Proposed Manuscript Chronology

[npcompl33t]

And I bet that, in fact, You are not allowed to view links. Register or Login to view..

I'll take that bet. I built groups from my 9 identified chronological groups, which fall almost entirely within single sections: Herbal A ×3, Pharma, Herbal B ×2, Stars ×2, Bio.

For each pair i took the mean JSD minus the average of the internal group spreads to estimate the squared distance between centroids. I then scored all 84 triples on ": Y lies between X and Z when X and Z are farther apart than either is from Y.


With the order held constant before the test:

• Only 7/84 fail
  
• the order is the unique best of all 181,440 orders
  
• every groups nearest neighbor are the ones next to it in the chronological order
  
• mean distance rises at every step of separation, roughly linearly (r2=0.98), exactly what accumulating drift looks like
  

In random controls, 9 unaligned centroids in 8 or 50d never got down to 7 in 2,000.

I tried grouping pages only by their illustration and currier labels, and kept the corresponding order fixed. 1 out of 20 fails, and the order is the unique best of all 360 combinaions, (p=0.003). It remains best even after 1k page resamples.

The alignment is there in R^n.

[MarcoP]

We know that the reason for "dialect" differences isn't different subjects (as defined by different illustrations) nor different scribes.

Do we?

From VoynichArchive search engine:

Tell me how Currier A and Currier B are related to supposed different scribes

Prescott Currier identified two distinct statistical patterns in the Voynich Manuscript's text, which he termed Language A and Language B, and also discerned two primary scribal hands, Scribe 1 and Scribe 2, in the botanical section of the manuscript. He noted a direct correlation between Language A and Scribe 1, and Language B and Scribe 2. [url=https://voynicharchive.com/#citation-t0-2][/url]Currier's work suggested that these differences in text statistics corresponded to variations in handwriting, implying the involvement of at least two authors.For example, Currier A rarely features the bigram /ed/, while Currier B uses it frequently. While Currier initially focused on two hands, he believed there could be as many as eight scribes involved. More recent analysis by Lisa Fagin Davis has identified five distinct scribal hands, with Scribe 1 primarily writing in Language A, and Scribes 2, 3, 4, and 5 writing in Language B

I realise it is more subtle but if I understand it correctly it is the main, strongest effect and the rest are nuances and refinements.

I just meant to say that recent Voynich studies agree about the significance of the several different dialects and that they cannot be explained by the different scribes alone: all these changes in the basic statistics of Voynichese deserve to be studied and understood. I agree that this might not have been clear to Currier fifty years ago.

You are not allowed to view links. Register or Login to view.

This could be an indication that the two Currier’s languages A and B [3] are only a major distinction within a group of (at least) five such languages.

(two of the five languages are Herbal-A and Pharmaceutical, both by Scribe 1)

You are not allowed to view links. Register or Login to view.

We find that computationally derived clusters match closely to a conjunction of scribe and subject matter (as per the illustrations) ... These analyses provide strong evidence that scribe, NMF topic, and Currier language are not the same. This, perhaps, provides a more convincing argument that NMF reflects distinct semantic and linguistic features, potentially also including differences in scribe and/or dialect.

(the authors believe that the variation in a scribe's output depends on different topics)

You are not allowed to view links. Register or Login to view.

The relationship between the various dialects is shown below. The arrows connect the two dialects that are most similar to each other.
   
…Possibly the most interesting observation here is, that scribe 3 has some output in almost all dialects.

You are not allowed to view links. Register or Login to view.

The text exhibits continuous development throughout the manuscript, with vocabulary, character usage, and word frequency distributions shifting gradually from beginning to end. This dynamic character is evidenced by a single, highly connected network of similar words spanning the entire manuscript, a strong correlation between word frequency and number of similar word forms and asymmetric vocabulary distribution indicating directional evolution.

[Jorge_Stolfi]

I'll take that bet.  ... For each pair i took the mean JSD minus the average of the internal group spreads to estimate the squared distance between centroids. I then scored all 84 triples on ": Y lies between X and Z when X and Z are farther apart than either is from Y. ... In random controls, 9 unaligned centroids in 8 or 50d never got down to 7 in 2,000.

Could you please give more details on these experiments?  Especially

• Which statistics do you compute for each page, and how many are there?
  
• How do you compute the distances between the centroids?
  
• How did you generate the random clouds?
  

Meanwhile, here is my attempt to reproduce your experiment, without the "intrinsic order"premise.

I created four roundish clouds in R^4, with centroids at the vertices of a regular tetrahedon.  Here are they in two different projections:
       
For each triple of clouds, I computed the ratio S = (dist(X,Y) + dist(Y,Z))/dist(X,Z), where dist is Euclidean distance in R^4 between cloud centroids, and X,Z are the two clouds in the triple with maximum dist(X,Z).  The ratio S can vary between 1 (when X,Y,Z are collinear in R^4) and 2 (when X,Y,Z are equidistant).

