Various Graphs and Analyses

[Jorge_Stolfi]

The table wasn't the best (and also used very bad scheme for the colorblind), so I made a new one. This is simply pair counts from a German text (Das Lob der Narrheit by Desiderius Erasmus)... I think this shows pretty clearly that there are sets of words that prefer the company of another set: (sie|sich)(nicht|in|mit) and (in|mit|von)(der|den|dem). (Never mind the heretical capitalization, I did it for normalization.) This is arbitrarily cut at 20 most paired words.

Thanks!  

Indeed the word pairs that can occur are only a small subset of all possible pairs; and the distinction allowed/forbidden  is quite well marked in most cases.  

Also, there is a fairly small number of 2x2 submatrices that have all four counts positive (that is, quadruples {A1,A2} and {B1,B2} where all four A-B pairs are allowed).  And only a subset of these really follow the ": : pattern" (with R close to zero). 

But only some of the 2x2 submatrices that you marked really fit the ": : pattern"

Bugs apart, here are some of them, sorted by increasing R:
('mit', 'von')  ('der', 'den')  [[18 10] [18 10]] D =    0 R = 0.0000

('sie', 'sich') ('nicht', 'in')  [[12 10] [16 14]] D =  -8 R = 0.0116
('mit', 'von')  ('den', 'dem')  [[10 17] [10 18]] D =  -10 R = 0.0134
('mit', 'von')  ('der', 'dem')  [[18 17] [18 18]] D =  -18 R = 0.0143
('sie', 'sich') ('in', 'mit')    [[10  7] [14 13]] D =  -32 R = 0.0636
('sie', 'sich') ('nicht', 'mit') [[12  7] [16 13]] D =  -44 R = 0.0717
('in', 'mit')  ('der', 'dem')  [[16 10] [18 17]] D =  -92 R = 0.0959
('in', 'von')  ('der', 'dem')  [[16 10] [18 18]] D = -108 R = 0.1093
('in', 'mit')  ('der', 'den')  [[16 20] [18 10]] D = -200 R = 0.1928
('in', 'von')  ('der', 'den')  [[16 20] [18 10]] D = -200 R = 0.1928
('in', 'mit')  ('den', 'dem')  [[20 10] [10 17]] D = -240 R = 0.2967
('in', 'von')  ('den', 'dem')  [[20 10] [10 18]] D = -260 R = 0.3097
[Sorry for the misalignment.  Blame this shitty forum software...]

Thus while {mit,von} pair up indifferently with {der,den}, the other quadruples show at last a bit of bias.  Some of that can be attributed to sampling error (17 is essentially the same as 18, etc.)  The most biased of those quadruples is {in,von} x {den,dem}:  "in" definitely prefers to be followed by "den", and "von" by "dem".

And, again, these biases are a common feature of texts in natural language.  

Now let me see again the table for Voynichese...

All the best, --stolfi

PS here is the code that created that table, if you care:

Code:

#! /usr/bin/python3 # Last edited on 2025-12-02 17:14:25 by stolfi from math import sqrt from sys import stdout as out, stderr as err def main():   submats = ( \     ( ('sie','sich'), ('nicht','in'),  ((12,10),(16,14)) ),     ( ('sie','sich'), ('nicht','mit'), ((12, 7),(16,13)) ),     ( ('sie','sich'), ('in','mit'),    ((10, 7),(14,13)) ),     ( ('in','mit'),  ('der','den'),  ((16,20),(18,10)) ),     ( ('in','mit'),  ('der','dem'),  ((16,10),(18,17)) ),     ( ('in','mit'),  ('den','dem'),  ((20,10),(10,17)) ),     ( ('in','von'),  ('der','den'),  ((16,20),(18,10)) ),     ( ('in','von'),  ('der','dem'),  ((16,10),(18,18)) ),     ( ('in','von'),  ('den','dem'),  ((20,10),(10,18)) ),                                           ( ('mit','von'),  ('der','den'),  ((18,10),(18,10)) ),     ( ('mit','von'),  ('der','dem'),  ((18,17),(18,18)) ),     ( ('mit','von'),  ('den','dem'),  ((10,17),(10,18)) ),   )     for A, B, M in submats:     ab, cd = M; a, b = ab; c, d = cd;     D, T, R = compute_R(a,b,c,d)     Af = f"{A}"; Bf = f"{B}"     out.write(f"{Af:25} {Bf:25} [[{a:4d} {b:4d}] [{c:4d} {d:4d}]]")     out.write(f" {D = :8d} {R = :6.4f}\n")   return   # ----------------------------------------------------------------------     def compute_R(a,b,c,d):      D = a*d-b*c   if D > 0:     D = -D     T = b + c   else:     T = a + d   L1 = abs(T/2 + sqrt(T*T/4 - D))   L2 = abs(T/2 - sqrt(T*T/4 - D))   R = min(L1,L2)/max(L1,L2)   return D, T, R   # ----------------------------------------------------------------------     main()