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Genetic Algorithm based Phrase Analysis

February 26, 2010 Leave a comment Go to comments

Hypothesis

The following hypothesis occurred to me while I was investigating a cipher theory proposed by Rich Santa Coloma. (This is not a new idea amongst Voynich researchers, but it was new to me!)

The VMs “words” are codes for plaintext character groups, probably trigraphs, digraphs and single characters.

How does  one use this system?

1) Take each word in the plaintext
2) Break it up into a sequence of one or more trigraphs, digraphs and single characters by referring to a code table
3) Write the code for each, separated by a space, and terminate the last  tri/di-graph/character code by a VMs “9”.

The labels are probably treated differently: there may well be a separate set of codes just for the labels.

As an example, take the following “sentence” of 33 “words” from the Herbal folios:

h1cok 2oe 1c9 4ohom 2oy 4ok1coe 1oyoy 2o82c9 4okd9 4okcc9 8am 4okC9 Kay o1c9 1oe 1oe 4ok1c9 8am 1okd9 8ae s19 k1c9 8am 8C9 ko8 8an 4okds 3o h1cc9 sam 1oh1oe 1oy Hos

Breaking the VMs “words” at each terminal “9”, this is deciphered to be a sentence of 13 words:

h1cok 2oe 1c
4ohom 2oy 4ok1coe 1oyoy 2o82c
4okd
4okcc
8am 4okC
Kay o1c
1oe 1oe 4ok1c
8am 1okd
8ae s1
k1c
8am 8C
ko8 8an 4okds 3o h1cc
sam 1oh1oe 1oy Hos

Each of these words is built of one or more codes. E.g. the first word in the list above is “h1cok 2oe 1c” and may be deciphered as

h1cok = “qui”,
2oe = “de”
1c = “m”

to make the Latin word “quidem”.

An interesting feature of this cipher/code is that you may have several choices of how to split each plaintext word into tri/di/mono-graphs, but without ambiguity for the decipherer. This may be an explanation for the different frequency distributions between the VMs folios and Currier hands: they were written by different scribes who tended to split the plaintext words differently.

Does the Theory fit the Data, for Latin?

We first take a substantial body of text from the VMs, e.g. the Recipes folios, and feed it through an application code that extracts all the VMs words, and groups them according to the procedure described above, using one or more arbitrary characters as word ending marks. Typically we use VMs “9”. Each sentence so derived is analysed: each of the tokens is analysed for n-gram content and frequencies are tallied.

At the end of the processing, the n-grams are sorted into frequency order: the most frequent n-grams appear first in the list.

At this point the application moves to its second stage. It ingests a large list of Latin phrases, generated by Knox (thanks, Knox!) and processes each word in each unique phrase for n-gram content, so extracting the n-gram frequencies for Latin. The phrases are placed in a sorted list: shortest first. The n-grams are sorted by frequency, most frequent first.

Here are the Latin phrase sizes used:

A total of 53834 different phrases of size >= 2
2 4405
3 28152
4 8524
5 3866
6 2227
7 1507
8 1085
9 813
10 633
11 513
12 424
13 356
14 300
15 252
16 209
17 177
18 150
19 130

The third stage of the application is to generate a set of Genetic Algorithm chromosomes. Each chromosome takes the Top N n-grams from the Voynich n-gram list and pairs them with a random selection of the n-grams from the Latin list.

For example, for a Chromosome of length 15 (in fact the GA uses much longer lengths, typically 200) the following table might be used:

V: am ay ae 1c8 4ohC oe 1c 4oham 8am 4ohan oham okam  oy 1c7  e
L: ed gi  n  de   et ae  p     s  du    tu   nd    d tio rum te

The chromosomes are “scored” by having them translate/decipher a training set of sentences from the input VMs folios. To calculate the score of each chromosome for each sentence, the sentence word tokens are converted to Latin n-grams using the chromosome’s table. Then the tokens are joined together to form the plaintext words. The plaintext words are looked up in the Latin dictionary: the chromosome’s score is increased for valid words, and decreased for invalid words. Once all the words in the sentence have been deciphered in this way, it is compared with each of the Latin phrases: if a Latin phrase appears in the sentence, the score of the chromosome is increased substantially.

The best chromosome found by a Monte Carlo method (basically generating random chromosomes, and retaining the best scoring chromosome) is placed at the top of a list, and then the remaining chromosomes needed for the Genetic Algorithm are generated.

The GA phase now begins: the chromosomes are genetically altered, mated and selected to optimise the best chromosome’s score on the training sentences. This phase is compute intensive.

