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Alfonso X’s Lapidario: Stones, Stars and Colours

October 13, 2016 6 comments

I’ve been down a bit of rabbit hole over the last couple of days which others may have already been down. I was looking once more at the Zodiac folios, in particular Taurus. The Taurus Light and Dark folios are both marked “may” in, as often remarked, a later hand. There are 15 figures in each Taurus folio, for a total of 30. However, as we well know, May has 31 days, so the figures probably don’t represent days. I thus went in search of 30-way splits of Zodiac signs ….

Alfonso X’s Lapidario

Looking at this old Spanish illustrated manuscript:

“Tratados de Alfonso X sobre astrología y sobre las propiedades de las piedras”

which is a treatise on astrology and the importance of stones/gems etc., we can see a circular Taurus diagram with 30 divisions.

lapidario_taurus_30

Each of these divisions is associated with a stone, of a noted colour, and one or a few stars in a constellation. There is a lengthy description of each division, its stone, its stars, the various ailments the stone cures, when the stone should be used, et cetera. There is a Spanish transcription of the text here, which I found very useful (combined with Google Translate):

Alfonso X Lapidario

Since a plausible language match to the month spellings as written in the Zodiac folios is Occitan which at one point covered part of Spain (please correct me on this, as I’m not sure), there seems to be a compelling regional match here, but I can’t quite figure it out.

From what I’ve read, Alfonso X assembled a team of scholars from all world regions, who worked on documents on a variety of topics. This website says of the Lapidario: “The Lapidario is a thirteenth century Castilian translation sponsored by King Alfonso X el Sabio, the Learned. The translation was done from an Arabic text which in turn is said to have been translated by the mysterious Abolays from an ancient text in the “Chaldean language”

Matching Stone Colours

Anyway, my first approach was to try to match the colours of the headgear or tunics of the clothed figures in the Taurus Light folio to the colours of the first and second fifteen stones mentioned in the Lapidario. It’s a little tricky, because although the stones are numbered, we don’t know which is figure 1 in the Taurus Light folio, and whether the inner ring precedes the outer. Even so, the patterns of colours in the stones sequence might reveal a match. I drew a blank.

Matching Stones with Voynich Star Labels

My second approach was to try to match the names of the stones with the labels on the figures, to see if there was some correlation between the label length, or its initial glyph, with the stones’ names. Very tricky.

Some of the stones that appear in the Taurus set of 30 also appear in other Zodiac signs in the Lapidario. For example, the ninth stone in Taurus is “esmeri(l)” (Latin), and esmeril is also the third stone of Libra, and the second stone of Aquarius.

This leads to the obvious question: is there a Figure in the both the Voynich Taurus and Libra roundels (Aquarius is missing) that shares the same label? If so, might that label be “esmeril”? And, are there other stones that appear in more than one sign which might be matched to duplicate stones in the Lapidario?

(As an aside, regarding the stones and colours, I was struck by the third stone of Taurus, called “camorica”, which is scarlet in colour and associated with the Pleiades.)

Another promising avenue is to compare the shapes and orientations of the stars in the constellations as they appear in the VM with how they appear in the Lapidario. Since the Pleiades are mentioned in the Lapidario, are they illustrated there, and does its illustration of the cluster match the apparent drawing of it in the VM (which differs in detail from its actual appearance in the night sky)? I need to investigate further, but my suspicion is that others have already been down this path 🙂

Chaldean Stones

I extracted the Chaldean stone names for each Zodiac sign, from the transcription I linked to above. The stones for Aries are shown below, as an example. (The whole set is available if anyone wants it.)

The first 12 sections in the Lapidario list the 30 stones for each zodiac sign, but a few signs appear to be truncated: Leo has only one stone, Pisces only has two stones, and Aquarius only 28.

There follow more sections, again one for each sign, but these each have only three stones. I’m not clear what they represent. I posted about all this at Voynich Ninja, and MarcoP was able to explain. Others also chimed in with some useful comments. The discussion is here.

Anyway, following those sections are several more that cover the stones of Saturn (4 stones), Jupiter (4 stones), Mars (4 stones), Venus (24 stones), Sun (9 stones) and Mercury (17 stones).

Here is an extract of the list I extracted for all the Zodiac stones: this is for Aries.

ARIES
1 magnitad
2 zurudica
3 gagatiz
4 miliztiz
5 centiz
6 movedor
7 goliztiz
8 telliminuz
9 milititaz
10 huye de la leche
11 alj?far
12 anetatiz
13 beruth
14 piedra de cinc
15 tira el oro
16 chupa la sangre
17 parece en la mar cuando sube Marte
18 tira el vidrio
19 annora
20 yzf
21 cuminon
22 astarnuz
23 belyniz
24 gaciuz
25 azufaratiz
26 abietityz
27 lubi
28 ceraquiz
29 berlimaz
30 annoxatir

In total I count 301 stones in the Lapidario’s Zodiac section, of which 291 are unique to a sign. The remainder appear more than once as follows:

bezaar [(9, 'G\x83MINIS'), (11, 'G\x83MINIS')]
azarnech [(12, 'SAGITARIO'), (13, 'SAGITARIO')]
pez [(7, 'LIBRA'), (30, 'LIBRA')]
plomo [(18, 'VIRGO'), (13, 'CANCRO')]
calcant [(10, 'VIRGO'), (11, 'VIRGO')]
aliaza [(23, 'TAURO'), (29, 'TAURO')]
parece en la mar [(15, 'SAGITARIO'), (15, 'TAURO'), (17, 'G\x83MINIS'), (17, 'ACUARIO')]
de la serpiente [(12, 'LIBRA'), (7, 'G\x83MINIS')]

e.g. “bezaar” is the 9th and the 11th stone in Gemini, “de la sepiente” is the 12th stone in Libra and the 7th in Gemini.

Turning to the Voynich Zodiac, I count 298 unique star labels of which 269 are unique to a sign. The labels that appear more than once are:

otal dar ['71r', '70v2'] Aries (Light) , Pisces , 
otal ['72r2', '73r'] Gemini , Scorpio , 
okeey ary ['72r1', '72r2'] Taurus (Dark) , Gemini , 
okal ['73v', '72r2', '72r2'] Sagittarius , Gemini , Gemini , 
okeos ['73v', '73r', '73r'] Sagittarius , Scorpio , Scorpio , 
okeoly ['70v2', '72v1'] Pisces , Libra , 
otaly ['70v2', '72v3', '73r'] Pisces , Leo , Scorpio , 
okaram ['70v2', '72r2'] Pisces , Gemini , 
okoly ['70v1', '72v3'] Aries (Dark) , Leo , 
okalar ['72r3', '72r2'] Cancer , Gemini , 
okary ['72v3', '73r'] Leo , Scorpio , 
okam ['72r2', '72v3'] Gemini , Leo , 
okeody ['73v', '73v', '73r', '72v2'] Sagittarius , Sagittarius , Scorpio , Virgo , 
ykey ['73v', '73v'] Sagittarius , Sagittarius , 
okaly ['70v2', '72r2', '72r2', '72v3'] Pisces , Gemini , Gemini , Leo , 
okaldy ['72r2', '72v3'] Gemini , Leo , 
otaraldy ['72r1', '72r2'] Taurus (Dark) , Gemini , 
otoly ['72v3', '73r'] Leo , Scorpio , 
oky ['73v', '72v3', '73r'] Sagittarius , Leo , Scorpio , 
oteody ['73v', '73v'] Sagittarius , Sagittarius , 
okedy ['72v1', '73r'] Libra , Scorpio ,

e.g. “otal dar” appears as a label on both the Aries(Light) and Pisces zodiac chart.

If the Voynich Zodiac charts are indeed showing stones (and the figure/star labels are their names), then there should be good matches between the two lists above.

One potential match is:

azarnech [(12, 'SAGITARIO'), (13, 'SAGITARIO')] 
ykey ['73v', '73v'] Sagittarius , Sagittarius ,

However, the two labels “ykey” on f73v are not adjacent, which they should be if they are stones 12 and 13.

Another:

azarnech [(12, 'SAGITARIO'), (13, 'SAGITARIO')] 
oteody ['73v', '73v'] Sagittarius , Sagittarius ,

in this case, the two labels “oteody” on f73v are adjacent to one another, but the figures/stars they label are in the group of four at the top of the folio: it’s a stretch to think their locations are 12th and 13th.

To be continued ….

 

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Common Words in Language A that are Rare in Language B

March 15, 2013 40 comments

The question was posed: which words are common in Language A but rare in Language B? And vice versa.

For this study I used the Herbal/Balneo folios that are Language A and B respectively (folios 1-25 and 75-84).

There are around 2900 unique words in total, with around 1600 being used in Language A, and 1630 in Language B.

Here are the results. The tables show the words in order of decreasing value of the frequency in A (B) divided by the frequency in B (A), and show the number of occurrences of each word in both Languages.

Common in A, rare in B

Common in A, rare in B

 

Common in B, rare in A

Common in B, rare in A

Conclusion? I have no idea … for now.

Categories: Features, Folios, Languages

Single glyphs in Language A and Language B

March 2, 2013 4 comments
As a sanity check, I looked at single glyphs (rather than nGrams > 1), searching for the mapping that takes all the Language B glyphs and maps them to Language A glyphs, so that the Language B words converted with the mapping most closely match the frequency of Language A words. I found the following:
Chromosome  ['o', '9', '1', 'a', 'H', 'c', 'e', 'h', 'y', 'k', '2', 's', 'm', '4', 'i', '(', '8', 'p', 'g', 'n']
ngramsA     ['o', '9', '1', 'a', '8', 'c', 'e', 'h', 'y', 'k', '2', 's', 'm', '4', 'g', 'i', 'K', 'p', '?', 'n']

This shows that most Language B glyphs map to the same glyph in Language A. However, there is some mixing going on here between “H”, “8”, “i”, “g”, “(“, “K” and “?”

It occurred to me that this may be due to GC’s choice of ascribing single glyphs where there should perhaps be several. In particular, he has:
“m” which looks like “iiN”
“n” which looks like “iN”
“M” which looks like “iiiN”
(I think EVA does a better job of recognizing these.) So I adjusted the GC transcription accordingly, replacing n,m,M with the i,N combinations above.
This resulted in a new mapping for B to A:
Chromosome  ['o', '9', '1', 'a', 'i', 'g', 'c', 'y', 'k', 'e', 'h', 'N', '2', 's', '4', '(', '8', 'p', 'f', 'H']
ngramsA     ['o', '9', '1', 'a', 'i', '8', 'c', 'e', 'h', 'y', 'k', 'N', '2', 's', '4', 'g', 'K', 'p', '?', 'H']
(There may be better mappings, but this is the best so far.) This has some interesting features:
  • e and y swap between languages
  • h and k gallows swap between languages
  • some mixing of g,8,(,K,f,? – some of these are relatively rare, so the statistics are poor, which may explain the mixing.
 Note that the simplification table I’m using for Voyn_101 is currently:
    seek = ["3",   "5",    "+",  "%",   "#", "6", "7",    "A", "X",  
            "I",   "C",    "z",  "Z",   "j", "u", "d",    "U", "P", 
            "Y",   "$",    "S",  "t",   "q",
            "m",   "M",    "n",  "Y",   "!"]
    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"]
(Thanks to Tony Gaffney for spotting an error in the conversion for C in a previous version.)
Categories: Algorithms, Languages

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 …

How was the Voynich Manuscript text written?

August 23, 2012 7 comments

I’ve spent many happy hours poring over the text, and am convinced that it is not as “simple” as it appears (i.e. the “words” are not words at all). Here are some conjectures:

  1. The lines look like they are written left to right i.e. the glyphs were written down from left to right, but were not.
  2. The scribe started with the drawing and started writing glyphs at various positions on the page.
  3. The method used for choosing each glyph and for deciding its position involved a mechanical apparatus, perhaps a set of co-rotating cipher wheels that were used to convert each character in the Latin plaintext into a VMs glyph and page position
  4. The apparatus is set to a new starting position for each folio/page (so e.g. Bettony labels on the three folios the plant appears on are different)
  5.  The density of ink is a clue to the order in which the glyphs were written (nib/quill freshly dipped and full of ink, or almost dry)
  6. At some point the scribe finishes writing the needed glyphs, and then fills out the spaces with pseudo-random words.
  7. There is no punctuation because what is seen are not words. What is seen makes no grammatical sense because the glyphs are not ordered and positioned linearly across the page.
  8. Perhaps the secret to unwinding the cipher is in the labels. The labels on one page are constrained to have been produced by the same initial position of the cipher apparatus, and they must come from the plaintext label.

There are so many clues as to what is going on, yet putting them all together is hugely challenging

For example, Jim Reeds suggested years ago that the order in which the text had been written on the sunflower page, f33v:

f33v

was first the text to the left of the left stalk, second the text in between the stalks, and finally the text to the right of the last stalk. This is compelling, since the ink density looks different, and the lines don’t line up well across the stalks. It becomes clearer if you saturate the image:

f33v Saturated

And in that image, what jumps out are the glyphs that are darker than the others. Those can be seen more clearly in black/white:

f33v monochrome drop

where the “o”, “y”, “8”, “e” stick out like sore thumbs. Most of those are in the left section, some in the middle, and fewer in the right. Why are these glyphs bolder, why are they inked more heavily? Were these the glyphs initially placed on the page, and contain the real information, and the rest, unimportant and pseudo-random, were all added later to make the text look “normal”?

Categories: 8, ay, Characters, e, f33v, Features, Jim Reeds, Latin, o, oy, Theories, Writing, y Tags: , ,

Frequency Distributions for Phonetic Codes

June 12, 2012 1 comment

Knox took the time to plot the frequency distributions from this post, where I looked at the theory that the VMs words are phonetic codes. Here are his results:

Where not included in the title, comparisons are to the Herbal Sections. VMs is in blue-black.

Comparison of phonetic code frequencies between VMs sections and various known texts.

With only 40 words to translate, there cannot be a meaningful series but it would be interesting to see the actual words in position, anyway. If this only shows the power of Genetic Algorithms to match something regardless of significance, why does the old Latin Herbal make the best matches to the Herbal and Astrological sections?

Copy and Conversion Errors

May 23, 2012 3 comments

Here is a piece of Greek from the Vienna Dioscurides.

Greek from the Vienna Dioscurides

Take the second line of text: we can make a simple substitution cipher to convert the Greek characters to Voynich glyphs:

One line glyph conversion

Now suppose there is a second step, where the Voynich glyphs are re-arranged into “words” according to some rules, and are then written into the manuscript.

So where am I going with this? Depending on how easily the original Greek characters are read (e.g. some lines are faint), and whether the characters are recognised correctly, would change the choice of which Voynich glyph to use. If a very old manuscript was being enciphered, this would probably be the case. Besides which, the mapping between a Greek character and a Voynich glyph might change depending on e.g. a table of equivalent characters/glyphs, or a choice of substitution cipher.

Thus if a) the original text is in a language unfamiliar to the scribe, and/or b) the original text is indistinct or otherwise hard to read, then the process of converting it to ciphertext causes errors. The same Greek letters might end up being enciphered differently depending on their readability.

Categories: Greek, Writing