[Blog Post] Rightward and Downward in the Voynich Manuscript - Patrick Feaster

[Emma May Smith]

Hi Patrick, I've been thinking more about your results and just wanted some clarification on how you calculate the rightwardness scores. You say in your post:

My usual method for calculating rightwardness tendencies for words has been to number the words in each line, starting at zero; then to divide these numbers by the quantity of words in the line (minus one), so that each word ends up assigned a value between 0 (first word in line) and 1 (last word in line); and finally to take the mean average of the values for all tokens of a particular word, or of some group of words sharing a common characteristic, so that higher values will correspond to greater overall rightwardness much as higher numerical temperatures correspond to greater heat.

So, for example:

1. If a word appears 10 times in position 5 of a 9 word sentence, it will have a score of .500.
   
2. If the same word appears one of those ten times in position 4 (rather than 5) in a 9 word sentence, it will have a score of .488.
   
3. If the same word appears one of those ten times in position 5 of a 10 word sentence (rather than a 9 word sentence), it will have a score of .494
   

In cases 2 and 3 the difference from case 1 will be .012 and .006 respectively. Is that correct?

Also, when you divided the line into ten parts, you give the word counts for each:

One option is to take our fractional measures of line position in a range from one to zero, multiply them by some factor, and then round each of them to the nearest integer.  The resulting groups will vary in size, but we can normalize for that in our subsequent calculations.  If we divide the line into ten groups as I’ve described, we find that they contain 4134, 2489, 3294, 3152, 2223, 4244, 3152, 3294, 2489, and 4107 words respectively.

There is quite a bit of difference between the number of words in some of these groups. I'm particularly interested in groups five and six, which have word counts of 2,223 and 4,244, respectively. That feels really "lumpy". Is there some reason why the number of words are distributed in this way? Is it just that the most common line lengths are such that some position deciles get more words than others?