--- Begin Message ---Received: from m2.deja.com (m2.deja.com [208.10.192.33]) by front7m.grolier.fr (8.9.3/No_Relay+No_Spam_MGC990224) with ESMTP id RAA12435 for <voynich@xxxxxxxxxxxxxxxx>; Mon, 6 Mar 2000 17:15:52 +0100 (MET) Received: from x36.deja.com (ix36.deja.com [10.2.1.236]) by m2.deja.com (8.8.5/8.8.5) with ESMTP id KAA22495 for <voynich@xxxxxxxxxxxxxxxx>; Mon, 6 Mar 2000 10:15:21 -0600 Received: (from www@xxxxxxxx) by x36.deja.com (8.8.7/8.6.12) id KAA16056; Mon, 6 Mar 2000 10:15:20 -0600 Message-Id: <200003061615.KAA16056@xxxxxxxxxxxx> From: antoine41@xxxxxxxxxxx To: voynich@xxxxxxxxxxxxxxxx Subject: The Voynich manuscript Date: Mon, 06 Mar 2000 16:15:17 GMT Reply-To: voynich@xxxxxxxxxxxxxxxx Newsgroups: sci.crypt NNTP-Posting-Host: 195.101.37.188 Organization: Deja.com - Before you buy. X-Article-Creation-Date: Mon Mar 06 16:15:17 2000 GMT X-Http-Proxy: 1.0 x28.deja.com:80 (Squid/1.1.22) for client 195.101.37.188 X-Http-User-Agent: Mozilla/4.7 [fr] (Win95; I) X-MyDeja-Info: XMYDJUIDantoine41 X-Mmail: \Recent X-M-Uid: 958.952359354 RULES IN THE Voynich MANUSCRIPT by Antoine CASANOVA ________________________________________________________________________ ___ Address ------- 6, Allee des erables, 93140 BONDY (France). E-mail ------ Voynich@xxxxxxxxxxxxxxxx Summary ------- >From the transcriptions of Captain Prescott Currier and William F. Friedman, we show that the terms of the Voynich manuscript are built with synthetic rules. The results which we obtain could lead us to consolidate the John Tiltman's assumption according to which the Voynich manuscript would be written with a synthetic universal language. Key words --------- Voynich manuscript, ciphers, ciphered manuscript, rules, structure, term. Theory ------ In the Voynich manuscript, it was noted by Currier [2] and by Tiltman [3] [5] that "words" or "sentences" differ from each other by only one symbol, as 8AR differs from SAR, although this characteristic is found in the written natural language, one does not note it within the same proportion. The assumption raised by Tiltman, and according to which the written language of the manuscript is probably a synthetic universal language, could be the cause of this characteristic. Indeed, in the universal language of Raymond Lulle but also in the universal language of Athanasius Kircher, Dalgarno or Wilkins, the words and the sentences are successively repeated and differ only on the substantive, the adjective, the verb of the proposal or on another symbol used as a changer of reference [4]. However, until now, it has not been proven yet that the Voynich manuscript was written with a synthetic language. Indeed, the manuscript may not be a real cryptogram for one could just as easily support the thesis of the use of a phonetic written form. We propose here to show that the terms of the Voynich manuscript are built with synthetic rules which exclude the assumption of a written natural language. Method ------ The method suggested rests on the calculation of the Hamming distance between the terms of the manuscript [1]. We extract the terms from the Voynich manuscript and we gather them according to their dimension. We obtain groups of terms. Each term has as many positions of substitution as it contains letters. In each group of terms we enter the Hamming distances equal to the unit on each possible position of each term. Results ------- At the conclusion of the operation of accounting we come to a table with two entries: The dimensions of the terms and the possible positions of the substitutions of letters within each term. At the intersection of these entries is the accounting of the Hamming distances equal to the unit. >From the two transcriptions, reviewed and corrected by the EVMT, made by Captain Prescott Currier and by William F. Friedman, we obtain two series of results which are shown in Table 1 and in Table 2. Term \ 1 2 3 4 5 6 7 8 Position 3 177 55 108 4 247 150 117 154 5 269 131 163 112143 6 130 67 86 49 52 70 7 40 21 27 29 17 11 18 8 1 2 6 6 2 2 2 3 Table 1 Currier's