[split] Does Voynichese evolve from A to B?

[Jorge_Stolfi]

I just want to be clear this is not what is happening in any of my fits. The curve is fitted in all 256d, I am just plotting it consistently with MDS1 on the x axis to make it easier to read.

I understand that the curve is fitted in R^256.  But what is the fitting algorithm, exactly?

The trivial way would be: pick a direction u in R^256 (naturally it would be MDS1, the direction of major extent). Project the data vector d(p) of each page p onto a line with direction u and let t(p) be the coordinate of the projection (that is, t(p) = dotprod(d(p),u).)  Then fit to the pairs (t(p),d(p)) a polynomial curve c(t) into R^256 by least squares.

Least squares fitting would minimize the squares of the Euclidean distances between c(t(p)) and d(p) along directions orthogonal to u.  In R^2 instead of R^d,  if u is the X-axis, that distance between c(t(p)) and d(p) is measured in the vertical Y direction.  This is not quite justified since the position t(p) too must be affected by errors.  Intuitively it would make more sense to recompute the parameter t(p) such that c(t(p)) is the point on the curve closest to d(p), and then adjust the curve so as to minimize the sum of the distances between these two points in R^256 -- and iterate until convergence.  

This process will probably yield better looking -- and maybe even more correct -- curve fittings. But it requires non-linear optimization, and there will often be several well-separated local minima: very different curves such that perturbing either of them in any way will make the fit worse.   

Considering your nice plots of the various curves used in your "stability" study, and the fact that the curves are not monotonic along MDS1, I guess that you are using this non-linear fitting method,  Is that correct?  In those plots we see two distinct families of curves, which must be two local minima of the fitting criterion, that surely must sort the points in different orders.

In fact, from what one can see in the MSD1..MDS3 plots, it seems that there should be at least three local minima of the fitting criterion, namely three curves that go through the clusters A,B,C in the order A-B-C or B-C-A or C-A-B:
   
Presumably your fitting algorithm chose the order A-B-C because its curve gave a better fit than the other two curves.  (Or maybe just because it started the non-linear optimization with the trivial least-squares fit using u = MDS1.)  But the difference between that curve and the other two must be small.

The VMS was surely composed by the Author as a draft on paper which was then transposed to vellum by the Scribe

Then the gradient would appear on the draft and would have been copied into the MS by the scribe.

But I explained why it is very unlikely that a gradient due to time would exist in the final draft.  Like us writing any paper or book, the Author must have gone back and forth over the draft, editing and re-editing pages that he wrote previously -- and applying to them any changes of spelling or nomenclature that he may have decided to make along the way.  

Just because the cloud of page data vectors of a section is elongated in some direction, you cannot assume that the elongation is due to passage of time.  It could be any factor that has perceptible effect on page statistics.  Like toxicity of the herb, or how much is is supposed to help extend one's years.  

In fact the "gradient" may be due to a non-linear dependency on such a variable.  For example, different words with -edy may be common on both harmless and very toxic plants, while certain words with -eody may be more common on plants with low toxicity.  That would elongate that cloud along the ed/eod direction -- but the position along the gradient would not be correlated with toxicity, even though this is its ultimate cause.

What is the opposite of pareidolia?

It is "real thing".  Like, Powell's Martian channels were just pareidolia, but Wegener's claimed match between the coastlines of Africa and South America was a real thing.