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Language A and B Again

March 13, 2013 12 comments

A tentative conclusion from comparing Language A and Language B  is that the non-gallows glyphs are used in the same way in both Languages.

That is to say, they appear to mean the same thing. So the “o” in A means the same as the “o” in B.
There is some persistent “mixing” between the e/y glyphs, which is illustrated by the example result below:
ABMixing
There is also some doubt about the “8” glyph, which sometimes seems to mix with the gallows glyphs (e.g. in some cases, the “8” appears in A to function in the same way as a gallows glyph in B and vice versa). This may simply be an error in the comparison method, or it may be that the “8” is a null, or it may be due to some other effect.
The gallows glyphs are different – they don’t appear to mean the same in A and B. I’m focussing on those glyphs now.
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Language “A” and “B” Conversions

March 5, 2013 12 comments

This is an update to my previous two posts on this topic.

I have been concentrating on searching for the correspondence between glyphs used in Language A, and glyphs used in Language B. As a reminder, the method is to take all words in, say, Language A, and “convert” them to words in Language B by changing the glyphs according to a candidate mapping table. The frequency of the converted Language B words is then compared with the original Language A words: the closer the frequencies, the better the mapping match.

Method Check using only Language A words

As a check of the method, I took the Herbal folios 1-25 (all in Language A) and split them into two groups: 1-12 and 13-25, and I then artificially labelled the latter group as Language B. Then I ran the matching procedure, which produced the following result:

Epoch 62 Best chromosome 0 Value= 5.62272615159e-05
Chromosome ['o', '9', '1', 'i', '8', 'a', 'e', 'c', 'k', 'y', 'h', 'N', '2', '4', 's', 'g', 'p', '?', 'K', 'H']
ngramsA    ['o', '9', '1', 'i', '8', 'a', 'e', 'c', 'h', 'y', 'k', 'N', '2', '4', 's', 'g', 'p', '?', 'K', 'H']

This is good and reassuring, since it shows that the words in folios 13-25 have essentially the same frequency distribution when their glyphs are mapped to the same glyphs in folios 1-12.

Removal of Glyph Variants in Voyn_101

As the tests progressed, it became clear that some of the glyphs GC defined in Voyn_101 were in fact variants of more common glyphs. The most obvious were the “m”, “n”, “N” glyphs mentioned before – with these included, the conversions between Language B and Language A were of much poorer quality than if they were expanded to “iiN”, “iN” and “iiiN” respectively. After some time weeding out these variants, the following table was arrived at:

seek =  ["3", "5", "+", "%", "#", "6", "7", "A", "X", 
         "I", "C", "z", "Z", "j", "u", "d", "U", "P", 
         "Y", "$", "S", "t", "q",
         "m", "M", "n", "Y", "!", ")", "*", "b", "J", "E", "x", "B", "D", "T", "Q", "W", "w", "V", "(", "&"]
repl =  ["2", "2", "2", "2", "2", "8", "8", "a", "y", 
         "ii", "cc", "iy", "iiy", "g", "f", "ccc", "F", "ip",
         "y", "s", "cs", "s", "iip",
         "iiN", "iiiN", "iN", "y", "2", "9", "p", "y", "G", "c", "y", "cccN", "ccN", "s", "p", "h", "h", "K", "9", "8"]

I am very confident that the glyphs remaining after using the above conversion table are the base set.  The base set of glyphs is thus:

Language A frequency order: 'o', 'c', '9', '1', 'a', '8', 'e', 'i', 'h', 'y', 'k', 's', '2', 'N', '4', 'g', 'p', '?', 'K', 'H', 'f', 'G', 'F', 'L', 'l', 'v', 'r', 'R'
Language B frequency order: 'c', 'o', '9', 'a', '8', 'e', '1', 'h', 'i', 'y', 'k', '2', 'N', 's', '4', 'g', 'p', 'f', '?', 'H', 'K', 'G', 'F', 'l', 'L', 'R', 'r', 'v'

where “?” represents all very rare glyphs (such as the “picnic table” glyph). There are thus 27 glyphs (15 gallows and 12 regular) excluding the rare special glyphs like the picnic table.

