By Gordon Rugg
There’s a new article about the Voynich Manuscript, by Marcelo A. Montemurro & Damián H. Zanette, on PloS One: Keywords and co-occurrence patterns in the Voynich manuscript: an information-theoretic analysis.
The authors claim to have produced evidence for the presence of real, meaningful text within the Voynich Manuscript. Unfortunately, the authors appear to have misunderstood some key issues. This article is a detailed discussion of some of these misunderstandings and their implications. It also addresses some unfortunate omissions in the Montemurro & Zanette (M&Z) article.
In brief, the article consists of three key assertions, all of which are seriously flawed.
Assertion 1: They have found statistical patterns in the Voynich Manuscript which are similar to the statistical patterns of real languages.
This assertion is true, but it’s hardly news. There’s a substantial amount of previous research which has reported similar results. As far as I know, all the serious researchers in the Voynich community take this as a well-established starting point.
The authors focus in particular on statistical patterns that extend across sections of the manuscript. This topic has received less attention, but it has been previously addressed. My article about textual structures in the Voynich Manuscript deals with precisely this point, for example.
Assertion 2: The statistical patterns they have found cannot be explained as the result of a hoax.
This assertion is completely mistaken. There’s plenty of published material showing that a hoax could easily produce just the sort of findings that they report, and more, from the level of syllable distributions to the level of regularities between and within sections of the entire manuscript (e.g. my article on textual structures in the Voynich Manuscript).
Assertion 3: Their results are consistent with the presence of meaningful text within the manuscript.
This assertion is sort-of true, but is seriously incomplete; it doesn’t mention the substantial literature discussing the problems with the “unidentified language” hypothesis, which have led most serious researchers to view this hypothesis as untenable. In addition, the M&Z results are also consistent with very different interpretations from the one that they reach.
In summary, this paper is at best inaccurate, and at worst likely to cause needless further confusion in a field that’s already complex by anyone’s standards.
What M&Z say
First, some quotes from the article that show what the authors are claiming, in their own words.
Quote 1: “We show that the Voynich manuscript presents a complex organization in the distribution of words that is compatible with those found in real language sequences. We are also able to extract some of the most significant semantic word-networks in the text. These results together with some previously known statistical features of the Voynich manuscript, give support to the presence of a genuine message inside the book.”
Quote 2: “The hypothesis that it is simply a nonsensical text either intended as a hoax or made up with any other purpose has debilitated [sic] in recent years, due to the increasing evidence of the text’s different levels of organizational structure.”
Quote 3: “Systematic studies supporting the hoax hypothesis have invariably overlooked the fact that any model for the hoax’s fabrication must, at the same time, explain in detail how such linguistic-like structures emerged from the process itself.”
Quote 4: “In summary, simple methods to generate random texts with some sort of local statistical structure may seem, under superficial scrutiny, rather convincing solutions to the problem presented by the Voynich manuscript. However, the statistical structure of the text at its various levels still requires an explanation that needs to go beyond reproducing local features like word forms or local word sequences. Here, we have contributed evidence of non-trivial statistical structure in the long-range use of words in the Voynich text. While the mystery of origins and meaning of the text still remain to be solved, the accumulated evidence about organization at different levels, limits severely the scope of the hoax hypothesis and suggests the presence of a genuine linguistic structure.”
All of these quotes contain serious problems, as discussed below.
The M&Z paper is based on two key underlying claims, set out in the quotes above:
Claim 1: There are non-random regularities in occurrences of words within and between sections of the Voynich Manuscript (VMS).
Claim 2: These regularities cannot be explained by the current hoax hypotheses.
How well do these claims stand up to scrutiny?
The claims and the evidence: the underlying statistics
Regarding the first claim, there has long been a consensus among the research community, including myself, that there are non-random features of “Voynichese” and that the statistics of Voynichese are similar to those of real human languages. For example, this was described by Gabriel Landini in 2001, whom M&Z cite, and was also described in detail by Jorge Stolfi, by Perakh, and others in numerous articles, not cited by M&Z. It’s surprising that the authors did not discuss this body of previous work in more detail. It’s a solid finding that’s stood the test of time; this particular claim is nothing new. It was, in fact, one of the starting points for my work, as described below.
