Qokeey and qokeedy in the stars section

Rene Zandbergen has pointed out that the word qokeey is very common on some pages of the stars section (ff 103r-116r) and rare on others. I believe the pattern discovered by him can be summarised thus:

• If a paragraph contains the word qokeey, there is a 38% chance that the next paragraph will contain the word qokeey.
• If a paragraph contains the word qokeey, there is a 40% chance that qokeey occurs more than once.
• If the current word is qokeey, there is a 6% chance that the next word will be qokeey.

High or low frequency of qokeey appears to be a feature of pages and sheets within the quire. In the following table, pages in the same row are on the same side of the same sheet of vellum. The string of numerals after each page number represents the paragraphs on that page and the occurrences of qokeey in each one (i.e. the first paragraph of f 103r has one occurrence of qokeey, the second has one, the third none and the final paragraph has four occurrences.

f103r	1100110004012211344	f116v	(not relevant)
f103v	40010012121000	f116r	0020010020
f104r	0000000000001	f115v	0100000000000
f104v	0000020010011	f115r	0000000010000
f105r	210000000000	f114v	000000000000
f105v	0000000000	f114r	00000000000000
f106r	000000100000000	f113v	010000001000001
f106v	000000001001200	f113r	00100100000000011
f107r	001000000000000	f112v	1002101000000
f107v	010200001000134	f112r	12501101000001
f108r	0200100100010301	f111v	1111000000010001210
f108v	01032010030233120	f111r	21210222120012111

A	Number of paragraphs: 331
B	Number containing qokeey: 99
C	Number containing qokeey more than once: 37 (as percentage of B: 37)
D	Number containing qokeey.qokeey: 10
E	Cases where previous paragraph contained qokeey: 44 (as percentage of B: 44)
F	Occurrences of qokeey: 156
G	Occurrences of qokeey.qokeey: 10 (as percentage of F: 6)

The word qokeedy conforms to a similar but not identical distribution.

f103r	0000000200002210210
f103v	11101100000000	f116r	0011000010
f104r	1100000000001	f115v	1000013100000
f104v	2010000000000	f115r	0110000010001
f105r	110000001000	f114v	100000000000
f105v	1000000000	f114r	00100001000000
f106r	000000210000001	f113v	010100000110000
f106v	000000000100001	f113r	00000100000000000
f107r	011000000000010	f112v	2022021002100
f107v	000000001010001	f112r	11010001000000
f108r	1100010101011225	f111v	0100000000000000100
f108v	12130001323521220	f111r	01021310121011010

A	Number of paragraphs: 331
B	Number containing qokeedy: 97
C	Number containing qokeedy more than once: 27 (as percentage of B: 27)
D	Number containing qokeedy.qokeedy: 9
E	Cases where previous paragraph contained qokeedy: 41 (as percentage of B: 42)
F	Occurrences of qokeedy: 135
G	Occurrences of qokeedy.qokeedy: 10 (as percentage of F: 7)

One possible explanation of this is that qokeey and qokeedy are names or reflect the occurrence of names in the underlying text.

Internal structure of the 'words'

Some 90 percent of the words in the B section can be generated from the regular expression

[dklprst]{0,1}[oa]{0,1}[lr]{0,1}[fkpt]{0,1}[SC]{0,1}[eE]{0,1}[dFKPT]{0,1}[ao]{0,1}[mnlM]{0,1}y{0,1}

subject to certain restrictions:

• q may only be followed by o or e
• the sequences pe and fe are forbidden
• the sequences le and re are forbidden
• the sequence rk is forbidden
• the sequences em en el em en er are forbidden
• only aiin ain al am an ol y (and very occasionally d) may be final

The transcription used here is a modified version of EVA, with S for sh, C for ch, E for ee, F for cfh, K for ckh, P for cph, V for cvh, m for iin, n for in and M for m.

