Analysis Section ( 2/5 ) - Character statistics
This page will first list a number of observations about the Voynich MS character statistics that may be found in the printed literature, and then concentrate on more quantitative analysis results.
2.2 Observations in the printed literature
Tiltman (1967) (1)
(Note: Tiltman treats
f as a variant form of
p as a variant form of
t. In the following, characters
or sequences in parentheses represent such variant forms).
appear to be infixes of
ch. The variant
symbol represented by
m appears most
commonly at the end of a line, rarely anywhere else.
Paragraphs nearly always begin with
(p), most commonly in the second
variant forms, which also occur frequently in words in the top lines of paragraphs where there is some extra space.
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
Hence my belief that these two have some separative or conjunctive function. (I have to admit, however, that
y also seems sometimes to take the place of o before
k or t (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
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.
l, usually preceded by a or o, is very commonly followed by d, much less commonly by t (p), with or without a space between.
Speaking generally, each character behaves as if it has 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.
Currier (1976) (3)
- These letters: o, d, y, s all seem to start with a 'c'-curve. [...] The forms all have counterparts starting with i: j , l , r, etc. We also have a = e + i.
- The final letters (that is, the ones I call finals, although they can also occur elsewhere) are in two series, one preceded by a and the other by
o, giving a series of sixteen:
n in iin iiin,
l (il) (iil) (iiil),
r ir (iir) (iiir),
m im (iim) (iiim).
The ones in parentheses are very low-frequency; the others all occur with respectable frequency. In addition, these combinations of symbols which appear as finals may occur separately — 'unattached finals,' as I call them. A large number of unattached finals is a characteristic of 'Language' B, and not 'Language' A, by the way.
- You can pick out resemblances between Latin abbreviations and other alphabets for most symbols except for the series t , k , p , f. [...] The last two [...] appear 90-95% of the time in the first lines of paragraphs, in some 400 occurrences in one section of the manuscript.
- One might conclude that p , f
are an elaborate form of t , k , with the same value. [...] But, not true! These two letters
p , f are not the same as those two t , k , as the statistics show. The letters t , k are followed anywhere in a 'word' by our little friend e about half the time (say 750 out of a total of 1500), including initially. These two, p , f, are never, ever, anywhere
in the manuscript, followed by e. [...] Therefore, p , f are not aberrant or variant forms of t , k
Currier's first observation has been noted independently by several people, and was taken up recently by Brian Cham, who developed the
out of it.
D'Imperio (1978) (4)
- The split gallows seem only to occur on first lines of paragraphs, and in labels.
- The same "word" may be repeated two, three or more times
- Many "words" differ by only one character and are found in each other's vicinity
Certain symbols occur characteristically at the beginnings, middles or ends of words, and in certain preferred sequences
- Certain symbols appear very rarely, and only on certain pages
There are very few doublets. Primarily: e
or i and occasionally also
There are very few single-letter words in the running text, primarily
Prefix-like elements are found in front of certain "words" that also occur commonly without them. Such prefix-like elements are:
- The symbol q almost always
precedes o, connected to it by an extension of the crossbar of the 4. This combination is found almost always at word start.
On most herbal folios, the first paragraph usually starts with
p or f,
usually immediately followed by ch,
Labels very rarely start with t,
or f . Instead, they often start with
y or sometimes
s or ch.
2.3 Character frequencies
Oddly enough, there is no consolidated set of this most basic statistic, due to the use of different transcription alphabets and different transcription sources. Several examples may be found in different sources.
One example is found in D'Imperio (1978)
(see note 4),
Fig. 28 on p.106, from several sources but none covering the entire MS text.
As a very short summary, the single character frequency distribution in the most important transcription alphabets is qualitatively similar to that of texts in normal European languages.
2.4 Vowel/consonant detection
An algorithm for detection of vowels and consonants was designed by B.V. Sukhotin, and Jacques Guy has experimented with this in the 1990's. He published a first English summary of the algorithm in Cryptologia
(see note 5),
. Results indicated that the characters that look like vowels (a,
o, y) also appeared statistically like vowels, though the confidence of the result was not very high. There is also a recent
>>blog entry related to running Sukhotin's algorithm on individual pages of the MS.
The concept of entropy has been explained in the introductory page and the reader should have read this introduction in order to have the full advantage of the following.
The entropy of the Voynich MS text was first analysed in detail by the Yale professor William Ralph Bennett Jr.
He develops the concept in many easy steps and in more detail than in the above-mentioned introductory page. He first analyses texts in common European languages and then addresses the Voynich MS with his own transcription alphabet
[...] the statistical properties of the Voynich Manuscript are quite remarkable. The writing exhibits fantastically low values of the entropy per character over that found in any normal text written in any of the possible source languages (see Table 5). The values of h1 [i.e. first order entropy - RZ] are comperable to those encountered earlier in this chapter with tables of numbers. Yet the ratio h1/h2 is much more representative of European languages than of a table of numbers alone.
