Similarity of Voynichese glyphs according to their immediate statistical environment

[Torsten]

Timm is probably using a different definition than mine because my results are quite different. For instance I find too that 'r' and 'm' have a moderately low average distance (0.26 in Herbal A), but 'n' is pretty far both from 'r' (av. distance = 0.63) and from 'm' (av. distance = 0.55). This because the distance according to the following character of 'n' from 'm' and 'r' is quite small (they are all mostly followed by space), but the distance according to the preceding character is high (1.1 and 1.08 respectively).

I find 'o' and 'a' to be 0.55 apart, moderately high, same for 'o' and 'y' (0.50): they are not grouped together. Same for 'r' and 's (0.52), while 's' and 'd' are moderately similar (0.39, they barely escaped the tables of my previous post, the threshold was 0.35).

I will check 'ee' vs. 'ch/sh', but I very much doubt they are similar. 'in', 'iin', 'iiin' might well be similar, but I need to test it before being sure.

One caveat is that the results depend on the section of the manuscript examined, ie. 'k' 't' 'p' and 'f' could indeed be seen as a single group in Herbal A (and 'ch', 'sh', 'cth', ckh', 'cph' and cfh' can be added to the mix, see the table You are not allowed to view links. Register or Login to view.), but in Balneological 'k/t', 'p/f' and 'ch/sh' are well separated.

Thank you for this analysis. The discrepancy between your distributional distances and my substitution rules is informative rather than contradictory — because I describe context-dependent rules:

"These rules for similar glyphs only apply with some restrictions. For instance 'o' and 'y' can replace each other only as the first or as the last sign. Another example is that 'o' is interchangeable with 'a' before 'l' and 'r' but not after 'q' or before 'k'." (You are not allowed to view links. Register or Login to view., p. 5). A word grid documenting the most frequent substitution relationships across the VMS vocabulary is available at You are not allowed to view links. Register or Login to view. (see also Timm 2014, pp. 66-82).

So "o" and "a" substitute in specific positions — as prefix elements before "l" and "r" — but not in all contexts. Their global distributional distance (0.55 in your measurement) is high because "o" after "q" has no "a" equivalent, pulling the global distances apart. But in the specific positions where they do substitute — "ol"/"al", "or"/"ar", "chol"/"chal" — they are interchangeable.

The same applies to "n" and "r" (0.63 in your measurement). Both appear word-finally, and in that position they substitute — dain/dair, sain/sair, okain/okair etc. But "r" also appears in other positions where "n" doesn't, making their global distributions different.

Your core pairs — ch/sh, k/t, p/f, r/l — show low distances because they substitute freely across many contexts. The pairs with higher distances in your analysis — o/a, o/y, n/r — substitute only in restricted positions, which dilutes their global similarity.

Note: Currier already noted in 1976 that the Voynich glyphs are constructed from shared base strokes — 'you can make up almost any of the other letters out of these two symbols i and e' (see The Nature of the Symbols in You are not allowed to view links. Register or Login to view.). Your distributional distances quantify this observation: glyph pairs with low distance are the pairs that share stroke structure.