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A Well-kept Secret of Mediaeval Science: the Voynich manuscript

Gabriel Landini (Lecturer in Analytical Pathology, School of Dentistry) and René Zandbergen (System Analyst and Consultant in the Space Sector, Darmstadt, Germany).

Note: this article first appeared in the July 1998 issue of 'Aesculapius', the journal of the University of Birmigham Medical and Dental Graduates Society, and has been published here with the kind permission of the editor.

Introduction

Imagine a book written in an unknown alphabet, in an unknown language, at an unknown date and place. Could such a book be read? Could one retrieve the information it contains, if any? This is not a trivial question and it has baffled historians and scientists alike for most part of this century, in the case of a particular mediaeval document, called "the Voynich manuscript".

Brief history

In 1912, Wilfrid M. Voynich (a rare book collector) bought a number of mediaeval manuscripts from an undisclosed source in Europe. Among these was a 235-page manuscript written in an unknown script and what appears to be an unknown language or a cipher. Understandably, Voynich wanted to have the mysterious manuscript deciphered and provided photographic copies to a number of experts. However, the book still remains unread. Since then, the manuscript has been known as the "Voynich manuscript".

It was eventually known that Voynich bought the manuscript from the Jesuit college at the Villa Mondragone, Frascati, in Italy and that it originally belonged to the Collegium Romanum. Attached to the manuscript was a letter in Latin dated 1666 (or 1665) from Johannes Marcus Marci of Cronland, rector of the University of Prague, to Athanasius Kircher S.J., a Jesuit priest and scholar in Rome, offering the manuscript for decryption and mentioning that it was bought by Emperor Rudolf II of Bohemia (1552-1612) for 600 gold ducats. The letter also implied that Kircher knew about the manuscript and had exchanged a letter and some transcribed portions with the previous owner who did not want to send him the whole manuscript. The letter further mentioned that Roger Bacon (the Franciscan friar who lived from 1214 to 1294) had been considered as the author, but in any case the manuscript had not been read.

A few pieces of circumstantial evidence connect the manuscript with John Dee (1527-1608) who visited the court in Prague in 1582-1586 and was an admirer of Bacon and collector of his mGnuscripts. Dee stated in his diary that he had 630 ducats in October 1586, (Keynes,1931) and his son remembered that while in Bohemia, his father owned a "…booke containing nothing butt Hieroglyphicks, which booke his father bestowed much time upon: but I could not heare that hee could make it out" (Browne, in Keynes, 1931). Could this be the manuscript? No other known manuscript fits this description. Furthermore, according to A. G. Watson (Roberts & Watson, 1990), the foliation numbering is in Dee's hand.

On the lower margin of the first folio of the manuscript, under special illumination, the erased ownership signature of Jacobus de Tepenecz and the word "Prag" were found. Tepenecz was the director of Rudolf's botanical gardens and he must have owned the manuscript between 1608, when he received his title "de Tepenecz", and 1619 when he fled from Prague. There is uncertainty as to whether he owned it before or after emperor Rudolf (who abdicated in 1611).

At this point the story is not very clear. The person who would not send the manuscript to Kircher is almost certainly the little-known alchemist Georg Barsch, who bequeathed his entire alchemical library to Marci. It is not fully certain what happened with the manuscript between the time of Marci's gift and 1912. Most probably Kircher, lacking the time to study it, filed it with his other correspondence. It was found by P. Beckx S. J. (1795-1887, general of the society of Jesus from 1853 to 1883), who seems to have rescued it from confiscation by Vittorio Emanuele's soldiers in 1870, together with other valuable manuscripts (among which was Kircher's collected correspondence). This collection, finally, was sold in 1912, in part to the Bibliotheca Apostolica Vaticana and in part to W. Voynich.

The book was then bought by H. P. Kraus (a New York book antiquarian) in 1961 for the sum of $24,500 and later valued at $160,000. Unable to find a buyer, he donated it to Yale University in 1969, where it remains to date at the Beinecke Rare Book and Manuscript Library with catalogue number MS 408.

Description of the manuscript

The manuscript counted at least 116 folios, of which 104 remain. The folio size is 6 by 9 inches, but some folios are two or three times that size and are folded. There is one large composite of six times this size (18 by 18 inches). Both the illustrations and the script of the manuscript are unique. As long as the script cannot be read, the illustrations are the only clue about the nature of the book. According to these illustrations, the manuscript would appear to be a scientific book, mostly an illustrated herbal with some additional sections.