transcription. On the basis of 4415 terms. Term \ 1 2 3 4 5 6 7 8 Position 3 194 120 158 4 397 308 195 253 5 459 263 315 208 276 6 238 143 171 164 121 170 7 81 40 58 42 38 43 43 8 8 2 9 5 8 9 5 7 Table 2 Friedman's transcription. On the basis of 6195 terms. To obtain more precision on the terms made up of seven and eight letters we synthesize these two tables in only one and we obtain the following table: Term 1 2 3 4 5 6 7 8 3 7,14 3,18 5,00 4 12,00 8,37 5,80 7,57 5 13,50 7,21 8,78 5,89 7,69 6 6,79 3,83 4,71 3,76 3,13 4,33 7 2,21 1,12 1,55 1,33 1,00 0,94 1,10 8 0,15 0,08 0,28 0,22 0,17 0,19 0,13 0,18 Table 3 Calculation based on the proportion of terms of each transcription. By considering the decreasing order of the ratios one obtains the table below. It describes the priorities or the order of the substitution of the letters within the terms. The diversity obtained by substituting the letters within the terms creates all the words of the dictionary used to write the text of the manuscript. Term 1 2 3 4 5 6 7 8 3 1 3 2 4 1 2 4 3 5 1 4 2 5 3 6 1 4 2 5 6 3 7 1 4 2 3 6 7 5 8 6 8 1 2 3 4 7 5 Table 4 Order of the substitution of the letters within the terms of the manuscript. We translate the table with inequalities to reveal the synthetic construction of the terms. Term 3 > < 4 > > < 5 > < > < 6 > < > > < 7 > < > > > < 8 > < > > < > < Table 5 We read them this way: For a word of three letters the first position is more substituted than the second position ?>? and the latter is less substituted than the third position ' < '. the structure is as follows: ' > < '. Rules ----- The manuscript contains terms with structures which are well ordered and dependent on one another. >From Table 4, one notices four rules governing the constitution of the terms comprising three, four, five, six and seven letters: 1. The first letter of a term is the most substituted. It represents the most important manpower of the various positions. 2. The penultimate position within a term is the least substituted position. 3. The third letter is the second letter which is the most substituted when it does not occupy the penultimate position within the term (Except for a term made up of eight letters for which we do not have sufficient statistical data to reveal its structure, Cf. Table 1 et Table 2). 4. The last position is systematically more substituted than the penultimate letter of the term. The remarks 1 and 2 lead to the following table: Term 1 2 3 4 5 6 7 3 1 3 2 4 1 2 4 3 5 1 4 2 5 3 6 1 4 2 5 6 3 7 1 4 2 3 6 7 5 Table 6 Rule 1 A term has the first position which is the most substituted. Rule 2 The penultimate position within a term is the least substituted position. These two rules are impossible to circumvent for the construction of a term. They have priority over any other rule. Table 5 shows us that the terms are built with the same logic of calculation. Rule 3 One passes from a term of dimension (n) to a smaller or larger term by withdrawing or by adding a unit to all the positions [2,n] of the initial term. Let us detail this operation and apply this methodology. Application of the rules ------------------------ Example 1 Research of the structure of a term made up of 5 letters starting from a term of 6 letters. Let us start by writing the order of the substitution of the letters for a term made up of n=6 letters. The order is written as such: 1 | n-2| n-4 | n-1 | n | n-3 If one wishes to know the order of the substitution of the letters for a term made up of n=5 letters then we realize the following operation: A 1 n-2 n-4 n-1 n n-3 B 0 1 1 1 1 1 A+B 1 n-2+1 n-4+1 n-1+1 n+1 n-3+1 Result 1 n-1 n-3 n n+1 n-2 The result of the operation cannot be lower than the unit or higher than the dimension of term (n), then the order (n+1) is impossible. Thus, there remains the following order: 1 | n-1 | n-3 | n | n-2 Which is the order of the substitution of a term made up of five letters (n=5): 1 | 4 | 2 | 5 | 3 Example 2 Research of the structure of a term made up of 4 letters starting from a term comprising 5 letters. This operation