A problem with this finding is that “similar to real languages,” is not the same as “identical to real languages”. Nor is it proof that the text in the Voynich Manuscript actually is a real language. This is a point to which we’ll return later.
Regarding the second claim, about the ability of the hoax hypothesis to explain this statistical similarity, the authors have missed a key point. This point was the topic of Andreas Schinner’s 2007 article, as well as much of my own work. I’ll quote from my book Blind Spot which came out earlier this year (pp 148 and 149).
“Stolfi had done a brilliant job of testing whether the manuscript had been produced the way almost all modern scientists would have put it together, if they had wanted to produce gibberish in large quantities. He checked whether the syllables in the Voynichese words had been randomly combined, and he showed that they hadn’t. What he and everyone else had missed was that when the manuscript was produced, nobody would be using random combinations, since the concept of randomness wasn’t discovered until centuries later.
“Instead, the hoaxer would be producing quasi-random combinations. It sounds like a nitpicky detail, but it’s a huge difference. At least one researcher has become rich by spotting that some lottery scratch cards use quasi-random rather than random numbers and working out how to pick the winning cards.”
The hoaxing mechanism that I described, the table and grille method, was designed specifically to produce text that wasn’t random in the strict statistical sense that’s at the heart of most standard statistical tests. Its mechanism meant that, for instance, the likelihood of two or more words co-occurring would be different from the likelihood expected by random chance. There’s a description of the table and grille method in my Scientific American article, here:
The significant feature of Schinner’s article was that he used his knowledge of advanced statistics to identify a statistical test that would handle this type of quasi-random distribution. His conclusion, when he applied this test, was that the text of the VMS was more similar to quasi-random meaningless text generated in the way I’d described than it was to the human languages he tested, or to the ciphertext that he tested.
In other words, when he used the appropriate statistical test, his results supported the hoax hypothesis.
So, the bottom line is that the authors have assumed that the hoax hypothesis depends on random combinations.
That’s a serious misunderstanding. In reality, my work is explicitly not based on those, but is instead based on quasi-random combinations, precisely because I had realised that random combinations didn’t explain the statistical features of Voynichese.
The authors are deeply mistaken in this assumption, and in the conclusions that depended on it.
Word distributions across sections of the VMS
What about the M&Z claim that the hoax hypothesis doesn’t explain or predict differences in word distributions within and between sections of the VMS? Similarly, what about the following claim elsewhere in their paper?
“In spite of recurrent claims in that sense, however, not a single piece of quantitative evidence has been advanced showing that such techniques are able to reproduce the features disclosed by statistical analysis of the text structure. It is also worthwhile remarking that the description of such features which the hoax’s fabricator should have been familiar with in advance were unquestionably out of reach of sixteenth-century mathematics.”
Again, there appears to be a significant misunderstanding; my work has explicitly addressed this topic in some detail, as described below.
The authors’ phrasing of “quantitative evidence” is unhelpful; my work showed qualitatively how the table and grille would produce various effects, and the M&Z wording about “quantitative” ignores those explanations.
The production mechanism and the word distributions
One of my recent blog articles examines syllable distributions across different sections of the VMS, and discusses how these are likely side-effects of the mechanism for producing text using the table and grille hoax method. There’s more about this in Blind Spot. It was also the topic of my talk at the Voynich centenary event in Italy. M&Z’s assertions in the previous paragraphs are simply mistaken.
Here’s the link to my previous blog article:
Here are the key illustrations of syllable distributions, from that article.
The first shows the distribution of these four common Voynichese syllables within the VMS.
Some syllable distributions in the Voynich Manuscript
The image is like a scaled-down picture of what the manuscript would look like if we printed it off as one huge scroll, and then went through it highlighting in red the syllable in question whenever it occurred. It’s clear that there are dramatic changes in the frequencies of the syllables at various points in the manuscript.