What is commonly called the Herbal section fills about half the volume. It consists of page-filling drawings of single plants with short paragraphs of text written beside them. Occasionally, two plants are shown on a single page. The layout is similar to that of traditional illustrated herbals. While some of the drawings do resemble existing plants, most of the drawings would appear to be fantastic compositions. Figure 1 shows a typical example (fol. 53r).

Following is a section with Astronomical and so-called Cosmological drawings. The astronomical pages feature drawings of circular design, with images of the sun, the moon and arrangements of stars. Cosmological drawings have a similar layout but include other more abstract features such as rosettas, tubes and pipes. A section of the astronomical pages (which is usually called the Astrological section) has illustrations of the zodiac, surrounded by circles of mostly nude female figures holding stars.

The next apparent section of the manuscript has been called Biological as it contains some odd, perhaps anatomical, drawings including pipes and tubes resembling blood vessels, together with

human figures, mostly nude females, similar to the ones in the astrological section. There have been suggestions that the illustrations represent medicinal baths. Figure 2, showing fols. 77v and 78r, is from this section.

Following, there are a few more herbal pages and a different section which has been called Pharmaceutical, as it includes pictures of labelled containers and many small parts of plants, mainly roots and leaves.

Finally, the manuscript closes with what has been called the Recipes section, as it contains many (324) short paragraphs, each with a star in the margin (on average 15 per page).There have been suggestions that this section was some sort of calendar (or almanac), although adding the two missing folios the total number of paragraphs would probably be higher than 360 or 365.

Figures 1 and 2 clearly show the style of the illustrations and the script used in the Voniych Manuscript. Some characters resemble those from the roman alphabet (a, o, c, n, m), some are like numbers (2, 4, 8, 9) and others are similar to symbols used as Latin abbreviations or in alchemy in the Middle Ages. In addition there are a few instances of extraneous writing (different from the main body of the manuscript), not in "Voynich script" and perhaps added later, such as the names of the months in the astrological section (in an unidentified Romance language) and three incomprehensible lines on the last folio, suggesting a key to decryption, or an attempted decryption by one of the previous owners.

The character set is discussed in more detail below.

Figure 1. A photostat of folio 53r from the Friedman collection. Folio 53r is part of the "herbal" section of the manuscript. Note the similarity of some of the characters to roman letters (c, a, e, i, o) and numbers (4, 8, 9). The number page (53) is supposedly in John Dee's hand. Reproduction by courtesy of the Marshall foundation, Lexington, Virginia.

Figure 2. A photostat of folios 77v and 78r from the Friedman collection. Folios 77v and 78r are part of the "biological" section. The drawings have been associated with sketches of anatomical organs: ovaries, uterus and blood vessels (top of f77v), intestinal tract (f77v, right) and male reproductive organs (Guy) (left). The numbering next to the text was added to the photostats probably by Friedman's team and it does not appear in the original. Reproduction by courtesy of the Marshall foundation, Lexington, Virginia.

Past attacks to the decipherment

When the manuscript was first shown to expert cryptologists, they thought that solving it would be easy as the text was composed of "words", some of which were more frequent and occurred in certain combinations (Kahn, 1967). This soon turned out to be a mistake; the text could not easily be converted into Latin, English, German or a host of other languages which might possible be at the base of this document.

A first "solution" was announced in 1919, by William Romaine Newbold (Newbold, 1921), who caused a sensation by claiming that the manuscript did indeed contain the work of Roger Bacon and that Bacon had known the use of the compound telescope and microscope, seeing the spiral structure of the Andromeda galaxy (!) only visible with modern telescopes and cell structures unknown in the 13th Century. This solution was finally disproved (Manly, 1931).

The attempts to crack the code, however, were not over. In 1931, Mrs. Voynich took a photostat copy of the manuscript to Catholic University in Washington where Fr. Theodore Petersen reproduced it photographically and started a complete hand transcription of the manuscript, with a card index to the words, and lists of concordances. The transcription alone was reported to have taken him 4 years. Unfortunately, it is not known what conclusion, if any, he reached.

In 1944, Hugh O'Neill, a renowned botanist at the Catholic University, identified various plants depicted in the manuscript as New-World species, in particular an American sunflower and a red pepper (O'Neill, 1944). This meant that the dating of the manuscript should be placed after 1493, when Columbus brought the first sunflower seeds to Europe. However, the identification is not certain: the red pepper is coloured green and the sunflower identification is equally contested.