Glyph Mixing Between A and B

I ran many trials using the base set of glyphs, comparing various sections of the VMs written in the different hands. In particular, the following folio collections were defined:

Special = {'HerbalRecipeAB': range(107,117) + range(1,26),
           'HerbalAB': range(1,57),
           'HerbalBalneoAB': range(1,26) + range(75,85),
           'HerbalAstroAB': range(1,13) + range(67,75),
           'PharmaRecipeAB': [88,89,99,100,101,102] + range(103,117),
           'AllAB': range(1,117)
 }

The collection I used the most was the one called “HerbalBalneoAB”, which contains Herbal folios written in Language A, and Balneo folios written in Language B. The nice feature of this collection is that the number of words is around the same for both Languages, which makes comparing counts very easy:

Total words =  2846  Total Language A =  1581  Total Language B =  1584

As an example, here is a trial result for HerbalBalneoAB:

Language B ['o', '9', '1', 'a', 'i', 'f', 'c', 'y', 'h', 'e', 'K', 'N', '2', 's', '4', 'g', 'p', '8', 'k', 'H']
Language A ['o', '9', '1', 'a', 'i', '8', 'c', 'e', 'h', 'y', 'k', 'N', '2', 's', '4', 'g', 'p', 'K', '?', 'H']

In all the tests I ran, there were some common features in the results:

  • Mixing between “e” and “y” – when writing Language A, the use of “e” appears to be equivalent to the use of  “y” in Language B, and vice versa
  • Mixing between  8,f,F,k,K,g,G,r,R,?  and so on – the Gallows glyphs swap amongst themselves, and “8”

Just about all trials showed the “e”/”y” mixing. Tony Gaffney pointed out that these two glyphs are quite similar in stroke construction. The appearance of “8” amongst the swapping Gallows glyphs is curious.

The Relationship Between Currier Languages “A” and “B”

March 1, 2013 24 comments

Captain Prescott Currier, a cryptographer, looked at the Voynich many moons ago, and made some very perceptive comments about it, which can be seen here on Rene Zandbergen’s site.

In particular, he noticed that the handwriting was different between some folios and others, and he also noticed (based on glyph/character counts) that there were two “languages” being used.

When I first looked at the manuscript, I was principally considering the initial (roughly) fifty folios, constituting the herbal section. The first twenty-five folios in the herbal section are obviously in one hand and one ‘‘language,’’ which I called ‘‘A.’’ (It could have been called anything at all; it was just the first one I came to.) The second twenty-five or so folios are in two hands, very obviously the work of at least two different men. In addition to this fact, the text of this second portion of the herbal section (that is, the next twenty-five of thirty folios) is in two ‘‘languages,’’ and each ‘‘language’’ is in its own hand. This means that, there being two authors of the second part of the herbal section, each one wrote in his own ‘‘language.’’ Now, I’m stretching a point a bit, I’m aware; my use of the word language is convenient, but it does not have the same connotations as it would have in normal use. Still, it is a convenient word, and I see no reason not to continue using it.

We can look at some statistics to see what he was referring to. Let’s compare the most common words in Folios 1 to 25 (in the Herbal section, Language A, written in Hand 1) and in Folios 107 to 116 (in the Recipes section, Language B, written in a different Hand):

Comparison between word frequencies in Languages A and B

Comparison between word frequencies in Languages A and B

So, for example, in Language A the most common word is “8am” and it occurs 192 times in the folios, whereas in Language B the most common word is “am”, occuring 137 times.

We might expect that these are the same word, enciphered differently. The question then is, how does one convert between words in Language A and words in Language B, and vice versa? In the case of the “8am” to “am” it’s just a question of dropping the “8”, as if “8” is a null character in Language A. In the case of the next most popular words, “1oe”(A) and “1c89″(B) it looks like “oe”(A) converts to “c89″(B). And so on.

If we look at the most popular nGrams (substrings) in both Languages, perhaps there is a mapping that translates between the two. Perhaps the cipher machinery that was used to generate the text had different settings, that produced Language A in one configuration, and Language B in another. Perhaps, if we look at the nGram correspondence that results in the best match between the two Languages, a clue will be revealed as to how that machinery worked.

This involves some software (I’m using Python now, which is fun). The software first calculates the word frequencies for Language A and B in a set of folios (the table above is an output from this stage). It then calculates the nGram frequencies for each Language. Here are the top 10:

nGramFrequencies

The software then runs a Genetic Algorithm to find the best mapping between the two sets of nGrams, so that when the mapping is applied to all words in Language B, it produces a set of words in Language A the frequencies of which most closely match the frequencies of words observed in Language A (i.e.  the frequencies shown in the first table above).

Here is an initial result. With the following mapping, you can take most common words in Language B, and convert them to Language A.

Table for converting between a Language B word and a Language A word

Table for converting between a Language B word and a Language A word

A couple of remarks. This is an early result and probably not the best match. There are some interesting correspondences :

  • “9” and “c” are immutable, and have the same function
  • Another interesting feature is that “4o” in Language B maps to “o” in Language A, and vice versa!
  • in Language B, “ha” maps to “h” in Language A, as if “a” is a null

In the Comments, Dave suggested looking at word pair frequencies between the Languages. Here is a table of the most common pairs in each Language.