The next image, for comparison shows the distribution of two common syllables in a German book with footnotes in English.
The short section at the end of each column with a lower frequency for the syllables is where the English footnotes occur. Within both the German section and the English section, the distribution of common syllables is very consistent, with no dramatic changes of syllable frequency within the same language.
What this shows is that there are differences in syllable frequencies between sections of the Voynich Manuscript that are much greater than the differences in syllable frequencies between the German and English texts above. The blog article discusses this in some detail.
In that article, I described how this sort of abrupt change in frequency is just what would be expected if the VMS had been produced using tables and grilles, as an unintended side-effect of the technology. Contrary to what M&Z assert, it’s perfectly possible to produce sophisticated statistical regularities in texts more or less by accident, as a side-effect of the technology being used. This was the topic of my presentation for the Voynich 2012 centenary event in Italy, a major event within the Voynich research community.
As a couple of examples, described in more detail below, the variant of table and grille method I described could produce entropy levels that were similar (but probably not identical) to those found in real languages. It has produced meaningless gibberish text with similar entropy levels to Voynichese (Stolfi, pers. comm. 2004). It could also easily produce words with a binomial word length distribution (highly unusual in real languages, but a key feature of Voynichese). This is discussed in another article on this side, about unintended complexity.
Both these statistical effects would be side-effects of the method, and would quite possibly be neither noticed nor intended by a hoaxer.
So how could this type of “accidental sophistication” be produced? That takes us into the practical details of how the table and grille method works.
Tables and grilles
The table and grille method that I proposed works as follows.
It’s well known to Voynich researchers that Voynichese words consist of up to three components, namely a prefix, a root and a suffix. Some Voynichese words contain all three components; many contain just two, such as a root and a suffix; some consist only of one, such as just a root, or just a prefix. There are a lot of regularities within Voynichese about which syllables occur in which places; for instance, the “4o” syllable almost always occurs only as a prefix, whereas the “89” syllable usually occurs as a suffix, but quite often also occurs as a prefix.
What I spotted was that a simple, low-tech method could produce just this sort of effect. It works like this. You need a big table of gibberish syllables, looking something like this.
There’s a deliberate structure in the table. Here’s how it works.
The table consists of sets of three columns. The first column in each set contains Voynichese prefixes. The second column in each set contains only Voynichese roots. The third contains only Voynichese suffixes. One of the illustrations below shows this in more detail.
What you now do is to use a grille to select a batch of three syllables, namely a prefix, a root and a suffix. A grille looks like this.
It’s a piece of card with three holes cut in it. You now lay it over the table, like this.
The holes in the grille show three cells from the table. The first cell is the prefix cell (labeled “P” at the top of the illustration). It happens to be empty. The second hole shows a root syllable, and the third hole shows a suffix syllable. If you’re a hoaxer, you now write down the word that the grille has put together, onto your page of vellum. You then move the grille three columns across, to show another combination of prefix, root and syllable, and write that down.
You obviously don’t systematically move the grille across horizontally every time; if you do that, it produces regular sequences of syllables that a codebreaker will spot very quickly indeed. Instead, you move the grille unsystematically – maybe across three columns, and down one row for the next word, then across three columns and up two rows for the next word.
When you get to the bottom of the table, you just start again at the top, this time using a grille with a different pattern of holes, such as this one.
So far, so good. However, there’s a problem. Even if you keep using different grille patterns, you reach a point where you’re at risk of repeating your text if you keep on using the same table. So what do you do? An obvious answer is to create a new table, with the same gibberish syllables in about the same proportions, but with those syllables in different places on the table. You can now start again, using the same grilles as before, and create a whole different set of words from your new table.