The ratio S of course came out the same for all triples, namely 2.0 exactly.

Then I repeated the test with the four centroids picked at random with uniform distribution within a cube of R^4:
   
The ratios S for the four distinct triples were 1.2744, 1.4229, 1.3460, 1.1910.  Are these numbers comparable to those in your "random" test?

Then I repeated the computation with the centroids in a regular tetrahedron, but stretched in an arbitrary direction of R^4 by a factor of 10:
   
The ratios S for the four distinct triples were 1.1810,  1.1013,  1.1013,  1.1810. 

Are those last values close enough to S = 1?

Note that in the second data set there still was no intrinsic order of the centroids.  The clouds are ordered along the direction of stretch, but that order is created by the stretching.  I could have obtained any of the 4!/2 = 3 possible orders by choosing different directions for the stretching.

The stretching is equivalent to picking the centroids in random order but with a strong correlation between their four R^4 data coordinates.  The same is expected to be the case when the points are VMS per-page statistics and the clouds are sections with same topic and text type.  It is undisputed that there are strong correlations between the frequencies of characters and digraphs over the sections.

All the best, --stolfi

[Rafal]

I just meant to say that recent Voynich studies agree about the significance of the several different dialects and that they cannot be explained by the different scribes alone: all these changes in the basic statistics of Voynichese deserve to be studied and understood.

If formulated this way, I can only agree with it.

My intuition is that there were several scribes and they had distinct "styles" but they influenced each other. It may explain some "transition pages" which are a mix of styles.

It could work this way:
- First some general method of text creation was created. At this moment it doesn't matter if it was a cipher or a way of creating fake words.
- The method wasn't totally deterministic and gave a user some freedom how to use it. One of the rules could be "You can break all the rules but don't do it often" 
- Then the Scribe 1 generated several pages using the method in his own way
- Then the Scribe 2 continued. He took the written pages by Scribe 1. In the first pages which he has written he used Scribe 1 work as an inspiration so these pages may contain traces of Scribe 1 style. But as Scribe 2 was writing more and more, he became more confident and his personal style was taking over.

Of course changes of subject could also matter if the text was meaningful.

[npcompl33t]

Could you please give more details on these experiments?  Especially

• Which statistics do you compute for each page, and how many are there?
  
• How do you compute the distances between the centroids?
  
• How did you generate the random clouds?
  

Meanwhile, here is my attempt to reproduce your experiment, without the "intrinsic order"premise.

Thanks for the response.

Statistics: 
I calculate two first order glyph transitions per page, essentially a 1st order markov representation, using the Zaterra 2022 slot alphabet. One is a pure word level , the second i concatenate all words in a line together. I did this because I noticed early herbal A in particular has low text, and using these different representations produces different but useful features to the top, so by combining them I get the unique distinctions each contains.

Distances:
I never compute centroid differences. The page-to-page distance is Jensen Shannon divergence between their transition matrices. I calculate the differences between each of the two independently, then average the distances together. JSD behaves like a squared Euclidean distance. D(X,Y) is the mean JSD over all page pairs across sections X and Y, and D(X,X) the mean over distinct pairs within X. D′(X,Y) = D(X,Y) − ½[D(X,X) + D(Y,Y)] is then an unbiased estimate of the squared distance between the two section centroids. For your S, use √D′.

Random Clouds
I compare best achievable orders. For a given ordering, a triplet fails if its two ends are not the farthest pair. I take the order with the fewest failures out of all, for the real sections and the random null draw. I didnt simulate fake word point clouds, I used the real 15 centroid distances shuffled among the network pairs, and six random centroids drawn from a standard gaussian distribution in 3, 5 and 50 dimensions, with those distances standing in for D′

Your Experiment
I was able to reproduce your numbers, however S measures straightness, not ordering, and it depends on the dimension. Random variance off the axis adds to every dimension equally. In 50d, the same x10 stretch gives S = 1.4, yet its best order leaves at most 1 triplet out of place 58% of the time. This is dramatically different from my results. My sections have S from 1.15-1.6. By pure S, they look like your random cube, but by order, they do not. 6 random centroid in 4 D leave two or more triplets out of place 96% of the time.

Your stretched cloud passes my test by construction, because it is only a 1 axis model. If that's the case, we agree on the overall geometry: sections differ mainly along one direction and the correlated character and digraph frequencies are that direction. I didn't tune a metric to pick this.