Common word pairs in Languages A and B

Common word pairs in Languages A and B

For clarity, I am using what I call the “HerbalRecipesAB” folios for this study i.e.

Using folios for HerbalRecipeAB : [107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]

More results coming …

Ink density and glyph order

July 31, 2012 4 comments

When using an ink pot and an old fashioned nib, one has to dip the nib in to the pot from time to time to replenish the ink. When the nib has just been dipped, the first few letters or so written often have more ink to them, as there is plenty on the nib.

If one were writing a string of identical letters, the frequency at which one has to re-dip the nib as it runs out of ink should be approximately constant. For example, if I’m writing “ooooooooooooo” then perhaps the nib holds enough ink for 5 “o”s before it needs replenishment. Then the appearance on the paper might be:

ooooooooooooooo

and so on.

On most folios of the VMs it’s apparent that some of the glyphs have been inked more heavily than others. Some possible explanations are:

  1. the nib has been refilled with ink just prior to these glyphs being written
  2. these glyphs have been re-inked for some reason
  3. these glyphs have been written at a different time with a different nib or ink or both

Here is a nice example of this feature

f49v

If the glyphs we see were written from the top down, from left to right, then the heavily inked glyphs are not spaced apart in the way expected by possibility 1 above.

One conclusion is that the glyphs we see were not written top down left to right, but in some other order.

Also, the glyphs that tend to be heavily inked are a subset of all the glyphs. “8” is very commonly heavily inked, but not always, even on the same folio. One of the gallows glyphs is also often heavily inked, but only on one side. Another is GC “1” and the downstroke on GC “y”.

(An interesting feature on this folio is the compound gallows that appears to have been constructed by first writing the standard gallows, then adding a line between each “c” that straddles it. Or perhaps the “c”s were written first, then the gallows was written and the “c”s joined later?)

Categories: f49v, Features, gallows Tags: , ,

Page Positional Gallows, Mk. II

June 29, 2012 3 comments

Here is a new set of images, for each of the folios in the VMs, that shows the positions of the various gallows glyphs.

To clarify – these “positions” are not the positions as seen on the image scans of the manuscript itself, they are the positions in terms of glyph position along each line.

The difference between these and the ones in the previous post is that these have Gallows “f” coloured blue, “g” coloured green, and the other gallows coloured red (as before).

Categories: Folios, gallows, Knox Tags:

The Page Positional Distribution of the Gallows

June 28, 2012 6 comments

Here is a set of images, for each of the folios in the VMs, that shows the positions on the page of the various gallows glyphs. Each image shows a set of lines corresponding to the lines on the folio: the gallows glyphs are coloured in red, other glyphs are coloured grey. Spaces between words are black. (The Java application that generates these images uses the Voyn_101 transcription file as input.)

Are there any tell-tale patterns, or does this just look like random noise?

Categories: Characters, Features, Folios, gallows Tags:

Current Status

March 3, 2010 6 comments

Current Status

This is my personal summary of where I am at the moment, in particular which theories I’ve rejected (for better or worse!)

  • Theory: VMs words are anagrams of a plaintext that has been enciphered into the VMs glyphs
    • Attempts to find solutions with many mappings (1- 2- 3-grams) and various languages/dictionaries fail to find even mediocre matches
    • Unusual prevalence of e.g. “8am 8am 8am” not explained by this theory
  • Theory: VMs words are in fact pieces of plaintext words, that need to be a) combined b) deciphered
    • Trials with delimiters like VMs “o” and “9” and with many mappings and languages/dictionaries fail to find good matches
    • But this would explain “8am 8am 8am” at a stretch
  • Theory: VMs words contain numeric codes, that use a Selenus type code table, with e.g. gallows characters used as multipliers
    • There are too many VMs characters: for this to work – only, say, 4 gallows characters and ten digits are needed for a minimal implementation – what are all the rest for?
    • Doesn’t explain “8am 8am 8am”
  • Theory: VMs words are phonetic codes for a reading of the manuscript
    • Mapping the words to Soundex or Double Metaphone and comparing with plaintexts produces a poor frequency match (but is this a good test – see e.g. Robert Firth’s notes)
    • This could explain “8am 8am 8am”
  • Theory: The text is produced by a polyalphabetic cipher with rotating/repeating sequences (a la Strong)
    • Multiple attempt to fit this theory using various alphabet lengths and sequence lengths fails to find a convincing match, although plausible results can be generated
    • Would explain “8am 8am 8am”
  • Procedure: since the cipher/code/whatever it is changes at least between sections, and possibly between folios (and maybe even within a folio), examining large quantities of VMs text for statistical properties is very misleading. Only text within a single side of a folio should be tackled for decryption.