Relations among pattern studies?

[pfeaster]

In my eyes the properties you describe as loops are caused by the network of similar vords. [see Timm & Schinner 2020, p. 4]. The general principle within this network of similar words is that "high-frequency tokens also tend to have high numbers of similar words. ... words (i.e. unconnected nodes in the graph) usually appear just once in the entire VMS while the most frequent token <daiin> (836 occurrences) has 36 counterparts with edit distance 1. [Timm & Schinner 2020, p. 6]. For this reason the most likely paths in your transitional probability matrix must result in frequently used words.

The cause for the network of similar words is "an existing deep correlation between frequency, similarity, and spatial vicinity of tokens within the VMS text" [Timm & Schinner 2020, p. 4] Or with other words "all pages containing at least some lines of text do have in common that pairs of frequently used words with high mutual similarity appear." [Timm & Schinner 2020, p. 3].

I definitely agree that there's a close connection between the patterns I was describing and the network you (and Schinner) have written about.  Still, I want to be careful when drawing conclusions about what's causing what.  You write here that the so-called "loop" properties are caused by the network (first paragraph), but then that the network is in turn caused by a "deep correlation between frequency, similarity, and spatial vicinity of tokens" (second paragraph).  Since I'd consider "deep correlation between frequency, similarity, and spatial vicinity of tokens" to be a reasonably good description of the system I was describing, those two paragraphs strike me as forming a little loop of their own.  So what came first, the chicken or the egg?

On the one hand, we have a network of similar words whose frequency correlates remarkably well with their degree of similarity to a few specific models.

On the other hand, we have a set of generative rules (involving glyph-by-glyph transitional probabilities) that would produce approximately that same set of words with approximately the same frequencies.  Other models (e.g., some "word paradigms") may be able to do the same.

If I understand things correctly, the self-citation hypothesis holds that the network exists due to the dynamics of copying words with minor changes, guided by the subjective / aesthetic preferences of the writer (and hence non-random).  Still, if we could identify a set of more concrete and specific rules, and had to account for its relationship with a network of words that just happened to follow those rules, I'd think Occam's razor would point to the rules causing the network rather than the network causing the rules.

From the perspective of the self-citation hypothesis, I suppose the rules (whether the ones I presented on, or any others) would then need to be interpreted as manifesting the subjective / aesthetic preferences of the writer, since they're not predictable in terms of a raw copying dynamic as such.  But even so, I'd presume any such rules would "really" have existed in the writer's mind to whatever extent grammatical rules exist in the mind of a speaker who's not consciously aware of them.

Of course the rules could take on other kinds of significance within other hypotheses.

One of your questions was why the repetition counts for [ol] are lower then the counts for [qokeedy] and for [chol]. Regarding this question it is interesting to look on folio 15v. On You are not allowed to view links. Register or Login to view. not only “oror” exists, there is also “oror or” and “or or oro r” immediately above each other on the first two lines. There are five instances for [oror], seven instances of [arar], even 15 instance for [olol], and 2 instances for [dydydy]. This means for shorter vords like [or], [ol], [dy] it is also possible to combine two instances of a word like [dy] into a new word like [dydy] or [dydydy].

These are all impressive cases of repeating / looping.  And yes, if we ignore spacing, it looks like there are well over 100 tokens of the glyph sequence [olol], which is clearly more than the 32 tokens of the glyph sequence [cholchol], based in both cases on a very hasty count.  My observation was limited to repetitions of whole discrete words, which I'll admit is a distinction I don't make for the rest of my analysis.

Another observation is that for longer words most transitions result in similar word that are recognizable. For instance is the similarity between [qokedy], [qokeedy] and [okeedy] still obvious. For shorter words the transition of a glyph automatically replaces a larger part of the word. If for instance [ol] transforms into [al], [or], or [kol] 50 or 33 % of the glyphs are different. Therefore sequences like [or.ar.y.kar.ol.al] on f34r.P.15 or [tor.ol.dol.or] on f54r.P.10 are maybe less eye catching compared to sequences like [qokeedy.qokeedy.chey.qokeedy.qokedy] on f108.P.37.

That's a good point, although [or.ar.y.kar.ol.al] also contains a lower proportion of "default" transitions than [qokeedy.qokeedy.chey.qokeedy.qokedy], which I'd take as indicating higher overall entropy.

Did that mean the it is necessary to assume different default loops for different pages?

To a point, yes.  Statistics for individual pages or bifolios of the VMS will often point to other default loops.  With a reduced dataset, two or more transitions will sometimes tie for top position, further complicating matters.  Like the network of related words with most of its "slots" filled in, default loops only emerge reliably from a larger-scale aggregate view.

For what it's worth, just three bifolios produce straightforward [qokeedy] loops all by themselves: 76+83, 104+115, and 108+111.  And only one bifolio produces a straightfoward [choldaiin] loop by itself -- 2+7 -- although for 3+6, 28+29, and 51+54, a tie leaves [choldaiin] as one of the loops.  Other bifolio-specific loops include [chol], [daiin], [qokedy], [ol], [chedy], [oldaiin], and even [qokaiinchedy].

That said, the transitional probability matrices as a whole tend to be more stable than the loops are.  To "break" a loop, it's only necessary for one transition to overtake another somewhere, which -- depending on how "close" things are -- can just be a matter of statistical noise.  But the question of how much variation there is in the whole system of transitional probability matrices from section to section, or even page to page, would be well worth investigating, and probably more informative than a survey of the "default" loops.