His computed values are as follows
||3.91 - 4.14
||3.01 - 3.37
||2.12 - 2.62
He finally identifies one language with a set of similarly low entropy values, namely Hawaiian, but is quick to point out that this does not make much sense.
Many more statistics related to entropy may be found in an on-line paper by
>>Dennis Stallings: understanding the second-order entropies of Voynich text.
This basically confirms the results of Bennett, and may be useful to those who have no access to a copy of Bennett's book.
An alternative method to compute entropy is the so-called 'commas' method, which has been used by Jim Reeds and later by Gabriel Landini. This will be included here shortly.
Jorge Stolfi has set up a tool to visualise the number of bits of entropy per character in the following location:
>>Jorge Stolfi: where are the bits?
Finally, I wondered about the question how it is possible that the character and digraph entropy of the Voynich MS text is so much lower than that of, say, Latin, while the word entropy (about which something will be said
is similar. This is addressed at this page:
From digraph entropy to word entropy,
which may be a bit hard to understand by itself (and I should re-do it). The short summary is that, counting from the start of each word, the entropy per character is higher for normal languages, but also drops much faster.
There is a critically important conclusion to be drawn from the first- and second-order entropy values reported by various authors. As already mentioned in the analysis section introduction, the entropy values do not change when one consistently replaces characters by others, i.e. in a simple substitution cipher. This tells us something about the possible plain text of the Voynich MS.
- It could be that the text is meaningless, i.e. there is no plain text language, and the anomalously low entropy is the result of whatever process was used to generate the strings of characters
- If there is a plaintext that was encoded using a simple substitution, then this plaintext must have the same anomalously low entropy values. This then excludes most of the typical languages that might be assumed for a European MS of the 15th Century. In fact, no candidate plaintext language could yet be identified. Hawaiian, the one identified by Bennett, does not match for other reasons (as will become apparent in later pages). Some languages like Hebrew, the various Arabic languages, Persian, Armenian etc. have not yet been tested quantitatively, to my best knowledge.
- If there is a plaintext in one of the known languages used in European MSs of the 15th Century, then this text must have been modified by some process changing the statistics quite drastically. This change is indeed so drastic that it is no longer possible to identify the plaintext language from the Voynich MS text, and any attempts of this nature will be invalid.
In general, and quite briefly, any attempt to translate the Voynich MS into something meaningful in Greek, Latin, English, etc. using a simple substitution must fail. As this is the first thing most people will try, we can begin to understand how the MS has resisted all translation attempts.
However, there is much more to this, as we shall see in the following
2.6 Other material
2.6.1 Line-initial/final and word initial/final character properties
Following observations are paraphrased from Currier's papers
(see note 3).
- In those pages where the text is presented linearly, the line is a functional entity. The following three bullets clarify this general observation
- 1: the frequency counts of characters at beginnings and endings of lines are markedly different from elsewhere. There are some characters that may not occur initially in a line. There are others whose occurrence is about one hundredth of the expected
- 2: the ends of lines seem to contain meaningless symbols: little groups of letters which don't occur anywhere else
There is one symbol
that occurs at the end of the last word of a line 85% of all of its occurances.
- 3: there is not one single case of a repeat going over the end of a line to the beginning of the next
- Skewed frequencies at beginnings of lines may be illustrated by the two letters ch and
Sh. If its occurrence as an initial were random, we would expect it to occur one seventh of the time in each word position of a line. Actually, it is a very infrequent word initial at the beginning of a line, except when there is an intercalated o. This applies only to 'Language' A.
- The 'ligatures' [ cKh cTh cFh cPh ] can never occur as paragraph initial, and almost never line initial.
The obsernation of Currier that the line appears to be a functional unit was further analysed in 2012 by Elmar Vogt, for which
One of the most obvious features he shows is that, when using the Eva alphabet, the first word tends to be on average 1 character longer than the second and following words.
2.6.2 Location of gallows (and other) characters
Julian Bunn highlighted the positions of the gallows characters on each folio of the MS in
>>a page at his blog, in colour coded graphics. They show a peculiar vertical pattern, which may be related to the observations of Andreas Schinner in his 2007 cryptologia paper
which is discussed in a
The following page by Sean V. Palmer gives a very visual representation of the feature that many characters have very preferential positions inside the words of the MS:
>>Voynich MS glyph position stacks.
- See Tiltman (1967).
- For Tiltman's roots and suffixes,
Additional observations are listed there.
- See D'Imperio (1978).
- See Guy (1991), also >> online here.
- See Bennett (1976), Chapter 4, pp. 103-198.
- For which see here.
- On p.193
- Combining Table 5 on p.140 and Table 12 on p.193
- For the curious reader: here.
- This statement is not fully understood, and it seems worthwhile to understand what he means. The only character that typically occurs at line ends is mentioned separately, so perhaps he means character combinations or groups..
- Currier almost certainly means m.
- See Schinner (2007).
Copyright René Zandbergen, 2016
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Latest update: 26/01/2016