12-08-2024, 11:41 AM
I believe that the mean edit distance should increase at a declining rate as changes accumulate, up to a distance of "equal change likelihood". Individual glyphs may "revert" closer to the original, but so long as the average edit distance is low any change is more likely to be away rather than toward. Only once words are more distinct from the initial state will a random change be equally likely to lower the edit distance than raise it. (I guess that the word patterns are more complex than the pages long, so that point would never(?) be reached in practice.)
So changing [qokeedy] to [okeedy] would give an edit distance of one. But given the number of possible further changes to [okeedy], all but one---the addition of [q]---will increase the edit distance further. It's not until we end up with a word like [ytcheo] that we can genuinely say that any possible change will lower the edit distance. But the mean will hover around an equal edit distance word like [otchody] (for example), where given changes might have a 50/50 chance to raise/lower the edit distance.
If that is right, then we shouldn't see large or continuous drops in edit distance, but only occasional blips in an upward trend until the "equal change likelihood" plateau. The first graph shows the kind of trend possible, but the second graph doesn't. Even were the second graph to show an overall increase in variation over lines, the pattern of leaps and falls in variation don't support the proposed method. (Though note that the scale is already higher, so it could represent a plateau. But that itself would invalidate the hypothesis which requires an initial sustained increase.)
Maybe I have it wrong though, so I would be happy to be corrected. The only possible excuse is the esthetic preference of the scribe somehow controls edit distance in a way which cannot be modeled.
So changing [qokeedy] to [okeedy] would give an edit distance of one. But given the number of possible further changes to [okeedy], all but one---the addition of [q]---will increase the edit distance further. It's not until we end up with a word like [ytcheo] that we can genuinely say that any possible change will lower the edit distance. But the mean will hover around an equal edit distance word like [otchody] (for example), where given changes might have a 50/50 chance to raise/lower the edit distance.
If that is right, then we shouldn't see large or continuous drops in edit distance, but only occasional blips in an upward trend until the "equal change likelihood" plateau. The first graph shows the kind of trend possible, but the second graph doesn't. Even were the second graph to show an overall increase in variation over lines, the pattern of leaps and falls in variation don't support the proposed method. (Though note that the scale is already higher, so it could represent a plateau. But that itself would invalidate the hypothesis which requires an initial sustained increase.)
Maybe I have it wrong though, so I would be happy to be corrected. The only possible excuse is the esthetic preference of the scribe somehow controls edit distance in a way which cannot be modeled.