Other people involved in the study of the manuscript were prominent cryptologists such as W. Friedman and J. Tiltman, who independently arrived at the hypothesis that the manuscript was written in an artificial, constructed language. This was based on the structure of the "words" as described below. Such artificial languages were devised at least a century after the probable date of the Voynich manuscript. Only the 'Lingua Ignota' of Hildegarde of Bingen (1098-1179) predates the Voynich manuscript by several centuries, but this language does not exhibit the structure observed by Friedman and Tiltman, and it provides only nouns and a few adjectives.

Friedman came to know Petersen who at some time presented his hand transcription and other material to him. After Friedman's death, all the material was moved to the W.F. Friedman collection of the Marshall Foundation. Recently, electronic versions of the transcriptions made by Friedman's groups were produced from the typed sheets and made available on the Internet (Reeds, 1995).

Later acclaimed solutions see in the manuscript a simple substitution cipher which can only decode isolated words (Feely, 1943), the first use of a more or less sophisticated cipher (Strong, 1945; Brumbaugh, 1977), a text in a vowel-less Ukrainian (Stojko, 1978) or the only surviving document of the Cathar movement (Levitov, 1987). No acceptable plaintext has ever been produced though.

Some interesting new insights into the manuscript were provided in the 70's by Prescott Currier, presenting some of his results at an informal Voynich manuscript symposium at the National Security Agency in Washington (D'Imperio, 1978). Basing his findings on the statistical properties of the text, he showed that the manuscript is written in two distinct "languages" which he simply called A and B. Each bifolio was written in one of the two, and bifolios in the same "language" were generally grouped together. Only in the herbal section there is a mixture of A and B folios. Based on the characteristics of the writing, he showed that the manuscript seems to have been written in two distinct "hands", and he even suggested there could be as much as five or even eight different hands. A significant feature is that the hand and language used on each folio are fully correlated. Currier's conclusion was that at least two people were involved in writing the Voynich manuscript, (which he considered a point against the "hoax theory" summarised below), although alternatively, the manuscript could have been written by one person, in two distinct periods.

Due to the lack of success in the decipherment, a number of people have proposed that the manuscript is a "hoax". The manuscript could either be a 16th century forgery, to be sold for a hefty sum to emperor Rudolf II, who was interested in rare and unusual items (Brumbaugh, 1977, deriving from earlier unpublished theories), or a more recent one by W. Voynich himself (Barlow, 1986). The latter is effectively excluded both by expert dating of the manuscript, and by the evidence of its existence prior to 1887.

One problem with the earlier hoax theory is that, as will be shown, certain word statistics (Zipf's laws) found in the manuscript are characteristic of natural languages. In other words, it is unlikely that any forgery from 16th century would "by chance" produce a text that follows Zipf's laws (first postulated in 1935).

Since 1990, a multidisciplinary group of varying size, generally between 100 and 200 individuals, dispersed all around the globe and connected through the Internet, has maintained an electronic mail forum on the decipherment of the Voynich manuscript. This has led to a lively exchange of ideas and the definition of two main goals: a machine readable transcription of the manuscript text and the study of the text through numerical experiments. The following sections relate to these issues.

Transcription

To be able to analyse the text with modern tools, a machine-readable representation of the text is needed. Some partial transcriptions were produced in the past, by study groups set up by Friedman (in particular his so-called First Study Group or FSG) and by Currier and D'Imperio. The authors decided to proofread the existing transcriptions and add the missing parts from the Petersen copy (with the kind permission of the Marshall Foundation) using a newly designed transcription alphabet. To facilitate the transcription process, this new alphabet (called EVA) assigns roman letters to the different characters such that the combinations that appear in the manuscript are mostly pronounceable.

Transcription of the Voynich manuscript is made difficult by a few problems. Since the alphabet is not known, one cannot be certain which are the basic components, i.e. the single characters. For the same reason, it is never clear whether two similar characters are really different, or in fact the same but with a variation in the handwriting. Over-differentiation leads to an excessively large character set and an extremely difficult transcription exercise, especially since the variations in the way characters are written is a continuum of possibilities and no clearly-defined rules for distinguishing one from the other can be given. Under-differentiation should, on the other hand, obviously be avoided because once two different characters are transcribed the same, the error can not be undone. Therefore, the transcription alphabet must be carefully designed.