Periodically, the GA will report on its progress:

Epoch 311 Cost/Ave 62.845588235294116/61.22993872549012 same 1 Mutated 21.608040201005025% New 1 MS 15
62.845588235294116 GAPhrases$Chromosome@41ec5a Good=128 / 408 = 31.37255% 40 phrases in 25 sentences
S: am ay ae 1c8 4ohC oe 1c 4oham 8am 4ohan oham okam  oy 1c7  e
R: ed gi  n  de   et ae  p     s  du    tu   nd    d tio rum te
Sentence 189
S: 2o ok1c - 1coe hc1 - 1Kc - ohan ae e hC - 4ohan 1cH - 1c7ay ap e2c - 2c7ae ohcay e hc8 - 1coehC - ehc - ohC - 4ohC - 4ohc - 4ohan ap -
T: endve la' binteua tunti nis te' pi et' in'* tunis

In this report, the GA has been running for 311 “epochs” (each epoch is a new generation of chromosomes). The cost (score) of the best chromosome is 62.8, whereas the average score of all the chromosomes in the population is 61.2. In this Epoch, there has been no change to the best chromosome since the last Epoch (“same 1”), 21% of the chromosomes have been mutated, a fresh chromosome (“New 1”) was inserted at this Epoch (to ensure diversity – this is not usually done in GA, but I find it produces more reliable training). “MS 15” means that the maximum number of no-change Epochs seen so far has been 15 … the larger this number is, the more stagnant the chromosome pool is, and the nearer to a solution we are.

The following line shows in detail how the best chromosome has scored: its table produces 128 valid Latin words, from a total of 408 translations i.e. about 31%. In the 25 sentences being used in training, 40 common Latin phrases have been found.

The next two lines show the first 15 n-grams in the mapping that the chromosome is using.

Then the status report shows how the chromosome fared on translating a sentence picked at random from the VMs folios. Since the GA is being trained only on the first few sentences, the remainder are essentially “unseen”, and so a valid, sensible translation in a non-trained sentence is significant.

The sentence picked is number 129 (the training set is the first 25 sentences in this run, so number 129 is well outside that). The VMs source sentence is shown with hyphens “-” separating the tokens that make up words. E.g. “2o ok1c” is the first word. Beneath is the Latin translation. A Latin word followed by a single quote means that that word appears in the Latin dictionary, and is thus valid. A star appearing after a set of valid Latin words indicates that the Latin phrase made up by the words is common, or at least appears in Knox’s list.

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  1. garlok
    June 20, 2011 at 8:31 am

    Dear Julian

    Please respect the following.

    The original concept behind VMS is much clearer than behind todays languages and writing systems. Indoeuropean languages (and much more – hungarian and bask too) are evolved from the same system than VMS.
    The VMS signs are close to that abstraction system that draws simple two dimensional representations of energy current flow (“wind”) in a 3D vector space. This 3D vector space is the universe, our whole body or our brain – the place of creation. The chinese geomancy discusses about the same 3D vector space. The viewpoint for 2D view was taken from a predefined point, so it must be an XYZ coordinate definiton before we can “read” a wind diagram. Wind diagrams drawn side by side represents the changing of wind in time. VMS includes many timeline of this type. These winds are energies of creation. Please see the hungarian word “szél” (wind) and the czech word “sil” (forces).

    Every wind representation is a spiral, or piece of spiral. In our handwriting we use many spiral too. But sometimes we use coordinate definiton too. Most handwritten latin letters seems like a geometricaly transformed arabic number “2”. But we can see that the egyptian eye of Horus symbol have a big “2” in it too.
    “S” and “Z” have only one coordinate definiton and the orientation is common. In hungarian we have “SZ”. “SZ” is double sign like “M” or “W”, “E” or arabic number “3”. These are wings, horns or flowers in our languages. The ancient word for these creation sources is “CE”, or in hungarian “SZi”. “M,E,W,3” are the four basic “CE” in the four basic direction. These are the four CE’s – the forces.

    Handwritten “R” and “k” have a 45 degree coordinate definition too but in common both are a “2” sign. Almost everything is a “2”.

    Every wind diagram has its own attributes. One of them the rotation. The direction of rotation can be represented in todays languages and writing systems with wovels. We can say – the wovel next to consonant determines the rotating direction (not only that) of given energy type (“a/e, 6/9”). A wovel configures a consonant. The position of the wovel is important too. This is not completely clear for me but i think it describes motivation context of given energy.

    So from my point of view every text is an abstract graphical equation.

    I think VMS isn’t the product of any language of the past few tausend years – modern languages are products of the same ancient philosophy too.

    We have only one language i think.

    Garlok

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