is possible for all the terms. But it is advisable to respect Table 6, Rule 1 and Rule 2. Indeed, when we compute the order of a term comprising four letters (n=4) we come to a result false for the suppression of an impossible order (n+1) justifies the order (n). We draw up the following table: A 1 n-1 n-3 n n-2 B 0 1 1 1 1 A+B 1 n-1+1 n-3+1 n+1 n-2+1 Result 1 n n-2 n+1 n-1 If we do not comply with the two basic rules we obtain the false result: 1 | n | n-2 | n-1 = 1 | 4 | 2 | 3 For indeed the construction { 1 | n | n-2 | n+1| n-1 } does not comply with the second rule. (n) must be in place of (n+1) and therefore the (n) cannot be in a second position. Thus, the construction becomes: 1 | n-2 | n| n-1 = 1 | 2 | 4 | 3 Example 3 Research of the structure of a term made up of 3 letters starting from a term comprising 4 letters. We continue this reasoning by seeking the structure of a term made up of three letters (n=3). A 1 n-2 n n-1 B 0 1 1 1 A+B 1 n-2+1 n+1 n-1+1 Result 1 n-1 n+1 n The case is identical to that of the determination of a term made up of four letters starting from a term comprising five letters. We notice here that (n+1) is impossible. According to the rule the penultimate position is necessarily occupied by (n). Here, the last position is taken by (n), this case is not allowed thus the construction of the term only can be: 1 | n | n-1 which is indeed the order: 1 | 3 | 2. Example 4 Explanation of an uncertainty. Research of the structure of a term comprising 8 letters starting from a term made up of 7 letters. We feel however uncertain about the order of the substitution of the letters in a term made up of eight letters (n=8, cf. Counts 3). We are going to determine if the fifth position is indeed smaller than the sixth position. The construction of a term made up of seven letters is: 1 | n-3 | n-5 | n-2 | n-1 | n | n-3. To determine the order of a term made up of eight letters we withdraw this time a unit instead of adding it. The operation is thus made: A 1 n-3 n-5 n-2 n-1 n n-4 B 0 1 1 1 1 1 1 A-B 1 n-3-1 n-5-1 n-2-1 n-1-1 n-1 n-4-1 Result 1 n-4 n-6 n-3 n-2 n-1 n-5 1 | n-4 | n-6 | n-3 | n-2 | n-1 |n-5 The (n) does not appear, but according to the rule the penultimate position is the least substituted position. Thus (n) is found integrated in this construction: 1 | n-4 | n-6 | n-3 | n-2 | n-1 |n | n-5 This sequence would be the order of the substitution of a term made up of eight letters (n=8). 1 | 4 | 2 | 5 | 6 | 7 |8 | 3 Conclusion ---------- The terms of the Voynich manuscript are built from synthetic rules which exclude the assumption from the use of a natural language for its writing. However, the rules which we have put forward could be the expression of a progressive modification, inspired from the discs of Alberti, from the encryption used by the writer(s) of the manuscript. But we must conclude that currently it is not possible yet to know this enigma for we have only come to the stage of the research of the structures of terms, words, sentences and of texts of their interactions and connections. As soon as we establish the building sets of this handwritten text we will be able to move to the following stage of research for inductive analogy between the internal structures of the manuscript and the possible natural languages underlying with the handwritten text. Bibliography ------------ [1] Antoine CASANOVA, Ph. D, University PARIS 8 (France), Méthode d?analyse du langage crypté : Une contribution à l?étude du manuscrit de Voynich, Paris, 1999. [2] Captain Prescott H. CURRIER, Some Important New Statistical Findings, Seminar on 30th November in Washington D.C, 1976. [3] John H. TILTMAN, Interim report on the Voynich MS : Personal communication to W. F. FRIEDMAN, 5 may 1951. [4] Umberto ECO, La ricerca della lingua perfetta nella cultura europa, Laterza, Roma-Bari, 1994. [5] Mary E. D'Imperio, The Voynich manuscript -An elegant enigma, Fort Meade, Maryland, National Security Agency, Central Security Service, 1978.
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