16-03-2016, 02:37 PM
Actually, what I meant here is character entropy as a general parameter, not related to any specific language, but to natural language in general. There might have been extinct languages, and they may have utilized less letters in the alphabet. Or this might have been an invented script for a language unknown to the scribe. I simply leave the validity of these assumptions out of scope.
The whole entropy discourse in respect to the VMS, to the extent which I am acquainted with, is a bit fuzzy and, I am afraid, this confuses many researchers who are not acquainted with the information theory.
To the consideration that I explained above, I would like to add (it seems that this fact is not well understood) that direct comparison of the character entropy between languages with different numbers of letters in the alphabet makes little sense, because entropy will depend upon the number of the letters in the alphabet. In other words, character entropy of English and character entropy of Hawaiian are not directly compatible, for to make any conclusions out of there. I guess what should be compared rather, is the degree (e.g. expressed in percentage) in which the character entropy reaches the maximum possible entropy. The maximum possible entropy is observed when all characters are equally probable to appear - hence, it depends on the size of the alphabet exclusively.
I have no access to Bennet's book (maybe anyone could provide a scan of the respective chapter if the copyright so allows) and don't know what comparisons were being made. As to the You are not allowed to view links. Register or Login to view., I would say that it is a bit wandering and, besides, I haven't time to examine it in detail, but he (albeit speaking of the 2nd order entropy), makes a strange statement (emphasis is mine):
From this explanation, I fail to understand wherefore this measure was not used, and also it seems that it was not used for first order entropy neither.
The whole entropy discourse in respect to the VMS, to the extent which I am acquainted with, is a bit fuzzy and, I am afraid, this confuses many researchers who are not acquainted with the information theory.
To the consideration that I explained above, I would like to add (it seems that this fact is not well understood) that direct comparison of the character entropy between languages with different numbers of letters in the alphabet makes little sense, because entropy will depend upon the number of the letters in the alphabet. In other words, character entropy of English and character entropy of Hawaiian are not directly compatible, for to make any conclusions out of there. I guess what should be compared rather, is the degree (e.g. expressed in percentage) in which the character entropy reaches the maximum possible entropy. The maximum possible entropy is observed when all characters are equally probable to appear - hence, it depends on the size of the alphabet exclusively.
I have no access to Bennet's book (maybe anyone could provide a scan of the respective chapter if the copyright so allows) and don't know what comparisons were being made. As to the You are not allowed to view links. Register or Login to view., I would say that it is a bit wandering and, besides, I haven't time to examine it in detail, but he (albeit speaking of the 2nd order entropy), makes a strange statement (emphasis is mine):
Quote:However, the H2(max) depends tremendously on m, the size of the character set chosen. For Voynich text, Currier has 36 characters and Basic Frogguy has 23 characters. Characters that are hardly ever used have little effect on h1 and h2, but could make a tremendous difference in H2(max). Therefore, this measure was not used.
From this explanation, I fail to understand wherefore this measure was not used, and also it seems that it was not used for first order entropy neither.