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

[pfeaster]

I've been experimenting with different strategies for displaying rightward/downward tendencies and thought I'd share a few examples of one particular kind of display I think seems promising.  My examples will involve statistics for individual glyphs.

I start by dividing paragraphs into five sectors: 1 = first line, 5 = last line, 2-4 = whatever remains in the middle, divided into thirds.  Next, I divide the lines into fifths (for a first analysis) and sevenths (for a second analysis), in each case splitting off the first and last adjacencies as well.  This maps positions onto a 2D grid with unequally sized "cells," 5x7 in one case, 5x9 in the other.

I then track pairs of glyphs adjacency by adjacency through each line, counting the first glyphs and second glyphs assigned to each line segment.  That may seem like a clunky approach, and it comes partly from re-using a script I designed with other things in mind; but still, it gives me totals for all glyph tokens in first position, second position, last position, and second-to-last position, as well as a pair of totals for each group in the middle with their "windows" offset by just one position.  The second and second-to-last glyphs are also factored into the outermost groups at either extremity.  Finally, I divide each result by the total count in each of the cells in the grid to normalize the figures for group size.

On the left of my display, I show the results for the first two positions; on the right, I show the results for the last two positions; and in the middle I show the results for intermediate positions, with the fifths and sevenths "interleaved," and with the pairs of measurements offset by a slight (arbitrary) distance along the x axis.  Each of the four "interleaved" series of plot points is connected by a separate line.  On the top, I show the separate results by paragraph sector color-coded in a way that's meant to suggest a blue-to-red spectrum: (1) dark blue, (2) light blue, (3) gray, (4) yellow-orange, (5) red.  On the bottom, in green, I show the aggregate values for all paragraph sectors lumped together.

Note: I count benched gallows and sequences of multiple [i] or [e] as single glyphs.

Here's a sample display showing data for [Sh] in Quires 1-3.



The bottom shows the composite curve for all paragraph positions sloping gently downward from around 4.5% to 2% of total glyphs by line position.  Meanwhile, the top shows further variation across paragraphs.  The points in dark blue indicate that [Sh] is disproportionately well-represented in the first lines of paragraphs, while the points in red show that it's disproportionately underrepresented in the last lines of paragraphs.  And then there's a snarl in the middle, although light blue (first third) seems to fall mostly below yellow-orange (last third).  Similar patterns turn up for [Sh] in other parts of the manuscript, especially that first-line-of-paragraph boost, which seems to be a constant.

Here's another sample, this one for [ii] in the whole of Currier B, as distinct from [i] and [iii].



There's not much to the aggregate (green) curve at the bottom, except for a shallow middle-of-the-line dip.  But the display at the top shows the different paragraph positions sorting rather nicely into order, not perfectly, but still perceptibly (I think): from the bottom, dark blue, light blue, gray, yellow-orange, red.  If wishful thinking isn't causing me to see things here, this would point to [ii] becoming more common the further downward we go in a paragraph.  For what it's worth, [i] doesn't appear to share this pattern.

Some may argue that Currier B is too heterogeneous to be meaningfully analyzed, so here's an equivalent graph limited to Quire 20:



A bit more mixed up, but blue still looks like it's sorting mainly to the bottom, and red and yellow to the top, and gray into the middle.

Other glyphs seem to have distinctive curve shapes more than simple rightward or leftward preferences that could be summed up in a single numerical score.  A case in point is [q]; here's a display for it across all of Currier B:



That odd double hump seems to be typical of [q] across different sections, and it looks a bit to me like the curves Marco plotted for words beginning [qo].  Once again, there's also notable variation by position within paragraphs -- particularly with the last line (red), although the fact that last lines are often atypically short might factor into the deviation in shape.

I can say more about other patterns these displays seem to be turning up on a glyph-by-glyph basis if there's interest, but I'm still not sure I've hit upon the best approach to visualizing what's going on.  Does anyone have other ideas about what an optimal display might look like?  What can't we get a good look at here yet?