In your model, each section sits at a point on the axis, and pages scatter around it at random. So two leaves of one bifolio, with different plants, should be no closer on the axis than any two pages of that section. However, this is not the case. In Herbal A, they land in the same batch 85% of the time. Pure random placement would only give 30%. The position on the axis I've identified follows the sheet the page was written on. This is exactly what an order based on production would predict, and one that a fixed topic axis does not.

Happy to answer any additional questions.

[Jorge_Stolfi]

In your model, each section sits at a point on the axis, and pages scatter around it at random. So two leaves of one bifolio, with different plants, should be no closer on the axis than any two pages of that section. However, this is not the case. In Herbal A, they land in the same batch 85% of the time. Pure random placement would only give 30%.

Can you please clarify here what you mean by "section" and "batch"?  Is "section" just Herbal-A or Herbal B, or all Herbal together?  Is "batch" Herbal-A or Herbal-B, or one of your 4(?) herbal blocks?

All the best, --stolfi

[npcompl33t]

Can you please clarify here what you mean by "section" and "batch"?  Is "section" just Herbal-A or Herbal B, or all Herbal together?  Is "batch" Herbal-A or Herbal-B, or one of your 4(?) herbal blocks?

Yes, sorry I could have been more clear. 

Section: I split sections using the illustrations and Courier label. So i separated Herbal A and Herbal B. 


For batch i was referring to my own labels. So for Herbal A, that is 

• 1a (38 pages), 
  
• 1b (31)
  
• 1.5a (19) 
  
• 2a (7 Herbal A pages, otherwise mostly Pharma)
  

[nablator]

For batch i was referring to my own labels. So for Herbal A, that is 

• 1a (38 pages), 
  
• 1b (31)
  
• 1.5a (19) 
  
• 2a (7 Herbal A pages, otherwise mostly Pharma)
  

Indeed. These are the golf_v21 assignment codes from your Voynich Clusters page.