That’s the theory. In practice, it’s horribly easy to make mistakes when you’re filling in a table by hand. For instance, you might lose your place, think that you’ve put in all the “4o” syllables you wanted, and then realise too late that you’d only put in half as many as you’d wanted. What do you do if that happens? Re-doing a table is boring hard work, especially if you know that you’re just producing meaningless gibberish anyway; there’s also the consideration that if you do begin again from scratch, you might well make a different mistake. So there’s a strong temptation just to use the new table as-is, and to accept that the pages you produce using it will have different syllable frequencies from the pages produced with the old table.
Which is just what you find in the Voynich manuscript; sudden transitions in syllable frequencies between different sections of the manuscript. These are hard to explain as part of a language, especially when the transitions are bigger than the transitions between English and German. But they’re very easy to explain as unintended side-effects of the table and grille method.
There are other features that you get as unintended side-effects of the table and grille. Suppose that you’ve got a couple of rare root syllables in the top left part of your table. This means that you’ll tend to get words containing those root syllables occurring on the same page as each other when you write down the words that you create with the grilles. It won’t always happen; sometimes the grille will show only one of those words, sometimes neither, but you will get them occurring on the same page at levels that are above random chance levels, precisely because this method generates quasi-random combinations as opposed to truly random combinations.
You can also end up producing the same entire words containing those rare root syllables on more than one occasion, via several routes; for instance, you might happen to reveal the same word twice by accident because of the deliberately non-random movement of the grille, or the same root syllable might happen to be combined with two different instances of the same prefix syllable.
One interesting side-effect of how you fill in a table is that you get variations in word length and repetitiveness depending on how systematic you are in filling in the table. For instance, if you put the syllable “4o” regularly into every fourth prefix cell, you get very different output from when you put the syllable “4o” into approximately every fourth cell – for instance, a gap of one cell on one occasion, and of seven cells on another occasion.This is something that I investigated with my student Laura Aylward. Here are two examples, both produced using software that simulated the table and grille technique, filling in the tables using the identical list of gibberish syllables and of syllable frequencies, but varying how systematically the syllables were located in the tables. The full stops show word boundaries; two full stops next to each other, or a full stop at the start of a line, show where the grille revealed only blank cells in all three holes, which occurred quite often in the first sample.
Aylward text samples
It’s apparent even without statistical analysis that these two samples are very different in word length; in other samples, we were also able to produce substantial differences in repetitiveness, which would lead to marked differences in entropy in the output texts.
In a related piece of work, an email from Jorge Stolfi in 2004 said that he had calculated entropy values for text that I had produced by hand using table and grille technique; he had found that those values were similar to those for Voynichese.
I’ll put the Aylward simulated text onto the Hyde & Rugg web site when I get time. It was computer generated, so it doesn’t have some of the subtleties that you get when using the manual version of table and grille, but it demonstrates the concept neatly.
Adding other complexities in a meaningless gibberish hoax
If you’re a moderately sophisticated hoaxer, you can do a lot more, in terms of producing plausible regularities. It’s easy, for instance, to add in meaningless gibberish “words” that look as if there’s cross-referencing between pages of the manuscript – for instance, you use one “word” at the start of a page so it looks like a title, and then in a later page you add that same word somewhere in the main text of the page, as if you’re referring back to the earlier page. From my experience of trying this out, it would only take about a couple of hours to set up this type of cross-referencing for a two hundred page manuscript. It’s not exactly rocket science in it terms of the skill required to do it, but it looks very plausible, and it would show up as exactly the sort of finding that M&Z are claiming as evidence for real meaningful text.
The M&Z conclusion: the “linguistic structure” argument
The M&Z paper reaches the conclusion that there is evidence suggesting “the presence of a genuine linguistic structure”. This conclusion needs to be interpreted very carefully. The meaningless gibberish produced using the table and grille method has linguistic structures in it, at both the level of syllable structure within words and at the level of which words tend to occur where on a page, and which words occur in which sections of the text. However, that structure doesn’t reflect any real meaning; it just reflects regularities in the gibberish, some of which are intended, and some of which are accidental side-effects of the table and grille method itself.