Another, smaller, problem is that the text includes what are obvious "ligatures" of basic characters, and some "rare" characters, which occur only a few times in the entire text (which is about 250,000 characters long). The EVA alphabet (designed by Zandbergen with the aid of Guy, priv.comm.) tends to break the text into smaller components than most of the previously existing alphabets. The basic alphabet which allows the transcription of the vast majority of the manuscript is displayed in Table 1, using a computer font designed by Landini. It includes some Voynich characters which are most probably single characters but represented in the transcription alphabet by several. The rarer characters, some of which are embellishments or variations of the basic characters, have been added as an extension to the alphabet, such that it can fully reproduce the manuscript (see the on-line document at http://web.bham.ac.uk/G.Landini/evmt/eva.htm).

Table 1. The transcription alphabet used by the authors.

Note: to display the characters of the Voynich script, the TrueType font 'EVA Hand 1' needs to be available to your browser

BASIC EVA CHARACTERS
EVA
script
EVA
script
EVA
script
'
'
m
m
sh
Sh
a
a
n
n
cth
cTh
b
b
o
o
ckh
cKh
c
c
p
p
cph
cPh
d
d
q
q
cfh
cFh
e
e
r
r
in
in
f
f
s
s
iin
iin
g
g
t
t
h
h
u
u
i
i
v
v
j
j
x
x
k
k
y
y
l
l
z
z

Ligatures are indicated by grouping several characters between parentheses, e.g. (c'y) or (ith), or by using capitals for characters which connect to the right, in these cases: C'y or ITh. These sequences look like C'y and ITh respectively. Rare characters are coded with the aid of numerical value contained between an ampersand and a semi-colon, e.g. (c&179;h) which looks like c³h. Words are separated by a full stop, while a comma is used when the word break is uncertain.

To illustrate the use of the EVA alphabet, the first paragraph of folio 53r (Figure 1) when transcribed using the EVA alphabet, and displayed using the computer font reads:

Table 2.
kodam,chocThody.oty
dol.dain.s,cho,She.oty
Sho,os.chokan.ody
ytchodaiin.yky.otchey.otod
okSh.otol.cFhy.cPhodol.ykody.qokchod. {plant drawing} otcho.qot.oty
ykeodar.oqoor.ocKi.odor.chain.qokod. {plant drawing} ykchdy.chees.dal
sodar.otos.qoy.tchy.otey.chos.okod. {plant drawing} ykchody.qokchy
qotchol.dar.qoty.chtor.oltSho.cTo. {plant drawing} ykeeod.o.y,toyd
otol.chol.cTheees.os.orol.chod.qoty=

The new transcription using the roman alphabet:
<f53r.1> kodam,chocthody.oty
<f53r.2> dol.dain.s,cho,she.oty
<f53r.3> sho,os.chokan.ody
<f53r.4> ytchodaiin.yky.otchey.otod
<f53r.5> oksh.otol.cfhy.cphodol.ykody.qokchod. -otcho.qot.oty
<f53r.6> ykeodar.oqoor.o(cki).odor.chain.qokod. -ykchdy.chees.dal
<f53r.7> sodar.otos.qoy.tchy.otey.chos.okod. -ykchody.qokchy
<f53r.8> qotchol.dar.qoty.chtor.oltsho.(cto). -ykeeod.o.y,toyd
<f53r.9> otol.chol.ctheees.os.orol.chod.qoty=

Analysis of the text

In the past, analysis of the Voynich manuscript text has been based either on visual inspection of the manuscript pages or by numerical analysis of partial transcriptions. Expert analysis of the manuscript has yielded surprisingly few hard facts. This is of course due to the uniqueness of the manuscript and the absence of the usual indications of provenance and age. The current belief about the provenance of the manuscript locates it in Central Europe while some experts narrow it down either to Germany or Italy. The age of the manuscript is given as late 15th to early 16th century, while others would not exclude the 13th or even the late 16th century. Proposed writers for the manuscript are Roger Bacon, an unknown North Italian or German alchemist or quack, John Dee, Giordano Bruno or Anthony Askham.

It seems clear that the best hope of solving the mystery of this manuscript is via a numerical analysis of the text, such as character and word statistics, concordances and correlations across the pages as well as identification of the captions (single words or 'labels' ) which occur near many of the illustrations in the manuscript. So far, there are some established facts:

Character statistics

The alphabet size appears to be of the order of 23-30, depending on what one calls a single character. It has not been possible to identify Voynich characters which obviously represent numbers. The frequency distribution of the single characters is rather similar to that of 'normal' languages, and it is possible to tentatively identify vowels and consonants such that the text is mostly pronounceable. Repeated single characters (doublets) are extremely rare, with the exception of i and e which usually occur two or three times in a row, and which perhaps represent single characters. For example the double or triple i (in and iin) closely resemble a cursive n or m respectively.