It is almost as if the Voynich language only contained words whose letters are in alphabetical order. The pattern emerges very clearly if consecutive words of the manuscript are printed in vertical columns with gaps inserted to indicate the null occurrence of a character. I have generated a vertical version of the first 25 lines of f 103r (the beginning of the stars section): the program was instructed to ignore word divisions but has mostly restored them from the regular expression).

Were the letters enciphered in order? The letter m

• m is a variant of another cipher letter. am looks much the same as al and has much the same distribution as ar al aiin ain (particularly the last two, which are never initial in a word).
  • But ar al aiin ain also occur finally in a line, and on the same page as am. It therefore seems not to be a variant of these four finals, but another letter in the same group.
• m is an abbreviation used where space is tight at the end of a line. am has a similar distribution to ali (common at the end of a line) and might be taken as an abbreviation of it.
  • But it occurs at the end of a line on f. 81r 19, where there is no illustration in the margin and ample space for the line to continue without abbreviation.
• m is a distinct individual letter which may appear anywhere in the plain text but is forced to the end of a line by the encipherment.
  • If the letters of the Voynich ms are encipherments of individual letters of a plaintext in the Roman alphabet, it is not possible that they have been enciphered in the original order. I speculate that m is an enciphering of a rare plaintext letter such as z and that the encipherment called for this letter to be entered into the ciphertext last of all.

Is it an anagram cipher?

Here is a transformation of plaintext into ciphertext which explains certain features of the Voynich "language".

1. Divide a plaintext into lines
2. Sort the words of each line into alphabetical order
3. Sort the letters of each word into alphabetical order

1. one thing led to another thing last night
2. another last led night one to thing thing
3. aehnort alst del ghint eno ot ghint ghint

1. The frequency distribution of words and letters is the same as in the natural language plaintext, but the distribution of two-letter groups and two-word groups is significantly altered.
2. Words at the beginning of a ciphertext line tend to start with letters at the beginning of the alphabet. Compare the high frequency of Voynich "d" at the beginning of a line.
3. If a letter near the end of the alphabet has a tendency to be word-initial in the plaintext (e.g. German "w"), it will have a strong tendency to be the last word in a line. Compare the high frequency of Voynich "m" at the end of a line.
4. The ciphertext versions of frequent words will tend to cluster together in a line. That is, where a word such as "thing" occurs twice in the plaintext line (as in the above example) the two word sequence "ighnt ighnt" will occur, but "ighnt" may also occur elsewhere in the line as an anagram of "night".
5. A one-letter word of ciphertext can only be an anagram of a single word of plaintext ("a" can only be an anagram of "a") and a two-letter word of ciphertext can only be an anagram of two possible words of plaintext ("et" can only be an anagram of "et" and "te"). This means that you cannot have a ciphertext line of the pattern "... i ... i ... " or of the pattern "... et ... et ... et ...". This principle largely holds good in the Voynich text: there are only six exceptions in the corpus of Currier's language B.

1. Voynichese words do not conform to a strict alphabetical ordering of letters (there are quite a lot of words of the pattern dshedy).
2. Voynichese words have a strong tendency to contain only one instance of a given letter, unlike any obvious candidate language for the plaintext.
3. The enciphering described is not unambiguously reversible (however I think it would work as a private aide-memoire, or as a means of establishing priority like Galileo's well known anagram announcing his discovery of the phases of Venus).

Here is an extract from a well known English novel modified in the way I have described:

adn as cddeeirt for efnortu adforrw i em my now aprt dehpsu amsw asw

adn adn bmoott by cdlou dopr eefl i egls elt my no efnot deit dinw

abel almost adn btu dfnou egno i i eglnor no egglrstu ot asw ehnw

aabdet adn by dehpt chmu my eflmsy morst eht hist eimt asw hiintw

a beefor cdeiiltvy got i i eilm aenr allms os ahtt eht ot adeklw asw

abotu accklo 'ccdejnortu eghit eeginnv i in ehors eht eht asw chhiw