had I been asked to review this paper, I would requested a justification.

[4] To wit, in the CMU dictionary, 17% of six-character words are an anagram of at least one other word, and there are no less than fifteen anagrams of the sequence AEIMNR.

[5] H&K claim that one can’t use the linear relaxation method to restore vowels. I don’t see why, though. If the hypothesis space is expressed as a single-state weighted finite-state transducer, and the plaintext vowels are simply mapped to epsilon, then everything proceeds as normal. In fact I am running such an experiment with a ciphertext consisting of an “abjad” (no-vowel) rendering of the Gettysburg Address. I use a variant of the Knight et al. (2006) approach with Baum-Welch training and forward-backward decoding rather than their Viterbi approximations (software here). Because the resulting lattice is cyclic, the shortest-distance computation during the E-step is more complex than normal, but it does basically work. This is to be expected: you prbbly hv lttl trbl rdng txt tht lks lk ths. Experimental results forthcoming.

References

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