There are also some serious problems with the “unidentified human language” hypothesis, which the M&Z article doesn’t mention. There has been a lot of discussion of this issue, and the general consensus in the Voynich research community is that if Voynichese is a real language, then it’s very different from any other known language. The differences are so pronounced that hardly any serious researchers think that this explanation is viable.
One example is the absence of word order in Voynichese. Real languages have regularities in word order. They may have some flexibility, but they also have a lot of regularities. In English, for instance, if you saw the words the, black and cat next to each other, you’d expect to see them in that order. You wouldn’t expect to see cat the black or black cat the. Yes, just once in a while you might see them in an unusual order, but the key point is that you would know it was unusual. Voynichese doesn’t have that sort of regularity; any word can occur next to pretty much any other word. That’s very unusual among human languages.
Also, in human languages it’s unusual to see the same word repeated, especially if the word is common – it would be the equivalent of “she she” in English. In Voynichese, however, this happens frequently; for instance, the common Voynichese word transcribed as dain in the EVA transcription system quite often occurs twice, and sometimes three times in a row, and the word transcribed as qokedy occurs four times in one six-word line.
The lines in the Voynich Manuscript are another odd feature. It’s long been recognised among Voynich researchers that the line is a significant unit within the manuscript; for instance, some characters are more common in one part of a line than others, and the second half of each line tends to be a different length from the first half. That’s very different from natural languages, where usually lines are just an arbitrary division of the text. The lines in Voynichese don’t show any of the features usually associated with poetry, such as end rhyme, or alliteration or scansion, so there’s no obvious explanation for why Voynichese should show this feature.
The “line as a unit” feature makes sense, however, if the manuscript was created using table and grille technique. The difference in word length between the first and second halves of lines is what you’d get if you filled in the table’s columns according to the length of the nonsense syllables you were using (for instance, starting with the shortest ones) and didn’t distribute them evenly across all the columns, so you ended up with (for instance) a higher proportion of long syllables in the later columns. Similarly, if you had a disproportionate number of syllables containing a particular character within a single column, then that character would tend to appear more often at a particular point in a line; for example, if the character appeared in the first “prefix” column of your table, then it would tend to appear in the first word of the line that you produced using that table (assuming that you’re starting each new line of text by moving your grille to the leftmost column of the table). In reality, these effects would probably be obscured by a combination of human error and of deliberate policy if the text was being produced by a knowledgeable hoaxer, who might begin a new line of text with the grille in the middle of the table, to hide just this sort of regularity (which would be a give-away if spotted by a knowledgeable analyst).
Another feature of Voynichese is that its word lengths form a binomial distribution, which is very unusual among real languages – it occurs in some Asian languages, but it’s very rare elsewhere. That might look like something that a hoaxer centuries ago would never think of hoaxing. However, it’s exactly what you’d expect as a completely unintended by-product if a tidy-minded hoaxer decided to use a tidy, symmetrical set of short, medium and long syllables for the prefixes, roots and suffixes in their meaningless gibberish. The binomial distribution would follow as a consequence, purely as a result of the mechanism that the hoaxer was using. I’ve described this in some detail in Blind Spot and in another article on the Hyde & Rugg blog site.
Yet another unsual feature of the Voynich Manuscript is the long-recognised presence of two “dialects” – Voynich A and Voynich B – which are very different from each other. However, they do not form an absolute divide; some sections of the manuscript show features of both A and B. Again, this is hard to reconcile with any known language; again, this is not mentioned as a potential objection by M&Z.
In summary, it’s been generally accepted among serious Voynich researchers that the “unidentified language” hypothesis has too many problems to be plausible. It’s unfortunate and surprising that M&Z do not discuss this topic, and its implications for their claims and conclusions.
It’s conceivable that the Voynich Manuscript might contain something that’s similar to natural language, such as an artificial language, of which several have been invented by philosophers and linguists, Esperanto being the most successful example. Again, there is a literature on this, and again, it’s not discussed by M&Z; again, the consensus among serious Voynich researchers is that this explanation is not plausible, for much the same reasons that the “unidentified human language” explanation is not plausible.