Character entropy

Entropy, in information theory terms, is a numerical measure of the uncertainty in a sequence or string of characters. For example the sequence "aaaaaaaaaaaa..." is very predictable (low entropy). There is a larger probability that the next character will be "a". The sequence "dkjtgarltsoy..." is not (high entropy). Interestingly, all natural languages have a certain degree of redundancy, which is also the case for the manuscript text. However the so-called second order entropy (the amount of uncertainty about the next character, given that the current one is known) is too low when compared to other European languages (Bennett, 1976). This is a reflection of the fact that the character sequences in the words tend to follow set patterns and it has been taken as an indication that the words are 'constructed' in a way similar to some of the artificial languages of the 16th century.

Word statistics

Assuming that the "spaces" between words are truly word separators, the word length distribution is somewhat shorter than that of Latin or English. There is a large amount of repetition in the text, and the same word may repeat itself up to four times. Additionally, words which only differ by one character are often found in each other's vicinity. It has been speculated that this sort of repetition could be due to coding numerical values (five, five), to prayers (amen, amen, etc.), or the presence of magical formulas or recipes. Because of the short word length, there are theories that the spaces do not separate words but rather syllables. Alternatively, because of the restricted set of word-initial or word-final characters, it is possible that the spaces are of an orthographic nature such as is the case in the arabic script. Still, both the number of different words and the number of words occurring only once in the text are within reasonable bounds for a text of this length.

Word distribution

In 1935 Zipf described a number of relationships in texts that he suggested were due to a "principle of least effort" in the use of language. He showed that in normal writing the frequency of a particular word is inversely proportional to its rank, once all the words have been sorted by decreasing frequency. Secondly that the number of infrequent words is inversely proportional to their frequency and finally that the number of syllables is inversely proportional to the frequency of use of a word. The first (and most important) characteristic is present in the Voynich manuscript text, as shown in Figure 3. The first Zipf law is represented by a straight line with a slope of -1. The characteristic small deviation from this line found in natural languages is also observed for the Voynich manuscript language.

Figure 3. A rank-frequency (Zipf's plot) of several texts: voynich (Friedman's first study group transcription), roget (Roget's Thesaurus), republic (Plato's Republic), Emma (Jane Austen), Alice (Alice in Wonderland, Lewis Carroll). Note that all, (except the Roget's Thesaurus which is a collection of very short definitions and cross referenced words) follow the same trend of a slope of -1 in the log-log plot. There are 2 more Zipf's "laws" which were also found in the Voynich manuscript (available at: http://web.bham.ac.uk/G.Landini/evmt/zipf.htm ).

Conclusion

It is possible that, if deciphered, the manuscript would reveal no more than the knowledge found in other mediaeval herbals and alchemy books. However, if the document is real it means that at least the people involved in the writing were able to read it. The fact that it still remains unread is quite unique and a challenge in cryptological terms. What was the method of encoding? What is the original underlying language ? Who wrote it? Why? It would also be interesting to know what kind of knowledge required such an amount of secrecy at the time of writing. It could even contain a subject completely unrelated to the drawings...

In any case, if a "readable" text is produced after some processing of the manuscript text, how can one be sure that the solution is correct? Could any of the solutions which have been announced be correct? On which basis to accept or reject a proposed a solution is quite a problem because there is no date, author, country or language associated with the manuscript. We will assume that:

  1. there is a meaningful text underlying the writing in the Voynich manuscript
  2. the language is a known one or closely related to a known one, and
  3. the text is encoded using a reversible method.

Without all of these being true, there seems to be no possibility of finding a solution.

No solution which fails to present a detailed description of how the "encoding" was done by the writer(s) of the manuscript can be accepted, and this is where most of the proposed solutions fail. It is also clear that neither the method of encoding nor the contents of the decoded text may conflict with the context of a manuscript written in medieval Europe (or elsewhere by a medieval European). Finally, the solution should clearly explain the many odd statistical properties found in the manuscript text, which could not be fully described here, but which may be found in the literature on the subject (Tiltman, 1967; Currier, 1976; D'Imperio, 1978).

It seems paradoxical that at the time of rising concerns about the public use of "uncrackable" security codes, a medieval manuscript probably cannot be read. Let's hope that it is not for too long.