#. page section currier golf_v21_assignment_code

1. f1r T A 1a
   
2. f1v H A 1.5a
   
3. f2r H A 1a
   
4. f2v H A 1a
   
5. f3r H A 1.5a
   
6. f3v H A 1.5a
   
7. f4r H A 1a
   
8. f4v H A 1a
   
9. f5r H A 1a
   
10. f5v H A 1b
    
11. f6r H A 1.5a
    
12. f6v H A 1.5a
    
13. f7r H A 1a
    
14. f7v H A 1a
    
15. f8r H A 1a
    
16. f8v H A 1a
    
17. f9r H A 1b
    
18. f9v H A 1b
    
19. f10r H A 1b
    
20. f10v H A 1a
    
21. f11r H A 1b
    
22. f11v H A 1b
    
23. f13r H A 1b
    
24. f13v H A 1b
    
25. f14r H A 1b
    
26. f14v H A 1b
    
27. f15r H A 1a
    
28. f15v H A 1b
    
29. f16r H A 1b
    
30. f16v H A 1b
    
31. f17r H A 1.5a
    
32. f17v H A 2a
    
33. f18r H A 1b
    
34. f18v H A 1b
    
35. f19r H A 1b
    
36. f19v H A 1b
    
37. f20r H A 1a
    
38. f20v H A 1a
    
39. f21r H A 1a
    
40. f21v H A 1a
    
41. f22r H A 1b
    
42. f22v H A 1b
    
43. f23r H A 1b
    
44. f23v H A 1b
    
45. f24r H A 1.5a
    
46. f24v H A 1.5a
    
47. f25r H A 1a
    
48. f25v H A 1a
    
49. f26r H B 3b
    
50. f26v H B 3b
    
51. f27r H A 1a
    
52. f27v H A 1a
    
53. f28r H A 1a
    
54. f28v H A 1a
    
55. f29r H A 1a
    
56. f29v H A 1a
    
57. f30r H A 1a
    
58. f30v H A 1a
    
59. f31r H B 3b
    
60. f31v H B 3b
    
61. f32r H A 1a
    
62. f32v H A 1a
    
63. f33r H B 3a
    
64. f33v H B 3a
    
65. f34r H B 3a
    
66. f34v H B 3a
    
67. f35r H A 1a
    
68. f35v H A 1a
    
69. f36r H A 1b
    
70. f36v H A 1b
    
71. f37r H A 1b
    
72. f37v H A 1b
    
73. f38r H A 1b
    
74. f38v H A 1a
    
75. f39r H B 3a
    
76. f39v H B 3a
    
77. f40r H B 3a
    
78. f40v H B 3a
    
79. f41r H B 3b
    
80. f41v H B 3b
    
81. f42r H A 1a
    
82. f42v H A 1a
    
83. f43r H B 3b
    
84. f43v H B 3b
    
85. f44r H A 1b
    
86. f44v H A 1b
    
87. f45r H A 1b
    
88. f45v H A 1b
    
89. f46r H B 3a
    
90. f46v H B 3b
    
91. f47r H A 1a
    
92. f47v H A 1a
    
93. f48r H B 3b
    
94. f48v H B 3a
    
95. f49r H A 1a
    
96. f49v H A 1a
    
97. f50r H B 3a
    
98. f50v H B 3a
    
99. f51r H A 1.5a
    
100. f51v H A 1.5a
     
101. f52r H A 1b
     
102. f52v H A 1.5a
     
103. f53r H A 1.5a
     
104. f53v H A 1.5a
     
105. f54r H A 1.5a
     
106. f54v H A 1.5a
     
107. f55r H B 3a
     
108. f55v H B 3a
     
109. f56r H A 1a
     
110. f56v H A 1a
     
111. f57r H B 3b
     
112. f57v C null
     
113. f58r S A 6
     
114. f58v S A 6
     
115. f65v H 3b
     
116. f66r T B 3b
     
117. f66v H B 3b
     
118. f67r1 A 5a
     
119. f67r2 A 2a
     
120. f67v2 C 5a
     
121. f67v1 A 5a
     
122. f68r1 A 2a
     
123. f68r2 A 2a
     
124. f68r3 A 5a
     
125. f68v3 C 5a
     
126. f68v2 A 5a
     
127. f68v1 A 5a
     
128. f69r C 5a
     
129. f69v C 5a
     
130. f70r1 C 5a
     
131. f70r2 C 5a
     
132. f70v2 Z 5a
     
133. f70v1 Z 5a
     
134. f71r Z 5a
     
135. f71v Z 5a
     
136. f72r1 Z 5a
     
137. f72r2 Z 5a
     
138. f72r3 Z 5a
     
139. f72v3 Z 5a
     
140. f72v2 Z 5a
     
141. f72v1 Z 5a
     
142. f73r Z 5a
     
143. f73v Z 5a
     
144. f75r B B 4a
     
145. f75v B B 4a
     
146. f76r T B 4a
     
147. f76v B B 4a
     
148. f77r B B 4a
     
149. f77v B B 4a
     
150. f78r B B 4a
     
151. f78v B B 4a
     
152. f79r B B 4a
     
153. f79v B B 4a
     
154. f80r B B 4a
     
155. f80v B B 4a
     
156. f81r B B 4a
     
157. f81v B B 4a
     
158. f82r B B 4a
     
159. f82v B B 4a
     
160. f83r B B 4a
     
161. f83v B B 4a
     
162. f84r B B 4a
     
163. f84v B B 4a
     
164. f85r1 T B null
     
165. f85r2 C B null
     
166. fRos C B 3d-c
     
167. f86v4 C B 3b
     
168. f86v6 T B 3c
     
169. f86v5 T B 3c
     
170. f86v3 C B 3c
     
171. f87r H A 2a
     
172. f87v H A 2a
     
173. f88r P A 2a
     
174. f88v P A 2a
     
175. f89r1 P A 2a
     
176. f89r2 P A 2a
     
177. f89v2 P A 2a
     
178. f89v1 P A 2a
     
179. f90r1 H A 1.5a
     
180. f90r2 H A 2a
     
181. f90v2 H A 2a
     
182. f90v1 H A 2a
     
183. f93r H A 1.5a
     
184. f93v H A 1.5a
     
185. f94r H B 3a
     
186. f94v H B 3a
     
187. f95r1 H B 3a
     
188. f95r2 H B 3a
     
189. f95v2 H B 3a
     
190. f95v1 H B 3a
     
191. f96r H A 1.5a
     
192. f96v H A 2a
     
193. f99r P A 2a
     
194. f99v P A 2a
     
195. f100r P A 2a
     
196. f100v P A 2a
     
197. f101r P A 2a
     
198. f101v P A 2a
     
199. f102r1 P A 2a
     
200. f102r2 P A 2a
     
201. f102v2 P A 2a
     
202. f102v1 P A 2a
     
203. f103r S B 4c
     
204. f103v S B 4c
     
205. f104r S B 3c
     
206. f104v S B 3c
     
207. f105r S B 3c
     
208. f105v S B 3c
     
209. f106r S B 3c
     
210. f106v S B 3c
     
211. f107r S B 3c
     
212. f107v S B 3c
     
213. f108r S B 4c
     
214. f108v S B 4c
     
215. f111r S B 4c
     
216. f111v S B 4c
     
217. f112r S B 4c
     
218. f112v S B 4c
     
219. f113r S B 3c
     
220. f113v S B 3c
     
221. f114r S B 3c
     
222. f114v S B 3c
     
223. f115r S B 3c
     
224. f115v S B 3c
     
225. f116r S B 4c