Similarly, the hypothesis that the VMS contains some form of aberrant human language, such as a schizophrenic rant, or speaking in tongues, runs into problems with the statistics of the text (particularly the binomial word length distributions, discussed earlier). These statistics can easily be explained by the hoax hypothesis as simple side-effects of the hoaxing mechanism, as described above, but are not easily explained by an “aberrant human language” explanation.
Another issue that M&Z do not address involves the implications of linguistic structures for possible codes. It has long been recognised that the presence of identifiable “words” within Voynichese is a severe constraint on the types of code that could be considered possible candidates. Most coding systems deliberately break up the text into four-letter or five-letter groups of characters, specifically so that would-be codebreakers can’t use word lengths as an easy way in to cracking the code. (For instance, if you were a codebreaker working on an enciphered text that was originally written in English, and you saw that one cipher character often occurred on its own in a one-letter word, then it wouldn’t be hard to work out that the cipher character probably stood for either “I” or “a”.)
Here’s a famous example of a modern-style code, the D’Agapayeff cipher.
It’s in neat, regular groups of five characters, with not a single identifiable word in sight. That’s how most strong codes work. There are a few ways of hiding a fairly strong code within text that contains identifiable words, but nobody’s found any sign of those approaches having been used within the Voynich Manuscript.
There are also other strands of relevant evidence which M&Z don’t mention, but which are highly relevant to this topic.
One is the absence of evidence for corrections in the VMS. There are a handful of places where text has been overwritten, but there are no examples of words being crossed out, or corrections added above a line, or of text being scraped off the vellum and then replaced with fresh text. The VMS is over two hundred pages long. It’s hard to imagine that anyone could write that much text without a mistake. Even Torah scribes, who are famous for their painstaking accuracy, make mistakes, which they correct by scraping out the mistake and then re-writing the correct text.
The implication is that either whoever produced the manuscript didn’t make any mistakes, which is extremely unlikely, or that they didn’t care about the mistakes they made. That’s hard to reconcile with a code or with meaningful language, but it makes a lot of sense if the manuscript is a hoax that contains only meaningless gibberish.
M&Z assert that their evidence is indicative of “genuine linguistic structure” but they do not explain precisely what they mean by this. This assertion gives no insights into just what form of language or code, if any, would be consistent with the unusual features of Voynichese described above. Given that previous researchers have grappled with precisely this problem for over a century without success, this is a serious omission.
Summary and conclusion
Unfortunately, the M&Z paper is a piece of work which will probably add confusion to an already complex area. It is based on key claims that are inaccurate or mistaken. The evidence that they present is consistent with numerous previous articles on the same topic, and can be explained by the hoax hypothesis. The paper reaches a conclusion that is not well supported by the evidence, and that faces numerous long-established objections that the authors do not address.
The paper would also have benefited greatly from more reference to the substantial literature on this topic, and from a more in-depth understanding of what was being argued by previous researchers. I hope that the authors’ future work will be a more positive contribution.
There’s a lot more detail about my work on this area in my book with Joe D’Agnese, Blind Spot. I’ll put some more background material and resources about my Voynich work online when time permits.
My article about accidental complexity, and producing binomial word length distributions without realising it, is here:
My article about textual structures in the Voynich Manuscript is here:
Blind Spot is available here:
If you want to try your luck on a couple of real codes that haven’t been cracked yet, you’re welcome to try these.
They’re codes that I’ve created, both of which deliberately break conventional assumptions of most modern codes. Neither of them is a super-code, but they should provide some entertainment. One of them, the Ricardus Manuscript, is deliberately modeled on the Voynich manuscript.
There’s an excellent recent overview of Voynich Manuscript research here:
A comprehensive overview of Voynich Manuscript research is available on René Zandbergen’s site:
Rich SantaColoma’s site contains some extremely interesting material and insights:
There’s a summary of the broader body of my work here: