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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 ….

 

Candidate Carrots and Castor Oil

March 26, 2010 7 comments

Here is a set of plausible coincidences, or strong evidence (depending on how gullible you are) that VMs words beginning “ok-” are enciphered from Latin words beginning “ca-“.

Evidence 1: Acorus Calamus – Sweet Flag

In my last post I referred to several labels in the VMs that appear on different folios. In particular,  “okoe89”, “okae89” and “okae9”. The question was “what do they all have in common?”. Two of the three “okae9” labeled objects are roots with distinctive shapes, strongly suggestive of “Acorus Calamus” (Sweet Flag):

Conjecture: “okae9” = “Calamus”

Evidence 2: Carrots

The three “okae89” labeled plants show similarities. The one on f101v2 looks very much like a carrot, and the other two could also be carrots:

Conjecture: “okae89” = “Carota”

Evidence 3: Castillum

And what about the third label “okoe89”? There are five objects labeled by this word. Three look like plants/roots, one is some sort of funnel (from the balneological pages) and the fifth is obviously a castle:

Castle in the Rosettes folios

Conjecture: “okoe89” = “Castellum”

From this evidence, a simple conclusion is that the prefix “ok” enciphers the Latin prefix “ca”.

Evidence 4: Castor and Pollux

If the “ok” prefix is enciphering “ca”, then we can search for labels beginning with “ok” and see whether there are any obvious matches to the labeled objects with words beginning “ca”. It turns out that there are.

On f68r3, which is popularly supposed to show the Pleiades star cluster, one of the map segments has a pair of stars labeled “okoy9” and “ohos”. These seem likely to be the famous pair Castor and Pollux. Moreover, in the opposite segment is a group of four stars, one of which also has the “ok” prefix, and is labeled “ok98*”. This is possibly the Behenian star Capella in the constellation of Auriga. (Note: if this is indeed the Auriga constellation, then one of the other stars should be “Alnath”. The star next to the Pleiades is supposed to be Aldabaran, and is enciphered as “81oe8a9”. The star next to Capella is labelled “8ayaee” – perhaps this is Alnath, and the VMs prefix “8-” encodes “al-“?)

Conjecture: “okoy9” = “Castor”, “ok98*” = “Capella”

Castor, Pollux, Capella and the Pleiades

Evidence 5: Castor Oil

Following on from the identification of Castor and Pollux on f68r3, we look for other instances of “okoy9” i.e. “Castor” and find one labeling a plant on f88v. The leaf of this plant looks very similar to that of the Castor Oil plant:

Summary

VMs Word Latin Word VMs Prefix Latin Prefix VMs Postfix Latin Postfix
okae9 calamus ok ca ae9 lamus
okae89 carota ok ca ae89 rota
okoe89 castellum ok ca oe89 stellum
okoy9 castor ok ca oy9 stor
ok98* capella ok ca 98* pella

Anagram Analysis

February 26, 2010 5 comments

Several people, notably Robert Teague and Philip Neal, have theorized that the cipher is based on anagrams. The idea is that to decipher the VMs text, you first convert the VMs symbols to alphabet letters, and then you find an anagram of those letters that makes a valid plaintext word.

Variations on this theme are that e.g. some of the plaintext letters in the target word are allowed to be missing and can be inferred from “context”, and/or that the VMs words are anagrams of the plaintext words that have letters arranged alphabetically.

For this analysis, we look at Folio68r3 in particular:

The labels on the stars are, from the ten o’clock pie slice going anti-clockwise, in the Voyn 101 encoding:

<68r3.pieslice_1>61oe7a9.8oay9.oae1coe=

<68r3.pieslice_2>oh1o89.8ayaee.ok98*.oK98=

<68r3.pieslice_3>ohoe19.1G9.179,9h9=

<68r3.pieslice_4>ohos.okoy9=

Anagrams: Combinations/Permutations

If you make the reasonable assumption that all the labels on the star shapes in f68r3 are star names, and you assume a target language, then this puts severe constraints on the cipher, since there are only so many star names and only so many cipher schemes that can be consistent amongst all the stars.

For each of the 12 star labels on f68r3 (61oe7a9 8oay9 oae1coe oh1o89 8ayaee ok98* oK98 ohoe19 1G9 179,9h9 ohos okoy9 ) there are a number of possible anagrams of the symbols (anagrams):

Label size 3 6 anagrams
Label size 4 24 anagrams
Label size 5 120 anagrams
Label size 6 720 anagrams
Label size 7 5040 anagrams

It appears like there is a lot of freedom: the first label “61oe7a9” can be rearranged 5040 different ways – and you can pick any letter for any of the 7 symbols! However, when you start actually choosing the mapping between symbols and alphabet characters, and require that at least one of  the anagrams for each deciphered label appears in a dictionary of star names, you rapidly eliminate many of the possibilities.

This is still true even if you allow that a single symbol in the label can map to two alphabet characters – the problem appears to be still over-constrained

For example, say you pick a mapping for the first label:

S: 6  1  o  e  7  a  9
R: d  r  e  ba an a  l
61oe7a9 -> drebaanal -> aldebaran

then you want to apply this to the next label “8oay9”. You already have the cipher for symbols o, a and 9 … they translate to e, a and l respectively – you know that the star name must contain e, a and l. You know that the star name must be between 5 and 7 characters long, and you just need to pick suitable letters for 8 and y.

Consulting a list of ~300 star names you find the following possibilities.

Alkes, Algedi, Alheka, Alhena, Elnath, Lesath, Alcyone, Algebar, Algorel, Ascella, Capella, Eltanin and Sheliak

(Since this Don Latham sent me a link to his list of star names at www.sixmilesystems.com/voynich , which I have simplified and removed any duplicates and non-alphabetic symbols from, and put here: http://pcbunn.cacr.caltech.edu/Voynich/StarNamesLatham.txt )

Choosing Alcyone (for reasons which will be obvious to some), you now have an extended mapping that includes 8 and y:

S: 6  1  o  e  7  a  9  8  y
R: d  r  e  ba an a  l  cy on
61oe7a9 -> drebaanal -> aldebaran
8oay9 -> cyeaonl -> alcyone

So far so good. Now we come to the third label: “oae1coe” which we can decipher all but one symbol of, to: “eabar?eba”.

Unhappily there are no 9 or 10 letter stars in the dictionary that can match this letter assortment. and so this eliminates our initial choice of mapping that gave us “aldebaran” for the first word, and “alcyone” for the second, because it cannot produce a dictionary word for the third label. Back to square one.

You can keep on doing this: selecting mappings, trying them out on the first two or three labels, and finding that there is no fit to the dictionary.

Although at first sight there seems to be a lot of flexibility from the use of anagrams in the cipher, in practice if an anagram of each and all the deciphered words is required to appear
in a dictionary, then that severely constrains the solution space.

Allowing Missing Characters

Looking again at the 12 star labels on f68r3:

61oe7a9 8oay9 oae1coe oh1o89 8ayaee ok98* oK98 ohoe19 1G9 179,9h9 ohos okoy9

There are 16 different VMs symbols used:

 o 9 1 e a 8 h y 7 k 6 c * K G s

Let’s assume that each of the VMs symbols maps to a single plaintext alphabet letter. Which 16 of the 26 letters in the alphabet will we choose to map? Let’s look at our list of star names and find the 16 most used alphabet letters:

 a i r e l s h n u t b k m d o c

(shown in order of frequency). How many different ways can we map the 16 VMs symbols to these 16 letters? That is:

Factorial 16 = 16! = 20,922,789,888,000

which is about 21 trillion (give or take), and is quite a lot. To explore this huge space of possibilities, we can use a Monte Carlo method. Basically we write a program to shuffle the 16 alphabet letters, look to see how that mapping works, then shuffle again, and so on. As we go, we keep track of the best mapping found so far.

Suppose we have the following mapping (cipher):

S: o 9 1 e a 8 h y 7 k 6 c * K G s
R: a e n c i l h r o s u d k t b m

Let’s go through the f68r3 star labels and convert them to plaintext using the cipher. After we convert them, let’s look the plaintext characters up in our list of star names using a “fuzzy match”. Here are the results:

61oe7a9 -> unacoie -> ?
8oay9 -> laire -> albireo (bo)
oae1coe -> aicndac -> ?
oh1o89 -> ahnale -> alhena ()
8ayaee -> liricc -> ?
ok98* -> aselk -> sheliak (hi)
oK98 -> atel -> elnath (nh)
ohoe19 -> ahacne -> achernar (rr)
1G9 -> nbe -> deneb (de)
1799h9 -> noeehe -> ?
ohos -> aham -> hamal (l)
okoy9 -> asare -> antares (nt)

Looking at the second label as an example, this is converted to plaintext characters “laire”. The fuzzy match looks up “laire” in the star names list, and finds a match with the star called “albireo”.

Fuzzy Match Rules

There is a match between the deciphered plaintext word and a dictionary word if

  1. All the letters in the plaintext word appear in the dictionary word
  2. There are no more than N missing letters in the plaintext word

In the example shown above, N is 2, so “laire” fuzzy matches “albireo”, with letters “bo” missing (shown in brackets)

Solutions

In the above example, 8 of the 12 VMs star labels have been matched to valid star names. The application continues exploring the 16! possible arrangements, trying to improve on the number of matches.

After looking at around 70 million arrangements (i.e. about 3 millionths of them), it finds this:

Iteration 67334517 Deciphered=9/12
S: o  9  1  e  a  8  h  y  7  k  6  c  *  K  G  s
R: a  e  l  b  r  h  c  d  o  t  i  u  n  s  k  m
61oe7a9 -> ilabore -> borealis (s)
8oay9 -> harde -> schedar (sc)
oae1coe -> arbluab -> ?
oh1o89 -> aclahe -> alphecca (pc)
8ayaee -> hrdrbb -> ?
ok98* -> atehn -> elnath (l)
oK98 -> aseh -> scheat (ct)
ohoe19 -> acable -> cebalrai (ri)
1G9 -> lke -> alkes (as)
1799h9 -> loeece -> ?
ohos -> acam -> almach (lh)
okoy9 -> atade -> tarazed (rz)

Just how interesting/plausible/believable is this? We can make a control experiment by using a dictionary of dog breeds of about the same size: does mapping the VMs labels on f68r3 to star names produce a better fit than mapping the labels to dog breeds?

We run the program for a few million mappings, first with the star names, then with the dog breed names. For about 4 million mappings, there is a slightly better (9 out of 12) mapping to dog breeds compared with star names (8/12):

Dogs

Iteration 3779182 Deciphered=9/12
S: o 9 1 e a 8 h y 7 k 6 c * K G s
R: e r o n h l b s d c a p t u i g
61oe7a9 -> aoendhr -> rhodesian (si)
8oay9 -> lehsr -> charles (ca)
oae1coe -> ehnopen -> ?
oh1o89 -> eboelr -> boerboel (bo)
8ayaee -> lhshnn -> ?
ok98* -> ecrlt -> central (na)
oK98 -> eurl -> tulear (ta)
ohoe19 -> ebenor -> redbone (d)
1G9 -> oir -> corgi (cg)
1799h9 -> odrrbr -> ?
ohos -> ebeg -> beagle (al)
okoy9 -> ecesr -> crested (td)

Stars

Iteration 4208178 Deciphered=8/12
S: o 9 1 e a 8 h y 7 k 6 c * K G s
R: a i e c o l b s t h n u r d k m
61oe7a9 -> neactoi -> ?
8oay9 -> laosi -> polaris (pr)
oae1coe -> aoceuac -> ?
oh1o89 -> abeali -> algieba (g)
8ayaee -> losocc -> ?
ok98* -> ahilr -> alphirk (pk)
oK98 -> adil -> alkaid (ka)
ohoe19 -> abacei -> cebalrai (lr)
1G9 -> eki -> keid (d)
1799h9 -> etiibi -> ?
ohos -> abam -> markab (rk)
okoy9 -> ahasi -> nashira (nr)

Of course, this doesn’t disprove that the labels on f68r3 are in fact star names: it may well be that one of the 16! combinations produces a perfect fit, with “61oe7a9” deciphered to “aldebaran” and “8oay9” deciphered to “alcyone” etc..

Character Position Based Cipher

Looking just at the star labels in Folio 68r, we can extract the letter/symbol frequencies as a function of position in the label.

Here’s what they look like:

1: o 1 8 4 9 k 2 A c y 7 W s ? G e 6 g ▐ h
2: o h k 1 c a 8 e y j C 9 K H 7 2 s u m J + f G ┘ W
3: o c 1 9 h a C e y 8 k K d U + 2 * s H n ª I 6 m Z J
4: o c 9 e a 8 y 1 C h i s k 7 A Q H 2 m J 3 ? d
5: 9 o 8 e y 1 c a m h s K * C 7 S 5 2
6: 9 e 8 a 1 y o 7 c s m i
7: 9 e a c y I o m p 1
8: 9 8 e y 7
9: a 9 e

In other words, the most likely symbol to find in the first position of any VMs label is “o” (this is the Voyn_101 encoding). Second most likely is “1” and so on. For the second symbol in the label, the most likely is again “o” in first position, then “k”, and so on.

This is another take on the Crust/Mantle business.

Clearly, the symbols at the ends of the words have a completely different distribution to those at the front.

Compare the VMs star labels with the English star names from Don Latham’s list of star names (simplified):

1: a  m  s  k  h  d  r  t  e  n  b  f  z  j  p  u  c  g  i  w  v  l  o  y
2: a  l  u  i  e  h  c  r  s  d  n  o  t  z  k  w  b  g  j  m  f  y  x
3: a  r  h  i  b  n  s  m  l  t  u  d  k  g  c  e  f  z  w  j  y  p  o  v
4: a  i  e  r  h  b  d  m  l  n  u  s  k  c  f  o  t  z  w  g  p  j  y  v
5: a  i  r  l  n  e  t  h  k  b  s  m  u  d  c  f  g  y  o  z  j  w  p
6: a  h  r  i  e  t  l  n  m  b  s  d  u  c  k  z  o  y  g  p  f  j  v
7: a  e  h  n  i  r  l  b  s  m  t  o  y  d  c  u  k  z  g  f  w  v
8: a  i  h  n  e  c  t  l  s  b  o  u  k  r  f  z  m  g  y  p
9: h  a  t  n  i  e  s  u  r  o  g  z  k  d  p  c  v  m  b

So the plaintext has a quite different letter distribution: basically “a” is always the most likely, regardless of the position in the word.

A hypothesis is that there is a different mapping being used depending on the character position in the word. E.g. if I am enciphering “aldebaran” I would use one mapping for the first “a”, a different mapping for the “l” and so on.

If we also allow a VMs symbol to map to two plaintext characters, we can generate a “likely” mapping as follows:

1T: a  al m  s  k  h  d  sa r  t  ha e  n  ma b  ka f  mi z  j
1S: o  1  8  4  9  k  2  A  c  y  7  W  s  ?  G  e  6  g  ▐  h 

2T: a  l  u  i  e  h  ar ha c  r  ab la al ai s  d  lg ub as n
2S: o  h  k  1  c  a  8  e  y  j  C  9  K  H  7  2  s  u  m  J 

3T: a  r  h  i  b  n  s  m  l  t  u  d  k  g  c  e  ra ha f  z
3S: o  c  1  9  h  a  C  e  y  8  k  K  d  U  +  2  *  s  H  n 

4T: a  i  e  r  h  b  d  m  l  n  u  s  ra k  at ar al ha en c
4S: o  c  9  e  a  8  y  1  C  h  i  s  k  7  A  Q  H  2  m  J 

5T: a  i  r  l  n  e  t  h  k  ah b  s  m  u  ar ra d  c  at f
5S: 9  o  8  e  y  1  c  a  m  h  s  K  *  C  7  S  5  2 

6T: a  h  r  i  e  t  l  n  m  b  ah s  d  u  c  k  an la ab ar
6S: 9  e  8  a  1  y  o  7  c  s  m  i 

7T: a  e  h  n  i  r  l  b  s  m  t  ah o  y  d  c  u  k  at an
7S: 9  e  a  c  y  I  o  m  p  1 

8T: a  i  h  n  e  c  t  l  s  in b  o  u  ch k  r  f  et at z
8S: 9  8  e  y  7 

9T: h  a  t  n  i  e  s  u  r  ha he o  to g  z  ze ab th ra k
9S: a  9  e

(where “T” labels the plaintext alphabet, and “S” labels the source VMs alphabet).

Using this set of mappings, we can translate all the labels to plaintext. The results are disappointing: there are no matches in the list of starnames to the deciphered labels, even allowing anagrams.

But we can then start shuffling the mapping order around for each character position, and use a Monte Carlo approach to see what we come up with. This is what I am trying now. It’s not clear to me that I should allow anagrams in the solutions, since shuffling the letters destroys the ordering in the tables above, that I have assumed.

Glyph Sequence Probabilities

February 26, 2010 2 comments

In the following tables, the probability (0..1) of finding a glyph following another glyph is shown, for various parts of the Voynich manuscript and also for some other texts.

In the tables, the ‘ ‘ character (blank) signifies the start or end of a word. The “#” character signifies a rare character not listed in the tables.

For example, in the Recipes table below (generated from the “Recipes” section of the VMs), the probability of finding “o” as the first character of a VMs word can be found by looking up the row for the ” ” (blank) in the first column, then moving along to the “o” column and reading off the probability = 0.2.

Some immediate features of Note:


1) The most probable glyph to find at the start of a word in the Recipes: “1”

2) In the Herbal: “1”

3) In the Labels: “o”

4) The glyph “4” is commonly found in the Recipes and Herbals text, and it is followed by “o” at least 90% of the time. It is very rarely found in the Labels.

5) The most probable glyph to find at the end of a word in the Recipes: “n”

6) In the Herbal: “m”

7) In the Labels: “p”

The most probable words

These tables allow us to generate the “most probable” words (i.e. just by taking the most probable transitions in turn)

1) Recipes: “1oe”

2) Herbal: “oe”

3) Labels: “oe”

4) Star names: “alalal….”

5) Thomas Hardy: “s”

6) Augustinus (Latin): “is”

Normalized Transition table: vertical = first character, horizontal = following character voyn_101Recipes_Sentences.txt

 

         ' '     'o'      'c'     'a'     '9'     '1'     'e'     '8'     'h'     'y'     'k'     '4'      '2'     '7'     'm'     'g'     's'     'n'     'p'     '#'
' ' :   0.0     0.2      0.0     0.05    0.05    0.13    0.07    0.03    0.03    0.01    0.04    0.12     0.04    0.0     0.0     0.04    0.01    0.0     0.0     0.06
'o' :   0.05    0.0      0.03    0.02    0.0     0.01    0.18    0.11    0.17    0.08    0.14    0.0      0.0     0.01    0.0     0.03    0.03    0.0     0.0     0.06
'c' :   0.01    0.22     0.13    0.05    0.12    0.02    0.0     0.21    0.02    0.0     0.01    0.0      0.0     0.08    0.0     0.0     0.01    0.0     0.0     0.03
'a' :   0.01    0.0      0.0     0.0     0.0     0.0     0.22    0.01    0.01    0.22    0.0     0.0      0.0     0.0     0.14    0.0     0.0     0.11    0.07    0.14
'9' :   0.81    0.0      0.0     0.0     0.0     0.03    0.01    0.0     0.05    0.0     0.02    0.0      0.01    0.0     0.0     0.0     0.0     0.0     0.0     0.01
'1' :   0.0     0.14     0.5     0.05    0.07    0.0     0.01    0.08    0.02    0.0     0.01    0.0      0.0     0.02    0.0     0.0     0.02    0.0     0.0     0.03
'e' :   0.3     0.07     0.0     0.06    0.03    0.11    0.01    0.02    0.2     0.01    0.02    0.0      0.04    0.0     0.0     0.0     0.01    0.0     0.0     0.04
'8' :   0.09    0.03     0.03    0.3     0.38    0.02    0.02    0.0     0.0     0.0     0.0     0.0      0.01    0.0     0.0     0.0     0.0     0.0     0.0     0.05
'h' :   0.01    0.04     0.42    0.22    0.05    0.11    0.01    0.0     0.0     0.0     0.0     0.0      0.02    0.0     0.0     0.0     0.0     0.0     0.0     0.06
'y' :   0.58    0.1      0.0     0.18    0.04    0.03    0.0     0.0     0.0     0.0     0.0     0.0      0.01    0.0     0.0     0.0     0.0     0.0     0.0     0.01
'k' :   0.01    0.08     0.32    0.22    0.05    0.18    0.0     0.01    0.0     0.0     0.0     0.0      0.02    0.0     0.0     0.0     0.0     0.0     0.0     0.05
'4' :   0.0     0.91     0.04    0.0     0.0     0.0     0.0     0.0     0.01    0.0     0.0     0.0      0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.01
'2' :   0.0     0.13     0.58    0.03    0.07    0.0     0.0     0.05    0.02    0.0     0.01    0.0      0.0     0.01    0.0     0.0     0.01    0.0     0.0     0.02
'7' :   0.03    0.0      0.02    0.28    0.57    0.0     0.01    0.0     0.01    0.0     0.0     0.0      0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.04
'm' :   0.93    0.02     0.0     0.01    0.01    0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0
'g' :   0.0     0.19     0.02    0.17    0.03    0.49    0.0     0.03    0.0     0.0     0.0     0.0      0.02    0.0     0.0     0.0     0.0     0.0     0.0     0.02
's' :   0.51    0.11     0.01    0.22    0.04    0.0     0.01    0.01    0.0     0.0     0.0     0.0      0.02    0.0     0.0     0.0     0.0     0.0     0.0     0.01
'n' :   0.95    0.0      0.0     0.01    0.01    0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0
'p' :   0.94    0.01     0.0     0.0     0.0     0.0     0.0     0.01    0.0     0.0     0.0     0.0      0.0     0.01    0.0     0.0     0.0     0.0     0.0     0.0
 '#'  :   0.24    0.09    0.14    0.11    0.1     0.11    0.02    0.03    0.01     0.01    0.0     0.0     0.0     0.01    0.0     0.0     0.02    0.0     0.0      0.02

Normalized Transition table: vertical = first character, horizontal = following character Voyn101_First10Herbal_Sentences.txt

 

         ' '     'o'     '9'     '1'     'a'     'c'     '8'     'h'     'k'      'e'     'y'     's'     'm'     '2'     '4'     'g'     'p'     'n'     'j'      '#'
' '  :   0.0     0.15    0.07    0.17    0.0     0.0     0.08    0.08    0.05     0.01    0.01    0.04    0.0     0.05    0.08    0.03    0.0     0.0     0.01     0.09
'o'  :   0.06    0.01    0.02    0.02    0.02    0.02    0.13    0.11    0.13     0.19    0.1     0.02    0.02    0.0     0.0     0.01    0.02    0.0     0.0      0.03
'9'  :   0.73    0.0     0.0     0.03    0.0     0.0     0.05    0.05    0.08     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.01
'1'  :   0.0     0.43    0.14    0.0     0.1     0.21    0.0     0.02    0.02     0.01    0.0     0.01    0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.01
'a'  :   0.01    0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.12    0.19    0.0     0.27    0.0     0.0     0.0     0.08    0.09    0.0      0.13
'c'  :   0.02    0.28    0.31    0.0     0.09    0.13    0.0     0.03    0.01     0.0     0.0     0.06    0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.0
'8'  :   0.08    0.09    0.29    0.04    0.35    0.02    0.0     0.01    0.0      0.01    0.0     0.0     0.0     0.02    0.0     0.0     0.0     0.0     0.0      0.02
'h'  :   0.0     0.23    0.12    0.22    0.19    0.12    0.0     0.0     0.0      0.0     0.0     0.0     0.0     0.06    0.0     0.0     0.0     0.0     0.0      0.02
'k'  :   0.01    0.29    0.13    0.23    0.15    0.09    0.0     0.0     0.0      0.0     0.0     0.0     0.0     0.03    0.0     0.0     0.0     0.0     0.0      0.02
'e'  :   0.46    0.09    0.06    0.04    0.01    0.0     0.09    0.02    0.03     0.0     0.0     0.06    0.0     0.03    0.0     0.0     0.0     0.0     0.0      0.03
'y'  :   0.68    0.05    0.08    0.08    0.06    0.0     0.0     0.0     0.0      0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.0
's'  :   0.48    0.12    0.07    0.08    0.14    0.04    0.0     0.01    0.0      0.0     0.0     0.0     0.0     0.01    0.0     0.0     0.0     0.0     0.0      0.0
'm'  :   0.96    0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.0
'2'  :   0.03    0.48    0.1     0.0     0.05    0.27    0.0     0.02    0.03     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.0
'4'  :   0.0     0.97    0.0     0.0     0.01    0.0     0.0     0.01    0.0      0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.0
'g'  :   0.02    0.21    0.13    0.43    0.06    0.04    0.0     0.0     0.0      0.0     0.0     0.0     0.0     0.08    0.0     0.0     0.0     0.0     0.0      0.0
'p'  :   0.93    0.02    0.0     0.0     0.0     0.0     0.02    0.0     0.0      0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.02
'n'  :   0.93    0.0     0.03    0.0     0.0     0.0     0.03    0.0     0.0      0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.0
'j'  :   0.0     0.33    0.09    0.42    0.09    0.04    0.0     0.0     0.0      0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.0
'#'  :   0.23    0.22    0.12    0.04    0.08    0.09    0.01    0.02    0.01     0.0     0.0     0.03    0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.03

 

Normalized Transition table: vertical = first character, horizontal = following character LabelsAll.txt

          ' '     'o'     'a'     '9'     'e'     'y'     '8'     'c'     'h'      '1'     'k'     's'     '7'     'm'     '2'     'p'     'n'     'j'     'g'      '#'
' '  :   0.0     0.48    0.05    0.04    0.01    0.0     0.12    0.01    0.01     0.05    0.01    0.09    0.01    0.0     0.01    0.0     0.0     0.0     0.0      0.03
'o'  :   0.03    0.0     0.0     0.0     0.21    0.14    0.08    0.02    0.14     0.01    0.16    0.03    0.01    0.01    0.0     0.0     0.0     0.02    0.02     0.04
'a'  :   0.02    0.0     0.0     0.0     0.27    0.36    0.01    0.0     0.02     0.0     0.0     0.02    0.0     0.05    0.0     0.06    0.05    0.0     0.0      0.06
'9'  :   0.82    0.0     0.0     0.0     0.0     0.0     0.05    0.0     0.04     0.0     0.03    0.01    0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.0
'e'  :   0.33    0.09    0.07    0.13    0.0     0.0     0.09    0.01    0.06     0.05    0.0     0.06    0.02    0.0     0.01    0.0     0.0     0.0     0.0      0.04
'y'  :   0.33    0.14    0.25    0.13    0.0     0.0     0.01    0.0     0.0      0.06    0.0     0.0     0.01    0.0     0.01    0.0     0.0     0.0     0.0      0.0
'8'  :   0.07    0.09    0.37    0.29    0.03    0.0     0.01    0.02    0.0      0.05    0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.03
'c'  :   0.01    0.3     0.05    0.11    0.0     0.0     0.12    0.08    0.04     0.01    0.02    0.04    0.08    0.0     0.0     0.0     0.0     0.01    0.0      0.04
'h'  :   0.01    0.24    0.27    0.11    0.0     0.0     0.0     0.17    0.0      0.13    0.0     0.0     0.0     0.0     0.02    0.0     0.0     0.0     0.0      0.0
'1'  :   0.0     0.26    0.03    0.14    0.0     0.0     0.14    0.26    0.0      0.0     0.0     0.01    0.05    0.0     0.0     0.0     0.0     0.0     0.0      0.01
'k'  :   0.01    0.31    0.2     0.11    0.01    0.0     0.01    0.19    0.0      0.11    0.0     0.0     0.02    0.0     0.01    0.0     0.0     0.0     0.0      0.02
's'  :   0.22    0.21    0.38    0.08    0.0     0.0     0.01    0.02    0.02     0.01    0.0     0.01    0.0     0.0     0.01    0.0     0.0     0.0     0.0      0.01
'7'  :   0.0     0.07    0.39    0.48    0.0     0.0     0.0     0.0     0.0      0.0     0.0     0.0     0.0     0.0     0.02    0.0     0.0     0.0     0.0      0.02
'm'  :   0.69    0.04    0.04    0.04    0.0     0.0     0.08    0.04    0.0      0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.04
'2'  :   0.04    0.34    0.0     0.08    0.0     0.0     0.17    0.21    0.0      0.04    0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.08
'p'  :   0.9     0.0     0.0     0.04    0.0     0.0     0.0     0.0     0.0      0.0     0.0     0.0     0.04    0.0     0.0     0.0     0.0     0.0     0.0      0.0
'n'  :   0.89    0.0     0.0     0.05    0.0     0.0     0.05    0.0     0.0      0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.0
'j'  :   0.0     0.15    0.15    0.15    0.0     0.0     0.1     0.1     0.0      0.31    0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.0
'g'  :   0.0     0.38    0.23    0.0     0.0     0.0     0.0     0.07    0.0      0.3     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.0
'#'  :   0.18    0.15    0.13    0.2     0.01    0.01    0.02    0.08    0.03     0.03    0.02    0.03    0.0     0.0     0.01    0.0     0.0     0.0     0.0      0.06

Normalized Transition table: vertical = first character, horizontal = following character StarNamesLatham.txt

          ' '     'a'     'i'     'h'     'e'     'l'     'r'     's'     'n'      'm'     'u'     't'     'b'     'k'     'd'     'c'     'z'     'f'     'o'      '#'
' '  :   0.0     0.26    0.01    0.04    0.03    0.0     0.04    0.1     0.03     0.1     0.01    0.04    0.03    0.06    0.04    0.01    0.02    0.02    0.0      0.07
'a'  :   0.09    0.01    0.05    0.07    0.0     0.16    0.1     0.04    0.06     0.03    0.02    0.07    0.05    0.04    0.03    0.02    0.02    0.01    0.0      0.04
'i'  :   0.1     0.06    0.0     0.02    0.02    0.05    0.09    0.07    0.11     0.06    0.0     0.03    0.07    0.04    0.05    0.03    0.01    0.02    0.01     0.07
'h'  :   0.29    0.35    0.09    0.0     0.11    0.0     0.01    0.0     0.0      0.0     0.04    0.0     0.0     0.0     0.0     0.0     0.0     0.01    0.03     0.0
'e'  :   0.12    0.01    0.03    0.01    0.02    0.15    0.09    0.05    0.13     0.04    0.03    0.06    0.04    0.02    0.05    0.03    0.02    0.0     0.0      0.04
'l'  :   0.14    0.19    0.09    0.04    0.07    0.02    0.0     0.04    0.0      0.04    0.02    0.03    0.03    0.02    0.01    0.04    0.0     0.03    0.0      0.1
'r'  :   0.21    0.31    0.09    0.0     0.06    0.0     0.02    0.02    0.03     0.0     0.05    0.02    0.0     0.03    0.02    0.0     0.01    0.02    0.01     0.01
's'  :   0.19    0.3     0.08    0.1     0.04    0.0     0.0     0.01    0.0      0.0     0.08    0.01    0.0     0.0     0.0     0.11    0.0     0.0     0.02     0.0
'n'  :   0.34    0.21    0.12    0.01    0.08    0.0     0.0     0.01    0.0      0.0     0.02    0.03    0.01    0.03    0.0     0.01    0.01    0.0     0.0      0.03
'm'  :   0.16    0.29    0.17    0.0     0.15    0.0     0.0     0.0     0.0      0.02    0.11    0.0     0.01    0.0     0.0     0.0     0.0     0.0     0.03     0.0
'u'  :   0.01    0.02    0.0     0.03    0.02    0.07    0.15    0.08    0.04     0.05    0.01    0.07    0.12    0.05    0.07    0.02    0.05    0.0     0.0      0.04
't'  :   0.28    0.28    0.05    0.18    0.04    0.0     0.0     0.0     0.01     0.0     0.03    0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.04     0.0
'b'  :   0.29    0.29    0.08    0.02    0.13    0.0     0.01    0.01    0.0      0.0     0.03    0.0     0.04    0.0     0.0     0.0     0.0     0.0     0.01     0.0
'k'  :   0.22    0.4     0.11    0.01    0.04    0.01    0.04    0.0     0.0      0.0     0.04    0.0     0.02    0.03    0.01    0.0     0.0     0.0     0.01     0.0
'd'  :   0.27    0.22    0.11    0.12    0.1     0.0     0.02    0.02    0.0      0.0     0.04    0.0     0.0     0.0     0.02    0.0     0.0     0.01    0.02     0.01
'c'  :   0.07    0.22    0.02    0.37    0.06    0.04    0.02    0.0     0.0      0.0     0.02    0.02    0.01    0.01    0.01    0.03    0.0     0.0     0.02     0.0
'z'  :   0.09    0.32    0.15    0.01    0.16    0.01    0.0     0.0     0.04     0.01    0.14    0.0     0.0     0.0     0.0     0.0     0.02    0.0     0.0      0.02
'f'  :   0.19    0.42    0.15    0.0     0.05    0.0     0.03    0.0     0.0      0.0     0.02    0.0     0.0     0.0     0.02    0.0     0.01    0.05    0.02     0.0
'o'  :   0.14    0.01    0.0     0.02    0.0     0.08    0.18    0.03    0.17     0.12    0.04    0.02    0.01    0.02    0.01    0.02    0.01    0.0     0.0      0.04
'#'  :   0.05    0.33    0.07    0.14    0.14    0.01    0.01    0.0     0.0      0.01    0.07    0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.03     0.06

Normalized Transition table: vertical = first character, horizontal = following character ThomasHardy.txt

          ' '     'e'     'i'     's'     'n'     'r'     'a'     't'     'o'      'l'     'd'     'c'     'g'     'u'     'h'     'p'     'm'     'y'     'f'      '#'
' '  :   0.0     0.03    0.03    0.11    0.02    0.04    0.05    0.05    0.02     0.03    0.05    0.08    0.02    0.01    0.04    0.06    0.04    0.0     0.04     0.16
'e'  :   0.15    0.03    0.0     0.1     0.09    0.14    0.06    0.02    0.0      0.04    0.14    0.03    0.0     0.0     0.0     0.01    0.02    0.0     0.0      0.06
'i'  :   0.0     0.04    0.0     0.08    0.31    0.04    0.02    0.08    0.07     0.05    0.04    0.05    0.03    0.0     0.0     0.01    0.03    0.0     0.01     0.06
's'  :   0.31    0.09    0.07    0.07    0.0     0.0     0.02    0.14    0.03     0.01    0.0     0.02    0.0     0.03    0.06    0.03    0.01    0.0     0.0      0.03
'n'  :   0.13    0.11    0.05    0.05    0.01    0.0     0.03    0.1     0.03     0.0     0.08    0.06    0.21    0.01    0.0     0.0     0.0     0.0     0.0      0.05
'r'  :   0.11    0.23    0.1     0.04    0.02    0.02    0.09    0.05    0.07     0.01    0.03    0.01    0.01    0.02    0.0     0.0     0.02    0.03    0.0      0.04
'a'  :   0.0     0.0     0.05    0.07    0.14    0.14    0.0     0.13    0.0      0.1     0.03    0.05    0.02    0.01    0.0     0.03    0.02    0.01    0.0      0.09
't'  :   0.17    0.17    0.17    0.03    0.0     0.06    0.07    0.03    0.03     0.02    0.0     0.01    0.0     0.03    0.09    0.0     0.0     0.03    0.0      0.02
'o'  :   0.01    0.0     0.01    0.04    0.21    0.12    0.01    0.04    0.04     0.04    0.02    0.02    0.01    0.11    0.0     0.03    0.06    0.0     0.01     0.12
'l'  :   0.1     0.19    0.11    0.01    0.0     0.0     0.1     0.02    0.08     0.1     0.03    0.0     0.0     0.02    0.0     0.0     0.0     0.14    0.0      0.03
'd'  :   0.45    0.15    0.12    0.03    0.0     0.03    0.02    0.0     0.02     0.02    0.02    0.0     0.0     0.02    0.0     0.0     0.0     0.01    0.0      0.02
'c'  :   0.02    0.16    0.05    0.0     0.0     0.04    0.1     0.09    0.18     0.04    0.0     0.02    0.0     0.05    0.11    0.0     0.0     0.01    0.0      0.07
'g'  :   0.42    0.11    0.05    0.02    0.01    0.06    0.05    0.0     0.03     0.04    0.0     0.0     0.02    0.02    0.08    0.0     0.0     0.0     0.0      0.0
'u'  :   0.0     0.03    0.03    0.14    0.14    0.17    0.03    0.07    0.0      0.1     0.02    0.03    0.04    0.0     0.0     0.03    0.04    0.0     0.0      0.03
'h'  :   0.11    0.28    0.13    0.01    0.0     0.02    0.14    0.06    0.13     0.0     0.0     0.0     0.0     0.03    0.0     0.0     0.0     0.01    0.0      0.01
'p'  :   0.04    0.21    0.08    0.01    0.0     0.14    0.13    0.03    0.1      0.08    0.0     0.0     0.0     0.02    0.04    0.06    0.0     0.0     0.0      0.0
'm'  :   0.06    0.23    0.13    0.02    0.0     0.0     0.17    0.0     0.11     0.0     0.0     0.0     0.0     0.02    0.0     0.1     0.03    0.01    0.0      0.05
'y'  :   0.75    0.05    0.03    0.03    0.0     0.0     0.01    0.0     0.02     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.01    0.0     0.0      0.04
'f'  :   0.04    0.13    0.13    0.0     0.0     0.06    0.14    0.03    0.14     0.08    0.0     0.0     0.0     0.1     0.0     0.0     0.0     0.0     0.07     0.0
'#'  :   0.15    0.2     0.11    0.06    0.02    0.02    0.09    0.03    0.07     0.05    0.0     0.0     0.0     0.03    0.02    0.0     0.0     0.0     0.0      0.03

Normalized Transition table: vertical = first character, horizontal = following character Augustinus_all.txt

          ' '     'e'     'i'     'a'     't'     'r'     's'     'u'     'n'      'm'     'o'     'c'     'l'     'd'     'p'     'b'     'v'     'f'     'g'      '#'
' '  :   0.0     0.04    0.09    0.09    0.04    0.03    0.09    0.01    0.03     0.05    0.02    0.08    0.03    0.07    0.09    0.0     0.05    0.05    0.01     0.03
'e'  :   0.13    0.0     0.0     0.01    0.06    0.2     0.08    0.0     0.14     0.07    0.0     0.05    0.02    0.03    0.01    0.05    0.0     0.0     0.01     0.03
'i'  :   0.08    0.04    0.0     0.05    0.12    0.02    0.14    0.04    0.12     0.04    0.05    0.05    0.03    0.03    0.01    0.04    0.01    0.0     0.02     0.01
'a'  :   0.1     0.07    0.0     0.0     0.15    0.09    0.05    0.02    0.11     0.12    0.0     0.04    0.04    0.02    0.01    0.06    0.01    0.0     0.01     0.0
't'  :   0.16    0.16    0.22    0.15    0.0     0.04    0.0     0.17    0.0      0.0     0.04    0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.01
'r'  :   0.12    0.24    0.16    0.15    0.04    0.02    0.01    0.07    0.01     0.01    0.04    0.0     0.0     0.01    0.01    0.01    0.01    0.0     0.0      0.0
's'  :   0.43    0.09    0.08    0.05    0.09    0.0     0.05    0.05    0.0      0.0     0.02    0.05    0.0     0.0     0.02    0.0     0.0     0.0     0.0      0.02
'u'  :   0.01    0.05    0.05    0.04    0.03    0.12    0.18    0.0     0.06     0.19    0.01    0.02    0.06    0.04    0.02    0.01    0.0     0.0     0.01     0.0
'n'  :   0.0     0.1     0.11    0.06    0.27    0.0     0.08    0.05    0.0      0.0     0.05    0.02    0.0     0.11    0.01    0.0     0.01    0.01    0.02     0.0
'm'  :   0.46    0.08    0.1     0.09    0.0     0.0     0.0     0.06    0.01     0.01    0.06    0.0     0.0     0.0     0.03    0.01    0.0     0.0     0.0      0.02
'o'  :   0.14    0.01    0.0     0.0     0.03    0.23    0.08    0.0     0.18     0.04    0.0     0.05    0.06    0.02    0.02    0.02    0.01    0.01    0.01     0.02
'c'  :   0.01    0.18    0.16    0.12    0.1     0.05    0.0     0.1     0.0      0.0     0.18    0.03    0.01    0.0     0.0     0.0     0.0     0.0     0.0      0.01
'l'  :   0.0     0.16    0.28    0.18    0.03    0.0     0.01    0.09    0.0      0.0     0.07    0.01    0.09    0.0     0.0     0.0     0.01    0.0     0.0      0.0
'd'  :   0.0     0.28    0.36    0.1     0.0     0.0     0.0     0.09    0.0      0.0     0.1     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.0
'p'  :   0.0     0.25    0.12    0.09    0.04    0.16    0.02    0.06    0.0      0.0     0.12    0.0     0.07    0.0     0.01    0.0     0.0     0.0     0.0      0.01
'b'  :   0.0     0.11    0.14    0.38    0.0     0.04    0.02    0.2     0.0      0.0     0.03    0.0     0.01    0.0     0.0     0.0     0.0     0.0     0.0      0.0
'v'  :   0.0     0.33    0.38    0.11    0.0     0.0     0.0     0.03    0.0      0.0     0.12    0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0      0.0
'f'  :   0.0     0.17    0.21    0.19    0.0     0.04    0.0     0.13    0.0      0.0     0.08    0.0     0.07    0.0     0.0     0.0     0.0     0.07    0.0      0.0
'g'  :   0.0     0.25    0.24    0.13    0.0     0.12    0.0     0.07    0.1      0.0     0.03    0.0     0.02    0.0     0.0     0.0     0.0     0.0     0.0      0.0
'#'  :   0.22    0.05    0.05    0.09    0.01    0.01    0.0     0.34    0.0      0.0     0.05    0.02    0.0     0.0     0.01    0.0     0.0     0.0     0.0      0.07
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