To make it clear, I was not arguing that the Voynichese is based on Roman numerals. I just wanted to quickly illustrate that various approaches to encoding words in the vocabulary (mind that all this discussion is within the framework of a "pure nomenclator" solution) can lead both to symmetric and asymmetric length distributions, and those symmetric can be close to normal.
Now, there are quantitative methods to assess how close is the given curve to the normal curve, such as calculating skewness and excess, but even without delving in that it is seen from the figures that the VMS fits the normal curve better than the Roman numbers system does.
Moreover, the larger the vocabulary size, the farther is the "Roman" distribution from normal, although it remains perfectly symmetric.
Here's the pic for the vocabulary size of 20000. In this graph frequency is shown in absolute, not relative, figures (to get relative, divide by 20000)
It's curious but it appears that there is the upper limit for the frequency of a particular word length, and it is 1000 (in my previous post where the size was 6818 the highest frequency was 934, i.e. not reaching the limit yet). This means that however large is the corpus of Roman numbers, there will be no more than 1000 of the same length. Which is counter-intuitive and really curious.
About numerical form representation in general. Yes: inspired by the fact that the VMS distribution is approximated by binomial of (N,K-1), Stolfi introduced this idea. However, it's not been shown that non-numerical systems cannot yield the same result.
About the second Stolfi article. Yes, I found it out yesterday via Rene's website after having written my post. I must say I fail to follow his linguistic interpretation, but it all looks tro me superfluous because he is too stuck with binomial. It's the more strange given that in this article (as opposed to the first article) he explicitly states that binomial will approach normal with large N, so I don't know why one should invent explanations for binomiality while the more obvious case would be just normality.
So the question would be: what's there in a writing system that makes its vocabulary word length distribution to be normal?
As Stolfi shows in his second article, there are some writing systems for natural languages that yield curves close to normal, such as Eastern-Asian romanizations.
I'm not familiar with anything Eastern-Asian at all, but I have the intuitive feeling that a language with more inflections will have distribution closer to normal. This can be checked against the batch of Human Rights Declaration texts in various languages.
(It is important to remember that each word form in this approach must be counted as a separate distinct word).
Now, there are quantitative methods to assess how close is the given curve to the normal curve, such as calculating skewness and excess, but even without delving in that it is seen from the figures that the VMS fits the normal curve better than the Roman numbers system does.
Moreover, the larger the vocabulary size, the farther is the "Roman" distribution from normal, although it remains perfectly symmetric.
Here's the pic for the vocabulary size of 20000. In this graph frequency is shown in absolute, not relative, figures (to get relative, divide by 20000)
It's curious but it appears that there is the upper limit for the frequency of a particular word length, and it is 1000 (in my previous post where the size was 6818 the highest frequency was 934, i.e. not reaching the limit yet). This means that however large is the corpus of Roman numbers, there will be no more than 1000 of the same length. Which is counter-intuitive and really curious.
About numerical form representation in general. Yes: inspired by the fact that the VMS distribution is approximated by binomial of (N,K-1), Stolfi introduced this idea. However, it's not been shown that non-numerical systems cannot yield the same result.
About the second Stolfi article. Yes, I found it out yesterday via Rene's website after having written my post. I must say I fail to follow his linguistic interpretation, but it all looks tro me superfluous because he is too stuck with binomial. It's the more strange given that in this article (as opposed to the first article) he explicitly states that binomial will approach normal with large N, so I don't know why one should invent explanations for binomiality while the more obvious case would be just normality.
So the question would be: what's there in a writing system that makes its vocabulary word length distribution to be normal?
As Stolfi shows in his second article, there are some writing systems for natural languages that yield curves close to normal, such as Eastern-Asian romanizations.
I'm not familiar with anything Eastern-Asian at all, but I have the intuitive feeling that a language with more inflections will have distribution closer to normal. This can be checked against the batch of Human Rights Declaration texts in various languages.
(It is important to remember that each word form in this approach must be counted as a separate distinct word).