References

Following are some of the more relevant works about the Voynich manuscript, which have been mentioned in the text. D'Imperio (1978) has a long bibliography of subjects which are possibly related to the manuscript. Furthermore, the most recent developments in the study of the Voynich manuscript may be found on the World-Wide Web, via the following sites:

http://web.bham.ac.uk/G.Landini/evmt/evmt.htm

Note: this site contains instructions on how to dowload the TrueType font 'EVA Hand 1' used in this article

http://www.geocities.com/Athens/Delphi/8956/

The most up to date bibliography about the Voynich manuscript is maintained on the WWW site of Reeds:

http://www.research.att.com/~reeds/voynich.html
  1. Barlow, M. The Voynich Manuscript - by Voynich?, Cryptologia, 1986, 10 (4): pp. 210-216.
  2. Bennett, W.R. Scientific and Engineering Problem Solving with the Computer, Englewood Cliffs: Prentice-Hall, 1976, pp. 103-198.
  3. Browne, Sir T. (citation) in Works, G. Keynes, ed., 1931, v.6, p. 325.
  4. Brumbaugh, R.S. The World's Most Mysterious Manuscript. Carbondale: Southern Illinois University Press, 1978. London: Weidenfeld and Nicholson, 1977.
  5. Currier, P. Papers on the Voynich Manuscript, Papers presented at: New Research on the Voynich Manuscript: Proceedings of a Seminar, 1976, Washington, D.C.
  6. Feely, J.M. Roger Bacon's Cipher: The Right Key Found. Rochester, NY., 1943.
  7. Guy, J.B.M. Private communication.
  8. D'Imperio, M.E. The Voynich Manuscript - an elegant enigma. Aegean Park Press, Laguna Hills, California, 1978.
  9. Kahn, D. The Codebreakers. New York: Macmillan, 1967, pp. 863-872, 1120-1121.
  10. Levitov, L. Solution of the Voynich Manuscript: A liturgical manual for the endura rite of the Cathari heresy, the cult of Isis. Laguna Hills, California: Aegean Park Press, 1987.
  11. Manly, J.M. Roger Bacon and the Voynich Manuscript. Speculum 6 (July 1931), pp. 345-91.
  12. Newbold, W.R. The Cipher of Roger Bacon. Proceedings of the College of Physicians and Surgeons of Philadelphia, 1921, pp. 431-74. Read April 20, 1921.
  13. Newbold, W. R. The Cipher of Roger Bacon, edited with foreword and notes by R. G. Kent. Philadelphia: University of Pennsylvania Press; London, H. Milford, Oxford University Press, 1928.
  14. O'Neill, H. Botanical Remarks on the Voynich MS. Speculum, 1944, 19: pp. 126.
  15. Reeds, J. Private communication.
  16. Reeds, J. William F. Friedman's Transcription of the Voynich Manuscript. Cryptologia, 1995, 19: pp. 1-23
  17. Roberts, R. J., Watson, A. G., eds. John Dee's Library Catalogue. London: The Bibliographical Society, 1990.
  18. Stojko, J. Letters to God's Eye, Vantage Press, New York, 1978. Lib. Congress No., 78-68893.
  19. Strong, L.C. Anthony Askham, the author of the Voynich Manuscript. Science, new series 101 (15 June 1945): pp. 608-9.
  20. Tiltman, J.H. The Voynich Manuscript. "The Most Mysterious Manuscript in the World", NSA Technical Journal, XII, 3 (July, 1967), pp. 41-85.
  21. Toresella, S. Gli erbari degli alchimisti. In: Arte farmaceutica e piante medicinali - erbari, vasi, strumenti e testi dalle raccolte liguri, Saginati L, ed. Pisa: Pacini Editore, 1996, pp. 31-70.
  22. Yale (Beinecke Library) catalogue of MS. 408 is electronically available at gopher://yaleinfo.yale.edu:7700/0R0-102421-YaleLibraries/Beinecke/manu/Beinpre/ms400-.gen
  23. Zipf G. K. The Psycho-biology of Language. Hought Mifflin Co, Boston, 1935, pp. 20-48.

Acknowledgements

The illustrations of the Voynich manuscript contained in this article show pages from W. Friedman's photostatic copy owned by the William and Elizebeth Friedman collection in the George Marshall Foundation, Lexington, Virginia, and were reproduced with the kind permission of the owner.

Most of the numerical analyses summarised in this article were performed by members of the Internet Voynich mailing list.

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