16-03-2026, 05:55 PM
Hi everyone,
First of all, thank you for your comments.
I have continued some experiments on the proximity between Voynich-like words and wanted to share some results that I think can contribute to the discussion.
Following Nablator's observation, I have repeated the experiments excluding all tokens of less than three characters and using a stricter similarity rule for short words. Specifically, for three-character words I only consider Levenshtein distance = 1, while for longer words I allow up to Levenshtein = 2.
With this filtering all connections between short words disappear. As expected, the bursts become noticeably smaller (the average size drops to about ~2.4, when before it was around ~5–6). However, several thousand small local clusters of similar words still appear. Therefore, the phenomenon does not seem to be simply an artifact caused by very short words.
Note: I worked with CUVA transliteration as it seems to slightly accentuate the results. As you know, CUVA is essentially a visual transformation of EVA that groups together some graphically very similar characters. For an analysis based on formal similarity it seems more appropriate to me. But as said, results in EVA are very simmilar.
Experiments:
1 Spatial proximity of similar words: The first experiment measures the spatial distance between similar words within the page. For each word I search for the closest similar word and measure the distance in two dimensions.
To check whether the result could simply be an effect of the overall word frequencies, I compared the real text with permuted versions of the text that maintain the same word distribution and line structure. The result is that in the real text similar words appear systematically closer than in the permutations.
For example:
mean Manhattan distance
real text ≈ 3.11
permuted text ≈ 3.39
The median also drops from 3 in the permuted text to 2 in the real text. In addition, there are more neighbors at very small distances (1 to 2 positions).
2. Direction of this proximity: I also looked at the direction of the nearest similar neighbor. If the main mechanism were copying words from the previous line, we would expect to see many exact column matches, that is, variants located exactly under the original word.
What appears is a little different. Exact column matches do not increase much with respect to permutations. However, the probability that the similar word appears in a very close column, for example a column to the right or left, does increase.
In other words, variants tend to appear in the same vertical area of the text, but not necessarily exactly under the previous word. The pattern seems more like local proximity than strict vertical copying.
3. Proximity in the flow of the text: If we look at the distance between variants in the linear flow of the text (in number of tokens), a similar pattern also appears. Variants tend to appear within relatively short windows of words.
This is compatible with a process with short textual memory, where one word can influence those written shortly afterwards.
4. Regarding René's question: René was asking if the “core word” tends to be more frequent than the variants.
In this study, I defined the core of the burst as the first word that appears in the sequence, because the goal is to see if the variants are generated from previous words in the text flow. Defining the core as the medoid (the word with the smallest total distance to the set), for example, completely eliminates directionality and is therefore not suitable for this type of question.
With this definition the results are:
Number of bursts analyzed: 3774
average frequency of the core ≈ 6
average frequency of the variants ≈ 70
Only approximately between 5% and 10% of the bursts have a core that is more frequent than its members.
That is, on average the variants are much more frequent than the initial word of the burst.
5. Provisional conclusion: The experiments seem to show three fairly consistent properties:
- variants appear spatially clustered
- this clustering is mostly local
- the first word of a burst is rarely the most frequent form of the set
This suggests some kind of local variant generation mechanism, but does not clearly point to strict vertical copying.
My (repetitive) intuition says that I have captured in numbers what other researchers had already detected in a more visual and less computational way. Nothing new with the analysis of the Vihnich text…
If anyone can think of other controls or tests that could help to better discriminate between possible models, they would be most welcome.
First of all, thank you for your comments.
I have continued some experiments on the proximity between Voynich-like words and wanted to share some results that I think can contribute to the discussion.
Following Nablator's observation, I have repeated the experiments excluding all tokens of less than three characters and using a stricter similarity rule for short words. Specifically, for three-character words I only consider Levenshtein distance = 1, while for longer words I allow up to Levenshtein = 2.
With this filtering all connections between short words disappear. As expected, the bursts become noticeably smaller (the average size drops to about ~2.4, when before it was around ~5–6). However, several thousand small local clusters of similar words still appear. Therefore, the phenomenon does not seem to be simply an artifact caused by very short words.
Note: I worked with CUVA transliteration as it seems to slightly accentuate the results. As you know, CUVA is essentially a visual transformation of EVA that groups together some graphically very similar characters. For an analysis based on formal similarity it seems more appropriate to me. But as said, results in EVA are very simmilar.
Experiments:
1 Spatial proximity of similar words: The first experiment measures the spatial distance between similar words within the page. For each word I search for the closest similar word and measure the distance in two dimensions.
To check whether the result could simply be an effect of the overall word frequencies, I compared the real text with permuted versions of the text that maintain the same word distribution and line structure. The result is that in the real text similar words appear systematically closer than in the permutations.
For example:
mean Manhattan distance
real text ≈ 3.11
permuted text ≈ 3.39
The median also drops from 3 in the permuted text to 2 in the real text. In addition, there are more neighbors at very small distances (1 to 2 positions).
2. Direction of this proximity: I also looked at the direction of the nearest similar neighbor. If the main mechanism were copying words from the previous line, we would expect to see many exact column matches, that is, variants located exactly under the original word.
What appears is a little different. Exact column matches do not increase much with respect to permutations. However, the probability that the similar word appears in a very close column, for example a column to the right or left, does increase.
In other words, variants tend to appear in the same vertical area of the text, but not necessarily exactly under the previous word. The pattern seems more like local proximity than strict vertical copying.
3. Proximity in the flow of the text: If we look at the distance between variants in the linear flow of the text (in number of tokens), a similar pattern also appears. Variants tend to appear within relatively short windows of words.
This is compatible with a process with short textual memory, where one word can influence those written shortly afterwards.
4. Regarding René's question: René was asking if the “core word” tends to be more frequent than the variants.
In this study, I defined the core of the burst as the first word that appears in the sequence, because the goal is to see if the variants are generated from previous words in the text flow. Defining the core as the medoid (the word with the smallest total distance to the set), for example, completely eliminates directionality and is therefore not suitable for this type of question.
With this definition the results are:
Number of bursts analyzed: 3774
average frequency of the core ≈ 6
average frequency of the variants ≈ 70
Only approximately between 5% and 10% of the bursts have a core that is more frequent than its members.
That is, on average the variants are much more frequent than the initial word of the burst.
5. Provisional conclusion: The experiments seem to show three fairly consistent properties:
- variants appear spatially clustered
- this clustering is mostly local
- the first word of a burst is rarely the most frequent form of the set
This suggests some kind of local variant generation mechanism, but does not clearly point to strict vertical copying.
My (repetitive) intuition says that I have captured in numbers what other researchers had already detected in a more visual and less computational way. Nothing new with the analysis of the Vihnich text…
If anyone can think of other controls or tests that could help to better discriminate between possible models, they would be most welcome.
![[+]](https://www.voynich.ninja/images/collapse_collapsed.png)