Re: VMs: Random Text Generation

[Nick Pelling <incoming@xxxxxxxxxxxxxxxxx>]

Hi Rob,

> My theory goes as follows -
>
> If an algorithm can be created that approximates Voynichese so well that 
> the generated text matches real Voynichese to, say, 90% accuracy (based on 
> letter, bigraph, trigraph, word frequencies, zipf laws, etc) AND it is 
> simultaneously found to be impossible to create a similar algorithm with 
> the same accuracy for a real language, the implication would be that the 
> VMS's scribe(s) used some sort of random word generation system.
>
> Is there any fundamental flaw in this logic?  I'm not out to prove one way 
> or the other whether the VMS is gibberish or not, but it seems to be a 
> means of determining this important fact.

An analogy: the approach I've always liked to use when writing computer 
games is to approximate constrained decision making (ie, AI) with bounded 
randomness. Of course, it's not true AI (though let's not get into a 
semantic discussion about what that would actually be :-)  ), but it can be 
very convincing... iff you tweak the parameters enough. :-)

I think that what you're suggesting may well be driving down the same road: 
creating a random walk through a Markov chain (or whatever) will - for sure 
- give you plausible-looking results, that can be made to get ever closer 
to Voynichese (or whatever language you're trying to simulate) as the 
complexity of your model increases.

And I suppose this is my point: what you are essentially proposing is to 
construct a generative model of Voynichese, by which plausible phrases (and 
even sentences) may be output randomly. There have been a number of these 
proposed already, that seem to be consistent with a large part of the 
corpus of the text... yet give no obvious indication why some words exist 
and others don't.

The problem is that many features of Voynichese seem to be somewhat at odds 
with the structure of existing languages - for example, the large number of 
unique (yet only slightly different) words relative to the size of the 
text. Why should some words (in the model's word-space) exist and others 
not? Tricky. :-|

> One could argue, I suppose, that any language could be modelled with an 
> algorithm, as long as no limit was set on the complexity of the algorithm.

Hmmm... I can see the exam question now: "Language is a social algorithm of 
indeterminate complexity. Discuss." :-)

> Our VMS scribe(s), however, would have been limited to something very 
> simple like a table of letter patterns and a knuckle-bone dice or two.

Though I don't recall this kind of idea (for example, of using dice to 
prompt an encipherer whether to insert a null in a ciphertext) as having 
been proposed or used in this general era: yes, it *is* possible... though, 
unless there's specific evidence to suggest otherwise, I'd say fairly 
unlikely. :-o

May I ask the more crypto-oriented participants here: has any statistical 
survey of null placements in C15-C18 ciphertexts has been done? It's the 
kind of thing that might have once come up in a Cryptologia footnote, I 
guess. :-)

My opinion is that you would need this kind of statistical bridge (between 
randomness and empirical cryptographic evidence) to exist to support your 
general proposition. :-o

But at the same time, trying to reconcile this with the (apparently) 
binomial distribution of VMS word lengths (as pointed out by Jorge Stolfi 
at the beginning of the year) is quite challenging:-

>       Actually, the fact itself still stands: the Voynichese word length
>       distribution is almost exactly like the binomial distribution
>       binom(9,k-1) (i.e. the number of distinct words with k letters
>       is proportional to the chance of obtaining k-1 heads in 9 coin 
tosses),
>       and quite unlike that of Latin, English, or any other "ordinary"
>       language.

Did the encipherer *really* flip a coin 9 times to get the word-length 
(erm, minus one)? This sounds fairly unlikely (especially as this would 
probably preclude "dain" from appearing so often, but not "d" or "ain" on 
their own).

However, note that the alternative would appear to be an enciphering (or 
similar transformation) process whereby this kind of distribution comes out 
as a side-effect. If my dating of 1450-1460 is even relatively close, there 
were few conceptual possibilities in the air then that would match this 
pattern.

However, the simplest system I can think of that may come close to fitting 
this single criterion would be a form of numbering scheme based (in part) 
on Roman numerals. As I've mentioned before, it would not surprise me in 
the slightest if the very core of the VMS' code were to prove to be no more 
than an embellished number code.

I have sometimes wondered, though, if some of Jorge's apparent binomial 
distribution arises in part from the EVA stroke transcription. If compound 
letters (such as EVA "aii", "aiii", "cc", and even "ccc") were to be 
converted into a single symbol each, would the resulting set of word 
lengths still conform to a binomial distribution?

Perhaps someone might like to test this out...? :-)

Cheers, .....Nick Pelling.....

PS: I don't currently know if any of the 15th Century number codes 
mentioned in the crypto literature (such as that used for the most part by 
the Strozzi) were ever written in Roman numerals - does anyone here know of 
any? This would seem to be a sensible place to start looking for possible 
structural similarities with the VMS' code...

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